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
Anastaziya [24]
2 years ago
15

A baby's crib has an area of 690:square inches and a perimeter of 106 inches.What are the dimensions of the crib

Mathematics
1 answer:
KengaRu [80]2 years ago
4 0

Answer:

The crib is 30 inches wide and 23 inches long.

Step-by-step explanation:

Assuming that the crib is rectangular, then the crib has a length L and a width W.

And remember that for a rectangle of width W and length L, the perimeter is:

P = 2*L + 2*W = 2*(L + W)

And the area is:

A = L*W

In this case, the perimeter is 106 in, then:

P = 106in = 2*(L + W)

And we also know that the area is 690 in^2

Then:

A = 690in^2 = L*W

Then we have a system of equations:

106in = 2*(L + W)

690in^2 = L*W

To solve this, first, we need to isolate one of the variables in one of the equations.

Let's isolate L in the first one:

106in/2 = L + W

53 in = L + W

53in - W = L

Now we can replace this in the other equation:

690in^2 = L*W = (53in - W)*W = 53in*W - W^2

690in^2 =  53in*W - W^2

Now we need to solve this for W.

This is a quadratic equation:

W^2 - 53in*W + 690 in^2 = 0

The solutions of this equation are given by Bhaskara's formula:

W = \frac{-(-53in)\pm \sqrt{(-53in)^2 - 4*1*(690in^2)}  }{2} =  \frac{57in \pm 7in}{2}

Then the two possible solutions of W are:

W = (53in + 7in)/2 = 30in

W = (53in - 7in)/2 = 23in

We can choose any one of these, so let's choose W = 30in

If we replace this in the equation: "53in - W = L"

We can find the value of L:

53in - 30in = 23in = L

Then we have:

W = 30in

L = 23in

You might be interested in
Help plz I've been stuck
stepladder [879]

Answer:

The answer is D. (\frac{1}{5} )^{2}

Step-by-step explanation:

5^{4} *(5^{-3} )^{2}

simplify the expression by multiplying

5^{4} *5^{-6}

calculate the product

5^{-2}

express with a positive exponent using a^{-n} =\frac{1}{a^{n} }

\frac{1}{5^{2} }

6 0
3 years ago
Read 2 more answers
Is it 5 or six units?
charle [14.2K]
I don't understand your question
<span />
7 0
3 years ago
Read 2 more answers
If you place a 10-foot ladder against the top of a 6-foot building, how many feet will the bottom of the ladder be from the bott
Anika [276]

Answer: 8 feet

Step-by-step explanation:

Draw a right triangle and label the sides using the given information. (Drawing below) Use pythagorean theorem to find the missing length:

a^2 + b^2 = c^2

(building)^2 + (missing piece)^2 = (ladder)^2

6^2 + x^2 = 10^2

36 + x^2 = 100. subtract 36

x^2 = 64. square root of both sides

x = 8

6 0
2 years ago
You have a photo that measures 1 in. wide by 3 in. tall. If you want to enlarge the photo so that the height is 18 in., what wil
kiruha [24]
6in... 3 times 6 is 18, so 1 times 6 is 6
4 0
2 years ago
If a person starts investing $100 per month starting at age 21, and that money earns a 5% return every year, how much will this
aalyn [17]

The formula for calculating compound interest with yearly contributions is:

Balance = X*(1 + Y)^n + Z((1 + Y)^(n + 1) - (1 + Y)/Y)

where the balance is the money earned after n years invested

Y is the interest rate as a fraction

Z is the yearly contribution

X is the starting investment

Therefore the calculation for this example is:

Balance = 1200*(1 + 0.05)^48 + 1200((1.05)^49 - (1.05)/05)

= $249,393.5


8 0
3 years ago
Read 2 more answers
Other questions:
  • Students were surveyed about their favorite colors 1/4 of the students preferred read 1/8 of the students preferred blue and 3/5
    10·1 answer
  • your friend works as a waitress at your local restaurant her income consists of an hourly wage plus tips. On Wednesday, your fri
    7·1 answer
  • Question 2 goes with question 1
    7·1 answer
  • 3,350 to the nearest ten.
    15·2 answers
  • Multiply (3b​ 2​+ 4​b​ + 8)(-2​b​ 2​+ ​b​ + 10).
    11·1 answer
  • Mary has 5/6 marbles that are striped and 1/6 marbles that are solid color. If Mary has 10 stiped marbles, how many marbles does
    5·1 answer
  • A cube+a square b+ ab square<br><br><br> Please help
    14·1 answer
  • Which expression has a value greater than 253?
    9·1 answer
  • After how many years will £6,000.00 yield a simple interest of £900.00 at 3%​
    12·2 answers
  • Multiply by<br> 3x10<br> Divide by<br> 6<br> Add<br> 2<br> Subtract<br> 4
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!