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3 years ago

Solve the equation. Show your work. 8x – 12 = 4x + 24

2 answers:

5 0

To find the value of x, we may add 12 to both sides of the equation and subtract 4x from the answer.
8x - 12 + 12 = 4x + 24 + 12
8x - 4x = 4x - 4x + 36
4x = 36
Divide both left hand and right hand side of the equation by 4 to give an answer of x = 9.

Len [333]3 years ago

3 0

Remember y ou can do anything to an equation as long as you do it to both sides

get 1x by itself

8x-12=4x+24
add 12 to both sides
8x=4x+36
minus 4x from both sides
4x=36
divide both sides by 4
x=9

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Find the volume. A. 103 yd B. 54 yd C. 74 yd D. 84 yd

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3 years ago

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How greater emphasis on public safety might reduce the risk for various groups of the population?

miss Akunina [59]

Answer:

Explained

Step-by-step explanation:

Emphasis on public safety can surely reduce the risk for various groups of population

1. Proper education and training must be provided to make them aware of the risks and how they can manage those risks.

2. Proper rules and regulation must be made and strictly followed for example traffic rules so as to avoid accidents.

3. Disaster management teams should to formed to ensure minimal loss of humans and resources during any natural calamity.

4.Eradication of poverty and illiteracy should be priority so as to ensure people focus on more important issues in life rather than involve themselves in trivial things.

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3 years ago

Y=4+4x fill in the table using this function rule x y 1 2 3 5

Feliz [49]

Answer:

1 2 3 4 5

4 8 12 16 20

Step-by-step explanation:

the x is 4 therefore, count by 4.

7 0

3 years ago

The volume of a sphere whose diameter is 18 centimeters is _ cubic centimeters. If it’s diameter we’re reduced by half, it’s vol

kaheart [24]

<h2>Answer:</h2>

First Part

Given that

$Volume = \frac{4}{3} \pi r^{3}$

We have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}$

Second Part

Given that

$Volume = \frac{4}{3} \pi r^{3}$

If the Diameter were reduced by half we have that

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}$

This shows that the volume would be $\frac{1}{8}$ of its original volume

<h2>Step-by-step explanation:</h2>

First Part

Gather Information

$Diameter = 18cm$

$Volume = \frac{4}{3} \pi r^{3}$

Calculate Radius from Diameter

$Radius = \frac{Diameter}{2} = \frac{18}{2} = 9$

Use the Radius on the Volume formula

$Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}$

Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s

$Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3$

We can see now that one of the 3s can be already divided by the 3 in the denominator

$Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3$

Finally, since we can't simplify anymore we just calculate it's volume

$Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}$

$Volume \approx 3053.63 cm^{3}$

Second Part

Understanding how the Diameter reduced by half would change the Radius

$Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}$

Understanding how the Radius now changes the Volume

$Volume = \frac{4}{3}\pi r^{3}$

With the original Diameter, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\$

If the Diameter were reduced by half, we have that

$Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}$

But we can see that the numerator is exactly the original Volume!

This shows us that the Volume would be $\frac{1}{8}$ of the original Volume if the Diameter were reduced by half.

3 0

2 years ago

What is -5/8 / 9/10 ? A. -25/36 B. -9/16 C. -45/80 D. -1/36

Ivenika [448]

Hi there, -5*10/9*8=-50/72, -50/72 simplified is -25/36. Therefore, the answer is A. -25/36

4 0

3 years ago