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Lady_Fox [76]
3 years ago
13

A builder cuts a rectangular hole in a ceiling to install an exhaust fan. The width is 3 in. less than the length and the area i

s 180 in². Find the length and width of the hole.
Mathematics
1 answer:
slavikrds [6]3 years ago
8 0

Area of a rectangle = l * w

A = Area of a rectangle

l = length

w = width

In our problem,

l = x

w = x - 3

A = 180 square inches

Plug our numbers into the area formula of a rectangle

180 square inches = x(x-3)

Distribute the x into (x-3)

180 square inches = x^2 - 3x

subtract 180 from both sides

0 = x^2 - 3x -180.

Factor the express on the left side of the equation

0 = (x-15) (x+12).

Set each term equal to zero and solve for x

x+12 = 0.

Subtract 12 from both sides

x = -12 <--- lengths of a rectangle cannot be negative, therefore, we need to check the other term we factored.

set x-15 equal to zero

x-15 = 0.

Add 15 to both sides

x = 15.

We know l = x so now we know that the length i = 15 inches.

We also know that the width = length - 3

w = 15 - 3

w = 12

The width is 12 inches and the length is 15 inches

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some friends went to a local movie theater and bought four large buckets of popcorn and six boxes of candy.The total for the sna
WARRIOR [948]

The total of 2 buckets of popcorn and 3 boxes of candy would be $23.25

To answer this question you need to form a set of simultaneous equations and solve them. We can do this by saying that a bucket of popcorn = P, and a box of candy = C. Then we can say:

4P + 6C = 46.50

P + C = 9.75

There are then two possible ways to solve; you can either say that C = 9.75 - P using the second equation and then substitute it into the first, or you can multiply the second equation by either 4 or 6 to cancel out P or C.

I’m going to multiply the second equation by 4:

4P + 4C = 39

Now we can subtract this for, the first equation:

4P + 6C = 46.50

4P + 4C = 39

2C = 7.50

C = 3.75

Now we can substitute this value of C into one of the equations to find P:

P + C = 9.75

P + 3.75 = 9.75

P = 6

And now to answer the question, you just multiply P by 2 and C by 3 and add them together, which gives you $23.25

I hope this helps! Let me know if you have any questions :)

6 0
3 years ago
Can somebody help me with this math question?
kap26 [50]

Answer:Hk and IJ

Step-by-step explanation:

They are parallel to eachother, hope this helped!

<!> Brainliest is appreciated! <!>

6 0
3 years ago
So sorry to ask another question but I need some help-
Vika [28.1K]

Answer:

14x + 23

Step-by-step explanation:

The lengths of three sides of a triangle are 5x + 9 feet, 2x + 14 feet, and 7x feet.

The perimeter of a triangle: the sum of all of its sides.

5x + 9 + 2x + 14 + 7x

14x + 23

It's the expression of the perimeter of the triangle. Once you will be asked to find x, you'll probably be given the exact perimeter of the triangle.

7 0
2 years ago
Help with this math problem, please!!
VMariaS [17]

Answer:

Step-by-step explanation:

that is hard

3 0
3 years ago
For online courses, like those in eCore, there is a positive correlation between the amount of time spent in the course and the
Troyanec [42]

Answer:

Regression Line is given by,

y = 22.909 + 0.209 x

The course grade of a student in the course who spent an average of 103 minutes in the course each week is: 22.909 + 0.209 × 103 = 44.436

Step-by-step explanation:

The equation of Regression equation is of the form of:

y = a + bx

where, a is intercept and b is slope

The formula for a and b is given by,

a=\frac{\sum Y \sum X^2-\sum X \sum XY}{n\sum X^2-(\sum X)^2}\\ and, b = \frac{n\sum XY -\sum X \sum Y}{n\sum X^2-(\sum X)^2}

Here, ∑X = 1149.8, ∑Y = 377.2, ∑XY = 93115.95, ∑X² = 320246.72

Thus, a = 22.909

and b = 0.209

Thus, Regression Line is given by,

y = 22.909 + 0.209 x

Thus, The course grade of a student in the course who spent an average of 103 minutes in the course each week is: 22.909 + 0.209 × 103 = 44.436

Now plotting these line:

6 0
3 years ago
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