Here is one possible system of equations to represent the information provided:
The system of equationsLet x be the number of apple pies, y be the number of pumpkin pies, and z be the number of key lime pies.
The number of apple pies is the same as the number of pumpkin and key lime pies combined, since both tables have the same number of pies: x = y + z
There are twice as many pumpkin pies as key lime pies: y = 2z
There are 5 more apple pies than pumpkin pies: x = y + 5
Solving for y in the second equation, we have: y = 2z
Substituting that into the first equation we have: x = 2z + z = 3z + 5
Substituting that into the third equation we have: x = y + 5 = 2z + 5
So we have a system of equations:
x = 3z + 5y = 2zNow we can solve for any of the variables. Let's find the number of PUMPKIN pies
y = 2z
We can substitute in any value of z to get y.
For example, if we let z=5, we can find that
y=2(5)=10 pumpkin pies
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if two distinct members of the set $\{ 2, 4, 12, 14, 21, 28, 98 \}$ are randomly selected and multiplied, what is the probability that the product is a multiple of 196? express your answer as a common fraction.
The probability that the numbers are selected and multiplied to be a multiple of 196 is 1/3.
196 is the multiple we require.We list the components of 196, which are 14*14=2*7*2*7.
Therefore, the required numbers that will be present in any product must have at least these as its factors.So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary.
So, we choose 98 now, and it's possible that all it takes to achieve 196 is to multiply that by 2. Therefore, if we take 98 as one of our numbers, the other numbers that must be multiplied are 2,4,12,14,28. That makes 5 pairs necessary. We can now take pairings like (21,28) and (14,28) based on the prime factorization (14,28).
The total number of possible pairs is ⁷C₂ = 21
Therefore, the required probability =7/21=1/3
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A team of 9 dodgeball players needs to choose
The function that would be needed for the team of dodgeball players to choose a co - captain and a captain would be a permutation.
When is a permutation needed ?The techniques used to determine how many outcomes are conceivable in certain circumstances are permutation and combination. Combinations and permutations are referred to as selections and arrangements, respectively. The sum rules and product rules, which are based on the basic concept of counting, make counting simple to use.
When an order or sequence of arrangement is required, permutations are used. There is an order that needs to be used here and that order is that a captain is picked to have more authority than a captain.
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The full question is:
Permutation, combination, or neither? A team of 9 dodgeball players needs to choose a co-captain and captain.
For questions 1-2, use the following scenario:
Some wooden chests are in a store. A green chest has a length of 180 centimeters (cm), a width of 75 cm, and a height of 20 cm.
1. If another box, a blue box, is proportional in size, what is its length if its width is 15 cm?
2. If another box, a red box, is proportional in size, what is its height if its length is 13 cm?
The measures are given as follows:
1. Length of 36 cm.
2. Height of 1.44 cm.
How to obtain the measures?The measures are obtained applying the proportions in the context of this problem.
The ratio between the length and the width is given as follows:
Length/Width = 180/75
Length/Width = 2.4
Length = 2.4 Width.
For a width of 15 cm, the length is given as follows:
15 x 2.4 = 36 cm.
The ratio between the length and the height is given as follows:
Length/Height = 180/20
Length/Height= 9
Length = 9Height
Height = Length/9
Hence the height if the length is of 13 cm is given as follows:
13/9 = 1.44 cm.
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The radius of a circle is 8 cm. Find its area to the nearest whole number.
Answer: 50.24 or 50
Step-by-step explanation:
the radius is half of a circle so the diameter is 16, the formula for area is diameter x pi
pi= 3.14
16 x 3.14 =50.24
Sam has some water in a jug. He pours all of this water into a second jug. Use the ruler tool to draw the correct level of water on the second jug
By using the ruler tool to draw the correct level of water on the second jug, the measurement of water is observed to be 500 ml or half litre.
The capacity and shapes of both the given jugs are different.
The first jug is measured in terms of millilitres and second jug is measured in terms of lites.
It is given that water is poured from one jug into the other. The measurement of the water level on both the jugs will be the same.
From the conversion of measurements, we know, 1 litre = 1000 millilitres
On the second jug into which water is poured, the first measurement line is 0.25 L. The second bigger line is 0.5 L.
The water level is observed to be till the second line in the second jug. Thus, the water on second jug is 0.5 L or 500 ml.
The question is incomplete. The complete question has the picture of two jugs. It is attached in the attachment below.
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Find the component form of the um of u and v with direction angle u and v.
Magnitude
u = 14
Angle
u = 45°
Magnitude
v = 70
Angle
v = 180°
(14cos45° + 70cos180°, 14sin45° + 70sin180°) = (17.9, -55.1) is the component form of the sum of u and v with direction angles u and v.
What's an angle?The amount of rotation that occurs between two planes or straight lines is what is meant to be meant by the geometrical term "angle." A full circle is 360 degrees, and an angle is measured in degrees. Right angles (90 degrees), acute angles (less than 90 degrees), and obtuse angles (more than 90 degrees) are the most prevalent types of angles. Depending on how they relate to one another, angles can also be broken down into complementary or supplementary categories. The sum of complementary and supplementary angles is 90 degrees, while the sum of the two is 180 degrees.
Component form :The vector addition formula can be used to determine the component form of the sum of u and v. According to this formula, the direction angle of the vector sum is equal to the arctangent of the ratio of the sum of the y-components of the two vectors to the sum of the x-components of the two vectors, while the magnitude of the vector sum of two vectors is equal to the square root of the sum of the squares of each vector's magnitude.
The component form of the sum of the given vectors u and v is as follows:
Magnitude = √(14²) + (70²)) = 70.45
The direction angle is arctan((14 × sin(45) + 70×sin(180)) / (14×cos(45) + 70×cos(180)))
= 153.43°
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please help me with this geometry question
Answer:
x = 4 cm
Area= 36 cm2
Step-by-step explanation:
x is the measurement of one side of the triangular shape above (4cm)
Area = (4)(9) = 36 (shaded face)
Hope this helps
aspen has 306 306306 green beads and 210 210210 silver beads. for every 5 cm 5cm5, start text, c, m, end text of a belt that aspen sews, they use 40 4040 green beads and 24 2424 silver beads. after how many centimeters of the belt will aspen have equal numbers of green and silver beads left?
After 30 cm of the belt sewn, Aspen will have equal numbers of green and silver beads left.
Aspen has 306 green beads and 210 silver beads.
For every 5 cm of a belt that Aspen sews, they use 40 green beads and 24 silver beads.
We can set up an equation to determine when Aspen will have equal numbers of green and silver beads left.
Let x be the number of centimeters of the belt Aspen will have sewn when they have equal numbers of green and silver beads left.
We can use the following equation:
306 - (40/5)x = 210 - (24/5)x
Solving for x, we get:
x = (306-210)/(40/5-24/5) = (96)/(16/5) = 96*5/16 = 30 cm
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If y varies directly as x and x = 33 when y = 22, find x when y = 32.
The value of x when y is 32 is 21.3
How to determine the value of x?From the question, we have the following parameters that can be used in our computation:
y varies directly as x
This means that
Y/X = y/x
From the question, we have the following values
x = 33 when y = 22
So, we have
33/22 = y/x
When x = 32, we have
33/22 = 32/x
Solve for x
x = 22 * 32/33
Evaluate
x = 21.3
Hence, the value of x is 21.3
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When the function f(x) is divided by 3x + 1, the quotient is 2x^2 + 2x - 9 and the remainder is 7. Find the function f(x) and write the result in standard
form.
Answer:
To find the function f(x), we need to use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial by x - a, the remainder will be equal to the value of the polynomial at x = a.
We know that f(x) divided by 3x + 1 leaves a remainder of 7, so we can set up the equation:
f(x) = (3x + 1)(2x^2 + 2x - 9) + 7
Expanding the left side of the equation, we get:
f(x) = 6x^3 + 2x^2 - 27x - 9 + 7
Simplifying, we get:
f(x) = 6x^3 + 2x^2 - 27x + 2
The function f(x) is in standard form.
Answer:
When the function f (x) is divided by 3x – 1, the quotient is 2x² – 3x + 6 a
Step-by-step explanation:
Step 1 Devisor = 3x - 1Quotient = 2x2 - 3x + 6Remainder = 7Dividend = f(
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
The final step in solving the inequality is: C. x < 3.
How Solve an Inequality?To solve an inequality means to find the possible value of a variable in in inequality statement, which will also make it true.
Given the inequality, –2(5 – 4x) < 6x – 4, we can solve as follows:
Step 1: Apply the distributive property
–10 + 8x < 6x – 4
Step 2: Subtract 8x from both sides
–10 < –2x – 4
Step 3: Add 4 to both sides
–6 < –2x
Step 4: Divide both sides by -2
-6/-2 > -2x/-2
3 > x
x < 3
The final answer of the inequality is: C. x < 3.
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Please help me solve this. I don’t understand it at all. Please explain and give me the answers please and thank you
The Pythagorean Theorem states that the square of the lengths of the two sides of a right triangle adds to the square of the length of the hypotenuse.
How do you prove Pythagorean triples?The Pythagorean Theorem states that a ² +b ² =c ² for a right-angled triangle ABC, right-angled at B. The whole integers a, b, and c form a Pythagorean triple if a and b are the lengths of the two sides of a right-angled triangle with hypotenuse c.
Draw a BD that is perpendicular to AC and meets at D. So, the Pythagorean theorem is established. Recall that the Pythagorean Theorem only applies to right-angled triangles. Two even numbers and one odd number, or all odd numbers, cannot form a Pythagorean triple. The square of an odd number is an odd number, and the square of an even number is an even number, hence this is true. A, B, and C are the three positive integers, and the Pythagorean triples are written as a ² +b ² =c ².
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Given: e || f and g is a transversal Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the corresponding angles theoremalternate interior angles theoremvertical angles theoremalternate exterior angles theorem. Therefore, 1 8 by the transitive property
We also know that 1 4 and 8 5 by the vertical angles theorem.
Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another. A vertical angle and the angle it is near to are also supplementary angles, which means their combined angle is 180 degrees.
The opposite angle, for example, is 45° when two lines intersect to form an angle, say X=45°. And the angle next to angle X will be 180 – 45, or 135 degrees.
Correct Question :
Given: e || f and g is a transversal.
Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the (corresponding angles theorem / alternate interior angles theorem / vertical angles theorem / alternate exterior angles theorem). Therefore, 1 8 by the transitive property.
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If C = G - 3F, find the trinomanial that represents C when F = 2x^2+6x-5 and G = 3x^2+4
The trinomial expression that represents C is
C = -3x² - 18x + 19
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
C = G - 3F ______(1)
F = 2x² + 6x - 5
G = 3x² + 4
Substituting F and G in (1)
C = 3x² + 4 - 3(2x² + 6x - 5)
C = 3x² + 4 - 6x² - 18x + 15
C = -3x² - 18x + 19
Thus,
The trinomial expression is
C = -3x² - 18x + 19
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A 6 ft. tall man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?
here we are given that a 6ft high man is flying a kite with a string of length 100ft at an angle of elevation 52° . We would like to calculate the height of the kite above the ground. For figure refer to the attachment. We would have to make use of trigonometric ratios here as ,
In ∆ ABE ,
[tex]\longrightarrow \sin 52^o = \dfrac{AB}{AE} \\ [/tex]
[tex]\longrightarrow 0.8 =\dfrac{y}{100ft} \\ [/tex]
[tex]\longrightarrow y =0.8(100ft) \\ [/tex]
[tex]\longrightarrow y = 80ft \\ [/tex]
Now the total height above the ground will be ,
[tex]\longrightarrow h = y + h_{man} \\ [/tex]
[tex]\longrightarrow h = (80 + 6)ft\\ [/tex]
[tex]\longrightarrow\underline{\underline{ h = 86\ ft. }} \\ [/tex]
And we are done!
S. Maya is spending money at the average rate of $3 per day. After 14 days she has $68 left. The amount left depends on the number of days that have passed. Hint: Is spending money a positive or negative.
1. Write an equation for the situation.
B. Use your equation to find out when she will have $35 left.
C. How much money does Maya have after 9 days?
C. How much money does Maya have after 9 days?
E. Explain what the slope and y-intercept represent for this problem
a) The slope equation representing Maya's spending situation is x - 3n = 68, where x is the initial amount Maya has and n is the number of days she has spent her money.
b) Using the above equation, after 25 days, Maya will have $35 left.
c) Using the above equation, after 9 days, Maya will have $83 left.
d) The slope is the average rate Maya spends per day, which is $3 while the y-intercept represents the initial amount she has.
What is a slope equation?A slope equation is written in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Maya's average spending rate per day = $3
The number of days Maya has spent money = 14 days
The amount left after 14 days = $68
Let the initial amount Maya has = x and the number of days she has spent her money = n
Equation:a) x - 3n = 68
x = 68 + 3n
x = 68 + 3(14)
x = 68 + 42
x = 110
= $110
b) 110 - 3n = 35
-3n = -75
n = 25
c) 110 - 3(9)
= 110 - 27
= 83
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Mrs. Wu uses a 25% off coupon to buy 1 adult ticket and 1 child ticket to a movie. She pays a total amount of $9.00. A child ticket without the coupon costs $4.00. Write an equation that can be used to find the cost of an adult ticket, x, without the coupon.
Answer:
$9 = (1-25%) * (x + 4)
Step-by-step explanation:
$9 = (1-25%) * (x + 4)
on a radio, min turned the dial until it was set to 96.3.what is 96.3 rounded to the nearest whole number?
In the given scenario, 96.3 rounded to the nearest whole number is 96.
A whole number is a number that does not have a fractional or decimal part, and is an integer greater than or equal to zero.
Whole numbers are often used to represent the count of discrete objects or items.
Examples of whole numbers include: 0, 1, 2, 3, 4, 5, and so on. Whole numbers are a subset of the set of integers.
To round a decimal number to the nearest whole number, look at the digit to the right of the decimal point.
If the digit is less than 5, round down. If the digit is 5 or greater, round up.
Rounding off is a method of approximating a number to a specified number of significant digits or decimal places.
The basic idea behind rounding off is to keep only the most significant digits of a number and discard the rest.
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Which of the following is a solution set for the following graph?
Substitute the sign for the symbol to graph the provided inequality.
What is the graph?Replace the symbol with the = sign to graph the specified inequality.
Create a table now.
y= 8x - 6.
Assume a random integer for x to determine y.
x y= 8x - 6.
-2 -4
0 -4
-6 8
We are now graphing the points. Connect the spots with the dotted line.
Now, we'll do shading.
Use the test point (8,6)
Therefore, we darken the area that doesn't include (8,6)
We are now graphing the points. Connect the spots with the dotted line.
Substitute the = sign for the symbol to graph the provided inequality.
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Find the proportion relating the side lengths of smaller quadrilateral to the lager quadrilateral
The ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be 4:5.
What is a quadrilateral?The quadrilateral has four sides and four angles. The sum of internal angles is 360 degrees.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The quadrilateral MLKJ is similar to the quadrilateral ABCD. Then the ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be given as,
Ratio = 12 / 15
Ratio = 4/5
The ratio of the lengths of the smaller quadrilateral to the larger quadrilateral will be 4:5.
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What value of g makes the equation true?
The value of the coefficient of the variable 'x' is 3. Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
(x + 7)(x - 4) = x² + gx - 28
Simplify the equation, then we have
(x + 7)(x - 4) = x² + gx - 28
x² + 7x - 4x - 28 = x² + gx - 28
x² + (7 - 4)x - 28 = x² + gx - 28
3x = gx
g = 3
The value of the coefficient of the variable 'x' is 3. Then the correct option is C.
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The complete question is given below.
Samuel buys 3 bottles of juice that each have an original price of 2.80. He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%. How much does Samuel pay 3 bottles of juice?
Samuel pay 5.81 for the 3 bottles of juice.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
Samuel buys 3 bottles of juice that each have an original price of 2.80.
And, He uses a coupon for 35% off. Then, he is changed sales tax at a rate of 6.5%.
Here, The original cost of 3 bottles of juice = 3 × 2.80
= 8.40
Now, He uses a coupon for 35% off.
Hence, The off price = 35% of 8.40
= 35/100 × 8.40
= 2.94
So, The amount of 3 bottles of juice = 8.40 - 2.94
= 5.46
And, He is changed sales tax at a rate of 6.5%.
Thus, The sales tax on bottles = 6.5% of 5.46
= 6.5/100 × 5.46
= 0.35
Thus, The actual amount of 3 bottles of juice = 5.46 + 0.35
= 5.81
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this is a camera toy
edge of the cube = 5cm
cylinder diameter = 4cm and
cylinder height = 20cm
1) find the clay required to make this toy
2)find the area to be painted
The total clay required is 376.2 cm³and area to be painted is given by 300.7 cm²
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr2h.
Given here: The dimensions of the edge of the cube as 5cm and the cylinder diameter is 4cm with a height of 20cm
We know the volume of the cube is given by a³ where a is the measure of the length of the cube
Thus a³=5³
=125 cm³
and surface area of the cube is given by 6a²=6×25
=150 cm²
Again the volume of the cylinder and surface area of the given cylinder is as follows:
Volume= 22/7×2²×20
=251.2 cm³
surface area = 2·π·2·10+2·π·22≈150.79645cm²
Thus the clay required to make the toy is=125+251.2
=376.2 cm³
And the area to be painted is given by =150.7+150
=300.7 cm²
Hence, The total clay required is 376.2 cm³and area to be painted is given by 300.7 cm²
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In rhombus RSTU diagonals RT and US intersect at point V, m
The length of US in the rhombus is 16 units
How to determine the length of USThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
RT = 6x + 4
SO = 7x - 6
By the properties of rhombus, we have
RT = 2 * SO
So, we have
6x + 4 = 14x - 12
Evaluate the like terms
8x = 16
So, we have
x = 2
This means that
US = 6 * 2 + 4
US = 16
Hence, the length is 16 units
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The variables x and y are proportional. When y=4,
x=1/2 or 1 over 2
. Find the constant of proportionality.
Answer:
Step-by-step explanation:
bro ima bout to drop out of highschool because of math '_'
I dont care what happeneds with me anymore
An urn contains 17 balls marked LOSE and 3 balls marked WIN. You and an opponent take turns selecting a single ball at random from the urn without replacement. The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN balls. If you draw first, find the probability that you win the game on your second draw
The probability that you win the game on your second draw is 1/1140.
We have an urn containing 17 balls marked LOSE and 3 balls marked WIN. You and the opponent take turns of a random selection of a single ball from the urn without replacement.
The person who picks the third WIN ball wins the game. It does not matter who picked the first two WIN balls.
If you first, we need to find the probability that you will win the game on your second draw.
Here we consider Y: you draw W first, O: opponent draws W first and
Y: you draw W second.
Then,
P(YOY) = P(W W W )
Where W is win.
P(YOY) = 3/20 × 2/19 × 1/18
P(YOY) = 1/1140
Therefore the probability that you win the game on your second draw is 1/1140.
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Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number
Ivanna earns $2,400 if she doesn't sell any copies of history is fun.
What is the difference between positive and negative number?Ivanna makes an extra $120 ($120) for each additional copy she sells and a loss of $120 ($120) for each fewer copy.
If Ivanna doesn't sell any copies of History is Fun, her total compensation is $2,400.
Ivanna makes a total salary of y = 2,400 + 120x, where x is the quantity of copies of her book History is Fun she sells.
We compare the compensation for two successive values of y to determine the change in Ivanna's pay.
We must estimate y when x exists of consecutive values i.e. 1, 2, 3, 4
We compute the value of y when x = 1, 2 and 3.
When x = 1, y = 2,400 + 120 (1) = 2,400 + 120 = $2,520.
When x = 2, y = 2,400 + 120 (2) = 2,400 + 240 = $2,640.
When x = 3, y = 2,400 + 120 (3) = 2,400 + 360 = $2,760.
To estimate the increase in her pay for a copy, we subtract y when x = 2 from y when x = 3.
(y when x = 3) - (y when x = 2) = $2,760 - $2,640 = $120.
So for every extra copy, Ivanna gets an extra $120.
To estimate the decrease in her pay for a copy, we subtract y when x = 3 from y when x = 2.
(y when x = 2) - (y when x = 3) = $2,640 - $2,760 = -$120.
So for every less copy, Ivanna loses $120.
To estimate her pay when she doesn't sell any copies of history is fun, we substitute the value of x as 0 in y.
When x = 0, y = 2,400 + 120 (0) = $2,400.
So Ivanna earns $2,400 if she doesn't sell any copies of history is fun.
The complete question is:
Ivanna is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2400+120x = y.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Ivanna's total pay for each copy of History is Fun she sells?
What is Ivanna's total pay if she doesn't sell any copies of History is Fun?
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Graph the function.
f(x)=-2x²
Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values.
Answer: The graph of the function f(x) = -2x² is a parabola that opens downward, with its vertex at the origin (0,0). The x-axis is the axis of symmetry for this parabola.
To plot five points on the graph of the function, we can substitute different x-values into the function and solve for y:
For x = 0, y = f(0) = -2(0)² = 0
For x = -2, y = f(-2) = -2(-2)² = 8
For x = -3, y = f(-3) = -2(-3)² = 18
For x = 2, y = f(2) = -2(2)² = -8
For x = 1, y = f(1) = -2(1)² = -2
So, the five points on the graph of the function are (0,0), (-2,8), (-3,18), (2,-8), (1,-2).
It's important to note that, the graph of f(x)=-2x² will be a parabola opening downward and passing through the points that we found.
Step-by-step explanation:
The graph shows the approximate U.S. box office revenues (in billions of dollars) from 2000 to 2012, where x = 0
represents the year 2000.
U.S. Box Office Revenue
ve (billions
Bollars) from 2000 to 2012, where x=0 represents the year 2000
Thank you! to anyone who finds it!!
The rise and run may be used to determine the slope. Discover the y-intercept.
What is the line's slope intercept equation?y= mx + bY= mx + b is the slope intercept form. Form of a Point Slope: y - y1 = mThe formula for a linear function is f(x)=mx+b.To determine a linear function's equation from its graph: The rise and run may be used to determine the slope. Discover the y-intercept. Put the value in the f(x)=mx+b function.When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. The y value of the y intercept point is denoted by the symbol b in the formula.where x = 0represents the year 2000.U.S. Box Office Revenueve (billionsBollars) from 2000 to 2012, where x=0 represents the year 2000To learn more about graph refer to:
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For the given graph, the slope is 2/9, t the U.S. box office revenue in 2018 is 12 billion.
Given a graph depicting approximations of US box office earnings (in billions of dollars) from 2000 to 2012, what would you conclude?
We must calculate the graph's slope and y-intercept.
In order to overcome the issue, we are employing the point-slope form. Two points are obtained from the graph: (x1,y1) = (0,8) and (x2,y2) = (9, 10).
Consequently, slope is m = y2 - y1 / x2 - x1
⇒ 10 - 8/ 9 - 0 = 2/9
This is the graph's straight line's slope.
The point-slope form is given by y-y1 = m. (x-x1)
Meaning: y - 8 = m(x - 0)
The line's equation is then y = 2x/9 + 8, with 8 serving as the y-intercept.
• In this case, the y-intercept provides the beginning value, or 8 when x = 0. Here, the year 2000 is represented by the number 0, and the U.S. box office took in $8 billion in that year.
2 • The graph's straight line shape and slope (m) indicate that the U.S. box office's revenue is rising at a steady rate of $2 billion every two years. 2 year 9 is on the x-axis.
• Using the equation, y = 2, we may get the precise income in any year from 2000 through 2012.
The x axis in the graph corresponds to the year;
hence, the point at x = 0 denotes the year 2000 and the one at x = 12 denotes the year 2012.
In order to get the income for 2018, we must determine the value of y when x equals 18.
The formula is y = 2x/9 + 8
y = 2(18)/9 + 8
y = 12
That is, 12 billion dollars will be made at the U.S. box office in 2018.
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Complete Question -
Condense 6 ln x +4 ln y.
The condensed form of 6 ln x + 4 ln y is ln ( x⁶ y ⁴ ).
What is a logarithmic function?The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.
Given a logarithmic function 6 ln x +4 ln y.
Using:
ᵃ log m = log mᵃ and
log a + log b − log c = log ( a b/ c )
In our case,
6 ln x + 4 ln y
=> ln x⁶ + ln y⁴
=> ln ( x⁶ y⁴ )
Therefore, ln ( x⁶ y ⁴ ) is The condensed form of 6 ln x + 4 ln y.
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