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18 days ago

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A store owner wants to give a pen to each customer who visits their store. The table shows the cost for the number of pens in a

pack that the store owner wants to buy. What is the best value?Number of Pens Cost 16 $8.64 18 $7.74 22 $6.82 30 $8.40 36 $9.00

1 answer:

PIT_PIT [12.4K]18 days ago

8 0

Answer:

$9 for 36

Step-by-step explanation:

To find the unit price, divide the total cost by the number of items. Here are the costs per item for each option:

1. $0.54

2. $0.43

3. $0.31

4. $0.28

5. $0.25

The best deal is $9 for 36 pens as it results in the lowest price of $0.25 per pen.

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Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Svet_ta [12734]

It's known that

When two lines are parallel, their slopes are identical.

The slope between any two points can be calculated using the following formula:

$m=\frac{y2-y1}{x2-x1}$

We will calculate the slope for each case to find the solution to the problem.

Case A) Point $B(5,2)\ C(7,-5)$

Determine the slope of BC

Insert the values into the formula:

$m=\frac{-5-2}{7-5}$

$m=\frac{-7}{2}$

$m=-3.5$

Thus,

The equation $y=-3.5x-15$ is parallel to the line that goes through the points $B(5,2)\ C(7,-5)$

Therefore,

the result for Part A) is

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

Case B) Point $D(11,6)\ E(5,9)$

Calculate the slope of DE

Plug the values into the formula:

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

Thus,

The equation $y=-0.5x-3$ is parallel to the line that goes through the points $D(11,6)\ E(5,9)$

Therefore,

the result for Part B) is

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

Case C) Point $F(-7,12)\ G(3,-8)$

Determine the slope of FG

Insert the values into the formula:

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

Thus,

Any linear equation with slope $m=-2$ will be parallel to the line through the points $F(-7,12)\ G(3,-8)$

Case D) Point $H(4,4)\ I(8,9)$

Calculate the slope of HI

Substitute the values in the formula:

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

$m=1.25$

Thus,

The equation $y=1.25x+4$ is parallel to the line through the points $H(4,4)\ I(8,9)$

Therefore,

the result for Part D) is

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

Case E) Point $J(7,2)\ K(-9,8)$

Determine the slope of JK

Insert the values into the formula:

$m=\frac{8-2}{-9-7}$

$m=\frac{6}{-16}$

$m=-0.375$

Thus,

Any linear equation characterized by slope $m=-0.375$ will be parallel to the line that runs through the points $J(7,2)\ K(-9,8)$

Case F) Point $L(5,-7)\ M(4,-12)$

Find the slope of LM

Substitute the values in the formula:

$m=\frac{-12+7}{4-5}$

$m=\frac{-5}{-1}$

$m=5$

Thus,

The equation $y=5x+19$ is parallel to the line connecting the points $L(5,-7)\ M(4,-12)$

Therefore,

the result for Part F) is

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

8 0

1 month ago

Read 2 more answers

What is the length of side PQ in this figure?

lawyer [12517]

I trust this will assist you.

5 0

2 months ago

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Find the value of x in the isosceles triangle shown below.

Leona [12618]

Solution:

x=8

Detailed explanation:

This isosceles triangle consists of two right triangles with sides equal to 8, $\sqrt{80}$ , and y

Considering we possess two sides of a right triangle, determining the third side can be achieved using the Pythagorean Theorem

$(\sqrt{80} )^2=8^2+y^2\\\\80=64+y^2\\\\y^2=16\\\\y=4$

Because it is an isosceles triangle, these two right triangles are the same, thus x=2y

Hence, x=2(4)=8

8 0

1 month ago

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Martha wrote an example of a quadratic function for a homework assignment. The function she wrote is shown. f(x) = 5x3 + 2x2 + 7

AnnZ [12381]

Answer:

The correct options are:

The term 5x³ can be removed

The power of the first term, 5x³, can be modified to 2 and combined with the second term, 2x²

Explanation:

The degree of an expression is identified by its highest exponent.

The expression in question is:

5x³ + 2x² + 7x - 3

Observing this, we see that the highest exponent is 3, indicating that the expression’s degree is 3.

A quadratic function is defined as having degree 2, meaning the highest degree must be 2.

Thus, Martha must eliminate the term with degree 3 (5x³) from her function.

This can be achieved through two methods:

1- She can simply remove the term with the third degree.

2- She can change the term with degree 3 to a lower degree and combine it with an existing like term.

Evaluating the options, we conclude the two accurate choices are:

- The term 5x³ can be eliminated.

- The exponent on the first term, 5x³, can be reduced to 2 and subsequently joined with the second term, 2x².

I hope this is helpful!:)

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1 month ago

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Mrs. Hernandez bought 18 pens for her class. Highlighters cost $3 each, and gel pens cost$2.50 each. She spent a total of $50. W

AnnZ [12381]

18*2.50=45
50-45=5
Highlighters are priced at $3, which means she bought only one highlighter.
5-3=2
45+3=48
(The last 2 dollars likely account for tax)

8 0

24 days ago