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3 years ago

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If the area of a rectangle 24a2b and the length is 8ab2, what would the width of the rectangle, given that width is found by div

iding area by length? Simplify the answer.

1 answer:

slava [35]3 years ago

5 0

Area of a rectangle: A = 24 a² b
Length: L = 8 a b²
Width: W = A / L = 24 a² b / 8 a b²
Answer: W = 3 a / b

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I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!

marissa [1.9K]

Answer:

2. Eunju is right

3. $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ .

Step-by-step explanation:

<u>Polynomial Remainder Theorem</u>

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

$f(x)=(x+b)^3+(x+c)^2-(b-c)$

To find out if x+b is a factor of f(x), we find f(-b):

$f(-b)=(-b+b)^3+(-b+c)^2-(b-c)$

Operating:

$f(-b)=(-b+c)^2-(b-c)$

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

$x^2+5x+6 =(x+2)(x+3)$

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

$f(x)=x^4+5x^3+2x^2-20x-24$

Find f(-2):

$f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24$

$f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0$

Find f(-3):

$f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24$

$f(-3)=81-5*27+2*9+60-24$

$f(-3)=81-135+18+60-24 =0$

Since both f(-2) and f(-3) are zero, $x^2+5x+6$ is a factor of $x^4+5x^3+2x^2-20x-24$ .

5 0

3 years ago

Please help if you can

Firdavs [7]

Answer:

4

Step-by-step explanation:

We just have to find the corresponding d(t) value when t=2. From the graph, we can see that when t = 2, d(2) = 4. Hope this helps!

7 0

3 years ago

What is the answer to this math problem.<br> FULL PROBLEM PLEASE!<br> 36m^4 + 40m + 28

Fofino [41]

You have to times 36 by itself 4 times, then add 40 and 28 to the answer you get.

The answer: 1679684.

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3 years ago

Solve for r. 60 = -24 + 12r

neonofarm [45]

Answer:

r = 7

Step-by-step explanation:

60 = -24 + 12r

<u>+24 +24</u>

84 = 12r

84 ÷ 12 = r

7 = r

Check:

60 = -24 + 12r

-24 + 12(7)

-24 + 84 = 60

3 0

3 years ago

Read 2 more answers

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-ciga

jasenka [17]

Answer:

The 90% confidence interval is (0.1897, 0.2285).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

From a July 2019 survey of 1186 randomly selected Americans ages 18-29, it was discovered that 248 of them vaped (used an e-cigarette) in the past week. This means that $n = 1186, \pi = \frac{248}{1186} = 0.2091$

Construct a 90% confidence interval to estimate the population proportion of Americans age 18-29 who vaped in the past week.

So $\alpha = 0.10$ , z is the value of Z that has a pvalue of $1 - \frac{0.10}{2} = 0.95$ , so $z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 - 1.645\sqrt{\frac{0.2091*0.7909}{1186}} = 0.1897$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2091 + 1.645\sqrt{\frac{0.2091*0.7909}= 0.2285$

The 90% confidence interval is (0.1897, 0.2285).

3 0

3 years ago