What is 7.5 quarts in pints

What is the slope of a line perpendicular to the line whose equation is Y=2x+5?

Oksanka [162]

B. slope is -1/2

This is because the m-value aka the slope is always the reciprocal if the line is perpendicular

8 0

2 years ago

Using the quadratic formula to solve x2 = 5 – x, what are the values of x?

Ivenika [448]

Answer:

x²=5-x

x²+x-5=0

1x²+1x²-5=0

[ax²+bx²+c=0]

∆=b²-4ac

∆=1²-4(-5)(1)=1+20=21

x=(-b±√∆)/2a

x=(-1±√21)/2

meaning:

x=(-1+√21)/2 or x=(-1-√21)/2

4 0

1 year ago

What is an equation of the line that passes through the points (0, -7) and (-8, 3)?

avanturin [10]

Answer (assuming it can be in slope-intercept form):

$y = -\frac{5}{4} x-7$

Step-by-step explanation:

1) First, find the slope of the line by using the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(3)-(-7)}{(-8)-(0)}\\m = \frac{3+7}{-8-0} \\m = \frac{10}{-8} \\m = -\frac{5}{4}$

So, the slope is $-\frac{5}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute real values for the $m$ , $x_1$ , and $y_1$ in the formula.

Since $m$ represents the slope, substitute $-\frac{5}{4}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine, it will equal the same thing at the end) and substitute its x and y values into the formula as well. (I chose (0, -7), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the following answer:

$y-(-7) = -\frac{5}{4} (x-(0))\\y + 7 = -\frac{5}{4} x\\y = -\frac{5}{4} x-7$

7 0

2 years ago

Can a percent of change problem have an answer over 100%?

gregori [183]

Yes it can have a change

4 0

2 years ago

Read 2 more answers

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is kn

loris [4]

Answer:

95 percent confidence interval for μ is determined by

(60.688 , 69.312)

a) be the same

Step-by-step explanation:

Step (i):-

Given data a random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph.

The sample size is n= 121

The mean of the sample x⁻ = 65mph.

The standard deviation of the population is 22 mph

σ = 22mph

Step (ii) :-

Given The 95 percent confidence interval for μ is determined as

(61.08, 68.92)

we are to reduce the sample size to 100 (other factors remain unchanged) so

given The sample size is n= 100

The mean of the sample x⁻ = 65mph.

The standard deviation of the population is 22 mph

σ = 22mph

Step (iii):-

95 percent confidence interval for μ is determined by

$(x^{-} - 1.96\frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} } )$

$(65 - 1.96\frac{22}{\sqrt{100} } , 65 + 1.96 \frac{22}{\sqrt{100} } )$

(65 - 4.312 ,65 +4.312)

(60.688 , 69.312) ≅(61 ,69)

This is similar to (61.08, 68.92) ≅(61 ,69)

Conclusion:-

it become same as (61.08, 68.92)

4 0

3 years ago