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just olya [345]

3 years ago

12

Find the average rate of change from x = 7 to x = 14 for the function f(x) = 0.01(2)^x and select the correct answer below.

1 answer:

Firdavs [7]3 years ago

3 0

Answer: 23.22

Step-by-step explanation:

Given function: $f(x)=0.01(2)^x$

At x=7

$f(7)=0.01(2)^7=1.28$

At x=14

$f(14)=0.01(2)^{14}=163.84$

We know that the rate of change from $x_1$ to $x_2$ of function is given by

$=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

Therefore, The rate of change of given function from x=7 to x=14

$=\frac{f(14)-f(7)}{14-7}\\\\=\frac{163.84-1.28}{14-7}\\\\=\frac{162.56}{7}\\\\=23.22$

Therefore, the average rate of change from x = 7 to x = 14 for the given function is 23.22

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Sophia purchased a cell phone for $25. This amount includes tax of 6%. What was the cost of the items before tax?

hram777 [196]

The sales price before tax was $23.58. Hope this helps!

4 0

2 years ago

Write the standard form of the line that has a slope of -3/4 and y-intercept of -2. Include your work in your final answer. Type

Nataliya [291]

3x + 4y = - 8

The equation of a line in standard form is Ax + By = C

where A is a positive integer and B, C are integers

Express the line in ' slope- intercept form '

y = mx + c → (m is the slope and c is the y-intercept)

here m = - $\frac{3}{4}$ and c = - 2

hence y = - $\frac{3}{4}$ x - 2 → equation in slope- intercept form

multiply all terms by 4

4y = - 3x - 8

add 3x to both sides

3x + 4y = - 8 → in standard form

7 0

2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2By%3D1%7D%20%5Catop%20%7Bx-2y%3D4%7D%7D%20%5Cright.%20%5C%5C%5Clef

brilliants [131]

Answer:

<em>(a) x=2, y=-1</em>

<em>(b) x=2, y=2</em>

<em>(c)</em> $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

<em>(d) x=-2, y=-7</em>

Step-by-step explanation:

<u>Cramer's Rule</u>

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

(c) The system to solve is

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

4 0

3 years ago

Tammy purchased a prepaid phone card for $15. Long distance calls cost 18 cents a minute using this card. Tammy used her card on

Mars2501 [29]

Answer:

46 minutes

Step-by-step explanation:

Sorry about not answering your question sooner, but here is your answer:

In order to get the answer, we have to subtract the original amount of money on the phone card by the amount left ver after the call:

15 - 6.72 = 8.28

Then, we divide this number by 0.18:

8.28 / 0.18 = 46

So, Tammy's call lasted 46 minutes

Hope this helps :)

5 0

3 years ago

Tom is 4 more than twice Andrews age.Sara is 8 less than 5 times Andrews age. If Tom and Sara are twins,how old is Andrew

Marrrta [24]

Andrew is 4 years old

4 0

2 years ago