2 Points

Consider m = y2 - y1/ x2 - x1 . Which x1 and x2-values would determine that the line is vertical? Justify your answer

Y_Kistochka [10]

Answer:

$x_2=x_1$

Step-by-step explanation:

We were given the slope formula;

$m=\frac{y_2-y_1}{x_2-x_1}$

This line is vertical if the denominator is zero.

That is when $x_2-x-1=0$

This implies that;

$x_2=x_1$

Justification;

When $x_2=x_1$ , then, the line passes through;

$(x_1,y_1)$ and $(x_1,y_2)$

The slope now become

$m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}$

The equation of the line is

$y-y_1=\frac{y_2-y_1}{0}(x-x_1)$

This implies that;

$0(y-y_1)=(y_2-y_1)(x-x_1)$

$0=(y_2-y_1)(x-x_1)$

$\frac{0}{y_2-y_1}=(x-x_1)$

$0=(x-x_1)$

$x=x_1$ ... This is the equation of a vertical line.

3 0

2 years ago

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confiden

Vlad [161]

Answer:

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.

This means that $n = 2161, \pi = \frac{1214}{2161} = 0.5618$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Margin of error:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}$

$M = 0.0209$

The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.

4 0

3 years ago

What is the equation of the line that passes through the points (1, −10) and (−4, −7)?

nignag [31]

Hi there! :)

First, let's find the slope using this formula:

m= $\frac{y2-y1}{x2-x1}$

m= $\frac{-7-(-10)}{-4-1} \\\frac{-7+10}{-5} \frac{3}{-5} =-\frac{3}{5}$

Now, use the Point-Slope formula:

y-y1=m(x-x1)

y-(-10)=-3/5(x-1)

y+10=-3/5x+3/5

y=-3/5x+3/5-10

y=-3/5x-9.4

Hope this helps..

~Just an emotional teen who listens to "Try Everything"

$SilentNature$

4 0

2 years ago

Francisca and Elizabeth are participating in a walk-a-thon fundraiser.

Ghella [55]

Francisca raises 76.50 and Elizabeth makes 43.50 together they makes 120

8 0

3 years ago

Solve each equation. Record your work and check your solution. a. 5(x-2)+(-9)= -7(1-x)

Daniel [21]

The solution for equation is x = -6

Solution:

Given equation is:

$5(x-2) + (-9) = -7(1-x)$

We have to solve the equation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

Therefore, solve for brackets in given equation

$5(x-2) + (-9) = -7(1-x)\\\\5x - 10 -9 = -7 + 7x$

Solve for terms in left hand side of equation

$5x - 19 = -7+7x$

Move the variables to one side and constants to other side

$7x -5x = -19+7\\\\2x = -12\\\\Divide\ both\ sides\ by\ 2\\\\x = -6$

Thus the solution for equation is x = -6

8 0

2 years ago