Audrey has $120 dollars to spend on a tennis racket and lessons. The racket costs $45 and the lessons cost $15 dollars per hour. Define a variable. The write and solve an equation to find how many hours of lessons she can afford.

Answers

Answer 1

45+15x=120
15x is the variable since it is a reoccurring fee.

Answer 2

x = how many hours she can afford
120 = 45 + 15x
first you subtract 45 from both sides
75 = 15x
divide both sides by 15
5 = x

so audrey can afford 5 hours of lessons

i hope this helps!!

Related Questions

Use the conversion factor 4 quarts / 1 gallon to convert 5.25 gallons to quarts

Answers

There are 21 quarts in 5.25 gallons.

Answer: 21 quarts

Step-by-step explanation: In this problem, we are asked to convert 5.25 gallons into quarts. To convert gallons into quarts, we use the conversion factor for gallons and quarts.

Conversion factor ⇒ 4 quarts = 1 gallon

Next, notice that we are going from a larger unit "gallons" to a smaller unit "quarts" and when we go from a larger unit to a smaller unit we multiply.

We will multiply 5.25 by the conversion factor which is 4 to get 21 quarts.

Therefore, 5.25 gallons is equal to 21 quarts.

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ? Enter your answer in the box.

Answers

y = x/4 + 5, slope = 1/4

perpendicular lines, slope is opposite and reciprocal
so slope = -4

passes through the point (2, 7)
y = mx + b
b = y - mx
b = 7 - (-4)(2)
b = 7 + 8
b = 15

equation
y = -4x + 15

answer
y = -4x + 15

The sides of an equilateral triangle are increasing at a rate of 10 cm/min. at what rate is the area of the triangle increasing when the sides are 30 cm long?

Answers

Area of a triangle is given by

[tex]Area= \frac{1}{2} ab\sin C= \frac{1}{2} s^2\sin C[/tex]

Since the sides of an equilateral triangle are equal.

Differentiating the area of the triangle, we have:

[tex] \frac{dA}{dt} = \frac{dA}{ds} \cdot \frac{ds}{dt} =(s\sin C) \frac{ds}{dt} [/tex]

where

[tex] \frac{ds}{dt} =10\,cm/min \\ s=30 \, cm[/tex]

[tex]\therefore \frac{dA}{dt} =(30\sin60)\times10=300\sin60=259.8\, cm^2/min[/tex]

Therefore, the rate is the area of the triangle increasing when the sides are 30 cm long is 259.8 cm^2 / min

When given the coordinates of the vertices of a triangle, can the slope formula be used to determine whether the triangle is a right triangle? if so, how?

Answers

I can use the Distance Formula to find the lengths of the each of the sides of the triangle, these lengths being the distances between the pairs of points. Then I can plus these distances into the Theorem to see if this triangle is a right triangle

A $360,000 building is depreciated by its owner. the value y of the building after x months is: y = 360,000 – 1,500 x. how many months will it take until it is completely depreciated

Answers

Final answer:

To find when the building will be completely depreciated, you solve for x in the equation y = 360,000 - 1,500x by setting y to 0. The solution is x = 240, meaning the building will be totally depreciated after 240 months or 20 years.

Explanation:

In this case, you are looking to find the value of x (the number of months) when the value of the building (y) becomes 0. The equation given is y = 360,000 - 1,500x. Set y = 0 and solve for x

First, replace y with 0 in the given equation: 0 = 360,000 - 1,500x. Next, move the term with x to the other side by adding 1,500x to both sides, which gives: 1,500x = 360,000.Finally, solve for x by dividing both sides of the equation by 1,500. This gives you: x = 360,000 / 1,500 = 240.

So, the building will be completely depreciated after 240 months or 20 years.

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Which value of x makes the numerical sentence true? 25^ 1/2 × 5 ^–3 = 5 ^x

Answers

5^-3=0.008
1/2=0.5
0.5*0.008=0.004
5/0.004=1250

25^1/2 × 5^–3 = 5 ^x
(5^2)1/2 × 5^–3 = 5^x
5^1 × 5^–3 = 5^x
5^-2 = 5^x
-2 = x
or
x = -2

answer
x = -2 makes the numerical sentence true

Which of the following expressions is a polynomial?

4a3+3a2+5a-9

32

y-3

x2-4x-2

Answers

x2-4x-2 is the answer

Convert 5460 feet per minute to miles per hour. Round to the nearest whole number

Answers

that's just for 1 set of 5460 ft and make sure u round

What is 0.125 written as a fraction in simplest form?

Answers

1/8

hopefully this is helpful

If f(x)=x^2+3x+5 what is f(3+h) ?

Answers

f(x)=x^2+3x+5
f(3+h)=(3+h)^2+3(3+h)+5
f(3+h)=9+6h+h^2+9+3h+5
f(3+h)=23+9h+h^2

f(x) = x^2 + 3x + 5
f(3+h) = (3+h)^2 + 3(3+h) + 5 ... replace every x with 3+h
f(3+h) = (3+h)(3+h) + 3(3+h) + 5
f(3+h) = (3^2+2*3*h+h^2) + (3*3+3*h) + 5
f(3+h) = (9+6h+h^2) + (9+3h) + 5
f(3+h) = 9+6h+h^2 + 9+3h + 5
f(3+h) = h^2 + (6h+3h) + (9+9+5)
f(3+h) = h^2+9h+23

Ali,s dod weighs 8 times as many as her cat.Together, the two pets weigh 54 pounds.HOW much does Ali's dog weigh

Answers

Ali dog = 8units
cat = 1 unit
total = 9 units
9u= 54
1u=6
8u= 48 pounds

There are a few steps in order to get the correct answer.

First you have to look at the facts about what we know:
- her dog is 8 times as much as her cat
- her dog and cat together equal 54 pounds

Now you need to create the equations based on what you know:
Let's say x is her dog and y is her cat

x+y=54 (both dog & cat equal 54)
x=8y (dog is 8 times as much as cat)

Step 1 -
Put in what we know x is for our first equation and solve for y (cat):

8y+y=54 (Combine like terms)
9y=54 (Divide by 9 on each side to get y by itself)
y=6
Now we have solved for y, but we still don't know what x is.

Step 2 -
Put in y into our first equation to solve for x (dog):

x+6=54 (Subtract 6 from both sides to get x by itself)
x=48
Now we have solved for x also. So now we have both x and y.

But to check our work we just have to put the numbers into the original equations:

x+y=54 ----> 48+6=54 (Correct)
x=8y ----> 48=8(6) (Correct)

You now have your final answer. Ali's dog weighs 48 pounds and her cat weighs 6 pounds.

What is the value of x? Answer it as a decimal

Answers

x / 97.5 = 49.5 / 71.5
71.5 x = 49.5 * 97.5
71.5 x = 4826.25
x = 4826.25 / 71.5
x = 67.5

I need help with a math question on my quick check. 0.24 x 13 A. 3.12 B. 4.62 C. 4.12 D. 3.10

Answers

This problem is simply a multiplication problem. All we have to do in this case is to multiply 0.24 by 13, or the other way around multiply 13 by 0.24. We can do this in the calculator which gives us:

13 x 0.24 = 3.12

Answer:

A. 3.12

Transitive property: if 3x plus y equals 7 and 7 equals 5x minus 2y then

Answers

3x + y = 7
7 = 5x - 2y

THEN 3x + y = 5x - 2y ... it's like you're taking out the middle man "7"

Transitive property states that if x = y and y = z then x = z.

3x + y = 7 and 7 = 5x - 2y

Using the transitive property we get,

3x + y = 5x - 2y.

What is transitive property?

It states that if x, y and z are the three quantities, and if x is related to y by a rule, and y is related to z by the same rule, then we can say x is related to z by the same rule.

Example:

x + 1 = 2 and 2 = x + 9 then x + 1 = x + 9

We have,

3x + y = 7 and 7 = 5x - 2y

Using transitive property we can say that,

3x + y = 5x - 2y

Thus using the transitive property we have,

3x + y = 5x - 2y.

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Option 1: $30 per month and $100 membership fee. Option 2: $25 per month and $150 membership fee.

Michael is trying to determine which tennis club to join. If Michael chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1? A) month 8 B) month 9 C) month 10 D) month 11

Answers

Let us say that m is the number of months. So that the equations for option 1 (O1) and option 2 (O2) are:

O1 = 30 m + 100

O2 = 25 m + 150

TO determine this, we equate O1 and O2 so that:

30 m + 100 = 25 m + 150

5 m = 50

m = 10

So at the 10th month, the cost for both options are equal. So we select month 11.

Answer:

D) month 11

find the greatest common factor of 15x^2y^3 and -20x^3yz

Answers

5x^2y is the greatest common factor

The greatest common factor of [tex]$15x^2y^3$[/tex] and [tex]$-20x^3yz$[/tex] is [tex]$5x^2y$[/tex].

To find the greatest common factor (GCF) of [tex]$15x^2y^3$[/tex] and [tex]$-20x^3yz$[/tex], we need to identify the highest power of each common factor that both terms share.

List the prime factors of each term:

[tex]$15x^2y^3 = 3 \times 5 \times x^2 \times y^3$[/tex]

[tex]$-20x^3yz = -1 \times 2 \times 2 \times 5 \times x^3 \times y \times z$[/tex]

Identify the common factors:

Common factors: [tex]$5$, $x^2$, $y$[/tex]

Find the lowest exponent for each common factor:

For (5), it appears in both terms, so we use the smaller exponent, which is [tex]$5^1$[/tex].

For [tex]$x^2$[/tex], it appears in both terms, so we use the smaller exponent, which is [tex]$x^2$[/tex].

For (y), it appears in both terms, so we use the smaller exponent, which is [tex]$y^1$[/tex].

Multiply the common factors:

[tex]$GCF = 5 \times x^2 \times y = 5x^2y$.[/tex]

So, the greatest common factor of [tex]$15x^2y^3$[/tex] and [tex]$-20x^3yz$[/tex] is [tex]$5x^2y$[/tex].

A computer password consists of 3 letters followed by two digits. none of the letters or digits repeat. how many different passwords can be created

Answers

751760.......................

Answer:

67,600

Step-by-step explanation:

What is (-3+2i)(-6-8i)

Answers

Do foil
First, outside, inside last

18 +24i - 12i + 16
(two i = -1)

18 - 12i + 16 is your answer

hope this helps

What is the simplest form of

Answers

Factor the numerator and factor the denominator.

[tex] \frac{x^2 + 5x - 36}{x^2 - 16} = \frac{(x +9)(x - 4)}{(x + 4)(x - 4)} = \frac{x+9}{x+4} [/tex]

Then you divide the numerator and the denominator by the common factor to reduce the fraction.

A solution containing 30 percent juice is mixed with a solution containing 10 percent juice to make 100 gallons of a 12 percent juice mixture. how much of the 30 percent juice solution was used

Answers

let there be x gallons of 30 percent juice, then there are (100-x) gallons of 12 percent juice.

0.30x+0.10(100-x)=100*0.12
0.3x+10-0.1x=12
0.2x=2
x=10

10 gallons of 30 percent juice should be used.

10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of 30% juice and y represent the amount of 10% juice, hence:

x + y = 100 (1)

Also:

0.3x + 0.1y = 0.12(100) (2)

From eqn 1 and 2:

x = 10, y = 90

10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.

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help me with algebra 2 homework

Answers

-10y + 9x = - 9....A
10y + 5x = - 5.....B

You should see right away that -10y and 10y cancel out.

We are left with

14x = -14

x = -14/14

x = -1

Plug x = -1 into EITHER equation A or B to find y.

I will use equation A.

-10y + 9(-1) = - 9

-10y - 9 = - 9

-10y = - 9 + 9

- 10y = 0

y = 0/-10

y = 0

Done!

What is the square root of 9/36 as a fraction?

Answers

1/12 the answer is 1/12 as a fraction

find the value of v......

Answers

you should get photomath (not promotion)

What is the side length b in the triangle below

Answers

12^2 +b^2 = 20^2 because of the Pythagorean theorem
144 + b^2 =400
B^2 =256
B=16

Answer:

Option B : 16

Step-by-step explanation:

Refer the attached file

Given :

In ΔABC , AB = b , BC = 12 , AC= 20

To Find : value of b i.e. Length of AB

Solution:

Since we are given a right angles triangle so we can use Pythagoras theorem i.e.

[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2} [/tex] ---(a)

Now in a given triangle AB is Perpendicular , BC is Base and AC is Hypotenuse.

So, putting values in (a)

[tex](AC)^{2} =(AB)^{2} +(BC)^{2} [/tex]

[tex](20)^{2} =(b)^{2} +(12)^{2} [/tex]

[tex]400 =(AB)^{2} +144 [/tex]

[tex]400-144 =(b)^{2} [/tex]

[tex]256 =(b)^{2} [/tex]

[tex]\sqrt{256} =b[/tex]

[tex]16=b[/tex]

Thus the value of b is 6

Hence Option B is correct.

URGENT NEEDS TO ME SUBMITTED BY MIDNIGHT!! The ratio of girls to boys in Mr. Hansen’s class is 4:5. The ratio of girls to boys in Ms. Luna’s class is 8:10. Which equation correctly compares these ratios?

Answers

If the ratio of girls to boys in Mr. Hansen's class is 4:5, and the ratio of girls to boys in Ms. Luna's class is 8:10, then the equation that correctly compares the ratio of both Mr. Hansen's class and Ms. Luna's class are 4/5 = 8/10.

4:5 ≡ 8: 10 is the correct way to compares these ratios.

What are equivalent?

" Equivalent means when two or more things have same value but different expression."

According to the question,

Ratio of girls to boys in Mr. Hansen's class = 4 : 5

Ratio of girls to boys in Ms. Luna's class = 8 : 10

Compare both the ratio's we get,

[tex]\frac{8}{10} =\frac{2}{2} * \frac{4}{5}[/tex]

Therefore,

4 : 5 ≡ 8 : 10

Hence, 4:5 ≡ 8: 10 is the correct way to compares these ratios.

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Show that each property of matrices is true for all 2 by 2 matrices scalar distributive

Answers

I don't know either. sorry.

A sample of n = 9 scores is obtained from a population with m = 70 and s = 18. if the sample mean is m = 76, then what is the z-score for the sample mean?

Answers

n times m equals the correcr answrr

Which symbol creates a true sentence when x equals 3?
8•3-4x_7(10-x)
A.<
B.=
C.>

Answers

Hi Tysona90!
Let's write it with the X as a 3
8*3-4*3_7(10-3) Now let's solve it 8*3 is 24 and 4*3 is 12 so then we do 24-12 which is 12. So now we have 12_7(10-3) so let's solve the other half which is 10-3 is 7 times 7 (since parenthesis can also mean multiplication) which is 49 so we now have 12_49 which means the answer is A.
Hope this helps!

20 points! If u can provide an explanation that would be great if not just tell me how certain that's the answer. Thanks a bunch

Answers

This is a linear programming problem. When I say "programming", I don't mean computers. This can be done without the use of a computer though I don't recommend doing it by hand.

Let
x = number of trays of corn muffins
y = number of trays of bran muffins

Given info: "baking a tray of corn muffins takes 4 cups of milk and 3 cups of wheat flour"
If we focus on the milk only then baking x trays of corn muffins means we use up 4*x (or simply 4x) cups of milk. Focus now on the wheat flour and it takes 3*x or 3x cups of wheat flour

Also given: "Baking a tray of bran muffins takes 2 cups of milk and 3 cups of wheat flour"
So we use up 2y cups of milk and 3y cups of wheat flour

-----------------

So far we have used 4x cups of milk for the corn muffins plus 2y more cups of milk for bran muffins giving a total of 4x+2y cups of milk used. We only have 16 cups of milk which means we can say this

4x + 2y <= 16

where the "<=" symbol without quotes means "less than or equal to". That inequality above is one of the constraints placed.

-----------------

Another constraint is this inequality

3x+3y <= 15

because
* we use 3x cups of wheat flour for the corn muffins
* we use 3y cups of wheat flour for the bran muffins
* we have a max of 15 cups of wheat flour

-----------------

Additional contraints are:
x >= 0
y >= 0
indicating that we cannot have x or y be negative

-----------------

The four constraints are:
4x + 2y <= 16
3x+3y <= 15
x >= 0
y >= 0

If you graph all of these inequalities and do the proper shading, you'll get what you see in the attached image. Specifically I'm talking about the blue shaded region. This region is known as the feasible region.

Now turn your attention to the red corner points aka the vertices. These points will be plugged into the objective function

P(x,y) = 3x+2y

This represents the profit (in dollars) of making x trays of corn muffins and y trays of bran muffins.
3x = 3*x = profit from just the corn muffins only
2y = 2*y = profit from just the bran muffins only
3x+2y = total profit (selling both corn and bran muffins)

The four corner points are:
A = (3,2)
B = (0,5)
C = (0,0)
D = (4,0)

Plug each of these points into P(x,y) = 3x+2y

-----------------------------

Plug in A = (x,y) = (3,2)
P(x,y) = 3x+2y
P(3,2) = 3*3+2*2
P(3,2) = 13

We earn a profit of $13 if we sell 3 trays of corn muffins and 2 trays of bran muffins

-----------------------------

Plug in (x,y) = (0,5) which is point B
P(x,y) = 3x+2y
P(0,5) = 3*0+2*5
P(0,5) = 10

The profit dropped to $10, so we can ignore point B. So far point A leads to the most profit.

-----------------------------

Plug in point C, which is (x,y) = (0,0)
P(x,y) = 3x+2y
P(0,0) = 3*0+2*0
P(0,0) = 0

The profit drops even further. Ignore this point.

-----------------------------

Plug in point D: (x,y) = (4,0)

P(x,y) = 3x+2y
P(4,0) = 3*4+2*0
P(4,0) = 12

The profit has gone back up but not at the same height as $13 back for point A. So we can cross this off the list too

-----------------------------

The max profit happens at point A which again was
(x,y) = (3,2)
x = 3 ----> selling 3 trays of corn muffins
y = 2 ----> selling 2 trays of bran muffins

----------------------------------------------------------
----------------------------------------------------------

So the final answer is choice A "3 trays of corn muffins and 2 trays of bran muffins"

Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker’s car at an average speed of 27 miles per hour. If Irina’s ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?

Answers

0.7 of an hour this is the correct answer if you put this in your quiz you will get a A for that question if you dont understand ask your teacher but this is the correct answer.

Answer:

0.7 an hour .

Step-by-step explanation:

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