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3 years ago

twice the sum of a number and 6 is equal to 3 times the difference of the number and 8. Find the number

Mathematics

1 answer:

Serhud [2]3 years ago

5 0

In order to solve this problem, we must solve an equation.

First, we need to define our unknown.

Let's call our number "n".

So, the sum of the number and 6 is the same as saying n+6

Then we need to multiply it by 2 (since it's twice the sum)

2(n+6)

This whole thing is equal to three times of the difference of the number and 8

n-8 is equal to the difference between the number and 8, then we need to multiply it by three.

3(n-8)

now, we set both sides equal and solve

$2(n+6)=3(n-8)\\2n+12=3(n-8)\\2n+12=3n-24\\12=n-24\\36=n$

The number is 36

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Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the me

mel-nik [20]

Answer:

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

$x+y=180^o$ ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

$x=2y$ ----> equation B

substitute equation B in equation A

$2y+y=180$

$y=60^o$

$x=120^o$

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

$b=12/2=6\ units$

The perimeter of the hexagon is given by the formula

$P=6b$

substitute

$P=6(6)=36\ units$

3 0

3 years ago

If the triangles are similar, what is the value of x?

Sav [38]

Answer:

the answer to your question is D. d=54

4 0

3 years ago

Find the general indefinite integral. (use c for the constant of integration. )

Vlada [557]

The indefinite integral will be $\int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)$

<h3 /><h3>what is indefinite integral?</h3>

When we integrate any function without the limits then it will be an indefinite integral.

General Formulas and Concepts:

Integration Rule [Reverse Power Rule]:

$\int x^ndx=\dfrac{x^{n+1}}{n+1}}+C$

Integration Property [Multiplied Constant]:

$\int cf(x)dx=c\int f(x)dx$

Integration Property [Addition/Subtraction]:

$\int [f(x)\pmg(x)]dx=\int f(x)dx\pm \intg(x)dx$

[Integral] Rewrite [Integration Property - Addition/Subtraction]:

$\int (7x^2+8x-2)dx=\int 7x^2dx+\int 8xdx -\int 2dx$

[Integrals] Rewrite [Integration Property - Multiplied Constant]:

$\int (7x^2+8x-2)dx=7 \int x^2dx+ 8 \int xdx -2\int dx$

[Integrals] Reverse Power Rule:

$\int (7x^2+8x-2)dx= 7(\dfrac{x^3}{3})+8(\dfrac{x^2}{2})-2x+C$

Simplify:

$\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C$

So the indefinite integral will be $\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C$

To know more about indefinite integral follow

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7 0

2 years ago

Find the percent of markup. 37.00 to 49.00

Wewaii [24]

So, 100 * (49-37) / 37..You always do whats in parenthesis first; 49-37=12. Then you do multiplication and division, since multiplication comes first we do; 100*12=1200/37. Rounding to the nearest tenth would be 32%

6 0

3 years ago

Read 2 more answers

Como se realiza eso?

amm1812

Answer:

english

Step-by-step explanation:

3 0

3 years ago