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
KATRIN_1 [288]
3 years ago
13

A pyramid has a rectangular base of length (3x + 1)cm and width xcm.

Mathematics
1 answer:
sergey [27]3 years ago
7 0

Answer:

The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3

Step-by-step explanation:

Given

Rectangle Pyramid

Base Length = 3x + 1

Base Width = x

Height = 12

Volume = 96

Required

Dimension of the base of the pyramid

Given that the volume of the pyramid is ⅓ of the base area * the height.

This is represented mathematical as

Volume = ⅓ * base area * height.

Where

Base area = width * length

Base area = (3x + 1) * x

Base area = 3x² + x.

So,

Volume becomes

Volume = ⅓ * (3x² + x) * 12.

Volume = (3x² + x) * 4

Substitute 96 for volume

96 = (3x² + x) * 4

Divide both sides by 4

96/4 = (3x² + x) * 4/4

24 = 3x² + x

Subtract 24 fr both sides

24 - 24 = 3x² + x - 24

0 = 3x² + x - 24

3x² + x - 24 = 0

Expand

3x² + 9x - 8x - 24 = 0

Factorize

3x(x + 3) - 8(x + 3) = 0

(3x - 8)(x + 3) = 0

3x - 8 = 0 or x + 3 = 0

3x = 8 or x = -3

x = 8/3 or x = -3

Recall that

Length = 3x + 1

Width = x

For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.

Substitute x = 8/3

Length = 3x + 1

Length = 3(8/3) + 1

Length = 8 + 1

Length = 9

Width = x

Width = 8/3

Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3

You might be interested in
The volume of construction work was increased by 60% but the productivity of labor increased by only 25%. By what percent must t
ss7ja [257]
<span>The number of workers must be increased by 28%.</span>
5 0
3 years ago
Find the slope of the line that would be parallel to the given original line 3x+y=10
Arturiano [62]
The answer is 3. If the lines are parallel then they would have the same slope. :)
7 0
3 years ago
Show work please find the volume of the following irregular space figure to the nearest whole number
artcher [175]

Answer:

144cm^3

Step-by-step explanation:

1) split the figure so you can find the volume of two rectangular prisms.

2) Find the volume of the first rectangular prism with the measurements of 2,       5, and 8. So the volume is 80

3) Find the volume of the second rectangular prism with the measurements of 4, 2, and 8. So you have 64

4) Add the two values 80+64.

5) Then that's your answer; 144

Hope this helps! :D

8 0
2 years ago
A system of equations that has an infinite number of solutions is called​ a(n) ______ system of equations.
GenaCL600 [577]
System of linear equations
A set of two or more linear equations containing two or more variables.

2x + 3y = −1
x − 3y = 4
8 0
3 years ago
Help with this math question please
Masja [62]
| -6x - 3 | > 15

This expression can be written as:

a) -6x - 3 > 15 
b) -15 > - 6x - 3

Solving a part:

- 6x - 3 \ \textgreater \  15 \\  \\ &#10;- 6x \ \textgreater \  18 \\  \\ &#10;x \ \textless \  -3

Solving b part:

-15 \ \textgreater \  - 6x - 3 \\  \\ &#10;-12 \ \textgreater \  - 6x \\  \\ &#10;2 \ \textless \  x

or we can write:
x > 2

So the solution to given inequality is:
x \ \textless \  -3  \\ or  \\ x \ \textgreater \  2

The second option correctly lists this solution.
7 0
3 years ago
Other questions:
  • A rectangular prism shaped toy box is 52 centimeters long. The perimeter of one side of the box is 90 centimeters. The height of
    7·1 answer
  • Sylvia walked​ 34 ​mi east from her house to the bank. Then she walked 13 ​mi west to a gift shop. From the gift shop, she walke
    14·1 answer
  • Can some help me pls<br> And fact
    12·2 answers
  • I need help what is 11 times 34,000​
    13·2 answers
  • Which of the following is equivalent to 5 · (7 · 4)? *
    7·1 answer
  • HELP NOW PLEASE A polygon on a coordinate was transformed using the rule (x,y) (x-4,y-3) Which of these desenbos this transforma
    15·1 answer
  • The Tigers, a football team, must gain 10 yards in the next four plays to keep possession of the ball. The Tigers lose 24 yards,
    13·1 answer
  • Please help!!! Will give brainliest
    10·1 answer
  • Carmen types at a rate of 16 words per minute. How many words does she type in 4 minutes?
    9·1 answer
  • A specific type of dwarfism is a genetically inherited recessive trait. based upon this pedigree. What is the probability that m
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!