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4 years ago

Factor 2x^2-128 completely

1 answer:

8 0

2x² - 128

2(x² - 64), but (x² - 64) = x² - 8² (difference of 2 squares),[a²-b²=(a-b)(a+b)]

2(x² - 64) = 2(x² - 8²) = 2(x-8)(x+8)

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Please help me asap!!!

Dmitry [639]

Answer:

So here is how we are going to get the measure of angle 2.

Since given that angle COE measures 55°, we will equate m∠2 = 2x and m∠3 = x+10 with 55. So, 55 = 2x + x + 10

55 = 3x + 10

55-10 = 3x

45 = 3x << divide both sides by 3 and the result is

15 = x

So now that we know x, we can now solve for angle 2.

m∠2 = 2x

m∠2 = 2(15)

m∠2 = 30°

I hope that this is the answer that you are looking for.

5 0

3 years ago

A store sells Brazilian coffee for $10 per lb. and Columbian coffee for $14 per lb. If the store decides to make a 150-lb. blend

Artemon [7]

Answer:

The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.

Step-by-step explanation:

Let "b" be the amount of Brazilian coffee, in pounds, required for the blend and "c" the amount of Colombian coffee required, in pounds.

Since there are two unknown variables a two-equation system is needed to solve the problem, we can set up one equation for weight and another for price as follows:

$b+c=150\\10*b+14*c=11*150$

Solve for "c" by multiplying the first equation by -10 and adding it to the second one:

$b+c=150\\10b+14c -10b-10c=11*150 -(10*150)\\4c=150\\c = 37.5$

Now, solve for b by replacing the value obtained into the first equation

$b+c=150\\b= 150 - 37.5\\b=112.5$

The store should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian cofee.

6 0

3 years ago

A large rectangular movie screen in an IMAX theater has an area of 8,364 square feet. Find the dimensions of the screen if it is

jeyben [28]

Answer:

The dimensions of the screen are

Length:102 feet

Width: 82 feet

Step-by-step explanation:

we know that

The area of the rectangle (movie screen) is equal to

$A=LW$

where

L is the length

W is the width

we have

$A=8,364\ ft^2$

$8,364=LW$ ----> equation A

The screen is 20 feet longer than it is wide.

$L=W+20$ ---> equation B

substitute equation B in equation A

$8,364=(W+20)W$

solve for W

$8,364=W^2+20W\\W^2+20W-8,364=0$

solve the quadratic equation by graphing

the solution is W=82 ft

see the attached figure

Find the value of L

$L=82+20=102\ ft$

therefore

The dimensions of the screen are

Length:102 feet

Width: 82 feet

7 0

4 years ago

All zeros of polynomial function 3x^4 +14x^2 -5

Marizza181 [45]

Answer:

Correct answer: x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

Step-by-step explanation:

Given:

3 x⁴ + 14 x² - 5 = 0 biquadratic equation

this equation is solved by a shift x² = t and get:

3 t² + 14 t - 5 = 0

t₁₂ = (-14 ± √14² - 4 · 3 · 5) / 2 · 3 = (-14 ± √196 + 60) / 6

t₁₂ = (-14 ± √256) / 6 = (-14 ± 16) / 6

t₁ = -5 or t₂ = 1 / 3

the solution t₁ = -5 is not accepted because it cannot be x² = -5

we accepted t₂ = 1 / 3

x² = 1 / 3 ⇒

x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

God is with you!!!

5 0

3 years ago

Maria mixes \frac{1}{4} cup white sugar and \frac{2}{3} cup brown sugar to make a topping for some muffins. She uses \frac{1}{12

Hoochie [10]

Answer: 11 muffins

Step-by-step explanation:

Since Maria mixes 1/4 cup white sugar with 2/3 cup brown sugar, this will give us a mixture of:

= 1/4 + 2/3

= 3/12 + 8/12

= 11/12

Ww are then told that she uses 1/12 cup of the mixture to top each muffin. Therefore, the number of muffins that she can top will be:

= 11/12 ÷ 1/12

= 11/12 × 12/1

= 12

She can top 11 muffins.

3 0

3 years ago