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Alex73 [517]
3 years ago
13

The length of a certain lot if 20 feet less than four times its width. the area of 4200 sq. ft. what are the dimensions of the l

ot?
Mathematics
1 answer:
tia_tia [17]3 years ago
3 0
The area of a surface is the number of square units present in the surface. For a rectangle, it is calculated from the product of the length and the width. To determine the length and width of the lot given above, we first assume that it is in a rectangular shape which is defined by its length and its width. We are given the following:

Area = 4200 square feet
Length = 4x - 20 feet
Width = x feet

From the definition of the area of a rectangle,

Area = length x width
4200 = (4x -20) (x)
4200 = 4x^2 - 20x
4x^2 - 20x - 4200 = 0
4(x^2 - 5x - 1050) = 0
x^2 - 5x -1050 = 0

Factoring the equation would lead to:
(x - 35) (x +30) = 0
x -35 = 0 ; x = 35
x + 30 = 0 ; x = -30

The width should not be a negative value so the width would be equal to 35 feet. So, the length would be 

Length = 4(35) - 20 = 120 feet

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monitta
Decimal point should be moved places to the right.
5 0
3 years ago
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When the new principal on a loan is $79,946.13 and the interest rate is 8 percent, the monthly payment is $587.20. Find the inte
lesya [120]

9514 1404 393

Answer:

  • to interest: $532.97
  • to principal: $54.23
  • new balance: $79,891.90

Step-by-step explanation:

The interest is found by multiplying the monthly rate by the balance on the loan. For the first month, the balance is the loan amount.

  $79,946.13 × 0.08 ×(1/12) . . . . . one month = 1/12 year

  = $532.97

The interest amount in the first payment is $532.97.

__

The amount of the first payment that goes to principal is what is left after the interest is paid:

  $587.20 -532.97 = $54.23 . . . amount to principal

__

The new balance is the previous balance less the amount to principal:

  $79,946.13 -54.23 = $79,891.90 . . . new balance

7 0
3 years ago
Veronica is choosing between two health clubs after how many months will the total cost for each health club be the same
Assoli18 [71]

Question:

Veronica is choosing between two health clubs. after how many months will the total cost for each health club be the​ same? yoga studio a: membership: $24.00 monthly fee: 21.50. yoga studio b: membership: $41.00 monthly fee: $17.25

Answer:

It takes 4 years for the total cost of each club to become equal

Step-by-step explanation:

Given:

For yoga studio A:

membership: $24.00

monthly fee: 21.50.

For yoga studio B:

membership: $41.00

monthly fee: $17.25

To Find:

Number of months after which the total cost for each health club be the​ same = ?

Solution:

Let   x be the number of months of membership, and   y  be equal the total cost.

For Yoga club A

y = 21.50 x + 24

For Yoga club B    

y = 17.25 x + 41.00

we know that the prices,   y , would be equal, we can set the two equations equal to each other.

21.50 x + 24 =17.25 x+ 41.00

Grouping the like terms,

21.50x - 17.25 x= 41.00 -  24

4.25x=17

x=\frac{17}{4.25}

x = 4

6 0
3 years ago
Assume that advanced students average 93% on an achievement test and regular students averaged 75%. If 100 advanced students and
Lemur [1.5K]
Average (mean) = (sum of all the data) / (# of data)

sum of all the data = (average)(# of data)

Thus for 100 students with an average of 93,
sum of all data = (93)(100) = 9300

and for 300 students with an average of 75,
sum of all data = (75)(300) = 22500

Therefore you would expect the overall average to be
(9300 + 22500) / (100 + 300) = 79.5 %

Now if there are x # of advanced students and y # of regular students, then

x + y = 90 (total # of students) and 93x + 75y = 87(x + y) (overall average)

The second equation can be simplified to x - 2y = 0

Subtracting the two equations yields

x = 60 and y = 90

Therefore you would need 60 advanced and 30 regular students.
7 0
3 years ago
Question 10 of 12
kenny6666 [7]

Answer:

x = 11

Step-by-step explanation:

x + 8 = 19        subtract both sides by 8

x = 11

4 0
3 years ago
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