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3 years ago

14

For what values of x is the rational expression below undefined? Check all that apply. A. 5 B. 4 C. 3 D. -3 E. -4 F. -5low equal

to zero. 20+2x/ 5-x

1 answer:

DiKsa [7]3 years ago

8 0

F is your answer or E

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Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured parallel to a line

Ber [7]

Answer:

The distance is:

$\displaystyle\frac{3\sqrt{142}}{10}$

Step-by-step explanation:

We re-write the equation of the line in the format:

$\displaystyle\frac{x+2}{3}=\frac{y+\frac{3}{2}}{2}=\frac{z+\frac{4}{3}}{\frac{5}{3}}$

Notice we divided the fraction of y by 2/2, and the fraction of z by 3/3.

In that equation, the director vector of the line is built with the denominators of the equation of the line, thus:

$\displaystyle\vec{v}=\left< 3, 2, \frac{5}{3}\right>$

Then the parametric equations of the line along that vector and passing through the point (-2, 3, -4) are:

$x=-2+3t\\y=3+2t\\\displaystyle z=-4+\frac{5}{3}t$

We plug them into the equation of the plane to get the intersection of that line and the plane, since that intersection is the image on the plane of the point (-2, 3, -4) parallel to the given line:

$\displaystyle x+y+z=3\to -2+3t+3+2t-4+\frac{5}{3}t=3$

Then we solve that equation for t, to get:

$\displaystyle \frac{20}{3}t-3=3\to t=\frac{9}{10}$

Then plugging that value of t into the parametric equations of the line we get the coordinates of the intersection:

$\displaystyle x=-2+3\left(\frac{9}{10}\right)=\frac{7}{10}\\\displaystyle y=3+2\left(\frac{9}{10}\right)=\frac{24}{5} \\\displaystyle z=-4+\frac{5}{3}\left(\frac{9}{10}\right)=-\frac{5}{2}$

Then to find the distance we just use the distance formula:

$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

So we get:

$\displaystyle d=\sqrt{\left(-2-\frac{7}{10}\right)^2+\left(3-\frac{24}{5}\right)^2+\left(-4 +\frac{5}{2}\right)^2}=\frac{3\sqrt{142}}{10}$

3 0

3 years ago

The circumference of a circle is 8pi What is the radius?

Mashcka [7]

Answer:

4

Step-by-step explanation:

5 0

2 years ago

I need help again :/

Kobotan [32]

Answer:

Hola

Step-by-step explanation:

Well if this is based off the first thing I answered, then 1. C

as I told you before, every time the x axis values go up one, the y values go up by x2 (aka times 2). Therefore it’s C.

2. It is linear because the unit change (amount it goes up aka slope) is the same since it’s alway x2. Hence the line on a graph would look linear

8 0

2 years ago

Please help with this question

Vera_Pavlovna [14]

This would be the equation:

Y= 5/2x+5

I hope I've helped!

7 0

3 years ago

Read 2 more answers

A game is played using one die. If the die is rolled and shows 5 5, the player wins $ 10 $10. If the die shows any number other

Verizon [17]

The expected value is -$0.33.

The probability of winning is 1/6. The probability of losing is 5/6.

If you win, your prize is 10-2 = 8, since you paid $2 to pay the game. If you lose, you lose the $2 you spent.

The expected value would be the probability of winning, 1/6, multiplied by the winnings, 8, added to the probability of losing, 5/6, multiplied by the loss, -2:
1/6*8 + 5/6(-2) = 8/6 - 10/6 = -2/6 = -0.33

5 0

2 years ago

Read 2 more answers