What is the largest factor of 16 that is also a perfect cube?

Answers

Answer 1

Answer:

The largest factor of 16 that is also a perfect cube is 2. When you factor out 16, you will get 4 times 4 and then factor out 4, you will also get 2 times 2 times 2 times 2. Other factors for 16 is 8 times 2 which can be further divided into 2 times 2 times 2 times 2. When you factor out 8, you get 2 times 2 times 2 and so 2 is a perfect cube.

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Solve the equation 8x-12=5x+15

Answers

8x-12=5x+15
add 12 to both sides

8x=5x+27
subtract 5x from both sides

3x=27
divide by 3

x=9

8x = 5x + 27 Add 12 to both sides

3x = 27 Subtract 5x from both sides

x = 9 Divide both sides by 3

Sandra conducted an observational study to learn how relationships with family affect happiness. She surveyed 500 people in her hometown and found that 85% say that positive relationships with family members make them happy. What could be the conclusion of her study?

Answers

She may conclude that in her hometown, a majority of people experience greater happiness thanks to positive relationships. However, in order to apply this to a greater population, she will have to use a larger sample of people.

Since this is an observational study and not an experiment, she can only conclude that there may be a link between closeness with family and happiness but we cannot say that closeness with family results in happiness.

What is the intersection of plane WZVS and plane STUV?

Answers

Answer: The required intersection is the line 'VS'.

Step-by-step explanation: We are given to find the intersection of the planes WZVS and plane STUV.

We know that,

If two planes intersect each other, then their intersection is a straight line.

As shown in the given figure, the point 'V' and 'S' lie on both the planes WZVS and STUV.

So, the line joining these two points, i.e., the line VS also lie on both the planes.

Therefore, the intersection of both the planes is the line 'VS'.

Thus, the required intersection is the line 'VS'.

An easy way to find this is to look at the cross section, and see where the lines meet

When Gail goes on a hike, she always packs a ratio of 20 protein bars to 15 water bottles in her backpack.Complete the statement about the ratio of protein bars to water bottles.

CLEARCHECK
For a short hike, Gail should pack
protein bars if she packs 3 water bottles.

Answers

The answer is 4 don’t listen to him

Simplify
-2(3x - 4y) +
5(x+3y)

Answers

Answer:

$- x + 23y$

Step-by-step explanation:

$- 2(3x - 4y) + 5(x + 3y) \n - 6x + 8y + 5x + 15y \n - 6x + 5x - 8y + 23y \n = - x + 7y$

Answer:

-x + 23y

Step-by-step explanation:

-2(3x - 4y) + 5(x+3y)

Expand the brackets.

-6x + 8y + 5x + 15y

Rearrange.

- 6x + 5x +8y + 15y

Add or subtract like terms.

- 1x + 23y

Solve the inequality:

4|x+5| -2 <10

Answers

4 |x + 5| - 2 < 10 4 |x + 5| - 2 < 10
4 |x + 5| < 12 4(x + 5) - 2 < 10
------------ ----- 4x + 20 - 2 < 10
4 4 4x + 18 < 10
|x + 5| < 3 4x < -8
-x - 5 < 3 ---- ------
-x < 8 4 4
---- --- X < -2
-1 -1
X > -8

-8 < x < -2

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