Simplify (3^3 x 5^3)^-2

kirill [66]

It's going to be kind of crazy, but you need to use Pythagorean's Theorem for this. That will look like this: $(2 \sqrt{x} +1)^2=( \sqrt{x} +1)^2+(2 \sqrt{x} )^2$ . FOIL out the left side to get $4x+4 \sqrt{x} +1$ . FOIL out the first of the 2 expressions on the right to get $x+2 \sqrt{x} +1$ , and the second of the 2 to get 4x. Our equation now looks like this: $4x+4 \sqrt{x} +1=x+2 \sqrt{x} +1+4x$ . Combine like terms to get an equation that still has square roots in it that we have to deal with: $4x-x-4x=-2 \sqrt{x}$ and $x=2 \sqrt{x}$ . We will square both sides to get rid of the square root sign. $x^{2} =2x$ . This is a polynomial now that can be factored to solve for x. Bring the 2x over by subtraction and set the polynomial equal to 0. $x^{2} -2x=0$ . Factor out an x, leaving us with x(x-2)=0. That means that x = 0 or x - 2 = 0 and x = 2. Of course if we are solving for the length of a side we know it can't have a side length of 0, so it must have a side length that is a multiple of 2. x = 2

3 0

2 years ago

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A certain company manufactures skateboards and rollerskates. It takes them 2 units of labor and 1 unit of materials to produce a

Alisiya [41]

Answer: The company should produce 7 skateboards and 16 rollerskates in order to maximize profit.

Step-by-step explanation: Let the skateboards be represented by s and the rollerskates be represented by r. The available amount of labour is 30 units, and to produce a skateboard requires 2 units of labor while to produce a rollerskate requires 1 unit. This can be expressed as follows;

2s + r = 30 ------(1)

Also there are 40 units of materials available, and to produce a skateboard requires 1 unit while a rollerskate requires 2 units. This too can be expressed as follows;

s + 2r = 40 ------(2)

With the pair of simultaneous equations we can now solve for both variables by using the substitution method as follows;

In equation (1), let r = 30 - 2s

Substitute for r into equation (2)

s + 2(30 - 2s) = 40

s + 60 - 4s = 40

Collect like terms,

s - 4s = 40 - 60

-3s = -20

Divide both sides of the equation by -3

s = 6.67

(Rounded up to the nearest whole number, s = 7)

Substitute for the value of s into equation (1)

2s + r = 30

2(7) + r = 30

14 + r = 30

Subtract 14 from both sides of the equation

r = 16

Therefore in order to maximize profit, the company should produce 7 skateboards and 16 rollerskates.

6 0

3 years ago

16 out of the 50 digital video recorders

IceJOKER [234]

Answer:

34

Step-by-step explanation:

6 0

3 years ago

Pls hurry i really i need to finish

Thepotemich [5.8K]

0,0
1,2
2,4
3,6
4,8
There u go hope u get it done

5 0

1 year ago

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12 (2 -2)+32 = (x +6) +2

Anestetic [448]

Answer: x = 24

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Step 1: Remove parentheses.

12 (2 − 2) + 32 = $x$ + 6 + 2

Step 2: Simplify 2 − 2 to 0.

12 × 0 + 32 = $x$ + 6 + 2

Step 3: Simplify 12 × 0 to 0.

0 + 32 = $x$ + 6 + 2

Step 4: Simplify 0 + 32 to 32.

32 = $x$ + 6 + 2

Step 5: $x$ + 6 + 2 to $x$ + 8.

32 = $x$ + 8

Step 6: Subtract 8 from both sides.

32 − 8 = $x$

Step 7: Simplify 32 − 8 to 24.

24 = $x$

Step 8: Switch sides.

$x$ = 24

~I hope I helped you! :)~

8 0

2 years ago

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