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
What is the equation of a circle with center (-3,-5) and radius 4?
kobusy [5.1K]

Answer:   D) (x + 3)² + (y + 5)²  = 16

<u>Step-by-step explanation:</u>

The equation of a circle is: (x - h)² + (y - k)² = r²    

where (h, k) = center   and    r = radius

Given: (h, k) = (-3, -5)  r = 4

Equation: (x - (-3))² + (y - (-5))² = 4²

                 (x + 3)²  +  (y + 5)²  = 16

8 0
3 years ago
P/90 = 4/18. What does p equal
Phoenix [80]
P/90 = 4/18
18P = 90*4 [cross-multiplication]
P = 360/18
P = 20
So, answer is P equals to 20
3 0
3 years ago
Read 2 more answers
Simplify the expression: <br>3+ – 5(4+ – 3v)
Mandarinka [93]

Answer:

The answer is

<h2>15v - 17</h2>

Step-by-step explanation:

3+ – 5(4+ – 3v) can be written as

3 - 5( 4 - 3v)

Expand and simplify

That's

3 - 20 + 15v

15v - 17

Hope this helps you

6 0
3 years ago
Two friends are renting an apartment. They pay the landlord the first month’s rent. The landlord also requires them to pay an ad
UNO [17]
So you could do $1725/3 (divided by) which would give you 575 then mulitply that by two and that will give you the months rent of, $1,150. I hope this helps!
5 0
3 years ago
Read 2 more answers
Oscar spent 2/3 hours each night doing homework for five nights this week. How many hours of homework did Oscar complete this we
jeka94
B because 2/3 hours is 40 mins 40 x 5 = 200 200 is 3 hours and 20 mins which is 1/3
3 0
2 years ago
Other questions:
  • A cheetah ran 275 feet in 3.23 seconds. How fast did the cheetah run in miles per hour? Round your answer to the nearest whole m
    12·1 answer
  • I really need help on this
    6·1 answer
  • Please solve!!!!!!!!!
    11·1 answer
  • Find the area of the rhombus if AE = 20 m and DE = 32 m
    15·1 answer
  • The side lengths of a square are each 3p. By adding 5 to the length and subtracting 5 from the width, a rectangle is made. What
    7·1 answer
  • Will give brainliest if corect please hurry im timed
    12·1 answer
  • What time is shown on the clock?
    15·1 answer
  • Dante it by 15 pounds of metal for $36 which purchase would have the same cost per pound is Dante purchase
    8·1 answer
  • Placement Assessment
    13·1 answer
  • Please help me with algebra 2 questions!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!