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3 years ago

The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

1 answer:

3 0

$\bf ~\hspace{10em}\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 8x^3-125~~ \begin{cases} 8=2\cdot 2\cdot 2\\ \qquad 2^3\\ 125=5\cdot 5\cdot 5\\ \qquad 5^3 \end{cases}\implies 2^3x^3-5^3\implies (2x)^3-5^3 \\[2em] [2x-5][(2x)^2+(2x)(5)+5^2]\implies (2x-5)(\stackrel{\stackrel{j}{\downarrow }}{4}x^2+\stackrel{\stackrel{k}{\downarrow }}{10}x+25)$

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Need help with this asap!

Brums [2.3K]

Answer:

The answer to your question is b = 8.06 cm

Step-by-step explanation:

Data

hypotenuse = c = 9 cm

long leg = b = ?

short leg = a = 4 cm

Process

This is a right triangle so we must use the Pythagorean theorem to find the length of the long leg (b)

c² = a² + b²

-Solve for b²

b² = c² - a²

-Substitution

b² = 9² - 4²

-Simplification

b² = 81 - 16

b² = 65

-Result

b = 8.06 cm

4 0

2 years ago

Read 2 more answers

PLS HELP: A box is 9 inches wide, 3 inches long, and 12 inches high. It is completely filled with blocks that are each 1 cubie i

LekaFEV [45]

Answer: 304

Step-by-step explanation: first you multiply 9, 3, and 12 which equals 324. Then you subtract 20 from 324 and you get 304.

3 0

2 years ago

What are the solutions of the equation x4 + 6x2 + 5 = 0? Use u substitution to solve.

klio [65]

Answer:

x = i and x = i $\sqrt{5}$

Step-by-step explanation:

Given

$x^{4}$ + 6x² + 5 = 0

Using the substitution u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Convert solutions back into terms of x

x² = - 1 ⇒ x = $\sqrt{-1}$ = i

x² = - 5 ⇒ x = $\sqrt{-5}$ = i $\sqrt{5}$

4 0

2 years ago

The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?

Mkey [24]

Question:

The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?

—————

Solution:

Call those two angles x and y, where x is the larger one.

If they are complementary, then their sum equals 90°:

x + y = 90° (i)

Also, the ratio between x and y is 3 : 2, so

x 3
—— = ——
y 2

Product of the extremes = product of the means:

2x = 3y

2x – 3y = 0 (ii)

Now, just solve this system of equations:

x + y = 90° (i)
2x – 3y = 0 (ii)

Solve it with elimination. Since you want to know the value of the larger angle, which is x, then eliminate the variable y by doing the following:

Multiply the equation (i) by 3,

3x + 3y = 270° (iii)
2x – 3y = 0 (ii)

then add both equations, so you cancel out the variable y:

3x + 2x + 3y – 3y = 270° + 0

3x + 2x = 270°

5x = 270°

 270°
x = ———
 5

x = 54° <——— this is the measure of the larger angle.

I hope this helps. =)

Tags: system of linear equations elimination method solve complementary angles algebra geometry

3 0

2 years ago

A college administration has conducted a study of 190randomly selected students to determine the relationship between satisfacti

almond37 [142]

Answer:

The probability that a student selected at random is on academic probation and is not satisfied with advisement is 0.1789

Step-by-step explanation:

Consider the provided information.

Out of 68 students on academic probation, 34 are not satisfied with advisement; That means 68-34=34 are satisfied with advisement.

If 68 students are in academic then the non academic students probation will be: 190-68=122

Only 25of the students not on academic probation are dissatisfied with advisement.

That means 122-25=97 students are satisfied.

According to the provided information draw the table as shown.

Satisfied Not satisfied Total

Academic probation 34 34 68

Non academic probation 97 25 122

Total 131 59 190

Now we need to determine the probability that a student selected at random is on academic probation and is not satisfied with advisement.

On academic probation and is not satisfied with advisement = 34

The total number of cases is 200.

$Probability=\frac{\text{Favourable cases}}{\text{Total number of cases}}$

Substitute the respective values:

$Probability=\frac{34}{190}\approx 0.1789$

Hence, the probability that a student selected at random is on academic probation and is not satisfied with advisement is 0.1789

4 0

2 years ago