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2 years ago

14

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet

of paper costs $0.34. How many sheets of paper can she buy? Show your
work

1 answer:

Montano1993 [528]2 years ago

6 0

She can buy 63 sheets and one scrapbook

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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.

Paraphin [41]

we know that

If two lines are parallel, then, their slopes are equal.

The formula to calculate the slope between two points is equal to

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

we will proceed to calculate the slope in each case, to determine the solution of the problem

<u>Case A)</u> Point $B(5,2)\ C(7,-5)$

Find the slope BC

Substitute the values in the formula

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

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

$m=-3.5$

so

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

therefore

<u>the answer Part A) is</u>

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

<u>Case B)</u> Point $D(11,6)\ E(5,9)$

Find the slope DE

Substitute the values in the formula

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

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

$m=-0.5$

so

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

therefore

<u>the answer Part B) is</u>

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

<u>Case C)</u> Point $F(-7,12)\ G(3,-8)$

Find the slope FG

Substitute the values in the formula

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

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

$m=-2$

so

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

<u>Case D)</u> Point $H(4,4)\ I(8,9)$

Find the slope HI

Substitute the values in the formula

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

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

$m=1.25$

so

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

therefore

<u>the answer Part D) is</u>

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

<u>Case E)</u> Point $J(7,2)\ K(-9,8)$

Find the slope JK

Substitute the values in the formula

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

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

$m=-0.375$

so

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

<u>Case F)</u> Point $L(5,-7)\ M(4,-12)$

Find the slope LM

Substitute the values in the formula

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

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

$m=5$

so

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

therefore

<u>the answer Part F) is</u>

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

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2 sandwiches and 3 croissants costs £11.

valentina_108 [34]

Answer:

The price of a sandwich is £2.5 and the price of a croissant is £2

Step-by-step explanation:

Let s be the number of sandwiches and c be the number of croissants

Then according to given statements the equations will be:

$2s+3c = 11\ \ \ \ \ \ \ Eqn\ 1\\3s+6c =19.50\ \ \ Eqn\ 2$

Multiplying equation 1 by 2 and subtracting equation 2 from the new equation

$2(2s+3c) = 11*2\\4s+6c = 22$

Now

$4s+6c-(3s+6c) = 22-19.50\\4s+6c-3s-6c = 2.5\\s = 2.5$

Putting s=2.5 in equation 1

$2(2.5)+3c = 11\\5+3c = 11\\3c = 11-5\\3c = 6\\\frac{3c}{3} = \frac{6}{3}\\c = 2$

Hence,

The price of a sandwich is £2.5 and the price of a croissant is £2

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