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telo118 [61]
3 years ago
13

A rectangular prism has a length of 5 1/8 feet, a width of 7 1/2 feet, and a height of 2 feet. What is the volume of the prism?

Enter your answer in the box. ___ft³
Mathematics
2 answers:
liberstina [14]3 years ago
7 0
Hey there!

The formula for volume is: 
l * w * h

Length = 5 1/8

Width = 7 1/2

Height = 2


First, multiply 5 1/8 and 7 1/2 . . .



5 1/8 = 41/8


7 1/2 = 15/2


41 * 15 = 615


8 * 2 = 16


= 615/16

Simplifying 615/16 . . .


615/16 = 38 7/16



Now, multiply 38 7/16 and 2 . . .



38 7/16 = 615/16


2 = 2/1


615 * 2 = 1230


16 * 1 = 16


= 1230/16

Simplifying 1230/16 . . .



1230/16 = 76 7/8 ←


Your answer:76 7/8 ft³



Hope this helps you,

Have a wonderful day! :)
koban [17]3 years ago
6 0
Hello! 

to find the volume you always have to do length times width times height so all you have to do is do 5 \frac{1}{8}  TIMES   7 \frac{1}{2}   and your answer should be   38 \frac{7}{16}  then  do    38 \frac{7}{16}   TIMES   2 and your answer should be   76 \frac{7}{8}  
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The slope of all parallel lines are equal.

The slope of a line in the form y=mx+c is m.

1. The given equation is: y=4x+2.  The slope of this line is m=4. The slope of the line parallel to this line is also 4.

2. The given equation is y=\frac{2}{7}x+1. The slope of this line is m=\frac{2}{7}.

The slope of the line parallel to it is also \frac{2}{7}.

3. The next equation is y+9x=13. The slope intercept form is y=-9x+13.

The slope of this is m=-13. The line parallel to it also has slope which is -13.

4. The given equation is y=-\frac{1}{2}x+4. The slope of this line and the line parallel to it is m=-\frac{1}{2}

5. The equation is 6x+2y=4. We simplify to get: 3x+y=2.

The slope-intercept form is y=-3x+2. The line parallel to this line has slope m=-3

6. Assuming the line is y=-3x+9, then the slope is m=-3

7. Assuming the line is -5x+5y=4, then the slope-intercept form is y=x+\frac{4}{5} and the slope of the line parallel to this line is m=1

8. The equation is 9x-5y=4. The slope intercept form is y=\frac{5}{9}x-\frac{4}{9}. The slope of the line parallel to this line is m=\frac{5}{9}

9. The given equation is -x+3y=6. The slope intercept form is y=\frac{1}{3}x+2. The line  parallel to this line also has slopem=\frac{1}{3}.

10.  Assuming the given line is 6x-7y=10, then y=\frac{6}{7}x-\frac{10}{7} and the line parallel to it has slope m=\frac{6}{7}

11. Assuming the line is y-x=-3, then y=x-3 and the slope of the line parallel to it is m=1

12. The given line is 3x-5y=6. This implies that y=\frac{3}{5}x-\frac{6}{5}

7 0
3 years ago
The graph of an exponential function is given. Which of the following is the correct equation of the function?
katen-ka-za [31]

Answer:

If one of the data points has the form  

(

0

,

a

)

, then a is the initial value. Using a, substitute the second point into the equation  

f

(

x

)

=

a

(

b

)

x

, and solve for b.

If neither of the data points have the form  

(

0

,

a

)

, substitute both points into two equations with the form  

f

(

x

)

=

a

(

b

)

x

. Solve the resulting system of two equations in two unknowns to find a and b.

Using the a and b found in the steps above, write the exponential function in the form  

f

(

x

)

=

a

(

b

)

x

.

EXAMPLE 3: WRITING AN EXPONENTIAL MODEL WHEN THE INITIAL VALUE IS KNOWN

In 2006, 80 deer were introduced into a wildlife refuge. By 2012, the population had grown to 180 deer. The population was growing exponentially. Write an algebraic function N(t) representing the population N of deer over time t.

SOLUTION

We let our independent variable t be the number of years after 2006. Thus, the information given in the problem can be written as input-output pairs: (0, 80) and (6, 180). Notice that by choosing our input variable to be measured as years after 2006, we have given ourselves the initial value for the function, a = 80. We can now substitute the second point into the equation  

N

(

t

)

=

80

b

t

to find b:

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

N

(

t

)

=

80

b

t

180

=

80

b

6

Substitute using point  

(

6

,

180

)

.

9

4

=

b

6

Divide and write in lowest terms

.

b

=

(

9

4

)

1

6

Isolate  

b

using properties of exponents

.

b

≈

1.1447

Round to 4 decimal places

.

NOTE: Unless otherwise stated, do not round any intermediate calculations. Then round the final answer to four places for the remainder of this section.

The exponential model for the population of deer is  

N

(

t

)

=

80

(

1.1447

)

t

. (Note that this exponential function models short-term growth. As the inputs gets large, the output will get increasingly larger, so much so that the model may not be useful in the long term.)

We can graph our model to observe the population growth of deer in the refuge over time. Notice that the graph below passes through the initial points given in the problem,  

(

0

,

8

0

)

and  

(

6

,

18

0

)

. We can also see that the domain for the function is  

[

0

,

∞

)

, and the range for the function is  

[

80

,

∞

)

.

Graph of the exponential function, N(t) = 80(1.1447)^t, with labeled points at (0, 80) and (6, 180).If one of the data points has the form  

(

0

,

a

)

, then a is the initial value. Using a, substitute the second point into the equation  

f

(

x

)

=

a

(

b

)

x

, and solve for b.

If neither of the data points have the form  

(

0

,

a

)

, substitute both points into two equations with the form  

f

(

x

)

=

a

(

b

)

x

. Solve the resulting system of two equations in two unknowns to find a and b.

Using the a and b found in the steps above, write the exponential function in the form  

f

(

x

)

=

a

(

b

)

x

.

EXAMPLE 3: WRITING AN EXPONENTIAL MODEL WHEN THE INITIAL VALUE IS KNOWN

In 2006, 80 deer were introduced into a wildlife refuge. By 2012, the population had grown to 180 deer. The population was growing exponentially. Write an algebraic function N(t) representing the population N of deer over time t.

SOLUTION

We let our independent variable t be the number of years after 2006. Thus, the information given in the problem can be written as input-output pairs: (0, 80) and (6, 180). Notice that by choosing our input variable to be measured as years after 2006, we have given ourselves the initial value for the function, a = 80. We can now substitute the second point into the equation  

N

(

t

)

=

80

b

t

to find b:

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

N

(

t

)

=

80

b

t

180

=

80

b

6

Substitute using point  

(

6

,

180

)

.

9

4

=

b

6

Divide and write in lowest terms

.

b

=

(

9

4

)

1

6

Isolate  

b

using properties of exponents

.

b

≈

1.1447

Round to 4 decimal places

.

NOTE: Unless otherwise stated, do not round any intermediate calculations. Then round the final answer to four places for the remainder of this section.

The exponential model for the population of deer is  

N

(

t

)

=

80

(

1.1447

)

t

. (Note that this exponential function models short-term growth. As the inputs gets large, the output will get increasingly larger, so much so that the model may not be useful in the long term.)

We can graph our model to observe the population growth of deer in the refuge over time. Notice that the graph below passes through the initial points given in the problem,  

(

0

,

8

0

)

and  

(

6

,

18

0

)

. We can also see that the domain for the function is  

[

0

,

∞

)

, and the range for the function is  

[

80

,

∞

)

.

Graph of the exponential function, N(t) = 80(1.1447)^t, with labeled points at (0, 80) and (6, 180).

Step-by-step explanation:

4 0
2 years ago
What is the slope of the line through (6,9) and (7,1)
pychu [463]

Answer:

-8

Step-by-step explanation:

m= y₂- y₁/ x₂-x₁

m= 1-9/7-6

m= -8/1

m= -8

8 0
3 years ago
Read 2 more answers
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