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3 years ago

Simplify:

1 answer:

8 0

Factoring is decomposing a higher powered expression into a lower powered expressions that are multiplied together. Since (a-b)(a^2+ab+b^2) is lower powered than a^3-b^3, (a-b)(a^2+ab+b^2) is more simplified.
The Difference of Cubes formula shows up frequently in mathematics courses and should be memorized.
The formula for factoring the difference of cubes is (a^3 - b^3)= (a-b)(a^2+ab+b^2). It works because if (a-b)(a^2+ab+b^2) is multiplied it out, then it becomes a^3 - b^3. This was probably originally determined by trial and error a long time ago.
Since x is cubed and 8 is 2^3 it factors with the Difference of Cubes Formula. (x^3-2^3)=(x-2)(x^2+2x+2^2)=(x^2+2x+4)

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vesna_86 [32]

Answer:

$m\angle y=35.69^o$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the right triangle of the figure

$sin(y)=\frac{7}{12}$ ----> by SOH (opposite side divided by the hypotenuse)

using a calculator

$m\angle y=sin^{-1}(\frac{7}{12})=35.69^o$

8 0

3 years ago

b. Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box.

Ainat [17]

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

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

Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:

We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.

⇒ $2x$

The third box contained two more pounds than the first box i.e.

⇒ $x+2$

The last box contained one-fourth the amount in the second box i.e.

⇒ $(\frac{1}{4})2x = \frac{x}{4}$

Therefore , Sum of pounds of candy are :

⇒ $\frac{x}{2} +x+2+2x+x=65$

⇒ $\frac{x}{2} +4x=63$

⇒ $\frac{9x}{2}=63$

⇒ $x=63(\frac{2}{9} )$

⇒ $x=14$

Therefore , Candy in each box is :

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

8 0

4 years ago

If John has 1107 bars of chocolate and wants to give each of his 10 friends an even amount each, what would each friend get? Wha

Nutka1998 [239]

Divide 1107 by 10, for example:

1107/10= 110.7

The decimal point means the remainder, this means John will only get 7 chocolate bars.

If You want it split evenly between ALL of them, divide by 1107 by 11, for example:

1107/11= 100.6, which would leave six bars left, so I think the logical offer would be the first answer I gave you.

I hope this helped!

7 0

3 years ago

On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the

FinnZ [79.3K]

Answer:

Step-by-step explanation:

Draw a picture!

You get a right triangle with hypotenuse = 20 ft and horizontal leg = 12 ft

Use the Pythagorean Theorem to find the length of the vertical leg:

vertical leg = √(20²-12²) = √256 = 16 ft

5 0

3 years ago

How many 3/4 foot pieces of string can be cut from a piece of string 4 1/2 feet long

Gnom [1K]

3/4 foot is 9 inches, and 4 1/2 feet is 54 inches, so, 54/9 makes exactly 6 pieces of string.

8 0

3 years ago