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BabaBlast [244]
2 years ago
6

At a school there are five lessons in a day in total the five lessons last 4 hours assume that each session lasts the same amoun

t of time how many minutes long is the final lesson
Mathematics
1 answer:
ikadub [295]2 years ago
7 0

Answer:

48 minutes long

Step-by-step explanation:

For a total amount of minutes the lessons are, take 4x60. 4 for the total time in the lessons and 60 for 60 minutes in an hour. 4x60= 240 minutes.

Take 240/5. 240 is the total number of minutes and with the five lessons being the same amount of time, you divide the total number of minutes by the number of lessons. 240/5= 48 minutes

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A hardware store sells rope at a fixed price per foot. A 50-foot piece of rope cost $12. Write an equation that relates C, the c
Masja [62]
C=6/25f
6/25 is the cost per foot
8 0
3 years ago
The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.
Ratling [72]
The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3).  The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).
8 0
3 years ago
You go out to eat with your family. The subtotal on your bill is $45.90. You must pay a 8% sales tax AND you would like to leave
Eddi Din [679]

Answer:

The answer is 57.83

Step-by-step explanation:

find 8% of 45.90 and add 18% of 45.90 and add them together.

8%*45.90=3.67

18%*45.90=8.26

Add, 45.90+8.26+3.67

The final price of your meal is 57.83

7 0
3 years ago
What is the best first step in solving the equation 3 + 3 sqrt 6x = 5
charle [14.2K]
X=268y bekaoownebeiwowobebr
3 0
3 years ago
The system of equations: 5x-4y=-3
Sophie [7]

Answer:

3)5x-4y=-3

6x+4y=14

Step-by-step explanation:

The system of equations is given

5x-4y=-3

3x+2y=7

Multiplying both sides of the lower equation by 2, we get

6x + 4y = 14

That means your answer 3)

5 0
3 years ago
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