What do the factors in the factored form represent?

Answers

Answer 1

Answer:

Answer:

The factored form tells you the times at which the object's height is zero (the roots). ... Write the equation for this parabola in vertex form, factored form, and general form. From the graph you can see that the x-intercepts are 3 and 5. So the factored form contains the binomial expressions (x 3) and (x 5).

Step-by-step explanation:

could u answer my newest question? ive been stuck on it for hours

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Suppose that you are in charge of evaluating teacher performance at a large elementary school. One tool you have for this evaluation is reports of the average student reading test score in each classroom. You also know that across the whole school, the average student reading score was 80 points and the standard deviation in scores was 10 points. Determine:(a) If each class has 25 students in it, what is the standard error of the classroom average score?(b) In what range do you expect the average classroom test score to fall 95% of the time?(c) What is the approximate probability that a classroom will have an average test score of 79 or higher?(d) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if there were only 15 students in a class? Explain your answer in 2-3 sentences.(e) Do you think the probability that a classroom has an average test score of 79 or higher would be greater or smaller if the standard deviation of individual student reading scores was only 5 points (instead of 10)?
In this triangle, what is the value of x?Enter your answer, rounded to the nearest tenth, in the box.x = yd
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Use the slope-intercept form to Graph y=-1/8x+2
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What is 5\8 times 16

Answers

5/8*16
the answer is 10

Are the series absolutely, conditionally convergent, or divergent?

Answers

Step-by-step explanation:

∑ sin(nπ/4) / (n³ + 3n)

This is less than 1 / n⁴ for all n > 1. 1/n⁴ is a convergent p-series, so the lesser series also converges. │aₙ│converges for the same reason, so this is absolutely convergent.

∑ (-1)ⁿ⁺¹ ln(n + 1) / (n + 1)

This is an alternating series. bₙ is positive and decreasing, and lim(n→∞) bₙ = 0, so the series converges. Now we need to check if│aₙ│converges. Using comparison test, │aₙ│is greater than 1/n for all n ≥ 6. 1/n is a divergent p-series, so the greater series│aₙ│also diverges. So this is conditionally convergent.

What is the slope of the function? –6 –4 4 6graph :
x
-2
-1
0
1
2

y
8
2
-4
-10
-16

Answers

to get the slope, all we need is two points, so let's pick two off the table.

$\bf \setlength{\fboxsep}{1pt}\begin{array}{rrll}x&y\n\cline{1-2}\n\boxed{-2}&\boxed{8}\n-1&2\n\boxed{0}&\boxed{-4}\n1&-10\n2&-16\end{array}~\hspace{5em}(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad(\stackrel{x_2}{0}~,~\stackrel{y_2}{-4})\n\n\n\slope = m\implies\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-8}{0-(-2)}\implies \cfrac{-4-8}{0+2}\implies \cfrac{-12}{2}\implies -6$

Answer:

-6 i got it right

Step-by-step explanation:

A 170-lb man carries a 20-lb can of paint up a helical staircase that encircles a silo with radius 30 ft. The silo is 90 ft high and the man makes exactly three complete revolutions. Suppose there is a hole in the can of paint and 8 lb of paint leaks steadily out of the can during the man's ascent. How much work is done by the man against gravity in climbing to the top

Answers

The work done by the man against gravity in climbing to the top is 16740 lb-ft

What is work done against gravity?

The work done against gravity relies on the height of the object and the weight at which the object is changing.

From the given information:

Taking the vertical y-axis when y = 0, then:

The weight of the paint w(y) becomes;

w(0) = 20 lb

w(90) = 20 - 8 = 12 lb

Provided that the paint leaks steadily, the function of y i.e. w(y) can be expressed as a linear function in the form:

w(y) = a + by ---- (1)

Thus;

w(0) = a = 20

w(90) = 20 + 90b = 12
b = (12 - 20)/90
b = -4/45

From equation (1)

w(y) = 20 - 4y/45

The total weight becomes;

w = w(y) + the man's weight

w = 20 - 4y/45 + 170

w = 190 - 4y/45

Therefore, the work done against gravity is computed as:

W = ∫ w dy

where;

y varies from 0 to 90

$\mathbf{W = \int ^(90)_(0)( 190 - (4y)/(45) )\ dy }$

W = 16740 lb-ft

Learn more about work done against gravity here:

brainly.com/question/12975756

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Find the area of the triangle Please help

Answers

Answer:

14m^2

Step-by-step explanation:

Area of a triangle is - 1/2 base times hight

two triangels find the srea of both and add them

4x4x1/2 = 16x1/2 = 8m

3x4x1/2 = 12x1/2 = 6m

6m + 8m = 14m

Prove the trigonometric identity
(tan x + cot x)/(csc x * cos x) = sec^2 x

Answers

Answer:

$(\tan x + \cot x)/(\csc x \cos x)=\sec^2 x$

$\boxed{((\sin x)/(\cos x) + (\cos x)/(\sin x))/((1)/(\sin x) \cdot \cos x)}=\sec^2 x$

$\boxed{((\sin^2 x)/(\sin x\cos x) + (\cos^2 x)/(\sin x \cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\boxed{((\sin^2 x+\cos^2 x)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\boxed{((1)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\boxed{(1)/(\sin x\cos x) \cdot (\sin x)/(\cos x)}=\sec^2 x$

$(1)/(\cos^2x)=\sec^2x$

$\sec^2x=\sec^2x$

Step-by-step explanation:

Given trigonometric identity:

$(\tan x + \cot x)/(\csc x \cos x)=\sec^2 x$

$\textsf{Use the identities\;\;$\tan x = (\sin x)/(\cos x)$\;,\;$\cot x=(\cos x)/(\sin x)$\;\;and\;\;$\csc x=(1)/(\sin x)$}:$

$\boxed{((\sin x)/(\cos x) + (\cos x)/(\sin x))/((1)/(\sin x) \cdot \cos x)}=\sec^2 x$

Simplify the denominator and make the fractions in the numerator like fractions:

$\boxed{((\sin^2 x)/(\sin x\cos x) + (\cos^2 x)/(\sin x \cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\textsf{Apply\;the\;fraction\;rule\;\;$(a)/(b)+(c)/(b)=(a+c)/(b)$\;to\;the\;numerator}:$

$\boxed{((\sin^2 x+\cos^2 x)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\textsf{Use\;the\;identity\;\;$\sin^2x+\cos^2x=1$}:$

$\boxed{((1)/(\sin x\cos x))/((\cos x)/(\sin x))}=\sec^2 x$

$\textsf{Apply\;the\;fraction\;rule\;\;$(a)/((b)/(c))=a \cdot (c)/(b)$}:$

$\boxed{(1)/(\sin x\cos x) \cdot (\sin x)/(\cos x)}=\sec^2 x$

Cancel the common factor sin x, and apply the exponent rule aa = a² to the denominator:

$(1)/(\cos^2x)=\sec^2x$

$\textsf{Use the identity\;\;$(1)/(\cos x)=\sec x$}:$

$\sec^2x=\sec^2x$

Answer:

The proof of the trigonometric identity:

We can start by expanding the numerator and denominator. In the numerator, we can use the trigonometric identities tan x = sin x / cos x and cot x = cos x / sin x.

In the denominator, we can use the trigonometric identity csc x = 1 / sin x. This gives us:

$((tan x + cot x))/((csc x * cos x) ) = (((sin x )/( cos x)) + ((cos x )/(sin x)))/(((1)/( sin x)) * cos x)$

`We can then cancel the sin x terms in the numerator and denominator. This gives us:

$((tan x + cot x))/((csc x * cos x) ) = (1 + 1)/(((1 )/(sin x)) * cos x)$

We can then multiply the numerator and denominator by sin x. This gives us:

$((tan x + cot x))/((csc x * cos x) ) = (sin x + sin x)/((1 )/(cos x))$

We can then simplify the expression. This gives us:

$((tan x + cot x))/((csc x * cos x) ) = (2sin x)/((1 )/(cos x)) = (2sin x)/(cos x) = 2tan x$

Finally, we can use the trigonometric identity tan^2 x = sec^2 x - 1 to get:

$2tan x =( 2tan^2 x )/( (sec^2 x - 1))$

This gives us the following identity:

$((tan x + cot x))/((csc x * cos x) ) = sec^2 x$

This completes the proof of the trigonometric identity.

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