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2 years ago

Let p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x. Define r(x) = p(x) \cdot q(x).

1 answer:

5 0

The roots of the entire polynomic expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6.

<h3>How to solve a product of two polynomials </h3>

A value of x is said to be a root of the polynomial if and only if r(x) = 0. Let be r(x) = p(x) · q(x), then we need to find the roots both for p(x) and q(x) by factoring each polynomial, the factoring is based on algebraic properties:

r(x) = (x + 6) · (x + 2) · x · (x² + 5 · x - 6)

r(x) = (x + 6) · (x + 2) · x · (x + 3) · (x + 2)

r(x) = x · (x + 2)² · (x + 3) · (x + 6)

By direct inspection, we conclude that the roots of the entire polynomic expression are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6. $\blacksquare$

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910

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Use the equation: y = 5x - 4 Write an equation in any form) of a line that passes through the point (-1,7) and is parallel to th

Tju [1.3M]

Answer:

y = 5x + 12

Step-by-step explanation:

Use the formula: y - y1 = m(x - x1)

Plug in all numbers into your equation: y - 7 = 5(x - -1)

Minus with a minus becomes a positive: y - 7 = 5(x + 1)

Distribute: y - 7 = 5x + 5

Add 7 to both sides: +7 +7

Answer: y = 5x + 12

7 0

3 years ago

Determine the slope of a line perpendicular to the line with equation 6x-4y= 30

UNO [17]

6x - 4y = 30
-4y = -6x + 30
y = 3/2x - 15/2....slope here is 3/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So ur perpendicular line will have a slope of -2/3 (see how I flipped 3/2 making it 2/3...and then changed the sign, making it -2/3)

answer : perpendicular line will have a slope of -2/3.

3 0

3 years ago

Read 2 more answers

In a survey, the planning value for the population proportion is . How large a sample should be taken to provide a confidence in

tatuchka [14]

Answer:

n=350

Step-by-step explanation:

Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.35$ estimated proportion (value assumed)

$p$ true population proportion

Confidence =0.95 or 95% (value assumed)

Me=0.05 (value assumed)

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.586$

And rounded up we have that n=350

4 0

3 years ago

Simplify. -9 -5 -7 х Y Z 2 6 3 X Y Z

krok68 [10]

Answer:

$= {x}^{ - 11} {y}^{ - 11} {z}^{ - 10}$

Step-by-step explanation:

$= \frac{ {x}^{ - 9} {y}^{ - 5} {z}^{ - 7} }{ {x}^{2} {y}^{6} {z}^{3} } \\ = {x}^{ - 9 - 2} {y}^{ - 5 - 6} {z}^{ - 7 - 3} \\ = {x}^{ - 11} {y}^{ - 11} {z}^{ - 10}$

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3 years ago

Samuel has an ant farm with a volume of 375 cubic inches. The width of the ant farm is 2.5 inches and the length is 15 inches. W

Alexxandr [17]

Answer:

Step-by-step explanation:

From the given information, it is clear that the shape of ant form is rectangular prism.

Let us write formula for volume of rectangular prism (ant form)

V = l x w x h

Use the formula to write an equation.

Plug V = 375, w = 2.5 and l = 15

375 = 15 x 2.5 x h

375 = 37.5 x h

Divide both sides of the equation by 37.5

375/37.5 = (37.5 x h)/37.5

10 = h

Hence, the height of the form is 10 inches.

6 0

3 years ago