Which of the following illustrates the truth value of the given conditional statement?

jeka94

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

For example

$x^{-2}=\frac{1}{x^2}$

or

$( \frac{2}{5} )^{-4}=( \frac{5}{2} )^4$

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$(8r^{-5})^{-3}$

$(8* \frac{1}{r^5} )^{-3} \\\\( \frac{8}{r^5} )^{-3}
 \\ \\ ( \frac{r^5}{8} )^3
\\\\ \mathrm{Apply\:exponent\:rule}:\quad *\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c} \ \ \ \ \ \ \ \ \ \ \ \ *(a^b)^c=a^{bc}
 \\\\( \frac{r^{15}}{8^3} )
\\\\( \frac{r^{15}}{512} )$

The answer is "D"

7 0

2 years ago

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.

Romashka [77]

By definition, the average change of rate is given by:
$AVR = \frac{f(x2)-f(x1)}{x2-x1}$
We will calculate AVR for each of the functions.
We have then:

f(x) = x^2 + 3x interval: [-2, 3]:
$f(-2) = x^2 + 3x = (-2)^2 + 3(-2) = 4 - 6 = -2

f(3) = x^2 + 3x = (3)^2 + 3(3) = 9 + 9 = 18$
$AVR = \frac{-2-18}{-2-3}$
$AVR = \frac{-20}{-5}$
$AVR = 4$

f(x) = 3x - 8 interval: [4, 5]:
$f(4) = 3(4) - 8 = 12 - 8 = 4 f(5) = 3(5) - 8 = 15 - 8 = 7$
$AVR = \frac{7-4}{5-4}$
$AVR = \frac{3}{1}$
$AVR = 3$

f(x) = x^2 - 2x interval: [-3, 4]
$f(-3) = (-3)^2 - 2(-3) = 9 + 6 = 15

f(4) = (4)^2 - 2(4) = 16 - 8 = 8$
$AVR = \frac{8-15}{4+3}$
$AVR = \frac{-7}{7}$
$AVR = -1$

f(x) = x^2 - 5 interval: [-1, 1]
$f(-1) = (-1)^2 - 5 = 1 - 5 = -4

f(1) = (1)^2 - 5 = 1 - 5 = -4$
$AVR = \frac{-4+4}{1+1}$
$AVR = \frac{0}{2}$
$AVR = 0$

Answer:
these functions from the greatest to the least value based on the average rate of change are:
f(x) = x^2 + 3x
f(x) = 3x - 8
f(x) = x^2 - 5
f(x) = x^2 - 2x

5 0

3 years ago

Pls help this should be the last thing

Lelu [443]

Answer:

1436 i believe

Step-by-step explanation:

7 0

2 years ago

Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values

Oduvanchick [21]

4x = 16log 4x = log 16 Take the common logarithm of both sides. (Remember, when no base is written, that means the base is 10.) What can you do with that new equation? log 4x = log 16x log 4 = log 16Use the power property of logarithms to simplify the logarithm on the left side of the equation. x log 4 = log 16Remember that log 4 is a number. You can divide both sides of the equation by log 4 to get x by itself.AnswerUse a calculator to evaluate the logarithms and the quotient.

3 0

3 years ago

the point (-3,2)is on the line given by which equation below A. y = 3x B.y = x-5 C.y = x+5 D.y = - 3 x need asap

Ipatiy [6.2K]

The answer is C. y=x+5

4 0

2 years ago