$\textbf{Given that,}\\\\~~~\dfrac{5^4}{5^7}\\\\\\=5^{4-7}~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~\dfrac{a^m}{a^n} = a^{m-n}\\\\\\=5^{-3}\\\\\\=\dfrac 1{5^3}~~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Apply exponent rule:}~ a^{-n} = \dfrac 1 {a^n},~~~a \neq 0 \\\\\\=\dfrac 1{125}\\\\\\=0.008$

5 0

2 years ago

Read 2 more answers

Write an inequality to model the situation.<br><br><br> A number exceeds 21

mezya [45]

It could be x > 21 im not sure

8 0

3 years ago

If the function f(x) = -1/2x - 7 were graphed, which of the following would be true?

Fittoniya [83]

ANSWER

D. As the x-values increase, the y-values would decrease

EXPLANATION

The given function is
$y = - \frac{1}{2} x - 7$

The slope of this function is
$m = - \frac{1}{2}$

Since the slope is negative, there is a negative or an inverse relationship between x and y.

As the values of x increases, the values of y decreases.

Also, as the values of x decreases, the values of y increases.

The first option is not true because as x is becoming bigger and bigger negatively, y will become positive.

For instance, when
$x = - 40$
$y = - \frac{1}{2} ( - 40) - 7$

This implies that,

$y = 20 - 7 = 13$

Options B is obviously not true because the function has a negative relationship between x and y.

Option C is also false because, x can be positive since it is the independent variable.

See graph

Therefore, the correct answer is option D.

5 0

3 years ago

Use synthetic division to find the remainder. When 3x^ 2 - 2x - 4 is divided by x - 3.

OlgaM077 [116]

ANSWER

a.)17

EXPLANATION

The given function is

$3 {x}^{2} - 2x - 4$

We want to find the remainnder when this function is divided by x-3 using synthetic division.

We write the coefficients of the given function and carry out the synthetic division as shown in the attachment.

The remainnder is 17.

The correct answer is A.

7 0

3 years ago