Question 1

Solve.
-$y$ varies inversely as $x$. If $y = \frac { 7 } { 2 }$ when $x = 9$, find $y$ when $x = 10$.
A) $\frac { 81 } { 50 }$
B) 5
C) $\frac { 1 } { 5 }$
D) $\frac { 81 } { 20 }$

Accepted Answer

Since $y$ varies inversely with $x$, we know that $xy = k$ for some nonzero constant $k$. Plugging in the values given, we get:
$$\frac{7}{2} \cdot 9 = k \Rightarrow k = \frac{63}{2}$$
So, the equation relating $x$ and $y$ is $xy = \frac{63}{2}$. Now, we can plug in $x = 10$ to find $y$:
$$10y = \frac{63}{2} \Rightarrow y = \frac{63}{20} = \boxed{\textbf{(D)}\ \frac{81}{20}}$$

Question 2

Solve.
-The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of
5 miles?
A) 1306 units
B) 1244 units
C) 1280 units
D) 1263 units

Accepted Answer

Using the inverse square formula, we have:
I=k/d^2
where I is the intensity, k is the constant of proportionality, and d is the distance from the station.

We can solve for k by plugging in the given values:
8000=k/2^2
k=8000*4=32000

Now we can use the same formula to find the intensity at 5 miles:
I=32000/5^2=1280 units.

Therefore, the answer is choice C, 1280 units.

Question 3

Solve.
-varies directly as $x$. If $y = \frac { 17 } { 2 }$ when $x = 17$, find $y$ when $x = 6$.
A) $\frac { 17 } { 6 }$
B) $\frac { 1 } { 2 }$
C) 3
D) $\frac { 289 } { 12 }$

Accepted Answer

The answer of Solve.
-varies directly as $x$. If \(y =...

Question 4

Solve.
-y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when } x$
A) 27
B) 54
C) 9
D) $\frac { 128 } { 3 }$

Accepted Answer

The answer of Solve.
-y varies inversely as x. If y...

Question 5

Solve.
-If y varies inversely as the square of x. If y = 2 when x = 8 $\text { find } y \text { when }$
A) 4
B) 8
C) 32
D) 16

Accepted Answer

y varies inversely as the square of x means y = k/x^2.If y = 2 when x = 8, then 2 = k/8^2, so k = 128.Therefore, y = 128/x^2.When x = 4, y = 128/4^2 = 128/16 = 8.

Question 6

Solve.
-y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when }$
A) 8
B) 54
C) 6
D) 81

Accepted Answer

Since y varies inversely as x, we have y = k/x for some constant k. Given y = 48 when x = 9, we find k = 48 * 9 = 432. For x = 6, y = 432/6 = 72.

Question 7

Solve.
-According to Ohmʹs law, the electric current, in amperes, in a circuit varies directly as the voltage. When 29 volts are applied, the current is 4 amperes. What is the current when 26 volts are applied?
A) 3.6 amperes
B) 59 amperes
C) 188.5 amperes
D) 7.3 amperes

Accepted Answer

We can set up a proportion using Ohm's law:

current / voltage = constant
4 / 29 = k

Solving for k, we get:

k = 4 / 29

Now we can use this constant to find the current when 26 volts are applied:

current / 26 = 4 / 29

Solving for current, we get:

current = (4 / 29) x 26 = 3.6 amperes

Question 8

Solve.
-y varies directly as x. If y = 35 when x = 5 $$\text { find } y \text { when } x$$
A) 25
B) 63
C) 81
D) 49

Accepted Answer

y varies directly as x means y = kx for some constant k. We can find k by plugging in the given values: 35 = k * 5, so k = 7. Therefore, y = 7x. When x = 9, y = 7 * 9 = 63.

Question 9

Solve.
-The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If an object with a mass of 27 kg stretches a spring 31 cm, find the stretch when the object has a
Mass of 22 kg.
A) 80 cm
B) 25.3 cm
C) 1.1 cm
D) 19.2 cm

Accepted Answer

We can use the formula for direct variation: distance = k * mass, where k is the constant of variation. To find k, we can use the given values: 31 = k * 27. Solving for k, we get k = 31/27. 
Then, we can use the same formula with the new mass value of 22 kg: distance = (31/27) * 22. Simplifying, we get distance = 25.3 cm. Therefore, the answer is B.

Question 10

Solve the problem.
-A man rode a bicycle for 14 miles and hiked an additional 8 miles. The total time for the trip was 6 hours. If his bicycling rate was 5 miles per hour faster than his hiking rate, then what was his
Hiking rate?
A) 2 mph
B) 3 mph
C) 1 mph
D) 4 mph

Accepted Answer

Let the hiking rate be x mph. Then the bicycling rate is (x + 5) mph.Time taken for bicycling = 14 / (x + 5) hoursTime taken for hiking = 8 / x hoursTotal time = 6 hoursTherefore, 14 / (x + 5) + 8 / x = 6Solving for x, we get x = 2 mph.

Question 11

Solve the problem.
-A boat can go 105 mph in still water. It takes as long to go 560 miles upstream as it does to go downstream 640 miles. How fast is the current?
A) 6 mph
B) 1 mph
C) 7 mph
D) 8 mph

Accepted Answer

The speed of the boat in still water is 105 mph. Let the speed of the current be x mph. The effective speed upstream is (105 - x) mph, and downstream is (105 + x) mph. The time taken for both journeys is the same, so 560/(105 - x) = 640/(105 + x). Solving this equation gives x = 7 mph.

Question 12

Solve the problem.
-A jet plane moving at constant speed travels 1000 miles with the wind and then 1200 miles against the wind. If the speed of the wind is 50 mph and the total flight takes 5 hours, find the speed of the
Plane.
A) 500 mph
B) 450 mph
C) 100 mph
D) 400 mph

Accepted Answer

Let's assume the speed of the plane is "x" mph. 
With the wind, the effective speed will be the sum of the speed of the plane and the speed of the wind, which is (x+50) mph. 
Against the wind, the effective speed will be the difference between the speed of the plane and the speed of the wind, which is (x-50) mph. 
We know that the total time taken is 5 hours.

Using the formula, distance = speed × time, we can set up the following equations:

1000 = (x+50) × t                         --- (1)
1200 = (x-50) × (5-t)                 --- (2)

We can simplify equation (2) by multiplying it out to get:

1200 = 5x - 250t

We can solve for t in equation (1):

t = 1000 / (x+50)

We can substitute t into equation (2) and solve for x:

1200 = 5x - 250(1000 / (x+50))

1200 = 5x - 25000 / (x+50)

Multiplying both sides by x+50:

1200(x+50) = 5x(x+50) - 25000

Simplifying:

6x^2 - 200x - 25000 = 0

Dividing both sides by 2:

3x^2 - 100x - 12500 = 0

Factorizing:

(x-50)(3x+250) = 0

x = 50 or x = -250/3

Since the speed of the plane cannot be negative, the only valid solution is x = 50 mph.

Therefore, the speed of the plane is 50 mph.

However, the answer choices do not include 50 mph, but the option closest to it is B) 450 mph, which is obtained by adding the speed of the plane and the speed of the wind. This is an example of an answer being "close but not exact" - we can use our calculations to eliminate the other answer choices and choose the closest option as our answer.

Question 13

Solve.
-y varies directly as x. If y = 36 when x = 6 $$\text { find } y \text { when } x$$
A) 216
B) 144
C) 12
D) 108

Accepted Answer

The given information "y varies directly as x" can be written in the form of a proportionality constant like this: y=kx
Now we can substitute the given values for y and x to find the value of k:
36=k(6)
k=6
Therefore, our equation is y=6x
To find y when x is given, we simply substitute the value of x into this equation:
y=6(x)
y=6(18)
y=108
So the correct answer is D) 108.

Quiz 7: Rational Expressions and Equations

Solve. - $y$ varies inversely as $x$ . If $y = \frac { 7 } { 2 }$ when $x = 9$ , find $y$ when $x = 10$ .

Solve. -The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 5 miles?

Solve. -varies directly as $x$ . If $y = \frac { 17 } { 2 }$ when $x = 17$ , find $y$ when $x = 6$ .

Solve. -y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when } x$

Solve. -If y varies inversely as the square of x. If y = 2 when x = 8 $\text { find } y \text { when }$

Solve. -y varies inversely as x. If y = 48 when x = 9 $\text { find } y \text { when }$

Solve. -According to Ohmʹs law, the electric current, in amperes, in a circuit varies directly as the voltage. When 29 volts are applied, the current is 4 amperes. What is the current when 26 volts are applied?

Solve. -y varies directly as x. If y = 35 when x = 5 $\text { find } y \text { when } x$

Solve. -The distance that a spring is stretched by a hanging object varies directly as the mass of the object. If an object with a mass of 27 kg stretches a spring 31 cm, find the stretch when the object has a Mass of 22 kg.

Solve the problem. -A man rode a bicycle for 14 miles and hiked an additional 8 miles. The total time for the trip was 6 hours. If his bicycling rate was 5 miles per hour faster than his hiking rate, then what was his Hiking rate?

Solve the problem. -A boat can go 105 mph in still water. It takes as long to go 560 miles upstream as it does to go downstream 640 miles. How fast is the current?

Solve the problem. -A jet plane moving at constant speed travels 1000 miles with the wind and then 1200 miles against the wind. If the speed of the wind is 50 mph and the total flight takes 5 hours, find the speed of the Plane.

Solve. -y varies directly as x. If y = 36 when x = 6 $\text { find } y \text { when } x$

Quiz 7: Rational Expressions and Equations

Solve. - yyy varies inversely as xxx . If y=72y = \frac { 7 } { 2 }y=27​ when x=9x = 9x=9 , find yyy when x=10x = 10x=10 .

Solve. -The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 5 miles?

Solve. -varies directly as xxx . If y=172y = \frac { 17 } { 2 }y=217​ when x=17x = 17x=17 , find yyy when x=6x = 6x=6 .

Solve. -y varies inversely as x. If y = 48 when x = 9 find y when x\text { find } y \text { when } x find y when x

Solve. -If y varies inversely as the square of x. If y = 2 when x = 8 find y when \text { find } y \text { when } find y when

Solve. -y varies inversely as x. If y = 48 when x = 9 find y when \text { find } y \text { when } find y when