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sertanlavr [38]
3 years ago
12

A rectangular sandbox cover will be built to protect an area of 72 square meters. Which are possible dimensions of the cover? Ch

eck all that apply.
2 m by 36 m
8 m by 9 m
8.5 m by 8.5 m
4 m by 18 m
6 m by 12 m
7.5 m by 9.5 m
Mathematics
2 answers:
Mama L [17]3 years ago
7 0

Answer:

2 m by 36 m

8 m by 9 m

4 m by 18 m

6 m by 12 m

Step-by-step explanation

Scrat [10]3 years ago
6 0
Answer:
A, B, D, E

Explanation:
You need to multiply them in order to get 72
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Use the model below to estimate the average annual growth rate of a certain country's population for 1950, 1988, and 2010, where
Morgarella [4.7K]

Answer:

The average annual growth rate of a certain country's population for 1950, 1988, and 2010 are 2.398, 0.9985 and 0.2236 respectively.

Step-by-step explanation:

The given equation is

Y=-0.0000084x^3+0.00211x^2-0.205x+8.423

Where Y is the annual growth rate of  a certain country's population and x is the number of years after 1900.

Difference between 1950 and 1900 is 50.

Put x=50 in the given equation.

Y=-0.0000084(50)^3+0.00211(50)^2-0.205(50)+8.423

Y=2.398

Therefore the estimated average annual growth rate of the country's population for 1950 is 2.398.

Difference between 1988 and 1900 is 88.

Put x=88 in the given equation.

Y=-0.0000084(88)^3+0.00211(88)^2-0.205(88)+8.423

Y=0.9984752\approx 0.9985

Therefore the estimated average annual growth rate of the country's population for 1988 is 0.9985.

Difference between 2010 and 1900 is 110.

Put x=110 in the given equation.

Y=-0.0000084(110)^3+0.00211(110)^2-0.205(110)+8.423

Y=0.2236

Therefore the estimated average annual growth rate of the country's population for 2010 is 0.2236.

8 0
3 years ago
What is the coordinates of the center of an ellipse defined by the equation 16x^2 + 25y^2 + 160x - 200y + 400 = 0 ? Please give
pickupchik [31]

16x^2 + 25y^2 + 160x - 200y + 400 = 0     Rearrange and regroup.

(16x^2 + 160x) + (25y^2 - 200y ) = 0-400.     Group the xs together and the ys together.

16(X^2 + 10x) + 25(y^2-8y) = -400.     Factorising.

We are going to use completing the square method.

Coefficient of x in the first expression = 10.

Half of it = 1/2 * 10 = 5. (Note this value)

Square it = 5^2  = 25.     (Note this value)


Coefficient of y in the second expression = -8.

Half of it = 1/2 * -8 = -4. (Note this value)

Square it = (-4)^2  = 16. (Note this value)


We are going to carry out a manipulation of completing the square with the values

25 and 16.  By adding and substracting it.


16(X^2 + 10x) + 25(y^2-8y) = -400

16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400

Note that +25 - 25 = 0.    +16 -16 = 0. So the equation is not altered.

16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = -400 +16(25) + 25(16)    Transferring the terms -16(25) and -25(16)

to other side of equation.  And 16*25 = 400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 25(16)


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 400

We now complete the square by using the value when coefficient was halved.


16(x-5)^2 + 25(y-4)^2  = 400

Divide both sides of the equation by 400


(16(x-5)^2)/400 + (25(y-4)^2)/400  = 400/400              Note also that, 16*25 = 400.


((x-5)^2)/25 + ((y-4)^2)/16  = 1

((x-5)^2)/(5^2) + ((y-4)^2)/(4^2)  = 1


Comparing to the general format of an ellipse.

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)  = 1


Coordinates of the center = (h,k).

Comparing   with above   (x-5) = (x - h) , h = 5.

Comparing   with above   (y-k) = (y - k) , k = 4.

Therefore center = (h,k) = (5,4).

Sorry the answer came a little late.  Cheers.

3 0
3 years ago
The discriminant for the equation f(x)=6x^(2)-x+c is 73. What is the value of c?
Andrews [41]

Answer:

c = -3

Step-by-step explanation:

The discriminant  is 73, that means we have:

(-1)^2-4*6*c=73

then: 1-24c=73

or -24c= 73 -1

-24c = 72

Then c = 72/-24= -3

The answer is -3

Hope that useful for you.

5 0
3 years ago
Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truc
Romashka [77]

Answer:

Payback is 7.3 years

NPV $3,099  

Step-by-step explanation:

The formula for payback period period=initial investment/annual cost savings

The initial investment is the amount of cash outflow that would be required to purchase the new delivery truck,which is $54,750,while on the other hand the  annual cost savings is $7,500

cash payback period=$54,750/$7,500=7.3 years

Ordinarily,the expected payback is 1/2 of 8 years=4 years.

The net present is the present worth of the future cost savings as well as the scrap value of the truck in year 8,calculated by multiplying the cash flows with the discounted factors for relevant years as below:

Years                 cash flow         DCF at 8%        Present values

0                      -$54,750            1                           -$54,750  

1-7 years            $7500             5.2064                  $39,048

8                        $34,800           0.54027               $18,801

NPV                                                                          $3,099  

Note that the  $34,800 =$7500+$27300

The year 1-7 factor is annuity factor for 8% 7 years

3 0
3 years ago
A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the s
skelet666 [1.2K]
The answer for part a would be 130

the answer for part b would be 60
8 0
3 years ago
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