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2 years ago

Solve the equation by expressing each side as a power of the same base and then equating exponents.

Mathematics

2 answers:

pickupchik [31]2 years ago

8 0

Hope it helped you.

alexdok [17]2 years ago

6 0

1/27 = 3^(-3)

3^(3x+6) = 3^(-3)

When bases are the same, all you need to do is set the exponents equal to each other:

3x+6 = -3
3x = -9
x = -3

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Find the equation of line passing through points A (1, 3) and B (3, 7).

Sidana [21]

Solution:

To find the equation of line passing through points A (1, 3) and B (3, 7).

we know that, to derive the equation of a line we first need to calculate the slope of the line. Slope m of a line at points $(x_{1} ,y_{1})$ and $(x_{2}, y_{2})$ is given by - $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

Slope of the line at point A(1,3) and B(3,7)

$m=\frac{7-3}{3-1}$ .

$m=\frac{4}{2}$ .

$m=2$ .

Equation of a line using a point and a slope , $y-y_{1}= m(x-x_1)$

$y-3= 2(x-1)$

$y-3= 2x-2$

$y= 2x-2+3$

$y= 2x+1$

The equation of line passing through points A (1, 3) and B (3, 7) : $y= 2x+1$

4 0

3 years ago

You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly sele

Damm [24]

Answer:

The margin of error for this estimate is of 14.79 yards per game.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.093

The margin of error is:

$M = T\frac{s}{\sqrt{n}}$

In which s is the standard deviation of the sample and n is the size of the sample.

You randomly select 20 games and see that the average yards per game is 273.7 with a standard deviation of 31.64 yards.

This means that $n = 20, s = 31.61$

What is the margin of error for this estimate?

$M = T\frac{s}{\sqrt{n}}$

$M = 2.093\frac{31.61}{\sqrt{20}}$

$M = 14.79$

The margin of error for this estimate is of 14.79 yards per game.

3 0

3 years ago

Find the equation of the line specified. The slope is -4, and it passes through ( 5, 8).

ollegr [7]

Answer:

B. y= -4x + 28

Step-by-step explanation:

To find the equation of this line first put it into slope-point form, $y-y_{1} =m(x-x_{1})$ where $y_{1}$ and $x_{1}$ are the y and x coordinates and m is the slope. So plug in the information to get the equation, y-8=-4(x-5). Then solve for y,