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2 years ago

Please help with the answer below

Mathematics

1 answer:

kenny6666 [7]2 years ago

3 0

Answer:

$f(x) = \frac{x + 7}{6 - x} \\ \frac{3}{2} = \frac{x + 7}{6 - x} \\ 3(6 - x) = 2(x + 7) \\ 18 - 3x = 2x + 14 \\ - 3x - 2x = 14 - 18 \\ - 5x = - 4 \\ \frac{ - 5x}{ - 5} = \frac{ - 4}{ - 5} \\ x = \frac{4}{5}$

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Paul can choose to be paid $50 for a job or he can be paid 12.50 per hour. Underwhat circumstances should he choose the hourly w

Advocard [28]

Option 1: $50
Option 2: $12.50 per hour.

50 ÷ 12.50 = 4

Paul can choose the hourly wage if he works more than 4 hours.
For example, he works 5 hours.

12.50 x 5 hours = 62.50

$62.50 is higher than the fixed rate of $50. Thus, hourly wage is the better option.

8 0

3 years ago

16) (1 Point) : Solve the equation

Marat540 [252]

Answer:

(B)

4 +/- 3 sqrt(2) or 4+3sqrt(2) and 4-3sqrt(2)

Step-by-step explanation:

4(c-4)^2=72

4(c-4)(c-4)=72

foil the parenthesis (first, outside, inside, last)

4(c^2 -4c -4c +16)=72

4(c^2-8c+16)=72

divide each side by 4

c^2-8c+16=18

subtract 18 from both sides

c^2-8c-2

use quadratic formula

((-b +/- sqrt((-b^2)-4ac)))/2a

((-(-8)+/-sqrt((-8)^2-4(1)(-2)))/2(1))

(8+/-sqrt(64-(-8)))/2

(8+/-sqrt(64+8))/2

(8+/-sqrt(72))/2

(8+/-sqrt(36 * 2))/2

(8+/-6sqrt(2))/2

4+/-3sqrt(2)

or 4+3sqrt(2) and 4-3sqrt(2)

3 0

2 years ago

Solve the system of equations. 7x+10y=36 y=2x+9 x = ______ y = ______

wel

Step-by-step explanation:

Substitute the y in the 1st equation with the 2nd equation.

7x + 10(2x + 9) = 36

7x + 20x + 90 = 36

27x + 90 = 36

3x + 10 = 4

3x = -6

x = -2

So now we can find y.

y = 2x + 9 = 2(-2) + 9 = (-4) + 9 = 5.

So x = -2, y = 5.

6 0

3 years ago

Read 2 more answers

Triangle ABC is similar to triangle FED, find the measure of x. A. X = 9 B. X = 11 C. X = 110 D. X = 231

just olya [345]

Answer:

$A+B+C=130$

$F+E+D=273$

Step-by-step explanation:

From the question we are told that:

Dimension of ABC

A=9

B=11

C=110

Dimension of FED

D=231

Generally the equation for the similar triangles is mathematically given by

$\frac{A}{F}=\frac{B}{E}=\frac{C}{D}$

Therefore solving for F

$\frac{9}{F}=\frac{110}{231}$

$F=\frac{9*231}{110}$

$F=18.9$

Therefore solving for E

$\frac{11}{E}=\frac{110}{231}$

$E=\frac{11*231}{110}$

$E=23.1$

Measure of $\triangle ABC$

$A+B+C=130$

Measure of $\triangle FED$

$F+E+D=273$

5 0

3 years ago

Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

$|u|=\sqrt{14^2+9^2}$ which is $\sqrt{277}$

$|v|=\sqrt{3^2+6^2}$ which is $\sqrt{45}$

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

$cos\theta=\frac{uv}{|u||v|}$ where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

$cos^{-1}\theta=\frac{96}{111.64676}$ which returns an angle measure of 30.7. Plugging that all into the dot product formula:

$u*v=\sqrt{277}*\sqrt{45}cos(30.7)$ gives you a dot product of 96

6 0

2 years ago