Is this true or false?

A function is given. h(t) = t2 + 3t; t = −1, t = 2

Arlecino [84]

Answer:

(a) The net change of the function is 12.

(b) The average rate of change of the function 4.

Step-by-step explanation:

The average rate of change of function $f(x)$ over the interval $a\leq x\leq b$ is given by this expression:

average rate of change = $\frac{net \:change \:in \:y}{change \:in \:x} = \frac{f(b)-f(a)}{b-a}$

It is a measure of how much the function changed per unit, on average, over that interval.

Given:

$h(t)=t^2+3t\\\\t=-1\\t=2$

(a) To find the net change of the function, first we calculate the values of $h(2)$ and $h(-1)$

$h(-1)=(-1)^2+3(-1)=-2\\\\h(2)=(2)^2+3(2)=10$

The net change is simply the difference

$h(2)-h(-1)=10-(-2)=12$

(b) The average rate of change takes the net change and divides it by the change in the $t$ value.

$\frac{12}{2-(-1)} =\frac{12}{3}=4$

5 0

2 years ago

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I WILL GIVE BRAINLEST AND CREATE A RANDOM QUE FOR U TO GET AN EXTRA !!!!!50!!!!! POINTS (ONLY IF YOU ACTUALLY SHOW YOUR WORK AND

Westkost [7]

I think the first one is a simple as it gets

for the second one it could be simplified to 6x^6-4 because u combine the x terms and distribute the power

8 0

2 years ago

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The vertices of a square CDEF are C(1,1), D(3,1), E(3,-1) and F(1,-1). What formulas prove that the diagonals are congruent perp

Oxana [17]

To prove that the diagonals are congruent, you need to formula to compute the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$

Using that formula, you may prove that $d(C,E) = d(D,F)$ , which means that the two diagonals have the same length.

To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by

$m = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

You can use this formula to prove that

$m_{CE} = -\cfrac{1}{m_{DF}}$

In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.

Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is

$y-y_0 = m(x-x_0)$

where $(x_0,y_0)$ is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:

$\begin{cases} y= m_{CE}x+q_{CE}\\ y = m_{DF}x+q_{DF} \end{cases}$

And use again the formula for the distance between two points to prove that

$d(A,C) = d(A,D) = d(A,E) = d(A,F)$

4 0

2 years ago

The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, t

12345 [234]

1 SD away from mean is 68% of data.
2 SD away from mean is 95% of data.
3 SD away from mean is 99.7% of data.

1 SD away:
190+30=220

2 SD away:
220+30=250

This shows we are on the outer 5 percent of the normal distribution.
Since you said "more", that means we only look at the right side of your 5%, which is only 2.5%

answer is D, 2.5%

4 0

2 years ago

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Evaluate the expression.

Liula [17]

Answer:

Step-by-step explanation:

Combine like terms

8+7y+2x+4y+4

11y+2x+12

8 0

2 years ago