All of the graphs and associated functions and equations serve as examples of quadratic functions.
The locations where the graph's line or curve crosses the x-axis are known as the zeros of a function. The line dividing a graph into equal halves is known as the axis of symmetry.
The minimum or greatest point on a graph is the vertex of a function. If a quadratic function expands upward, its vertex is lowest; if not, it is maximum.
The worksheet is given below:
Using the stated definitions, the worksheet's answers are:
Graph 1
Zeros: -4 and 0
Axis of symmetry: x = -2
Min or Max: Maximum
Vertex: (-2, 4)
Graph 2
Zeros: 2
Axis of symmetry: x = -2
Min or Max: Minimum
Vertex: (-2, 0)
Graph 3
Zeros: -3 and 3
Axis of symmetry: x = 0
Min or Max = Minimum
Vertex: (0, -9)
Graph 4
Zeros: -5 and -3
Axis of symmetry: x = -4
Min or Max = Maximum
Vertex: (-4, -1)
Graph 5
Zeros: 3 and 7
Axis of symmetry: x = 5
Min or Max = Minimum
Vertex: (5, -4)
Graph 6
Zeros: None
Axis of symmetry: x = 24
Min or Max = Minimum
Vertex: (2, 5)
Graph 7
Zeros: 1 and 5
Axis of symmetry: x = 3
Min or Max = Minimum
Vertex: (3, -4)
Graph 8
Zeros: -2 and 0
Axis of symmetry: x = -1
Min or Max = Maximum
Vertex: (-1, 1)
Graph 9
Zeros: 5
Axis of symmetry: x = 5
Min or Max = Minimum
Vertex: (5, 0)
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What is the answer? Please explain how you got the answer too!!
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The function is,
⇒ f (x) = x
Here, The graph of the parent function of f (x) = x is shown in figure.
Hence, We get;
The correct sentence to describe in the parent function is,
⇒ Shifted up.
⇒ Horizontal stretch
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Student A and student B were given the following graph and asked to find the value of f(x) when x = 2. Student A gave an answer of 0 while student B gave an answer of −6. Who is incorrect? Drag and drop the correct option into each box to complete the explanation of the error.
Student A is incorrect. The student started at 0 on the y-axis, did not need to move horizontally on the graph, and so moved horizontally to 2 on the x-axis. The student should have started at 0 on the x-axis, moved horizontally to the graph, and then moved vertically to -6, which student B did.
How to obtain the numeric value from the graph?The value of x at which we want to find the numeric value of the function is given as follows:
x = 2.
Tracing a vertical line through x = 2, it will cross the graph of the function at y = -6, hence the numeric value is given as follows:
f(2) = -6.
Meaning that student B is correct.
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8x=x+35
y=8x
what is x and what is y?
The solution of the system is x = 5 and y = 40.
What is the system of equations?A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.
Given:
system of equations,
8x=x+35 {equation 1}
y=8x {equation 2}
From equation 1,
8x = x+35
7x = 35
x = 5
Substituting the value of x to the equation 2,
And y = 8(5)
y = 40
Therefore, the solution is x = 5 and y = 40.
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How do i solve this?
a factory bottles 360 bottles of juice in minutes. find the factory's unit rate of bottles per minute.
A factory produces 72 bottles of juices in one minute.
Meaning of rate:
A rate is a special ratio in which two words are expressed using different units. The price is $69 for 12 ounces of corn if a 12-ounce can costs that much. This is not a ratio of two comparable units, like shirts, for example. This is a ratio between the units of cents and ounces.
We must divide the quantity of bottles produced by the time it takes to make them in order to determine the factory's production rate in bottles per minute. The factory in this instance produced 360 bottles in 5 minutes, resulting in the following production rate:
= 360 bottles / 5 minutes
= 72 bottles/minute
This means that the factory produces 72 bottles of juice per minute.
Hence, the factory produces 72 bottles of juice per minute.
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The following question may be like:
A factory bottles 360 bottles of juice in 5 minutes. Find the factory's unit rate of bottles per minute.
What is the measure of x
Answer:
x = 6.6
Step-by-step explanation:
Proportions:
6.8 ⇒ 8.2
5.5 ⇒ P
P = 8.2 * 5.5 / 6.8
P = 6.6 (Rounded to the nearest tenth)
Please help me mark u brainliest anuthing please i beg u :
in the interval 0 x 360 find the values of x for which tan x =-0. 6745
The required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.
The interval of angle is given as 0° ≤ x ≤ 360°.
The value of x for which tan x is given as, tan x = - 0. 6745.
We have tan negative in two of the four axes, they are second (90° - 180°) and fourth quadrants (270° - 360°).
So, tan x = - 0. 6745
x = tan⁻¹ (- 0. 6745) = -33.9
As periodicity of tan x is 180°, x = 180-33.9 = 146.1°
x = 360-33.9 = 326.1°
Thus, the required values of x in the interval 0° ≤ x ≤ 360° are 146.1° and 326.1°, when the value of tan x is given.
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Expand to write an equivalent expression: LaTeX: -\frac{1}{2}\left(-2x\:+\:4y\right)
On expanding the expression "(1/2)(-2x + 4y)" , the equivalent expression is -x + 2y .
An expression is defined as the sentence that have a minimum of two numbers or variables and at least one math operation in it.
For Example : 2x + 3y is an expression .
The expression is : "(1/2)(-2x + 4y)" ;
By using distributive property which means that a(b+c) = ab + ac ,
we multiply by (1/2) with both the terms ;
⇒ (1/2)(-2x) + (1/2)(4y) ;
Simplifying further ,
we have ;
⇒ -2x/2 + 4y/2 ;
Further simplifying we get ⇒ -x + 2y ;
Therefore , the equivalent expression is -x + 2y .
The given question is incomplete , the complete question is
Expand to write an equivalent expression: (1/2)(-2x + 4y) .
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A man bought a $250 suit and four shirts for $398. How much did he spend per shirt?
Answer:
Step-by-step explanation:
To find out how much the man spent per shirt, you need to divide the total cost of the shirts by the number of shirts.We know that the man spent $250 on the suit and $398 on the four shirts. To find the total cost of the shirts, you can add these two amounts:$250 + $398 = $648To find the cost per shirt, you need to divide the total cost of the shirts by the number of shirts:$648 / 4 = $162So the man spent $162 per shirt.
if distance between points p(3,a) and q(3,1 is 4 units find the value of a
Answer: -3 AND 7
Step-by-step explanation: very important to include the and, as it that point could be to the right or left of (3,1)
A recipe for lemonade is shown. Select the two true statements about the ratios in this recipe.
Lemonade recipe
2 cups sugar
3 cups lemon juice
8 cups water
There is 14 cup of sugar for each cup of water.
There are 2 cups of sugar for each cup of water.
There are 4 cups of water for each cup of sugar.
There are 8 cups of water for each cup of sugar.
Answer:
it is There are 4 cups of water for each cup of sugar
Step-by-step explanation:
complete the description of the piecewise function graphed below
The description of the piecewise function y is -2x + 3.
Find the description of the piecewise function?It is necessary to optically estimate the coordinates of the points because not everything is visible (particularly for the leftmost point).
We have the following considerations, I believe:
(-6, 1.5) (-3, 3) (-3, 3)
(-3, 2) (1, 2) (1, 2)
(1, 1) (6, -9) (6, -9)
the basic function definition appears on all three segments.
y = ax + b
X is always a factor of a, which is the line function's slope.
When a point on a line moves from one end to the other, the ratio y/x shows how many units change when x moves by a specific number of units.
b represents the y-intercept, or the value of y when x = 0.
(-6, 1.5) is followed by the first part and then (-3, 3).
x is modified by +3 units (from -6 to -3).
y shifts by 1.5 or 3/2 units (from 1.5 to 3).
the line has a slope of 3/2/3, which is 3/(23) = 1/2.
supplying the initial portion
y = (1/2)x + b
When we solve for b using a single point's coordinates (for example, -3, 3), we obtain b:
3 = (1/2)×-3 + b
3 = -3/2 + b
6/2 + 3/2 = b
9/2 = b
total equation is
y = (1/2)x + 9/2 = (x + 9)/2
The second portion is a straight line with no slope at all.
y = 2
Third segment, from (1, 1) to (6, -9)
5 units are added to x. (from 1 to 6).
By, y shifts
y = -2x + 3.
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1,3,8,17,31,51.....next value
The next value in the sequence is 80.
In arithmetic, what are sequences?
Sequences are ordered sequences of numbers, also referred to as "terms," such as 2,5,8. Some sequences adhere to a particular pattern that can be exploited to make them infinitely long. For instance, 2,5,8 conforms to the pattern "add 3," thus we can now proceed with the sequence. Formulas for sequences can be used to locate any term inside the sequence.
What does a mathematical series mean?
A series is the cumulative total of a given set of terms in mathematics. However, considerably more generality is possible. Typically, these phrases refer to real or complex numbers.
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Would anyone know this ?
There are two possible options for points and distances:
M = - 14, AM = 0, MB = 49, AB = 49M = 6, AM = 20, MB = 29, AB = 49How to determine the coordinates of point M and distances between points
In this problem we need to determine the location of point M and distances between points A, M and B. This can be done by means of differences on number line and algebraic equations:
M - A = x² - x
M - (- 14) = x² - x
M + 14 = x² - x
M = x² - x - 14
B - M = 5 · x + 4
35 - M = 5 · x + 4
M = 31 - 5 · x
Then, we eliminate M and find the solutions to the resulting quadratic equation:
x² - x - 14 = 31 - 5 · x
x² + 4 · x - 45 = 0
(x + 9) · (x - 5) = 0
x = - 9 or x = 5
Finally, we determine the possible values for M based on the fact that M is between - 14 and 35:
x = - 9
M = 31 - 5 · x
M = 31 - 5 · (- 9)
M = 31 - 45
M = - 14
AM = - 14 - 14
AM = 0
MB = 35 - (- 14)
MB = 49
x = 5
M = 31 - 5 · x
M = 31 - 5 · 5
M = 31 - 25
M = 6
AM = 6 - (- 14)
AM = 20
MB = 35 - 6
MB = 29
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Part B How many of each type of pepper will Andrew use for each type of sauce? Explain.
Andrew intends to make a second batch of Sauce 1 and Sauce II with 3,180 green peppers and 5,560 hot chili peppers.
What is the pepper will Andrew use?You've tried poblanos and like the heat they provide to homemade salsa, but you're ready to branch out. The good news is that there are more than 4,000 different varieties of chili peppers in the world, and more are constantly being created.
Andrew prepares hot salts. his first batch will have 4 chili peppers and 6 green peppers, while his second batch will contain 3 green peppers and 10 chili peppers. We therefore need to know how many of each he requires.
To give you an idea of how many peppers to use per bottle of hot sauce, we suggest using at least two really hot peppers per bottle for a sauce with a lot of heat. In addition, habaneros can be made with 4-6 peppers.
Therefore, 975 green peppers and 1,250 hot peppers are purchased by Andrew. He uses all of those peppers to make both types of sauce.
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How to factor -25-15mn
The factorization of -25-15mn is -5(5+3mn)
What is factorization?Factorising is the reverse process of expanding brackets. To factorise an expression fully, means to put it in brackets by taking out the highest common factors. The simplest way of factorising is: Find the highest common factor of each of the terms in the expression.
For example 5( 3x+ 2y+ 4z) can be expanded into 15x + 10y + 20z and moreover 15x + 10y + 20z can be transformed by finding the factors between each terms, here the factor is 5; 5( 3x + 2y +4z)
Similarly to factorize -25-15mn we find the factor that is common to -25 and - 15 . The common factor is -5.
therefore factorizing -25-15mn we bring -5 out of -25 and -5
= -5( 5+3mn)
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Help please! God bless the person who helps
Answer:
3/2
Step-by-step explanation:
slope is rise over run:
3/2
A t shirt vender is thinking about changing the number of tshirts he brings to an event. To make sure he doesnt run out, he plans to bring more of the size most likely to be sold
The seller ought to bring more medium-sized shirts because these are the best-selling size.
From the graph we can see that total small shirt sold = 160
Total number of sale of small shirt = 225
Now remaining shirts = Total small shirt sold/Total number of sale
Now remaining shirts = 160/225 × 100
Now remaining shirts = 71
Total medium shirt sold = 335
Total number of sale of medium shirt = 375
Now remaining shirts = Total shirt sold/Total number of sale
Now remaining shirts = 335/375 × 100
Now remaining shirts = 89
Total large shirt sold = 275
Total number of sale of large shirt = 325
Now remaining shirts = Total shirt sold/Total number of sale
Now remaining shirts = 275/325 × 100
Now remaining shirts = 85
Total X-large shirt sold = 125
Total number of sale of X-large shirt = 175
Now remaining shirts = Total shirt sold/Total number of sale
Now remaining shirts = 125/175 × 100
Now remaining shirts = 71
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The complete question is given below:
Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12. 28%, compounded monthly. Charles will also be responsible for 6. 88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid. ) Dodge Cars in Good Condition Model/Year 2004 2005 2006 2007 2008 Viper $7,068 $7,225 $7,626 $7,901 $8,116 Neon $6,591 $6,777 $6,822 $7,191 $7,440 Intrepid $8,285 $8,579 $8,699 $9,030 $9,121 Dakota $7,578 $7,763 $7,945 $8,313 $8,581 a. 17. 64% b. 15. 67% c. 16. 70% d. 12. 86% Please select the best answer from the choices provided A B C D
Percent of the total amount a per the given list price, documentation fee , registration fee and other payment paid by Charles is given by :
Option c. 16.70%
Cost of his old 2004 Dodge Neon = $6591
Sales tax = 6.88%
Dealer gives 80% trade in price on hos car
After tax selling price of the car
= 6,591 × (80/100) × [ 1 - (6.88/100) ]
= $4910.03
= $4,910
Vehicle registration amount = $1,089
List price of car = $21,450
Documentation fee = $124
Total cost of the car
= $21,450 + $1,089 + $124
= $22,663
Net amount Charles needs to pay
= $22,663 - $4,910
= $17,753
Monthly payment at the rate of 12.28% compounded monthly for 3 years
= 17753 [ 12.28%( 1+ 12.28%)^3 / [( 1+ 12.28%)^3 -1 ]
= $592
Total amount paid by Charles
= $592 × 36
= $21,312
Total interest paid by Charles
= $21,312 - $17,753
= $3,559
Percent of the total amount
= ( $3,559 / $21,312 ) × 100
= 16.699%
= 16.70%
Therefore, the percent of the total amount paid by Charles is equal to Option c. 16.70%.
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Payton did not spend $15.00 at the grocery store. Write an inequality to represent the amount Payton spent. Then wrote two examples of amounts Payton might have spent.
A possible inequality to represent the amount Payton spent is x >15, and two examples of the possible amount of money Payton spent are $30 and $6.
What is inequality?This is a mathematical expression that represents a situation using symbols such as ≥ (greater or equal to) or < (less than).
What is a possible inequality in this case?A possible inequality is 15 >x or 15 <x, which means the amount of money spent was less than or more than 15.
Some possible values within this range are:
$10
$2
$6
$30
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ec
19. Lennon bought two books for $21.00. One book
cost $8.00. Solve the equation 21 = b + 8 to find
b, the cost of the other book.
Answer:
b = 13
Step-by-step explanation:
21 = b + 8 Subtract 8 from both sides
21 - 8 = b + 8 - 8
13 = b
Answer: 13
Step-by-step explanation:
He bought two books for $21, and one of the books was $8. With this, we know that if we subtract 8 from 21, we can get "b", or the cost of the other book
21 = b + 8
-8 -8
13 = b
b = 13
Therefore, b = 13, or $13 for the other obok
Formulate but do not solve the following exercise as a linear programming problem. Ace Novelty manufactures Giant Pandas and Saint Bernards. Each Panda requires 1. 5 yd2 of plush, 30 ft3 of stuffing, and 5 pieces of trim; each Saint Bernard requires 2 yd2 of plush, 35 ft3 of stuffing, and 8 pieces of trim. The profit for each Panda is $20 and the profit for each Saint Bernard is $30. If 3600 yd2 of plush, 66,000 ft3 of stuffing and 13,600 pieces of trim are available, how many of each of the stuffed animals should the company manufacture to maximize profit P in dollars? (Let x represent the number of Giant Pandas to be manufactured and y represent the number of Saint Bernards to be manufactured. ) Maximize P = 20x+30y subject to the constraints plush stuffing trim x ≥ 0 y ≥ 0
The system of equations for the stuffed animals should the company manufacture to maximize profit P in dollars is P = 20x + 30y
The term equation in math is called as an expression or a statement that comprises two algebraic expressions with the same value and are separated by an equal symbol in between them.
Here we know that we have to determine the number of each of three types of souvenirs to be made.
Here let us consider that x, y, and z denote the respective numbers of type-A, type-B, and type-C souvenirs to be made.
Here we know that the total amount of time that machine I is used is given by 2x + y + z minutes and must equal 180 minutes.
Here the known details will leads to the equation
=> 2x + y + z = 180
While we take the similar considerations on the use of machines II and III lead to the following equations which is written as
=> x + 3y+2z = 300
=> 2x + y + 2z = 240
Here we have also identified the the stuffed animals should the company manufacture to maximize profit P in dollars as,
=> P = 20x+30y
Here we know that the subject to the constraints plush stuffing trim x ≥ 0 y ≥ 0.
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graph y=|x+4|
Please help!!
The graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=|x+4|.
Graph the absolute value using the vertex and a few selected points.
Plot the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2)
Therefore, the graph for the points (-6, 2), (-5, 1), (-4, 0), (-3, 1) and (-2, 2) is plotted as below.
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An equation 3 (2x - 7) = 3
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work.
The solution of the equation 3(2x - 7) = 3 is x = 4 and the equation has a single solution.
How to solve equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, let's solve the equation as follows:
3(2x - 7) = 3
open the bracket
3(2x - 7) = 3
6x - 21 = 3
add 21 to both sides of the equation
6x - 21 = 3
6x - 21 + 21 = 3 + 21
6x = 24
divide both sides by 6
6x / 6 = 24 / 6
x = 4
Therefore, the equation has only one solution. The solution of the equation is x = 4.
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Help me please! (Worth 30 points!)
Question 8: A system of equations is given.
-2y = 2 - 3x
-5y = 10 - 5x
Part 1: Use elimination to solve the system of equations & show all work.
Part 2: Identify the values for x & y by filling in the blanks below.
x = ______
y = ______
The solution of the system of equation using elimination method is x = -2, y = -4
How to solve system of equations using elimination method?The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.
-2y = 2 - 3x --- (1)
-5y = 10 - 5x ---(2)
To eliminate y, multiply (1) by -5 and multiply (2) by -2. Then subtract the result. That is:
-5 × (-2y = 2 - 3x) => 10y = -10 + 15x
-2 ×(-5y = 10 - 5x) => 10y = -20 + 10x
.......................................................................
0 = 10 +5x
.........................................................................
0 = 10 +5x
5x = -10
x = -10/5
x = -2
put x = -2 in (1):
-2y = 2 - 3x
-2y = 2 -3(-2)
-2y = 2 + 6
-2y = 8
y = -8/2
y = -4
Thus, x = -2, y = -4
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find x and y
7x+y=17
-9x-y=-21
The value of x and y is solved in the equation 7x + y = 17 and -9x - y = -21 to get
x = 2 y = 3How to solve for x and yThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
7x + y = 17
-9x - y = -21
adding the equations will result to
-2x + 0 = -4
x = 2
substitute x = 2 into 7x + y = 17
7x + y = 17
7 * 2 + y = 17
14 + y = 17
isolating y
y = 17 - 14
y = 3
therefore x = 2 and y = 3
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Brainly to correct answer
Jaidon counted dishes in the kitchen cabinet. The table shows what was found.
Plates 10
Bowls 8
Cups 14
Write a ratio to compare plates to all dishes.
10:14
10 over 22
32 to 10
10 over 32
Answer:
10/32
Step-by-step explanation:
10+8+14 = all dishes = 32
10 = how many plates
In a ratio: 10/32
a logarithm is defined as the power to which a base must be raised in order to equal a given number, why can't we have negative bases
Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.
Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.
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On the screenshot is my question.
The solution is Option A.
The inequalities have one common solution
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equations be represented as A and B
The value of A is
( 1/2 )x + 8 ≤ 10 be equation (1)
-3x - 24 ≤ - 36 be equation (2)
On simplifying the equation (1) , we get
Subtracting 8 on both sides of the equation , we get
( 1/2 )x ≤ 2
Multiply by 2 on both sides of the equation , we get
x ≤ 4
And , on simplifying the equation (2) , we get
Adding 24 on both sides of the equation , we get
-3x ≤ -12
Multiply by -1 on both sides of the equation , we get
3x ≥ 12
Divide by 3 on both sides of the equation , we get
x ≥ 4
So , the common solution to the inequalities is x = 4
Hence , the inequalities have solution at x = 4
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data collected at the same, or approximately the same point in time are a. time series data. b. approximate data. c. approximate time series data. d. cross-sectional data.
Data collected at the same, or approximately the same point in time are Cross- sectional data
In statistics and econometrics, cross-sectional data, or a cross section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.
For instance, if we wanted to determine the prevalence of obesity in a population, we could randomly select a sample of 1,000 people (also referred to as a cross section of that population), measure their height and weight, and then determine what proportion of that sample falls under the definition of obesity. With the use of this cross-sectional sample, we are able to get a current picture of that group. Be aware that based on a single cross-sectional sample, we cannot determine whether the prevalence of obesity is rising or falling; we can only describe the current proportion.
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