1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alenkinab [10]
3 years ago
8

The length of a rectangle is 8 feet more than the width. If the width is increased by 4 feet, and the length is decreased by 5 f

eet, the area remains the same. Find the dimensions of the original rectangle.
Mathematics
1 answer:
SVEN [57.7K]3 years ago
7 0

Answer:

Width = 12 feet

Length = 20 feet

Step-by-step explanation:

The area of a rectangle is A = l*w. Here the length is 8 feet more than the width or 8 + w and the width is w. So the area is A = w(8+w) = 8w + w²

If the dimensions are changed then the expressions will change. The width is increased by 4 feet. This means the width w becomes w + 4. The length is decreased by 5 feet. This means the length becomes 8 + w - 5 = 3 + w. So the area of the new triangle is A = (w+4)(3+w) = w² + 7w + 12.

Since the areas are the same, set them equal to each other and solve for w.

w² + 7w + 12 = 8w + w²                Subtract w² from both sides.

7w + 12 = 8w                                 Subtract 7w from both sides.

12 = w

The original width w is 12 feet. This means the original length which was 8 + w = 8 + 12 = 20 feet.

You might be interested in
Choose the correct vertex for the following quadratic function.
frez [133]

Answer:

U (2,-1)

Step-by-step explanation:

if you replace x to 2, your answer will come out to be -1

7 0
2 years ago
Read 2 more answers
A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample
marusya05 [52]

Answer:

The margin of error for her confdence interval is of 0.3757.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 2.8982

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

Standard deviation of 0.55 meters.

This means that s = 0.55

What is the margin of error for her 99% confidence interval?

M = T\frac{s}{\sqrt{n}}

M = 2.8982\frac{0.55}{\sqrt{18}}

M = 0.3757

The margin of error for her confdence interval is of 0.3757.

7 0
2 years ago
What is the slope of the line graphed above​
erma4kov [3.2K]
Answer:
B

Explanation:
Slope = rise/run = -2/2 = -1
3 0
3 years ago
Read 2 more answers
Help me please!!!! The question is in the picture^^^
Aleksandr [31]

Answer:

7,173

x = 7

Step-by-step explanation:

Within the question it gives two examples.

x = 0 corresponds to 2000

x = 1 corresponds to 2001

If you pay close attention the x-value is always the same as the last digits in the year. So with 2007 the last digit is 7, which then leads us to determine that

x = 7

f (x) = -327 (7) + 9462

f (x) = -2289 + 9462 = 7173

6 0
3 years ago
Lauren has gross pay of $765 and federal tax withholdings of $68. Determine Lauren's net pay if she has the additional items wit
Romashka-Z-Leto [24]
<span>gross =768
 fed = 68
 ss = 6.2/100 times 765
 med = 1.45/100 times 765
state = 22/100 times 68
gross - ( sum of all deductions) = net pay
</span><span>Subtract 6.2% of $765 = 0.062 * $765 = 48.67
</span><span>Subtract 1.45% of $765 = 0.0145 * $765 = 11,0925
</span><span>Subtract 22% of $68 = 0.222 * $65 = 14.43
</span>Social security tax = 765 * 6.2% = 47.43
Medicare tax  = 765 * 1.45% = 11.09
State tax (22% of federal tax) = 68 * 22% = 14.96

765 - 68 - 47.43 - 11.09 - 14.96 = 623.52

 net pay is 623.52

8 0
2 years ago
Read 2 more answers
Other questions:
  • Use your graphing calculator to find the value of f ′(1) for f(x) = x2 + Ln(x).
    8·1 answer
  • Emily and a friend bought two tickets to see a soccer game. Each ticket cost $8.25. The friends paid a total of $24.50, which in
    5·1 answer
  • Your mother bought a three-liter bottle of water. When she got home, she discovered a small leak in the bottom and asked you to
    6·2 answers
  • What 1,055 to the nearest tenth
    13·2 answers
  • Ed genuity
    5·2 answers
  • Please help! find the area is the parallelogram.​
    11·2 answers
  • PLEASE HELP EMERGENCY have a great day
    6·1 answer
  • a plane can fly 450 miles in the same time it takes a car to go 150 miles. if the car travels 100 mph slower than the plane, fin
    14·1 answer
  • Plz help me with these 2 problems
    14·2 answers
  • Solve using geometric mean theorem
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!