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3 years ago

Describe how to substitute an ordered pair into an equation.

1 answer:

5 0

Let's say you have the equation

5x + 3y = 11

You are asked to test the ordered pair (1, 2) to see if it is a solution of the equation. A solution of the equation will make the equation a true statement. The ordered pair (1, 2) has 1 as its x-coordinate and 2 as its y-coordinate.
Substitute 1 for x and 2 for y in the equation. Then work it out to see if it is a true statement.

5x + 3y = 11

5(1) + 3(2) = 11

5 + 6 = 11

11 = 11

Since 11 = 11 is a true statement, the ordered pair (1, 3) is a solution of the equation.

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Prove algebraically that (m + 2)2 – m 2 – 12 is always a multiple of 4

Julli [10]

Answer:

$(m + 2)^{2} - m^{2} - 12 = 4(m - 2)$

Step-by-step explanation:

Step 1:

Write the expression

$(m+2)^{2} - m^{2} - 12$

Step 2: Expand $(m + 2)^{2}$

$(m+2)^{2} - m^{2} - 12\\(m+2)(m+2) - m^{2} - 12\\m^{2} + 2m + 2m + 4 - m^{2} - 12$

Step 3: Collect similar terms

$m^{2} - m^{2} + 4m + 4 - 12\\4m - 8$

Step 4: Factor 4 out of the expression to prove that the expression is a multiple of 4.

$Therefore\\4m - 8 = 4(m - 2)\\Hence,\\(m+2)^{2} - m^{2} - 12 is a multiply of 4 because the expression is equal to 4(m-2)$

3 0

2 years ago

Find the midpoint of the line segment that has endpoints at (10,8) (-3,-10)

dem82 [27]

Hey there! :)

Answer:

(3.5, -1).

Step-by-step explanation:

Use the midpoint formula to solve this problem:

$(x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Plug in the coordinates given:

$(\frac{10-3}{2}, \frac{8-10}{2})$

Simplify:

$(\frac{7}{2}, \frac{-2}{2})$

Therefore, the coordinates of the mid-point are:

(3.5, -1).

7 0

2 years ago

Mae sells newspaper subscriptions door-to-door. In addition to a fixed salary, she earns a commission for each subscription that

Lady_Fox [76]

<span>The answer is y = 10x + 125</span>

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2 years ago

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shtirl [24]

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2 years ago

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2 find the probability of getting a sum 9 when two dice are thrown simultaneously.

Cloud [144]

Answer:

The answer is 11.1

Step-by-step explanation:

First you need to figure out what all of the possible combinations of the two dice being thrown then divide it by the number of faces on both dice and you get your probability.

3 0

2 years ago