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Aliun [14]
3 years ago
8

Solve for the variables

Mathematics
1 answer:
Pani-rosa [81]3 years ago
8 0

Step-by-step explanation:

{x}^{2}  =  {30}^{2}  -  {18}^{2}  \\ x =  \sqrt{900 - 324}  \\ x =  \sqrt{576}  \\ x = 24

{y}^{2}  =  {24}^{2}  +  {10}^{2}  \\ y =  \sqrt{576 + 100}  \\ y = \sqrt{676}  \\ y = 26

<h3>#CMIIW</h3>

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19. If a school board determines that there should be 3 teachers for every 50 students, how many teachers are needed for an enro
WINSTONCH [101]

Answer:

324 teachers

Step-by-step explanation:

3 teachers of every 50 students

__ teachers of 5400 students

so,

5400 \div 50 = 108

therefore,

3 \times 108 = 324

7 0
3 years ago
Read 2 more answers
Write equations for the vertical and horizontal lines passing through the point (7,4)
Softa [21]
X=7 and y=4 are the correct equations
8 0
3 years ago
Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 270 em
allsm [11]

Answer:

The number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.

The explanation of the answers is now provided as follows:

Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:

U + A + W = 270 ………………………. (1)

Since United Continental had three times as many empty seats as American, this implies that:

U = 3A ………………………………… (2)

Substituting U = 3A into equation (1), we have:

3A +A + W = 270

4A + W = 270

W = 270 - 4A ………………………….. (3)

For the cost, we have:

3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33

0.447A + 0.146A + 0124W = 38.33

0.593A + 0.124W = 38.33 ………………… (4)

Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:

0.593A + 0.124(270 - 4A) = 38.33

0.593A + 33.48 - 0.496A = 38.33

0.593A - 0.496A = 38.33 - 33.48

0.097A = 4.84

A = 4.84 / 0.097

A = 49.8969072164948

Rounding to a whole number, we have:

A = 50

Substituting A = 50 into each of equations (2) and (3), we have:

U = 3 * 50 = 150

W = 270 - (4 * 50) = 70

Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Download pdf
6 0
2 years ago
Write the equation of the line in fully simplified slope-intercept form.
Bad White [126]

Answer:

y = -\frac{2}{5} x-6

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula m =\frac{y_2-y_1}{x_2-x_1}. Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5} \\  

So, the slope of the line is -\frac{2}{5}.

2) Next, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the m, x_1 and y_1 into the formula.

Since m represents the slope, substitute -\frac{2}{5}  in its place. Since x_1 and y_1 represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6

6 0
3 years ago
What is 607-568 rounded off to the nearest 100
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