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3 years ago

What are the zeros of the polynomial function? F(x)= x^2 + 12x +20

Mathematics

1 answer:

vampirchik [111]3 years ago

3 0

Answer:

Step-by-step explanation:

$F(x)=x^2+12x+20\\\\\text{The zeros:}\\\\F(x)=0\iff x^2+12x+20=0\\\\x^2+2x+10x+20=0\\\\x(x+2)+10(x+2)=0\\\\(x+2)(x+10)=0\iff x+2=0\ \vee\ x+10=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x+10=0\qquad\text{subtract 10 from both sides}\\\boxed{x=-10}$

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WOULD VERY MUCH APPRECIATE THIS PLEASE HELP

Sindrei [870]

Answer: the area of a figure is 85.13 in²

Step-by-step explanation:

The area of a figure S consists of the area of a semicircle S₁ and the area of a parallelogram S₂

$\displaystyle\\S_1=\frac{\pi D^2}{4*2} \\\\S_1=\frac{\pi (8)^2}{8} \\\\S_1=\frac{64\pi }{8} \\\\S_1=8\pi \\\\S_1\approx25.13\ in^2\\\\S_2=10*6\\\\S_2=60\ in^2\\\\Thus,\\\\S=25.13+60\\\\S=85.13\ in^2$

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1 year ago

SOMEONE PLEASE HELP ALL THE QUESTIONS R ATTACHED AS WELL AS THE ANSWERS!!!!!!!!!!!!!!

Reil [10]

The error is in <em>Step-4</em>.

A negative exponent does NOT mean that the number turns negative. A negative exponent means the number is in the denominator.

(4)⁻⁴ means (1/4⁴) . That's (1/256) . All positive numbers.

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3 years ago

Volume and surface area are often compared by manufacturers in order to maximize how much of something can go inside of a packag

notka56 [123]

We have no dimensions to work with. I'll pick some and try and comply with the conditions of the problem.

Suppose you have an object that is 14 by 22 by 27 cm. These three numbers have no common factor so they cannot be reduced any further, which is helpful for this problem.

Find the Volume
Volume

l = 27 cm
w = 14 cm
h = 22 cm

V = 27 *14 * 22
V = 8316 cm^3

Find the surface area
SA = 2*l*w + 2*l*h + 2*w*h
SA = 2*27*14 + 2*27*22 + 2*14*22
SA = 756 + 1188 + 616
SA = 2558

Just looking at these numbers The surface area is about 1/3 of the volume. I don't think this is always true.

$\frac{SA}{V} = \frac{2*L*W + 2*L*H + 2*W*H}{L*W*H}$

Another way to do this is to consider a cube which might give you a more useful result.

s = L = W = H all three dimensions are equal in a cube.
The volume of a cube is s*s*s = s^3
The surface area of a cube is 2*s*s + 2*s*s + 2s*s = 6s^2

$\frac{SA_cube}{V_cube} = \frac{6s*s}{s*s*s}$
$\frac{SA}{V} = \frac{6}{s}$

That means whatever the side length, the Surface Area to volume = 6/the side length which is kind of an interesting result.

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2 years ago

Simplify (15q^6 + 5q^2)(5q^4)^-1

saveliy_v [14]

The answer should be:

3q4 + 1 /q2

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3 years ago

A study investigated the effectiveness of meditation training in reducing trait anxiety. The study evaluated subjects trait anxi

Setler79 [48]

Answer:

The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.7787.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.7787\frac{6.9}{\sqrt{27}} = 3.7$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.9 - 3.7 = 1.2.

The upper end of the interval is the sample mean added to M. So it is 4.9 + 3.7 = 8.6.

The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).

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2 years ago