What is a variable that cannot be controlled?

Suppose you need to get the dent in your car fixed. You see the ads in the newspaper above (mikes repair shop $100 service charg

Norma-Jean [14]

Answer:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295, so I will take the car to Amy's shop

Point of intersection: (x,y) = (4,360)

Explanation:

Part 1 )

Let x = number of hours worked

Let y = total cost to you

Determining where to take the car:

Total Cost at Amy's shop is $280 which is less than the total cost at Mike's shop which is $295

Mike's repair shop:

Service fee: $100

Per hour rate: $65

Let x is the number of hours worked on. Total cost will be equal to the service fee plus hourly charges. Charges per an hour are $65, so for x hours the charges will be 65x.

Therefore, total cost for Amy's repair shop can be written as:

y = 100 + 65x ------(1)

For 3 hours work: y = 100 + 65(3)

Cost at Mike's, y = $100 + $195 = $295

Amy's repair shop: 

Service fee: $40

Per hour rate: $80

Charges per an hour are $40, so for x hours the charges will be 80x.

Therefore, total cost for Amy's repair shop can be written as:

y = 40 + 80x ------(2)

For 3 hours work: x = 3

y = 40 + 80(3)

Cost at Amy's, y = $40 + $240 = $280

Part 2)

Find the point of intersection

Using elimination method:

y = 100 + 65 x ------1

y = 40 + 80x ------2

As the y coefficients are equal we will subtract eq1 from eq2

y - y = 40 + 80x - 100 - 65x

0 = -60 + 15x

60 = 15x

x = $\frac{60}{4}$

x = 4

put x = 4 in eq 1

we get y = 100 + 65 (4) = 100 + 260 = 360

x = 4, y = 360

Point of intersection: (x,y) = (4,360)

8 0

3 years ago

AB≅BC≅CD≅DE, AD = 8x - 4, AB = x + 2 solve for AB

Levart [38]

Just solve for , then substitute back into either expression and calculate either BC or AD. The other one is then the same amount.

The one about the square is the same thing except you don't care how the figure is named because all 4 sides are equal anyway. Just set the two expressions equal to one another and then solve for

4 0

3 years ago

Read 2 more answers

A state income tax is 9% of any amount earned over $15,000. What state income tax does a person earning $24,500 pay?

ehidna [41]

Answer:

the answer is C. $2,205

3 0

3 years ago

Solve for g. -3 + 5 + 6g = 11 - 3g

Veronika [31]

The answer would be I believe
$g = 1$

8 0

3 years ago

A plot of land doubles in size by adding x meters to the length and x meters to the width of the land. If the orgininal plot had

stellarik [79]

Hey :)

The answer is 100.
The overall area will be the length times the width:
200 times 300 = 60000.
If the plot of land doubles in size, then the resulting area will be 120000. To get to 120000, the question is saying that the same number was added to both 200 and 300, which were then multiplied together. The equation will look like this:
(x+200) times (x+300) = 120000
Now, you will multiply these together in a process called FOIL (which means you multiply the first numbers in each parentheses, then the outside numbers, then the inside numbers, then the last numbers):
x^2 (this means x squared, or x times itself) + 300x + 200x + 600 = 120000
Then, you will add together like terms:
x^2 + 500x + 600 = 120000
Next, you will subtract 120000 from both sides to get 0 on one side of the equation:
x^2 + 500x - 6000 = 0
Next, you will essentially perform the opposite of FOIL (now you're trying to get the right side of the equation into two parentheses):
(x + 600) times (x - 100) = 0 (you can check if this is correct by performing FOIL and making sure that product is the previous equation)
Now, set both of the parentheses equal to 0 and solve:
x + 600 = 0 ----> x = -600x - 100 = 0 ----> x = 100
Lastly, you will have to choose which value for x satisfies the initial question. Since the question is asking for a value within the real world, a negative answer will not work (you cannot give someone -600 meters of land). So, the answer is 100.

Hope this helps! :)

3 0

3 years ago