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3 years ago

What is the solution to this equation?

Mathematics

1 answer:

Anettt [7]3 years ago

6 0

Answer:

B. a = 5

Step-by-step explanation:

3(a - 4) + 1 = 9 - a

Distribute the 3 into the parenthesis.

3a - 12 + 1 = 9 - a

Add -12 and 1.

3a - 11 = 9 - a

Add a to both sides.

4a - 11 = 9

Add 11 to both sides.

4a = 20

Divide both sides by 4.

a = 5.

Proof:

3(a - 4) + 1 = 9 - a

Substitute variable.

3(5 - 4) + 1 = 9 - 5

Subtract inside parenthesis.

3(1) + 1 = 9 - 5

Multiply 3 and 1.

3 + 1 = 9 - 5

Add 3 and 1.

4 = 9 - 5

Subtract 5 from 9.

4 = 4.

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3 years ago

Read 2 more answers

Find the measures of the interior

Ainat [17]

Answer:

Angle 1 = 108°

Angle 2 = 72°

Angle 3 = 120°

Angle 4 = 96°

Angle 5 = 144°

Step-by-step explanation:

We need to find the measures of the interior angles in a pentagon if the measure of each consecutive angle is in the ratio 9:6:10:8:12.

Let x be the common ratio

So, we can write:

Angle 1 = 9x

Angle 2 = 6x

Angle 3 = 10x

Angle 4 = 8x

Angle 5 = 12x

We know that the <em>sum of all angles of pentagon = 540</em>

So, adding all angles and equal them to 540, we can find value of x

$9x+6x+10x+8x+12x=540\\45x=540\\x=\frac{540}{45}\\x=12$

So, we get the value of x: x=12

Now, calculating the angles by putting x=12:

Angle 1 = 9x = 9(12) = 108°

Angle 2 = 6x = 6(12) = 72°

Angle 3 = 10x = 10(12) = 120°

Angle 4 = 8x = 8(12) = 96°

Angle 5 = 12x= 12(12) = 144°

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3 years ago

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3 years ago

What is the distance between the points (5, 1) and (-3,-5)?

Reil [10]

Answer: THIRD OPTION.

Step-by-step explanation:

For this exercise you need to use the formula for calculate the distance between two points. This is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Given the following points:

$(5, 1)$ and $(-3,-5)$

You can identify that:

$x_2=-3\\x_1=5\\\\y_2=-5\\y_1=1$

Knowing these values, the next step is to substitute them into the equation for calculate the distance between two points and then evaluate.

Therefore, the distance between $(5, 1)$ and $(-3,-5)$ is:

$d=\sqrt{(-3-5)^2+(-5-1)^2}\\\\d=10$

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3 years ago