If ED = 10 and DB = 3x – 8, what is the length of mc084-2.jpg?

The area of a rectangular lot that is 50 feet wide by 100 feet deep is:

ziro4ka [17]

The area of a rectangle can be directly calculated using the formula:

A = l * w

Where l is the length or the depth while w is the width

Therefore,

A = 50 feet * 100 feet

<span>A = 5000 square feet</span>

8 0

2 years ago

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

2 years ago

PLEASE HELP WORTH 50 POINTS

VashaNatasha [74]

Answer:cos( A + B ) = cosAcosB - sinAsinB ;

cos( A + B ) / ( cosAsinB ) = ( cosAcosB - sinAsinB ) / ( cosAsinB ) = ( cosAcosB ) / ( cosAsinB ) - ( sinAsinB ) / ( cosAsinB ) = cosB / sinB - sinA / cosA = cotB - tanA ;

tan²(x) - sin²(x) = sin²(x)/cos²(x) - sin²(x)

… = sin²(x) (1/cos²(x) - 1)

… = sin²(x) (sec²(x) - 1)

… = sin²(x) tan²(x)

Step-by-step explanation:

5 0

1 year ago

A linear function contains the following points.

stich3 [128]

Answer:

The answer is C. The slope is 3 and y-intercept is (0,-1(

6 0

2 years ago

In the New York State Numbers Lottery, you pay $1 and can bet that the sum of the numbers that come up is 13. The probability of

Harman [31]

Answer:

The expected value of profit is -0.5125. This is expected loss as value is negative.

Step-by-step explanation:

We are given the following in the question:

P(winning) = 0.075

Thus,

P(Loosing) =

$1 - 0.075 = 0.925$

If we win we gain a profit of $5.50 and if we loose the lottery, we loose $1.

Thus, we can form the probability distribution in the following manner:

Event: Winning Loosing

Profit(x): +5.50 -1

P(x): 0.075 0.925

We have to calculate the expected value of the profit.

$E(X) = \displaystyle\sum x_i(P(x_i))\\E(x) = +5.50(0.075) + (-1)(0.925)\\E(x) = -0.5125$

Thus, the expected value of profit is -0.5125. This is expected loss as value is negative.

7 0

2 years ago