36k² - 1 What are the steps to completing this

lesantik [10]

$\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}$

3 0

3 years ago

34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

skad [1K]

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

$m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-1 for $x_{1}$ , and 4 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

$y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$$

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation $y-4=\frac{1}{3} x-\frac{1}{3}$ , and simplify as follows,

$y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$$

This is the required linear equation.

5 0

2 years ago

Valeria has been training for the Charlestown cruisers bike race. The first week she trained, she rode 5 days and took the same

ira [324]

The number of miles covered every evening obtujwd using a system of equation is 15 miles.

Let the number of miles per evening = m

Number of days = 5

Number of miles per morning = 8 miles

Total miles covered = 115 miles

Using the expression below :

Number of days(miles per morning + miles per evening) = 115 miles

5(8 + m) = 115

40 + 5m = 115

5m = 115 - 40

5m = 75

m = 75 / 5

m = 15 miles

Therefore, the Number of miles covered per evening is 15 miles.

Learn more : brainly.com/question/18796573

8 0

3 years ago

Dan is organizing a trip to the airport for a group of 75 people.

eduard

6 large taxis x 7 people per large taxi = 42 people. In total there are 75 people. 75-42=32 people left. If you want to divide these people over small taxis, you divide 32 by 4, 32/4=8, so you need 8 small taxis

6 0

3 years ago

what is the image of the point (4,-8) after a rotation of 270 degrees counterclockwise about the orgin

marysya [2.9K]

Answer:

(-8,-4)

Step-by-step explanation:

(y,-x)

8 0

3 years ago