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3 years ago

Write a paragraph, flowchart, or 2-column proof for the following:

Mathematics

1 answer:

lawyer [7]3 years ago

7 0

Answer:

see the procedure

Step-by-step explanation:

we know that

m∠1+m∠2=180° -----> supplementary angles (form a linear pair)

we have

m∠1=27°

substitute the measure of m∠1 in the equation above and solve for m∠2

27°+m∠2=180°

Subtract 27° both sides

27°+m∠2-27°=180°-27° ----> by subtraction property of equality

m∠2=153°

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Write the equation of the line passing through the points (-4,-1) and (2,8)

klio [65]

<h3>Explanation:</h3>

Calculate the slope with two given coordinate points by using rise over run.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let these points

$\begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}$

$m = \frac{8 - ( - 1)}{2 - ( - 4)} \\ m = \frac{8 + 1}{2 + 4} \Longrightarrow \frac{9}{6} \Longrightarrow \frac{3}{2} \\ m = \frac{3}{2}$

Slope-Intercept

$y = mx + b \\ m = slope \\ b = y - intercept$

Substitute the value of m in the equation.

$y = \frac{3}{2} x + b$

Substitute any coordinate points that are given or part of the graph in the equation.

$(x_, y) = ( - 4, - 1)$

$- 1 = \frac{3}{2} ( - 4) + b$

Solve the equation for b-term.

$- 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b$

Rewrite the equation by substituting the value of b in the equation.

$y = \frac{3}{2} x + 5$

<h3>Answer</h3>

$\large \boxed{y = \frac{3}{2} x + 5}$

If you have any questions related to the answer, feel free to ask via comment.

7 0

3 years ago

Cedric and doug each had an equal amount of money. After cedric spent $35 and doug spent $28, the ratio of cedrics money to doug

uysha [10]

Answer:

Each of them had $49 at first.

Step-by-step explanation:

Given:

Cedric and Doug each had an equal amount of money.

Let the number of money they had at first be x

Cedric spent = $35

Doug spent = $28

Cedric Money left = $x-35$

Doug Money left = $x-28$

the ratio of Cedric money to Doug money was 2:3

Hence the expression can be made as;

$\frac{x-35}{x-28}=\frac{2}{3}$

Now by cross multiplication method we get;

$3(x-35)=2(x-28)$

Now we will use distributive property to elaborate the same;

$3x-105=2x-56$

Combining common terms we get;

$3x-2x=105-56$

Using Subtraction property we get;

$x= 49$

Hence $49 they each had at first.

8 0

3 years ago

Given angle BEJ~RUW, what is RU?

harina [27]

RU is 34. To find the answer you can use a proportion. In this problem the proportion would be 60/51 = 40/x. You can then cross multiply giving you 51*40=60x. You can then solve for x which is your answer.

5 0

3 years ago

The volume of a rectangular prism has 5376 cubic inches the prism is 14 in long and 16 in wide how tall is the prism

Mkey [24]

Answer:

The height of the prism is $24\ in$

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

$V=LWH$

In this problem we have

$V=5,376\ in^{3}$

$L=14\ in$

$W=16\ in$

substitute in the formula and solve for H

$5,376=(14)(16)H$

$H=5,376/[(14)(16)]$

$H=24\ in$

4 0

3 years ago

The watering can contained 5 1/2 quarts of water. After all the plants were watered, only 4 cups remained. How many cups of wate

Ivahew [28]

Answer: 9.5 cups of water

Step-by-step explanation:

5 1/2 + 4

5 1/2= 11/2

11/2+4=9.5

3 0

3 years ago