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
SOVA2 [1]
3 years ago
9

Pat wishes to fence in a rectangular area, using the wall of her garage as one side, so only three sides need to be fenced. If s

he has 80 ft of fencing available, what is the maximum area that can be fenced in?
Mathematics
1 answer:
natali 33 [55]3 years ago
8 0

Answer:

The maximum area is 800 ft².

Step-by-step explanation:

Lets call L the length of the side parallel to the garage and M the length of the other two sides. The total amount to fence is 2M+L and the area is L*M.

Since Pat got 80ft of fence, then 2M+L = 80, hence L = 80-2M. By replacing the value of L in the formula of the area, we get that

A(M) = M*(80-2M) = -2M² + 80M

The maximum of this function can be obtaining throught derivation, but since it is a quadratic with negative main coefficient, we know that the maximum is the vertex. The x-coordinate of the vertex is '-b/2a' = -80/2*(-2) = 20. The y-coordinate (which represents the maximum area),  as a result, is A(20) = -2*20²+80*20 = 800.

800 is the maximum area that can be fenced. Note that M = 20 and L = 80-2L = 40.

You might be interested in
It is given that cos 0 = -0.4209 and 0° 0 < 360°. Calculato the values of 0​
beks73 [17]

Answer:

114.89 degrees

245.11 degrees

Step-by-step explanation:

cos is negative in the second and third quadrant ("pointing" on the x-axis to the left).

so, the first answer for the second quadrant is

114.89 degrees.

the answer for the third quadrant is then backwards the same angles from a full 360 degree rotation

360 - 114.89 = 245.11 degrees

5 0
3 years ago
Me.jhonson sells erasers for $3 each he sold 96 erasers last week and he sold 204 eraser this week about how much more money did
Sveta_85 [38]
Step 1:
96 divided by $3 = $32

Step 2:
204 divided by $3= $68

Step 3:
$68-$32=36

He made $36 more this week
5 0
3 years ago
Scientists have calculated that the earth is 4 540 000 00 years old. How many billion years is this
djyliett [7]

Answer: Earth's age at approximately 4.54 billion years.

5 0
3 years ago
Read 2 more answers
Angela had $6w. AFter buying some books at $17 each, she had $w left.
kkurt [141]

Answer:a) W=-17x/-5

Step-by-step explanation:

Number of books = x

6W-(X×17)=W

6W -17X = W

Collect like terms

-17X= W-6W

-17X = -5W

Divide both sides by the coefficient of W

-17X÷ -5 = -5W÷ -5

W = -17X÷ -5

B) W = 34

W = -17X ÷ -5

34 = -17X ÷ -5

Cross multiply

-17X = 34× -5

-17X = -170

Divide both sides by the coefficient of X

X = -170 ÷ -17

X = 10

∴ Angela bought 10 books

3 0
2 years ago
Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands
Black_prince [1.1K]
When the rock hits the ground, y = 0

-.005x^2 +0.41x -5.1 = 0

Multiply equation by (-200)

x^2 -82x +1020 = 0

Use quadratic formula:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{82 \pm \sqrt{82^2 -4(1)(1020)}}{2} \\  \\ x = \frac{82 \pm 51.4198}{2} \\  \\ x = 15.29 , 66.71

Since the ball is initially below the ground, on its way up it will reach the point where y=0 but still be in the air, therefore the ball lands the second time y=0 or when x is larger.

Answer:  66.71 feet
6 0
3 years ago
Read 2 more answers
Other questions:
  • I WILL GIVE BRAINLIEST!!! PLZ HELP ASAP!!!!!
    15·2 answers
  • Completely factor the following expression t^2+4tv+4^2
    15·1 answer
  • In a group of 36 children, there are twice as many boys as girls, how many girls are there?
    15·1 answer
  • the area of the continent North America is about 9540000 square miles right 9540000 in expanded form using exponents to show the
    5·2 answers
  • Y varies directly with X. When X=5, Y=40. What is the value of Y when X increases to 7.
    11·1 answer
  • 6 mg of 20 mg is what​
    10·1 answer
  • A manager recorded how many hours each of 11 cashiers worked in a week. Which interval contains the median number of hours worke
    15·1 answer
  • What number will give me 0 if I divide it by -3
    15·1 answer
  • Help really fast round 93.0129 to the nearest thousandth
    8·2 answers
  • PLS HELP I'LL GIVE THE BRAINLEST
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!