Hi

A line goes through the points (5, -1) and (7, -5). What is a possible equation to a new line that is perpendicular?

Leya [2.2K]

Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5).

First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y."

5x+4y=2

-5x -5x (subtract 5x from both sides to move it to the right side of your equation)

4y = 2 - 5x

/4 /4 /4 (divide all the terms by 4 to get "y" by itself)

y = (1/2) - (5/4)x ... I suggest leaving your slope as a fraction.

Now, we know that our slope, m , is going to be -(5/4).

Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know:

y = 5

m = -(5/4)

x = 7

y=mx+b

5=(-5/4)(7) + b -> I plugged in what we knew for y, m, and x.

5 = -(35/4) + b -> I multiplied the numbers in the numerator (5 x 7) to get 35/4

20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4)

+(35/4) +(35/4) -> I add (35/4) to both sides to isolate b

55/4 = b ... or b = 13.74

Answer:

m = -(5/4)

b = 13.75

7 0

3 years ago

Simplify. 9x^8-18x^6

GrogVix [38]

You cannot simplify this but you can factorise it:

9x^6 (x^2 - 2)

7 0

3 years ago

A runner is preparing for a marathon that is cut into 5 equal sections. The marathon is 42.95 kilometers long. How long is each

Lisa [10]

Your answer is 21.475km

5 0

3 years ago

Read 2 more answers

In the 1980’s, a clinical trial was conducted to determine if taking an aspirin daily reduced the incidence of heart attacks. Of

zubka84 [21]

There is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.

Given sample size of patients take aspirin 11037, sample size of patients who have assigned placebo group be 11034. 104 doctors who take aspirin had a heart attack, 189 doctors had placebo had heart attacks.

First we have to form hypothesis.

$H_{0} :p{1} -p_{2} =0$

$H_{1}:p_{1} -p_{2} < 0$

We have to find the respective probabilities.

$p_{1}$ =104/11037

=0.0094

$p_{2}$ =189/11034

=0.0171

Now their respective margin of errors.

$s_{1}$ = $\sqrt{ {(0.0094*0.9906)/11037}$

=0.0009

$s_{2}$ = $\sqrt{0.0171*0.9829}$

=0.0011

Hence the distribution of the differences,they are given by:

p= $p_{1} -p_{2}$

=0.0094-0.0171

=-0.0077

S= $\sqrt{s_{1} ^{2}+s_{2} ^{2} }$

= $\sqrt{(0.0009)^{2} +(0.0011)^{2} }$

=0.00305

z=(p -f)/S (In which f=0 is the value tested at the null hypothesis)

=(-0.0077-0)/0.00305

=-2.52

p value will be 0.005.

p value of 0.05 significance level.

z=1.96.

1.96>0.005

So we will reject the null hypothesis which means it cannot reduce the whole chance of becomming a heart attack.

Hence there is enough evidence to conclude that taking aspirin cannot reduces the chance of cancer.

Learn more about t test at brainly.com/question/6589776

#SPJ4

6 0

2 years ago

a. Show that the system of rational expressions is closed under addition, or give an example showing the contrary.

otez555 [7]

A "rational expression" is a fraction in which the numerator and the denominator are both polynomials. The sum of two such expressions will always produce another such expression, viz.,
p(x)/q(x) + r(x)/s(x) = [p(x)s(x) + q(x)r(x)] / [q(x)*s(x)]. 
The numerator and denominator of the sum will both be polynomials when fully expanded

7 0

3 years ago