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3 years ago

Steven is solving the equation 3(8−2x)+40=34. He begins with the following two steps.

Mathematics

2 answers:

STatiana [176]3 years ago

7 0

Answer:

Step-by-step explanation:

3(8 - 2x) + 40 = 34 use the distributive property a(b + c) = ab+ ac

3(8) + 3(-2x) + 40 = 34

24 - 6x + 40 = 34 combine like terms

-6x + (24 + 40) = 34 Answer: Add 24 and 40

-6x + 64 = 34 subtract 64 from both sides

-6x = -30 divide both sides by (-6)

x = 5

yarga [219]3 years ago

5 0

Answer:

Add 24 and 40.

Step-by-step explanation:

Steven is solving the equation $3(8-2x)+40=34$

Step 1:

$3(8)+3(-2x)+40=34$

Step 2:

$24-6x+40=34$

So, according to pemdas, the next step is Add 24 and 40.

Then this becomes:

Step 3:

$64-6x=34$

So, the answer will be option 2: Add 24 and 40.

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Step-by-step explanation:

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3 years ago

Factor completely: 64 - y^3

madam [21]

From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is $4^{3}$ , and $y^{3}$ .

There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.

That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are $a^{3}$ and $b^{3}$ . The difference of those two cubes is:
$a^{3} - b^{3} = (a - b)( a^{2} + ab + b^{2})$

In our problem, a = 4 (since $a^{3}$ = 64) and b = y (since $b^{3} = y^{3}$ . Plug these values into the rule to find the factor of $64 - y^3$ :
$64 - y^3 \\
= (4 - y)( 4^{2} + 4y + y^{2}) \\
= (4 - y)( 16 + 4y + y^{2})$

-----

Answer: $(4 - y)( 16 + 4y + y^{2})$

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2 years ago

Item 16 A sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. What is the difference of the vol

Zigmanuir [339]

Answer:

$672\pi \text{ cm}^3$ .

Step-by-step explanation:

We have been given that a sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. We are asked to find the difference of the volumes of the spheres.

We will use volume formula of sphere to solve our given problem.

$\text{Volume of sphere}=\frac{4}{3}\pi r^3$ , where r is radius of sphere.