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
kolbaska11 [484]
3 years ago
12

The volume of a rectangular prism is b^3 + 8b^2 + 19b + 12 cubic units, and its height is b + 3 units.

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
7 0
The answer is (b² + 5b + 4).

The volume of a rectangular prism (V) is:
V = l · w · h              (l - length, w - width, h - height)

The base of the rectangular prism is the product of length and width, so the area of the base is:
A = l · w

Since V = l · w · h and A = l · w, then:
V = A · h
It is given:
V = b³ + 8b² + 19b + 12
h = b + 3
⇒ b³ + 8b² + 19b + 12 = A · (b + 3)
⇒ A = (b³ + 8b² + 19b + 12) ÷ (b + 3)

Now, we have to present the volume as multiplication of factors. One of the factors is b+3. So:
b³ + 8b² + 19b + 12 = (b · b² + 3b²) + (5b² + 15b) + (4b + 3·4) =
                                =    b²(b + 3)    +   5b(b + 3)   +  4(b + 3) =
                                = (b + 3)(b² + 5b + 4)

A = (b³ + 8b² + 19b + 12) ÷ (b + 3) = (b + 3)(b² + 5b + 4) ÷ (b + 3)

(b + 3) can be cancelled out:
A = (b² + 5b + 4)
You might be interested in
What is the sum of -7(-5+x)
vesna_86 [32]

Answer:

35-7x

Step-by-step explanation:

Multiply parenthesis by -7

3 0
3 years ago
Lem is playing a board game and needs to roll two dice and get a six on both die in order to win the game. What is the probabili
tangare [24]

The probability of getting a 6 on one dice is 1/6

The probability of getting a 6 on both dice would be 1/6 x 1/6 = 1/36

Answer: 1/36

3 0
3 years ago
Find c. Round to the nearest tenth.
bija089 [108]

Answer:

Step-by-step explanation:

A = 150°

B = 12°

C = 180 - (150 + 12) = 18°

b = 10 cm

Apply the sine rule:

\frac{b}{sin(B)} = \frac{c}{sin(C)}

Plug in the values

\frac{10}{sin(12)} = \frac{c}{sin(18)}

Multiply both sides by sin(18)

\frac{10}{sin(12)}*sin(18) = \frac{c}{sin(18)}*sin(18)

\frac{10*sin(18)}{sin(12)} = c

c = 14.9 cm (nearest tenth)

7 0
4 years ago
What times what equals 6 but when added equals 5
ArbitrLikvidat [17]
2 & 3
2+3=5
2x3=6
Hope this helps
6 0
4 years ago
Read 2 more answers
Which is the only fraction that must be represented by a nonterminating decimal?
Aleks04 [339]
A is incorrect - In decimal form, 7/5 is 1.4

B is incorrect - In decimal form, 7/4 is 1.75

D is incorrect - In decimal form, 7/2 is 3.5

The answer is C. 7/4; In decimal form, 7/4 is 2.33333333.... (this represents a terminating decimal)
3 0
3 years ago
Other questions:
  • A car is traveling at a speed of 75 km/h. Compute the speed of the car in m/s.
    8·2 answers
  • Janice and patty spent more than 175 shopping. Janice spent 34. How much did patty spend. Write a inequality.
    5·1 answer
  • The cost for a pack of
    11·2 answers
  • 1.What effect does changing the function f(x) = 1/2 sin (x) +2 to the function g(x) = 2 sin (x) +8 have on the graph of f(x)?
    15·1 answer
  • Bryan had typed his English essay at a constant speed from beginning to end. If he typed
    12·1 answer
  • What is the value of c in the equation y = 4x^2 -10x + c if the y-coordinate of the vertex is -7
    6·1 answer
  • Just find BC that’s all
    7·1 answer
  • What is the mean number of points scored be these players?<br> A. 7<br> B. 8<br> C. 9<br> D. 10
    14·2 answers
  • PLEASE HELP!! Worth 15 points
    11·1 answer
  • The given figure is a solid object formed by a cylinder and a hemisphere. If the total length of that solid object is 64 cm and
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!