All categories

3 years ago

PLEASE HELP!!!

Mathematics

1 answer:

AlekseyPX3 years ago

3 0

Answer:

Step-by-step explanation:

Find the average rate of change of each given function over the interval [-2, 2]]:

✔️ Average rate of change of m(x) over [-2, 2]:

Average rate of change = $\frac{m(b) - m(a)}{b - a}$

Where,

a = -2, m(a) = -12

b = 2, m(b) = 4

Plug in the values into the equation

Average rate of change = $\frac{4 - (-12)}{2 - (-2)}$

= $\frac{16}{4}$

Average rate of change = 4

✔️ Average rate of change of n(x) over [-2, 2]:

Average rate of change = $\frac{n(b) - n(a)}{b - a}$

Where,

a = -2, n(a) = -6

b = 2, n(b) = 6

Plug in the values into the equation

Average rate of change = $\frac{6 - (-6)}{2 - (-2)}$

= $\frac{12}{4}$

Average rate of change = 3

✔️ Average rate of change of q(x) over [-2, 2]:

Average rate of change = $\frac{q(b) - q(a)}{b - a}$

Where,

a = -2, q(a) = -4

b = 2, q(b) = -12

Plug in the values into the equation

Average rate of change = $\frac{-12 - (-4)}{2 - (-2)}$

= $\frac{-8}{4}$

Average rate of change = -2

✔️ Average rate of change of p(x) over [-2, 2]:

Average rate of change = $\frac{p(b) - p(a)}{b - a}$

Where,

a = -2, p(a) = 12

b = 2, p(b) = -4

Plug in the values into the equation

Average rate of change = $\frac{-4 - 12}{2 - (-2)}$

= $\frac{-16}{4}$

Average rate of change = -4

The answer is D. Only p(x) has an average rate of change of -4 over [-2, 2]

You might be interested in

Jovita divides $12,000 into three investments: a savings account paying 4% annual interest, a bond paying 6%, and a money market

xenn [34]

Answer:

$2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

Step-by-step explanation:

Let a, b, and c be the fractions of the $12,000 that is invested in the savings, bond, & money fund respectively.

Let S1, S2, S3 be the total monies from the savings, bond, & money fund after the year with interest respectively.

We know that a+b+c=1

and

S1+S2+S3 = 12000 + 860

S1+S2+S3 = 12860

From, the question, we know that b = 2a, and c = 1 - 3a based on the condition of 2 times more in the bond account that the savings account.

Thus;

S1 = a(12000)(1.04) = 12480a

S2 = 2a(12000)(1.06) = 25,440a

S3 = (1 - 3a)(12000)(1.09) = 13080 - 39240a

We already know that;

S1+S2+S3 = 12860

Thus, Adding the 3 equations gives;

12480a + 25,440a + 13080 - 39240a = 12860

Thus, simplifying gives;

13080 - 12860 = 39240a - 12480a - 25,440a

220 = 1320a

a = 220/1320

a = 0.1667

So,b = 2 x 0.1667 = 0.3334

c = 1 - (3 x 0.1667)

c = 1 - 0.5

c = 0.5

Thus,

S1 = 12480a = 12480 x 0.1667 ≈ $2080

S2 = 25,440a = 25440 x 0.1667 ≈ $4241

S3 = 13080 - 39240(0.1667) ≈ 6539

So, $2080 was invested in the savings account, $4241 was invested in the bond account, & $6539 was invested in the money fund.

3 0

3 years ago

Read 2 more answers

Ignore circled one and work it out please

mash [69]

Answer:

a. $\frac{(x-7)}{x^2+x-30}$

Step-by-step explanation:

$\huge \frac{x^2-3x-28}{(x^2+10x+24)(x-5)} \\\\\huge {=\frac{x^2-7x+4x-28}{(x^2+6x+4x+24)(x-5)}}\\\\\huge {=\frac{x(x-7)+4(x-7)}{\{x(x+6)+4(x+6)\}(x-5)}}\\\\\huge {=\frac{(x-7)(x+4)}{(x+6)(x+4)(x-5)}}\\\\\huge {=\frac{(x-7)}{(x+6)(x-5)}}\\\\\huge {=\frac{(x-7)}{x^2+(6-5)x+6(-5)}}\\\\\huge {=\frac{(x-7)}{x^2+x-30}}$

3 0

2 years ago

The sum of 5 times a number is 7

IRISSAK [1]

Answer:

5*x=7

The answer is made by division

x=7/5

x=1.4

Step-by-step explanation:

7 0

3 years ago

If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a

Karolina [17]

Let h = height of the box,
x = side length of the base.

Volume of the box is $V=x^{2} h = 115$ .
So $h = \frac{115}{ x^{2} }$

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
$S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x$
$= 2 x^{2} + \frac{460}{x}$
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

$S' = 4x- \frac{460}{ x^{2} } = 0$
$4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86$
Then $h= \frac{115}{4.86^{2}} = 4.87$
So the box is 4.86 in. wide and 4.87 in. high.

5 0

3 years ago

Read 2 more answers

Jay took out a small-business loan for 210,000. The terms of the loan are 5% annual interest for four years.

Marta_Voda [28]

5% of 210000=
(210000/100)5= $10500 anually

so 4 years will be $42000

he'll pay 42000 + 210000
$252000
answer is B

4 0

3 years ago

Read 2 more answers