All categories

3 years ago

Perform the indicated operation. (w 3 + 64) ÷ (4 + w)

Mathematics

2 answers:

Aloiza [94]3 years ago

5 0

Answer:

The expression $\frac{\left(w^3+64\right)}{w+4}$ becomes $w^2-4w+16$

Step-by-step explanation:

Given : Expression $\frac{\left(w^3+64\right)}{w+4}$

We have to find the simplified value of given expression.

Consider the given expression $\frac{\left(w^3+64\right)}{w+4}$

Rewrite 64 as $4^3$

$=w^3+4^3$

$\mathrm{Apply\:Sum\:of\:Cubes\:Formula:\:}x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)$

$w^3+4^3=\left(w+4\right)\left(w^2-4w+4^2\right)$

Simplify,

$=\left(w+4\right)\left(w^2-4w+4^2\right)$

Given expression becomes,

$=\frac{\left(w+4\right)\left(w^2-4w+16\right)}{w+4}$

Cancel common factors, we have,

$=w^2-4w+16$

Thus, The expression $\frac{\left(w^3+64\right)}{w+4}$ becomes $w^2-4w+16$

pantera1 [17]3 years ago

4 0

W³ + 64 = w³ + 4³ = (w+4)³ - 3*w*4(w+4) = (w+4)[(w+4)² - 12w]

(w³ + 64) ÷ (w+4)
=(w+4)[(w+4)² - 12w] ÷ (w+4)
= (w+4)² - 12w
= w² -4w + 16

You might be interested in

The product (5x+8-6x)(4+2x-7)

Mashutka [201]

Answer:

(8 - x) • (2x - 3)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Problem page the longer leg of a right triangle is 1ft longer than the shorter leg. the hypotenuse is 9ft longer than the shorte

LenKa [72]

Hello,

To solve this problem we want to use the Pythagorean Theorem.
The pythagorean theorem states that for a 90° triangle,

$a^{2} + b^{2} = c^{2}$

where a and b represent the two legs of the triangle, and c represents the hypotenuse.

Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1.

If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c.

Doing this, we have:
$a^{2} + b^{2} = c^{2}$
$(b+1)^{2} + b = (b+9)^{2}$

Expanding this, we get $b^{2} + 2b + 1 + b^{2} = b^{2} + 18b + 81

 2b^{2} + 2b + 1 = b^{2} + 18b + 81

 b^{2} + 1 = 16b + 81

 b^{2} = 16b + 80
 
b^{2} - 16b - 80 = 0

$

Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20.

However, we should check this with the original question to make sure it checks out.

a = b + 1
a = 20 + 1 = 21

c = b + 9
c = 20 + 9 = 29

So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:

$21^{2} + 20^{2} = 29^{2}$
441 + 400 = 841
841 = 841, checks out.

So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet.

Hope this helps!

7 0

3 years ago

Please help, our teacher wasn’t here and we got no explanation on how to do it

nasty-shy [4]

Help with what? there isn’t anything there

8 0

3 years ago

Read 2 more answers

Help me guys fast as

Viktor [21]

cos(180-x)=-cosX

$\\ \rm\Rrightarrow tan^2135-cosec^260=-xcos45.sin45.cot60$

$\\ \rm\Rrightarrow (-1)^2-(\dfrac{2}{\sqrt{3}})^2=-\dfrac{x}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{3}}$

$\\ \rm\Rrightarrow 1-\dfrac{4}{3}=\dfrac{-x}{2\sqrt{3}}$

$\\ \rm\Rrightarrow \dfrac{3-4}{3}=\dfrac{-x}{2\sqrt{3}}$

$\\ \rm\Rrightarrow \dfrac{-1}{3}=\dfrac{-x}{2\sqrt{3}}$

$\\ \rm\Rrightarrow \dfrac{1}{\sqrt{3}}=\dfrac{x}{2}$

$\\ \rm\Rrightarrow x=\dfrac{2}{\sqrt{3}}$

4 0

2 years ago

What happens as the triangle goes from obtuse to acute

jeka57 [31]

Answer: the degree will go down 90 degrees

Step-by-step explanation: An obtuse triangle is one that has an angle greater than 90°. An acute triangle is defined as a triangle in which all of the angles are less than 90°.

7 0

3 years ago