5. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture?

The vertex form of the expression is y = (x-4)²-1

What is vertex form?

In this little tutorial, we'll look at how to change a standard form into a vertex form and vice versa. A parabola's equation can be shown in various ways, including standard form, vertex form, and intercept form. Any of these forms can be changed into either of the other two depending on the situation. We will discover how to convert in this article.

The vertex form is y = (x-h)² + k

The only term with x with 2hx from the vertex form and 8x in order to form a standard form.

The given expression is x²-8x+15,

So 2hx = -8x

h = 4

Substituting  in the original expression we will have

y = (x-4)²-1

Hence this is in vertex form.

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Let the selling price for walnuts be x and the selling price for the almonds be y.

On the first day, Erick sold 2 pounds of walnuts and 4 pounds of almonds for $28. This implies that

On the second day, 4 pounds of walnuts and 3 pounds of almonds for $31.

The value of x is 0.94 or 3.34 with the functions given.

The function is given as:

f = (x, 4 x - 17)

g = (x, (2 x + 8) / 5)

We get that:

g⁻¹ (x) = (2 x + 8) / 5

f o f (x)

= f (f (x))

= (4x [ 4x - 17] - 17)

= 16 x² - 68 x - 17

ATQ:

16 x² - 68 x - 17 = (2 x + 8) / 5

80 x² - 340 x - 85 = 2 x + 8

80 x² - 342 x - 93 = 0

Solving the equation:

D = b² - 4 ac

D = (-342)² - 4 (80) (-93)

D = 36681

x = (342 ± √36681) / 2(80)

x = (342 ± 191.52) / 160

x = 0.94 or x = 3.34

Therefore, the value of x is 0.94 or 3.34 with the functions given.

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Ratio of the length of a tile in model to length of actual tile is 1/9 and Ratio of Area of tile to area of actual tile is 1/ 81

Given,

Length of each tiles = 2/3 in

Width of each tiles = 1/2 in

The actual tiles have length = 1/2 ft = 6 in {1 foot = 12 inch }

Width of actual tiles = 3/8 ft = 4.5 in

Ratio of length of tile in the model to the length of an actual tile =

length of tile / length of an actual tile

= [tex]\frac{2/3}{6} = \frac{1}{9}[/tex]

Area of tiles = area of rectangle = length × width

= 2/3 × 1/2

= 1/3 in²

Area of actual tile = 6 × 4.5 = 27 in²

Ratio of the area of a tile in the model to the area of an actual tile =

Area of tile / area of actual tiles

= [tex]\frac{1/3}{27} = \frac{1}{81}[/tex]

Another way of finding ratio is by Dilation ,

Ratio of lengths = 1 / 9

according to the property of dilation,

Ratio of area of tiles to area of actual tiles = (1/9)² = 1/81

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The solution of the given system of equations is x =1 and y = -1.

In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Given is a system of equations; 4x+2y=2 and y=-3x+2

Solving the equation by substitution, we get,

4x+2(-3x+2) = 2

4x-6x-4 = 2

-2x+4 = 2

-2x = -2

x = 1

Put x = 1 in any of the given equation,

y = -3*1+2

y = -3+2

y = -1

Hence, The solution of the given system of equations is x =1 and y = -1.

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There 6 quarters and 24 nickels of each coins that John Carlo has.

There are 5 cents in a nickel and 25 cents in a quarter. Let us represent the number of quarters as x so that the number of nickels that John Carlo has will be 4x.

Thus, 4x(5 cents) + x(25 cents) = 270 cents

20x cents + 25x cents = 270 cents

45x cents = 270 cents

divide through by 45

x = 270/45

x = 6

and thus there are 4(6) = 24 nickels.

Therefore, John Carlo has 6 quarters and 24 nickels each of coins.

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Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]

Alicia has at most $196 this means that her amount of money is less or equal than $196, we can express this as an inequality, like this:

Where x represents the cost associated with the hat and the gloves and y is the money that left after the purchase of these articles

Given

The line segment with end points (-8, -7), (-7, -8).

To find:

The midpoint of the given segment.

Explanation:

It is given that,

The line segment with end points (-8, -7), (-7, -8).

That implies,

Hence, the midpoint of the line segment is (-15/2, -15/2).

Explanation

The unit rate os obtained as shown as follows:

Answer is A. The unit rate is equal to $17.

EXPLANATION

Let's see the facts:

%Earns= 13% commission/week

Last week sold = $7,500

In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:

$Earns = 0.13 (decimal form)*$7,500

Earns = $975

Last week, he made $975 in commission.

If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year

Answer:

(0,-88) (0,-88)

Step-by-step explanation:

For dilations just multiply the pre-images coordinates by the scale factor to get the image's coordinates.

Given:

Let's select the number line that could show this value.

To select the number line, let's first simplify the expression.

We have:

The number line that will represent this value must have a dot on the point 10.

This is because the value √101 is approximately 10.

Therefore, the number line that could show this value is the number line with a point on 10.

The correct number line is:

ANSWER:

The graph of the function:

Can be obtained by using the parent function:

Whose graph is shown below:

We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:

And the graph is:

Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:

The graph is shifted 4 units to the right as shown:

The highest possible price that a customer could have paid for their meal that evening exists $ 757. Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

When determining the mean (average) of a group of values, we add up the values in the group and divide that total by the number of values in the group. As a result, the average of the set's values divided by the total number of values is equal to the set's values' sum.

Let n represent how many people were in the store that evening. Thus, a total of 56n was paid that evening by all customers. The bill for the last customer's meal was $70.00. There were (n-1) customers who had already paid a total of (56n-70) dollars before this one arrived. The average cost per customer at that time was $55 dollars.

From the above information, we get

[tex]$\frac{56 n-70}{n-1} &=55 \\[/tex]

simplifying the above equation, we get

56n - 70 = 55(n - 1)

56n - 70 = 55n - 55

n = 15

Since n = 15, it follows that there were 15 customers that evening, and the total amount paid by all customers stood therefore 56 n = 56(15) = 840 dollars.

To estimate the highest possible price that a customer could have paid for their meal that evening, we will assume that 13 of the customers paid the lowest possible price of $ 1. Then the remaining customer would have paid 840 - 13 × 1 - 70 = 757 dollars.

Therefore, the highest possible price that a customer could have paid for their meal that evening exists $ 757.

Since this is a fundraiser, $ 1 exists probably a very small amount and $757 would be considered a very generous donation for a meal.

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Given:

The inequality is,

Required:

To choose the correct value for the given inequality.

Explanation:

Consider the given inequality,

Consider the first option, 6

Put x=6 in to the given inequality, we get

Clearly the statement is false.

Now consider the next option, 4

Put x=4 in to the given inequality, we get

Clearly the statement is false.

Now consider the next option, 0

Put x=0 in to the given inequality, we get

Clearly the statement is false.

Final Answer:

There is no values in the given options .

3 + √97/2 , -3 ±√97/2 are the dimensions of rectangle .

What is rectangle?

let width = x

length = x + 3

area = 22

 area of rectangle =  l * w

           22 =  x * ( x + 3 )

          22 = x² + 3x

       x² + 3x - 22 = 0

    x = -3 ± √3² - 4 .1 (-22)/2.1

   x = -3 ± √9 + 88/2

    x = -3 ±√97/2

width =  -3 ±√97/2

length =  x + 3  =  -3 +√97/2 + 3 = 3 + √97/2

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EXPLANATION

The sum of 79 and 34 is

Answer: 113

The modulus of |-r| means that it is an absolute value. Therefore, the answer is "s".

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, thus, |-2| = |2| = 0, and has vertex(turning point) at (0,0). Then the range is from the y-coordinate of the vertex to positive infinity.

WE have given as s=l-r l

When we add a positive or negative number in between the lines then; it is;

|-r| goes through = -r = -s

|-r| goes through = r = s

The modulus of |-r| means that it is an absolute value. Therefore, the answer is "s".

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A solution to a system of linear equations in two variables is an ordered pair that makes BOTH equations true.

When is the system of equations is said to be consistent?

If there is at least one combination of values for the unknowns that satisfies each equation in the system—that is, makes each equation hold true as an identity—then a system of equations, whether linear or nonlinear, is said to be consistent.

When is the system of equations is said to be non-consistent?

If there isn't a set of values for the unknowns that solves every equation, then the system of equations is said to be inconsistent.

Ex: Consider a system of linear equations:

x+3y=6                    

x=-3y+6                       …..(1)

2x+8y= -12                  …..(2)

Substitute equation (1) in (2)

2(-3y+6)+8y=-12

-6y+12+8y=-12

           2y=-24

            y=-12              ….(3)

Substitute equation (3) in (1)

x+3(-12)=6

x-36=6

x=42

Here, the order pair (x,y)=(42,-12) is the solution of the given linear equations and satisfy equations (1) and (2)

> 42+3(-12) = 42-36             .....From (1)

                  = 6 = RHS

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We were told that Amber had 5/6 of a book of postage stamps. If she used 2/6 of the book of postage stamp, then the fraction of the book of postage stamp that she has left is

5/6 - 2/6

= 3/6

She has 3/6 now

The scale factor of the drawing will be 1/3 inch per foot.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

Jane drew a scale drawing of a game room. The pool table is 3 inches long in the drawing. The genuine pool table is 9 feet in length.

The scale factor of the drawing is calculated as,

Scale factor = 3 / 9

Scale factor = 1/3 inch per foot

The scale factor of the drawing will be 1/3 inch per foot.

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From the given option (1,10), (5,6) and (7,4) are ordered pairs that formed from combining a term in Pattern A with its corresponding term in Pattern B.

In the given question,

Pattern A follows the rule "add 2" and Pattern B follows the rule subtract 2

Pattern A: 1, 3, 5, 7, 9

Pattern B: 10, 8, 6, 4, 2

We have to find which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B.

From the given question,

Pattern A:  1, 3, 5, 7, 9

Pattern B:  10, 8, 6, 4, 2

As given in the pattern A all numbers are 2 number up from the previous one and in pattern B each number is 2 number down from the previous one.

We have to combine a term in Pattern A with its corresponding term in Pattern B.

We have to combine with corresponding terms that means we combine one term from pattern A and one from pattern B.

Now the term after combining are

1, 10, 3, 8, 5, 6, 7, 4, 9, 2

So the combination of terms that can be formed are

(1, 10), (10,3), (3, 8), (8,5), (5, 6), (6,7), (7, 4), (4,9), (9,2)

Hence, from the given option (1,10), (5,6) and (7,4) are ordered pairs that formed from combining a term in Pattern A with its corresponding term in Pattern B.

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Answer:

49

Step-by-step explanation:

10 to 23 is 13, and 23 to 36 is 13. so you just add 13 to 36 to get 49

⇒ Note we can answer the question without having to calculate anything if we know what is meant by a y-intercept and x-intercept.

y-intercept is a point in the y-axis where the x coordinate is 0 given by (0,y)

x-intercept is a point is the x-axis where y is equal to 0.(x,0)

If we are to check in the diagram⇒ for y-intercept the point in the

(0,-6)

For x-intercept, the point on the x- axis where y is 0 is (-8,0)

Given the expression:

Let's solve the expression using distributive property.

To use distributive property, distribute the term ouside the parentheses to the terms in the parentheses.

Apply distributive property:

Distribute 4 to the values inside the parentheses:

ANSWER:

68

The 100th term of the arithmetic sequence is 203.

Let the first term of the arithmetic sequence be a and the common difference be d.

The general term of the sequence is given by

[tex]T_{n} = a + (n-1)d[/tex]

It is given that the 6th term is 15, we have :
[tex]T_{6} = a +5d[/tex]  

a + 5d = 15......equation(1)

It is given that the 9th term is three times the 2nd term, we have :

[tex]T_{9} = 3*T_{2} \\a + 8d = 3(a +d)\\a + 8d = 3a +3d\\a -3a = 3d -8d = -5d\\-2a = -5d\\2a = 5d\\a = \frac{5d}{2}[/tex]

Putting this value in equation(1)

[tex]\frac{5d}{2} + 5d = 15 \\\\5d + 10d = 30\\15d= 30\\d = \frac{30}{15} = 2[/tex]

a = 5*2/2 = 5

Hence, the first term is 5 and the common difference is 2.

Now, evaluating the 100th term of the sequence, we have :

[tex]T_{n} = a +(n-1)d\\T_{100} = a +99d\\T_{100} = 5 +99*2 = 5 +198 = 203[/tex]

Hence, the 100th term of the arithmetic sequence is 203.

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Answer:

4x - 3y = 36

Step-by-step explanation:

⅔x-½y=6

just multiply both sides by the LCM which is 6

6×⅔x-6×½y=6×6

4x-3y=36