After using the npr formula, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
There are a total of 13 players on the youth basketball team, and there are five different positions that need to be filled. To determine the number of ways that the players can be assigned to these positions, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of players, and r is the number of positions. In this case, n = 13 and r = 5. Plugging these values into the formula, we get:
P(13, 5) = 13! / (13 - 5)!
= 13! / 8!
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (13 * 12 * 11 * 10 * 9) / 1
= 154440
Therefore, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
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Lanny got a short term job selling computers. He is paid on
commission. In order to impress customers, he bought a few nice suits. If he has
$20 000 in sales, he will lose $140. If he has$30 000 in sales, he will make a $90
profit. Determine the:
a. rate of change and initial value
b. the amount he needs to sell to break even
c. The amount he needs to sell in order to make $1000 profit
The rate of change and initial value are 0.023 and -600 respectively.
The amount he needs to sell to break even is $26,086.96.
The amount he needs to sell in order to make $1000 profit is $69,565.22.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided, a system of equations that models the situation is given by;
-140 = 20,000x + c ...equation 1.
90 = 10,000x + c ...equation 2.
By subtracting equation 1 from equation 2, we have:
230 = 10,000x
x = 0.023
For the initial value, we have:
90 = 10,000x + c
c = -140 - 20,000(0.023)
c = -600.
In order to break even, y must be equal to 0;
y = 0.023x - 600
0 = 0.023x - 600
x = 600/0.023
x = $26,086.96.
In order to make $1000 profit, Lanny must sell the following:
y = 0.023x - 600
1,000 = 0.023x - 600
x = 400/0.023
x = $69,565.22.
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21. *
21
Andy made a servings of tacos and
15 servings of nachos, and wants to set
up identical tables for the tacos and
nachos. He also doesn't want any left
over tacos or nachos. What is the most
number of tables Andy can set up?
10 poi
Andy can set up a maximum of 12 tables, each with 3 servings of tacos and 3 servings of nachos.
Let's assume that there are a limit of n servings per table. We need to get the greatest number of n that divides both 21 and 15 without leaving a remnant because Andy doesn't want any leftover tacos or nachos. In comparison to the factors of 15, which are 1, 3, 5, and 15, the factors of 21 are 1, 3, 7, and 21. Three is the highest number that divides both 21 and 15.
Thus, a maximum of three dishes can be placed on each table. We divide the total servings by the maximum servings per table to get how many tables Andy can set up:
Servings total: 21 + 15 = 36
3 serves maximum per table.
Amount of tables = Total Servings / Maximum Servings Per Table = 36 / 3 = 12
Hence, Andy can only put up a maximum of 12 tables, each with 3 tacos and 3 nachos.
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The daily cost of production in a factory is calculated using ()= 200+ 16, where is the number of complete products manufactured. Which set of numbers best defines the domain of ()?
Integers
positive real numbers
positive rational numbers
whole numbers
The domain of the function is positive integers. The function () = 200 + 16 represents the daily cost of production in a factory, where x is the number of complete products manufactured.
Since the production of products cannot be negative or fractional, the domain of the function is restricted to non-negative integers.
Therefore, the domain of the function is the set of positive integers:
{1, 2, 3, 4, ...}
Any value outside this set would not make sense in the context of the problem, as a fraction or a negative number of products cannot be produced.
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Larry owns a shoe store. his starting balance was 17,300 his ending balance was 14,700 what is Larry's burn rate.
Larry's burn rate, which represents the amount of money he spent per unit of time, is $2,600 per month based on the starting balance of $17,300 and the ending balance of $14,700.
Larry's burn rate can be calculated as the amount of money he spent per unit of time, which is usually expressed as a monthly or annual rate. To calculate his burn rate based on the given information, we need to know the time period for which the difference between the starting and ending balances represents.
Assuming that the starting balance of $17,300 represents the beginning of a month or some other specific time period, and that the ending balance of $14,700 represents the end of the same time period, we can calculate Larry's burn rate as follows:
Burn rate = (Starting balance - Ending balance) / Time period
If we assume that the time period is one month, then:
Burn rate = ($17,300 - $14,700) / 1 month = $2,600 per month
Therefore, Larry's burn rate is $2,600 per month. This means that he spent an average of $2,600 per month to run his shoe store during the time period in question.
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There are 6000 registered voters in Roseville and 3/4 of these voters are registered Democrats. A survey indicates that 2/3 of the registered Democrats are in favor of Bond Measure A and 3/5 of the other registered voters are in favor of this measure.
The total number of voters in favor of Bond Measure A is 3900 voters in favor of Bond Measure A.
How to find out how many voters are in favor of Bond Measure A.First we need to calculate the total number of voters who are registered Democrats and the total number of voters who are not registered Democrats, and then calculate the number of voters in favor of the measure for each group and add them together.
Total number of registered Democrats:
3/4 of 6000 registered voters = 4500 registered Democrats
Number of registered Democrats in favor of Bond Measure A:
2/3 of 4500 registered Democrats = 3000 registered Democrats in favor of the measure
Number of registered Democrats not in favor of Bond Measure A:
4500 - 3000 = 1500 registered Democrats not in favor of the measure
Total number of voters who are not registered Democrats:
6000 - 4500 = 1500 voters who are not registered Democrats
Number of voters who are not registered Democrats and in favor of Bond Measure A:
3/5 of 1500 voters who are not registered Democrats = 900 voters who are not registered Democrats and in favor of the measure
Therefore, the total number of voters in favor of Bond Measure A is:
3000 registered Democrats in favor + 900 other registered voters in favor = 3900 voters in favor of Bond Measure A.
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11. F(x) = 2x2² - 12x +9
a. Concave
Narrower / Wider / Same
b. Axis of Symm.
(Show work here. )
C. Vertex
(Show work here. )
Width: (Circle One)
d. Domain:
_/2
10637910-y
Range:
/2
Inlo4 lemobib A
-/2
$
T
-3
t
m
$43
N
P
3
-5
e. Y-intercept & Reflection:
n
Additional Point & Reflection: _______
(Show work here. )
C
/3
/2
a. To establish whether the function is concave up or concave down, we must obtain the function's second derivative. F(x) = 2x2 - 12x + 9 F'(x) = 4x - 12 F"(x) = 4x - 12 F"(x) = 4.
The function is concave up because the second derivative has a constant value of 4, which is positive. Since the coefficient of x2 is more than one, the function is narrower than the conventional parabola y = x2. b. The equation x = -b/2a gives the parabola's axis of symmetry, where a and b are the coefficients of the x2 and x terms, respectively.A = 2 and b = -12 for the function F(x) = 2x2 - 12x + 9. As a result, the axis of symmetry is x = -12/(2*2) = 3. c. The point at which The coordinates (h, k) define the parabola, where h = -b/2a and k = f. (h). We already determined that the axis of symmetry for the function F(x) = 2x2 - 12x + 9 is x = 3. So, h = 3. To find k, enter h = 3 into the function: F(3) = 2(3)^2 - 12(3) + 9 = -9 As a result, the vertex is (3, -9). Width: The parabola's width is the distance between the x-intercepts, which may be calculated using the quadratic formula.
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Zach has to cut wooden molding into 9 pieces that are each half a yard long. What is the total length of the molding in yards written as a mixed number?
Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.
what is length ?A measurement of length is the distance between two points on an item. It is one of the essential physical quantities used in physics and a fundamental idea in geometry. Typically, length is expressed in terms of meters, centimeters, feet, inches, or kilometers. Rulers, measuring instruments, and laser rangefinders are just a few of the tools that can be used to determine an object's length. When describing the size of geometric objects like lines, segments, or curves, length is frequently used in mathematics.
given
The overall length of the molding can be calculated by multiplying the length of each piece by the number of pieces, for example, if Zach needs to cut wooden molding into 9 pieces that are each half a yard long:
Total length equals each piece's length times the number of parts.
Overall length is 9 + (1/2 yard)
length overall: 9 2 yards
We can divide 9 by 2 and write the outcome as a mixed number to represent this:
with a residue of 1, 9 2 = 4
Zach has to cut the wooden molding into 9 sections, resulting in a total length of 4 1/2 yards in various numbers.
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what’s the zeros of the function of f(x)=x^2+49
Answer:
This function has no zeroes
Step-by-step explanation:
To understand this problem we need to first understand what the zeroes of a function is; the zeroes of a function is the point at which the y value of a solution is equal to zero. So in this scenario all we need to do is plug 0 in for y:
[tex]0 = x^2 +49[/tex]
Subtract 49 from both sides:
[tex]-49 = x^2[/tex]
Now we can notice that [tex]x^2[/tex] is equal to -49; to our surprise there is no possible value for [tex]x^2[/tex] to be equal to a negative number. Therefore this function has no roots.
Step-by-step explanation:
a zero of a function means what value of x causes a functional value of 0 ?
so,
0 = x² + 49
-49 = x²
x = ±sqrt(-49)
this tells us that there is no solution in real numbers, because no square of any real number can be negative.
but the function still has 2 zeroes. they are numbers of the set of imaginary or complex numbers.
that means they base on the square root of -1, called i.
x = ±sqrt(49×-1) = ±7×sqrt(-1) = ±7i
A Level III video editor takes 20 hours to add special effects to a movie. A Level II video editor takes 26 hours and a Level I video editor takes 32 hours. Find how long it would take them to add the special effects if they all work together.
It would take them about 8.4 hours to add the special effects if they all work together.
What is formula for work done?1/T = 1/T1 + 1/T2 + 1/T3 +... + 1/Tn, where T is the time it takes for all n persons to complete the task and T1, T2,..., Tn are the times it takes for each person to do the task individually, is the formula for addressing issues involving work done by several people. This equation is based on the premise that each person's contribution to the activity is inversely proportionate to the time it takes them to do it. In other words, a person contributes more effort to the entire task the faster they work. This method may be used to determine how long it will take all n persons working together to do the assignment in total.
The work done is calculated by:
1/T = 1/T1 + 1/T2 + 1/T3
Here, we have T1 = 20, T2 = 26 and T3 = 32 hours for work done separately.
Substituting the values:
1/T = 1/20 + 1/26 + 1/32
1/T = (32/640) + (24/640) + (20/640)
1/T = 76/640
T = 640/76
T ≈ 8.4 hours
Therefore, it would take them about 8.4 hours to add the special effects if they all work together.
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Tom will run at least 30 miles this week. So far, he has run 22 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t .
pls put ur answer written pls help me this is so hard I'm crying
The calculated number of additional miles he would run must not exceed 8 miles
How many additional miles should he run?The following are symbols for inequalities and their corresponding meanings:
> signifies a value that is larger than another value< signifies a value that is smaller than another value≥ signifies a value that is larger than or equal to another value≤ signifies a value that is smaller than or equal to another value.The inequality format that expresses the information in the question is as follows:
Tom's minimum required running distance must be greater than or equal to the sum of the distance he has already run and the distance he plans to run.
Using this inequality, we can derive the equation
30 ≥ 22 + t
Where t represents the distance Tom plans to run.
To determine the value of t, we must simplify the equation by combining similar terms.
We can subtract 22 from both sides, resulting in
8 ≥ t.
Therefore, the maximum distance Tom plans to run is 8 miles.
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For what ranges of values, holding all else constant, could each of the objective function coefficients be changed without changing the optimal solution? (
The optimal solution of an objective function does not change when its coefficients are changed within a certain range of values. This range of values for each coefficient depends on the function itself and the value of other coefficients.
For example, if the objective function is 3x + 2y, then the range of values for the coefficient of x (3) can be changed from 2 to 4 without changing the optimal solution. Similarly, the coefficient of y (2) can be changed from 1 to 3 without changing the optimal solution.
Therefore, the ranges of values for each coefficient of the objective function, holding all else constant, can be changed without changing the optimal solution.
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PLEASE SOMEBODY HELP: Generate a symbolic rule for locating the point that divides a line segment into two parts so that the ratio of the lengths is m: n, with the point closer to the left endpoint.
Step-by-step explanation:
Let the coordinates of the left endpoint of the line segment be (x1, y1) and the coordinates of the right endpoint be (x2, y2). Let the point dividing the line segment be (x, y). Then the distance between the left endpoint and (x, y) is mx/(m+n) and the distance between (x, y) and the right endpoint is nx/(m+n).
Using the distance formula, we have:
[tex]distance \: between \: (x1, y1) \: and \: (x, y) = \sqrt{((x - x1)^2 + (y - y1)^2)} = \frac{mx}{(m+n)} [/tex]
[tex]distance \: between \: (x, y) \: and \: (x2, y2) = \sqrt{((x2 - x)^2 + (y2 - y)^2)} = \frac{nx}{(m+n)} [/tex]
Squaring both equations, we get:
[tex](x - x1)^2 + (y - y1)^2 = \frac{mx}{(m+n)^2}[/tex]
[tex](x2 - x)^2 + (y2 - y)^2 = \frac{nx}{(m+n)^2}[/tex]
Expanding the squares, we get:
[tex]x^2 - 2x1x + x1^2 + y^2 - 2y1y + y1^2 = \frac{mx}{(m+n)^2} [/tex]
[tex]x^2 - 2x2x + x2^2 + y^2 - 2y2y + y2^2 = \frac{nx}{(m+n)^2}[/tex]
Rearranging and simplifying, we get:
[tex]x = \frac{(mx2 + nx1)}{(m+n)} \: and \: y = \frac{(my2 + ny1)}{(m+n)}[/tex]
Therefore, the point that divides the line segment into two parts so that the ratio of the lengths is m: n and the point is closer to the left endpoint is:
[tex](x, y) = \frac{(mx2 + nx1)}{(m+n)}, \frac{(my2 + ny1)}{(m+n)}[/tex]
Express 0939 as a fraction.
According the given question 0.0939 as a Fraction equals 939/10000.
What is fractiοn?Fractiοns are referred tο as a whοle's cοnstituent parts in mathematics. A single item οr a cοllectiοn οf items can be the cοmplete. When we really cut a slice οf cake frοm the cοmplete cake, the cοmpοnent represents the percentage οf the cake. The wοrd "fractiοn" cοmes frοm Latin.
To write 0.09390 as a fraction you have to write .09390 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
.09390 = .09390/1 = 0.939/10 = 9.39/100 = 93.9/1000 = 939/10000
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Complete Question:
Express 0.09390.0939 as a fraction.
Classify the quadrilateral by its most specific name. Explain your reasoning.
To classify a quadrilateral by its most specific name, we need to examine its sides and angles.
What is a quadrilateral?A quadrilateral is four-sided polygon with four angles. It is closed shape with straight lines that do not cross each other.
Here are the most common types of quadrilaterals and their defining characteristics:
Parallelogram - quadrilateral consist of two pairs of parallel sides.
Rectangle - parallelogram with four right angles.
Rhombus - parallelogram with four congruent sides.
Square - rectangle and a rhombus, with four right angles and four congruent sides.
Let's consider an example.Suppose we are given a quadrilateral with four sides of equal length and two pairs of opposite parallel sides. This means that it has the characteristics of a parallelogram and a rhombus.
Reasoning: The quadrilateral has four equal sides, which makes it a rhombus. Additionally, it has two pairs of parallel sides, which satisfies the criteria for a parallelogram. However, since a rhombus is a type of parallelogram with additional properties, it is the most specific name for this quadrilateral.
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A microwave was originally sold for $137 and has been marked down to $66. What is the percentage decrease for the microwave? ____%
The percentage decrease in the price of the microwave is 51.82%.
What is the percentage decrease?Percentage is used to determine the relative value of a digit as a number out of a hundred. The sign that is used to represent percentages is %. In order to express a value as a percentage, multiply the number by 100. Percentage is a measure of frequency.
Percentage decrease = (change in price / initial price) x 100
Change in price = initial price - new price
$137 - $66 = $71
(71/137) x 100 = 51.82%
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What single percentage change is equivalent to a 11% increase followed by a 21% decrease?
Answer:
Step-by-step explanation:
-10 perecent
because 21-11=10
simplify the expression x + 8 and = 3: x by the power of 2 - xy
The given expression can be simplified to x2 - xy = 3.
What is expression?Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.
This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as x2 - xy = 3.
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The given expression can be simplified to 25 + 5y + 4.
What is expression?Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.
To simplify the expression x + 8 and = 3, we must first subtract 8 from both sides of the equation to get x = -5. We can then substitute -5 for x in the expression x2 - xy + 4, resulting in (-5)2 - (-5)y + 4.
Simplifying further, we get 25 - (-5)y + 4, or 25 + 5y + 4. Therefore, the simplified expression is 25 + 5y + 4.
This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as 25 + 5y + 4.
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Billy ran 52 yards. How many feet did he run?
Answer:
The answer to your problem is, 156
First lets find out how many feet or in one yard ?
Well 1 yard = 3 feet.
Now that we know that we can use our knowledge to answer the next question:
If Bill ran 52 yards, how many feet did he ran?
We can do math to solve our answer. :
1 x 52 = 52.
Now we need to multiply 52 x 3.
That is a little bit to much, so lets make the problem easier!
By breaking up the problem \/ to make it more easier.
50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150
3 x 2 = 6.
Next add:
150 + 6 = 156.
Thus the answer to your problem is, 156
A) Given: Regular pyramid KO ⊥ (ABCD) KO = 10. 2, m∠AKO = 38º Find: V
The standard pyramid KO has a volume of roughly 64.88 cubic units.
To find the volume of the given regular pyramid KO, we need to know the area of the base and the height of the pyramid. Since the pyramid is regular, the base is a square. Let the side of the square base be x.
Now, we can use trigonometry to find the height of the pyramid. Draw a line from vertex K to the center O of the base. This line is perpendicular to the base, so it splits the base into two equal parts. Let M be the midpoint of side AB. Then, we have right triangle KMO with hypotenuse KO, and angle MKO equal to half of angle AKO (19 degrees).
We can use the trigonometric function tangent to find the height h of the pyramid:
tan 19 = h/5 (where 5 is half of x, the side length of the base)
h = 5 tan 19 ≈ 1.98
Now, we can use the formula for the volume of a pyramid:
V = (1/3) * area of base * height
Since the base is a square, its area is x². Substituting the known values, we get:
V = (1/3) * x² * h
V = (1/3) * x² * 1.98
V = (0.66) x²
We are given that KO = 10.2, which is the slant height of the pyramid. Using the Pythagorean theorem, we can find x:
x² + (5/2)² = 10.2²
x² = 104.04 - 6.25
x² = 97.79
x ≈ 9.89
Substituting this value for x into the equation for the volume, we get:
V = (0.66) * 9.89²
V ≈ 64.88
Therefore, the volume of the regular pyramid KO is approximately 64.88 cubic units.
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Which list shows these numbers in order from least to greatest?
0. 009854 1. 98 V9 30%
The list that shows these numbers in order from least to greatest is:
0.009854, 30%, 1.98, V9
The reason for this order is as follows:
0.009854 is the smallest number, since it is a decimal between 0 and 1 with four digits after the decimal point.30% is the next smallest number. It is larger than 0.009854 but smaller than the other two numbers in the list. Note that "30%" is equivalent to the decimal 0.3.1.98 is the next largest number. It is larger than both 0.009854 and 30%, but smaller than "V9"."V9" is the largest number in the list, but we cannot directly compare it to the other three numbers since it is not a numerical value. Without additional context, we cannot determine its relative magnitude.For more such questions on Mathematical comparison: brainly.com/question/29006160
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5
The diagram shows a sector of a circle of racus 24 cm
Not drawn
accurately
24 cm
Work out the are length AB
(Worked out wrong )
The value of the variable x given the perimeter is 44°.
What is the sector?A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Given: radius = 24cm
perimeter (total) of sector = 68cm
Total perimeter of sector=68cm
Radius = 24 cm
24 + x = 68 cm
x =68 - 24
x = 44°
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A diagram shows a sector of a circle of radius 24 cm and perimeter of 68cm. Find the value of x.
very confused please help explan the answer
Answer:
[tex]a_{n}[/tex] = 3 + 5(n - 1)
Step-by-step explanation:
there is a common difference between consecutive terms , that is
8 - 3 = 13 - 8 = 18 - 13 = 5
this indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 3 and d = 5 , then
[tex]a_{n}[/tex] = 3 + 5(n - 1) ← is the explicit formula
Graph the function. Make sure to find the axis if symmetry, vertex, and 5 total points in order to graph. f(x)=x^2−8x+13
The axis of rotation is a perpendicular line that passes through the vertex, meaning the lowest point in the graph [tex](4, -3)[/tex].
Describe the vertex.A vertices is a place on a polygons where two ray or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the lines A, B, C, E, etc E in the aforementioned figures are vertices.
A vertex in a mathematical graph is what?A node of a graph, or one of the vertices from which a graph is formed and that can be connected by graph, is referred to as a "vertex" in computing. Moreover, the words "point," "junction," and "0-simplex" are employed.
To graph the function [tex]f(x) = x^2 - 8x + 13[/tex], we need to find its axis of symmetry, vertex, and a few other points.
Find the axis of symmetry
[tex]x = -b/2a[/tex]
In this case, [tex]a = 1[/tex] and [tex]b = -8[/tex], so the axis of symmetry is [tex]x = -(-8)/(2*1) = 4[/tex].
Find the vertex
[tex]f(4) = 4^2 - 8(4) + 13 = -3[/tex]
So the vertex is [tex](4, -3)[/tex].
To find other points,
When [tex]x = 0, y = 13[/tex]
When [tex]x = 1, y = 6[/tex]
When [tex]x = 2, y = 1[/tex]
When [tex]x = 3, y = -2[/tex]
When [tex]x = 5, y = 2[/tex]
These points cannot be connected on a graph to form a basic picture of the function.
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I’ll give brainlyyyyyy
(a) Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units.
Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4).
(b) Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).
Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0).
How to complete the statement(a)
Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units. The -4 in the second equation means shifting downward 4 units
Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4). hence the y intercept is -4
(b)
Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).
Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0). In this case both graphs intercepts the y-axis at same point which is at the origin
The graphs are attached
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Write the equation of a circle given a center of (-5,-12) and a radius of 7
Answer:
(x+5)^2 + (y+12)^2 = 49
Step-by-step explanation:
(x-h)^2 + (y-k)^2 = r ^2 is the general equation for circles, where r is the radius and h,k are the center's coordinates.
The distance between two points on a map is 20 cm. The actual distance is 980 m. What is the unitless scale of the map in simplest form?
In Linear equation, 196000 cm is the unitless scale of the map in simplest form.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
h = 1/2 t²
here
g = 980 m/sec²
t = 20 sec
Therefore, the distance h is: 196000 cm
h = 1/2 * 980 * 20² = 196000 cm
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8) Is \( f(x)=6 x^{2}-\frac{4}{x} \) odd, even or neither? You must show all of your algebra. 10 points 9) Find the equation of the line that goes though \( (-1,3) \) and \( (2,-4) \). 10 points
This function is neither odd nor even. To show this, we can take the algebraic approach.
The definition of an odd function is that for every \( x \), \( f(-x) = -f(x) \).
Therefore, we can substitute \( -x \) for \( x \) and see if this statement is true.
\( f(-x) = 6(-x)^{2}-\frac{4}{-x} \)
\( f(-x) = -6 x^{2}+\frac{4}{x} \)
Since this is not equal to \( -f(x) \), which is \( -6 x^{2}-\frac{4}{x} \), this function is neither odd nor even.
9) The equation of the line that goes through the two points \( (-1,3) \) and \( (2,-4) \) is \( y = \frac{1}{3}x + \frac{17}{3} \).
To find the equation, we can use the point-slope formula. The slope of the line is \( \frac{-7}{3} \), which we can find using the two points.
\( m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-4-3}{2-(-1)} = \frac{-7}{3} \)
The point-slope formula for the equation of the line is \( y - y_{1} = m(x - x_{1}) \). We can substitute in the slope and the point \( (-1,3) \) to get the equation.
\( y - 3 = \frac{-7}{3}(x - (-1)) \)
\( y - 3 = \frac{-7}{3}(x + 1) \)
\( y = \frac{-7}{3}x - \frac{7}{3} + 3 \)
\( y = \frac{1}{3}x + \frac{17}{3} \)
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25 POINTS
Where do the graphs of f of x equals cosine of the quantity x over 2 and g of x equals square root of 3 minus cosine of the quantity x over 2 intersect on the interval [0, 360°)?
300°
150° and 210°
60°
30° and 330°
The graphs of f of x equals cosine of the quantity x over 2 and g of x equals square root of 3 minus cosine of the quantity x over 2 intersect on the interval [0, 360°) at: D. 30° and 330°.
What is a point of intersection?In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
In this context, we can logically deduce that the point of intersection of the graphs would be at function f(x) = function g(x):
[tex]cos(\frac{x}{2} )=\sqrt{3} -cos(\frac{x}{2} )\\\\\sqrt{3}=cos(\frac{x}{2} ) + cos(\frac{x}{2} )\\\\\sqrt{3}=2cos(\frac{x}{2} )\\\\cos(\frac{x}{2} )=\frac{\sqrt{3}}{2} \\\\cos(\frac{x}{2} )=\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{\sqrt{3}} \\\\cos(\frac{x}{2} )= \frac{3}{2\sqrt{3}}[/tex]
x/2 = 15
x = 15(2)
x = 30
x/2 = 165
x = 2(165)
x = 330.
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Find the equation of a line that passes through the points (1,-3) and (3,-4).
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-4 +3}{2} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{1}) \implies y +3 = - \cfrac{ 1 }{ 2 } ( x -1) \\\\\\ y+3=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}\implies y=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}-3\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x-\cfrac{5}{2} \end{array}}[/tex]
Answer: First, let's find the slope of the line:
slope = (change in y) / (change in x)
slope = (-4 - (-3)) / (3 - 1)
slope = -1/2
Now, let's choose one of the points, say (1,-3), and use the point-slope formula:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) are the coordinates of the point.
So, substituting in the values we get:
y - (-3) = (-1/2)(x - 1)
Simplifying this equation, we get:
y + 3 = (-1/2)x + 1/2
Subtracting 3 from both sides, we get:
y = (-1/2)x - 5/2
Therefore, the equation of the line that passes through the points (1,-3) and (3,-4) is y = (-1/2)x - 5/2.
Your welcome.
Step-by-step explanation:
Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))Solve the system of equations algebraically. Verify your answer using the graph.
y = 4x – 5
y = –3
What is the solution to the system of equations?
((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))
Answer:
Step-by-step explanation:
To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:
y = 4x – 5 (equation 1)
y = -3 (equation 2)
Substitute equation 2 into equation 1:
-3 = 4x – 5
Add 5 to both sides:
2 = 4x
Divide both sides by 4:
x = 1/2
Now, we can substitute this value of x back into either equation to find y:
y = 4(1/2) – 5 = -3
Therefore, the solution to the system of equations is (1/2, -3).
To verify this solution using the graph, we can plot the two equations on the same set of axes:
y = 4x – 5 (red line)
y = -3 (blue line)
The two lines intersect at the point (1/2, -3), confirming our solution.
Therefore, the answer is (B) (1/2, -3).