# The table represents the start of the division of 8x^4+2x^3-7x^2+3x-2 by the indicated divisor. Find the quotient.

Explanation:

1) Question: divide 8x⁴+2x³-7x²+3x-2 by 4x² - x + 1

2) First term of the quotient

8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x²                   2x²
----------------------------------
4x³ - 9x² + 3x - 2

3) Second term of the quotient:

8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x²                   2x² + x
----------------------------------
4x³ - 9x² + 3x - 2
-4x³ +  x² -   x
----------------------------
- 8x² + 2x - 2

4) third term of the quotient:

8x⁴ + 2x³ - 7x² + 3x - 2     | 4x² - x + 1
---------------------
-8x⁴ + 2x³ - 2x²                   2x² + x - 2
----------------------------------
4x³ - 9x² + 3x - 2
-4x³ +  x² -   x
----------------------------
- 8x² + 2x - 2
8x²  - 2x + 2
-------------------------
0

5) Conclusion: since the remainder is 0, the division is exact and the quotient is
2x² + x - 2

You can verify the answer by multiplying the quotient obtained by the divisor. The result has to be the dividend.

Answer: 2x² + x - 2 (the first option)

Step-by-step explanation:

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## Related Questions

For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed that 62% of employers are likely to require higher employee contributions for health care coverage this year relative to last year. Suppose the survey was based on a sample of 800 companies likely to require higher employee contributions for health care coverage this year relative to last year. At 95% confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answer to four decimal places.) Compute a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answers to four decimal places.)

95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage.

(0.5868 , 0.6532)

Step-by-step explanation:

Step(i):-

Given the survey was based on a sample of 800 companies

Given size 'n'  = 800

A recent survey showed that 62% of employers are likely to require higher employee contributions for health care coverage this year relative to last year

sample proportion

p⁻ = 0.62

Step(ii):-

The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage.

M.E  = 0.017 X 1.96

M.E = 0.03

Step(iii):-

95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage.

( 0.62 - 0.0332 , 0.62+0.0332)

(0.5868 , 0.6532)

The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is approximately 0.0245. The 95% confidence interval for the proportion of companies likely to require higher employee contributions is (0.5955, 0.6445).

### Explanation:

To compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage, we can use the formula:

Margin of error = Z * sqrt((p * (1-p)) / n)

where Z is the Z-score corresponding to the desired confidence level (95% in this case), p is the proportion of companies likely to require higher employee contributions, and n is the sample size. Substituting the given values into the formula, we have:

Margin of error = 1.96 * sqrt((0.62 * (1-0.62)) / 800)

Calculating this value gives us a margin of error of approximately 0.0245.

To compute the 95% confidence interval for the proportion of companies likely to require higher employee contributions, we can use the formula:

Confidence interval = p ± margin of error

Substituting the given values into the formula, we have:

Confidence interval = 0.62 ± 0.0245

Calculating this value gives us a confidence interval of (0.5955, 0.6445).

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1. (5 points) At 6pm, ghost A is 5 kilometers due west of ghost B. Ghost A is flying westat 15 km/hr and ghost B is flying north at 20 km/hr. How fast is the distance between
the ghosts changing at 10pm?

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

Step-by-step explanation:

At first we assume that north and east directions both represent positive quantities. Let suppose that and . If both ghosts moves at constant velocity such that and , then the final positions of both ghosts are, respectively:

Ghost A

(Eq. 1)

Ghost B

(Eq. 2)

Where is the time, measured in hours.

Then, the equations of motion of each ghost are, respectively:

Ghost A

Ghost B

Then, the distance between both ghosts is:

(Eq. 3)

The magnitude of the relative is represented by the following Pythagorean identity:

Then, we find the rate of change of the relative distance (), measured in kilometers per hour, by implicit differentiation:

(Eq. 4)

If we know that , then the rate of change of the relative distance at 10 PM is:

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

93% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

To solve the problem shown in the figure above you must keep on mind the following information:

1. The figure shows a parabola whose vertex is (0,0).

2. The x² indicates that the red parabola shown in the figure is vertical

3. and the sign - indicates that the red parabola opens down.

Therefore, you can conclude that the red parabola has the equation f(x)=-x²

If we observe the graph of F(x) and G(x), F(x) can be obtained by shifting the graph of G(x) 4 units down.

Shifting 4 units down means subtracting 4 from the function value.

So, G(x) = 4 - x²

Thus,

F(x) =  G(x) - 4
F(x) = 4 - x² - 4 = - x²

Therefore, the correct answer is option B

Convert to fractions and write in simplest form.A) 0.02
B) 12%
C) 0.5%
D) 1.12

Given below.

Explanation:

A) 0.02 = =

B) 12% = = =

C) 0.5% = =

D) 1.12 =

PLEASEEE HELP FAST! One solution each is given on four quadratic equations. Assuming that each quadratic equation has two solutions, what is the second solution for each equation?

Step-by-step explanation:

If one solution of a quadratic equation is a complex number (a + bi),

Other solution of the equation will be the conjugate of the first solution.

So the other solution will be in the form of (a - bi)

If one solution is, x = -4 - 5i

Other solution will be, x = -4 + 5i

If one solution is, x = 4 + 5i

Other solution will be, x = 4 - 5i

If one solution is, x = 5 - 4i

Other solution will be, x = 5 - 4i