A container holds 2 gallons of lemonade. How much is this in pints?

Write an equation in slope-intercept form of the line that passes through the point (-2,1) and is perpendicular to the equation

blondinia [14]

Let's convert the equation into slope-intercept form.

3x + 18y = 4
Subtract 3x from both sides.
18y= -3x + 4
Divide both sides by 18.
y = -3/18x + 4/18
Simplify.
y = -1/6x + 2/9

To make a line perpendicular, we need the slope to be the reciprocal of the other. Flip the denominator and numerator, and change the sign. We also have to change the b to make the line go through (-2, 1)

-1/6 to +6/1, or 6.

y = 6x + b

Input the x and y values and solve for b.

1 = 6(-2) + b
1 = -12 + b
Add 12 to both sides.
13 = b

y = 6x + 13

5 0

3 years ago

Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

2 years ago

Rita's family is moving to Grand Junction to Dallas. The moving van averages 60 miles each hour. About how many hours does the v

Eddi Din [679]

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}$

$\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}$

$\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}$

$\text{Time taken to reach Dallas}=16.3333\text{ Hour}$

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

$0.3333\times 60=19.998\approx 20$

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

5 0

2 years ago

What are the solutions of x^2+5x=2? Check all that apply

astraxan [27]

X^2+5x=2
you then solve by completing the square using the formula (b/2)^2 in order to create the new term. Solve for x by using this term to complete the square.
Your answer is then
x=-5/2+-√33/2

3 0

3 years ago

Read 2 more answers

Identify all sequences of transformations that results in similar figures.

Rus_ich [418]

A is the answer. Reflection and rotation.

7 0

2 years ago