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lisabon 2012 [21]

3 years ago

5

Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of meas

urement. f(x)=x2−3f(x)=x 2−3; [1, 3].

1 answer:

Nastasia [14]3 years ago

3 0

Answer:

4

Step-by-step explanation:

Average Rate of Change Formula: $\frac{f(b) - f(a)}{b - a}$

Simply plug in our interval:

[(3² - 3) - (1² - 3)]/(3 - 1)

[9 - 3 - 1 + 3]/2

8/2

4

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The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to

satela [25.4K]

Part A:

Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

$\frac{y-2}{x} = \frac{-5-2}{1} =-7 \\ \\ \Rightarrow y-2=-7x \\ \\ \Rightarrow y=-7x+2$

Thus, p(x) = -7x + 2

</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

$\frac{y-1}{x-4} = \frac{-3-1}{2-4} =\frac{-4}{-2}=2 \\ \\ \Rightarrow y-1=2(x-4)=2x-8 \\ \\ \Rightarrow y=2x-7$

Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is (1, -5)

Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).

Part C:

From part A, we have that p(x) = -7x + 2, given that $g(x) = 1 + 1.5^x$

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

3 0

3 years ago

Identify the solution(s) of v2+11v−26=0.

miss Akunina [59]

Answer:

i solved for v and got

v = 2, -13

i hope this helps :]

4 0

3 years ago

Desiree works 28 hours per week. She has a monthly income of $120 from investments. Desiree also plays in a band one night a wee

Oksi-84 [34.3K]

So hmmm let's see
she has a monthly income of 120 from investments, now, there are 12 months in a year, so her yearly income from investments are 120*12 or
$1440

she plays on a band, and makes 200 a week, now, there are 52 weeks in a year, so her yearly income from band playing is 200 * 52, or
$10400

her total annual income is 49696, now, if we subtract the band and investment income, we'd be left over with only what comes from her job payrate
so 49696 - 1440 - 10400 is 37856

so, she makes from her job, $37856 annually

now, she only works 28 hours weekly, how much is that yearly? well, 52 weeks in a year, she works 28*52 hours a year, let us divide 37856 by that

37856 ÷ ( 28 * 52) well, it ends up as 26

so, her hourly payrate is $26 per hour

now, she wants to ask for a raise, to make 51880 annually

well, if we check the difference of 51880 and 49696, that'd leave us with the difference in pay, or the raise annual amount

51880 - 49696 = 2184

ok, so she wants $2184 annually more from her work
how much is that in the hours she works annually? well 2184 ÷ ( 28 * 52)

7 0

3 years ago

Read 2 more answers

Find the volume of a right circular cone that has a height of 9 m and a base with a

AlladinOne [14]

Answer:

that is the solution to the question

3 0

3 years ago

Use the discriminant to describe the roots of each equation. Then select the best description. x2 - 5x + 7 = 0

miv72 [106K]

The general form of a quadratic (second degree) equation is

$a x^{2} +bx+c=0$ , where

$D= b^{2}-4ac$ is called the Discriminant.

The Discriminant determines how many roots the equation will have as follows:

i) if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.

In our equation, $x^{2} -5x+7=0$ , a=1, b=-5, c=7

so the discriminant is D=(-5)^2-4*1*7=25-28<0

Thus the equation has no roots.

Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.

5 0

3 years ago