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3 years ago

Given the following table, find the rate of change between f(-4) and f(0).

Mathematics

1 answer:

Virty [35]3 years ago

3 0

Answer: The correct option is (B) $\dfrac{1}{2}.$

Step-by-step explanation: We are given to find the rate of change between f(-4) and f(0) from the following table:

x -4 -2 0 2 4

f(x) -2 -1 0 1 2

The average rate of change of a function f(x) from x = a to x = b is given by

$A=\dfrac{f(b)-f(a)}{b-a}.$

From the given table, we have

f(-4) = - 2 and f(0) = 0.

Therefore, the average rate of change between f(-4) and f(0) is given by

$A=\dfrac{f(0)-f(-4)}{0-(-4)}=\dfrac{0-(-2)}{0+4}=\dfrac{2}{4}=\dfrac{1}{2}.$

Thus, the required rate of change is $\dfrac{1}{2}.$

Option (B) is correct.

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What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the la

olga55 [171]

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the two smaller ones are a and a+1, the larger one is a+2

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2 years ago

The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2/3x + 6. What is the point-

Elena-2011 [213]

$y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so hmmm then we know the slope of that line is -2/3, so we're really looking for the point-slope form of a line with a slope of -2/3 and that passes through (-3 , 8)

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{(-3)})\implies y-8=-\cfrac{2}{3}(x+3)$

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1 year ago

A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. Th

NikAS [45]

<h2>Answer:</h2>

$6\frac{1}{2}$ <u>, "six and one over two ft".</u>

<h2>Step-by-step explanation:</h2>

Let's considerate the fact that the garden has a <u>square shape</u>.

<h3>1. Finding values of interest.</h3>

Amount of fence that the gardener already has: $4\frac{1}{2}$ ft.

Length of one side: $2\frac{3}{4}$ ft.

If one side measures $2\frac{3}{4}$ ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

$4*(2\frac{3}{4})=\\ \\4*(2+\frac{3}{4})=\\ \\(4*2)+(4*\frac{3}{4})=\\ \\8+(\frac{12}{4} )=\\ \\8+3=\\ \\11$

The gardener already has $4\frac{1}{2}$ , which equals $4 + \frac{1}{2}$ . Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that:

$11-(4+\frac{1}{2} )=\\ \\11-(\frac{8}{2} +\frac{1}{2} )=\\ \\11-\frac{9}{2}= \\ \\\frac{22}{2} -\frac{9}{2}=\\\\ \frac{13}{2}$

<h3>3. Express your result.</h3>

$\frac{13}{2} =\\ \\\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{1}{2}= \\ \\6+\frac{1}{2}=\\ \\6\frac{1}{2}$

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1 year ago

PLEASE HELP ASAP - ILL GIVE BRAINIEST

Mars2501 [29]

10. x*x + 10x + 21 = x + 3 * length

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This is the expression bro!

100% sure

Plz mark me brainliest

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2 years ago

Read 2 more answers

.Which one of the following is true when ds/dt=3t^2/2s

ser-zykov [4K]

1) Given: ds / dt = 3t^2 / 2s

2) Separate variables: 2s ds = 3t^2 dt

3) Integrate both sides:

∫ 2s ds = ∫ 3t^2 dt

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=> s^2 = t^3 + constant

=> s = √ (t^3 + constant)

Answer: option B.

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3 years ago