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algol [13]
3 years ago
5

You are building a curio cabinet in the form of a rectangular prism that must be 4 feet tall with a volume of 48 cubic feet. The

length and with each must be no more than tot. Which of the following dimensions are the possible width and length of the cabinet? a) 15 foot by feet b) 24 feet by 5 foot c) 25 feet by 4.8 feet d) 3 feet by 4 feet e) 4 feet by 12 feet 19
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
7 0

Answer:

d) 3 feet by 4 feet

Step-by-step explanation:

Volume of the prism = 48 feet³

Height if the prism = 4 feet

To determine the possible values of the length and width of the prism let's divide the volume by the height.

So 48/4 = 12

So we'll be looking for a product of two numbers to give us 12

And it's between 12 and 1, 4 and 3 , and 6 and 2.

We have only 4 and 3 in the option.

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Write an exponential model given the points ( 7, 12 ) and ( 8, 25 ). Round to the nearest hundredth.
inna [77]

Answer:

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

Step-by-step explanation:

The exponential model can be modelled by the following mathematical expression:

y = A\cdot e^{B\cdot x} (1)

Where:

x - Independent variable.

y - Dependent variable.

A, B - Coefficients.

If we know that (x_{1}, y_{1}) = (7,12) and (x_{2}, y_{2}) = (8,25), then we get the following system of equations:

A\cdot e^{7\cdot B} = 12 (2)

A\cdot e^{8\cdot B} = 25 (3)

If we divide (3) by (2), we calculate the value of B:

e^{B}=\frac{25}{12}

B = \ln \frac{25}{12}

B \approx 0.734

And by (2), we determine the value of A:

A = 12\cdot e^{-7\cdot B}

A = 0.0704

The exponential model is y = 0.07\cdot e^{0.73\cdot x}.

4 0
3 years ago
If y varies directly with x and y=2 when x=15. Find x when y=8.
andreyandreev [35.5K]
Since the two numbers vary directly, if Y is quadrupled, X will do the same.  2 times 4 is 8, 15 times 4 is 60.

X = 60.

Hope that helps!! :)


8 0
3 years ago
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Have some free points OwO
hram777 [196]

Answer:

YAY

Step-by-step explanation:

4 0
4 years ago
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What are the solutions of the equation?
yKpoI14uk [10]

Answer:

Option (b) is correct.

The solution of the quadratic equation x^2+4x=21  is -7 and 3

Step-by-step explanation:

Consider the given quadratic equation x^2+4x=21

This can be rewritten as, x^2+4x-21=0

We can solve the quadratic equation using middle term splitting method,

4x can be written as 7x-3x , we get,

\Rightarrow x^2+4x-21=0

\Rightarrow x^2+7x-3x-21=0

Taking terms common, we get,

\Rightarrow  x(x+7)-3(x+7)=0

Thus, \Rightarrow (x-3)(x+7)=0

Thus, we get (x-3)= 0 or (x+7)= 0  

this gives x = 3 or x = -7

Thus, the solution of the quadratic equation x^2+4x=21  is -7 and 3

7 0
3 years ago
The isosceles triangle has two sides of equal length , a , that are longer than the length of the base , b. The perimeter of the
bija089 [108]

Answer:

Step-by-step explanation:

Since the length of one of the longer sides, a, has been given to be 6.3, plug it into the equation.

2(6.3) + b = 15.7

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b = 15.7 - 12.6

b = 3.1

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3 years ago
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