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
Bogdan [553]
3 years ago
11

A cuboid with a volume of 924cm^3 has dimensions

Mathematics
1 answer:
Leona [35]3 years ago
3 0

The values of x are -22 and 10

The dimensions are 4 cm , 11 cm , 21 cm

Step-by-step explanation:

The given is:

  • A cuboid with a volume of 924 cm³
  • It has dimensions  4 cm , (x + 1) cm and (x + 11) cm

We want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions

The volume of a cuboid is the product of its three dimensions

∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)

∴ Its volume = 4(x + 1)(x + 11)

- Multiply the two brackets and then multiply the product by 4

∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)

∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms

∴ (x + 1)(x + 11) = x² + 12x + 11

∴ Its volume = 4(x² + 12x + 11)

∴ Its volume = 4x² + 48x + 44

∵ The volume of the cuboid = 924 cm³

- Equate the expression of the volume by 924

∴ 4x² + 48x + 44 = 924

- Subtract 924 from both sides

∴ 4x² + 48x - 880 = 0

- Simplify it by dividing all terms by 4

∴ x² + 12x - 220 = 0

Now let us factorize it into two factors

∵ x² = x × x

∵ 220 = 22 × 10

∵ 22(x) - 10(x) = 12x ⇒ the middle term

∴ x² + 12x - 220 = (x + 22)(x - 10)

∴ (x + 22)(x - 10) = 0

- Equate each factor by 0 to find x

∵ x + 22 = 0 ⇒ subtract 22 from both sides

∴ x = -22

∵ x - 10 = 0 ⇒ add 10 to both sides

∴ x = 10

∴ The values of x are -22 and 10

We can not use x = -22 because there is no negative dimensions, then we will use x = 10

∵ The dimensions are 4 , (x + 1) , (x + 11)

∵ x = 10

∴ The dimensions are 4 , (10 + 1) , (10 + 11)

∴ The dimensions are 4 cm , 11 cm , 21 cm

Learn more:

You can learn more about the factorization in brainly.com/question/7932185

#LearnwithBrainly

You might be interested in
Hey I’m struggling with number 13 so please show your work. Thx
Dafna11 [192]

Answer:

\frac{5}{12}

Step-by-step explanation:

Because \frac{3}{5} is being multiplied by S, we can divide \frac{3}{5} from both sides of the equation. This will give us:

\frac{1}{4}÷\frac{3}{5}

But, that looks a bit hectic. Instead of dividing, you can multiply by the reciprocal (which is essentially how to divide fractions). So, instead of \frac{1}{4}÷\frac{3}{5}, you get:

\frac{1}{4}×\frac{5}{3}

When multiplying fractions, remember you can just multiply straight across-- numerator x numerator, then denominator x denominator.

By doing that, you get the fraction \frac{5}{12}

\frac{5}{12} cannot be simplified any more, so S=\frac{5}{12} is your answer :)

I hope this helps

6 0
3 years ago
Solve for m: <br> 8(m + 2) = 3(12 - 4m)
Tema [17]

Answer:

m=1

Step-by-step explanation:

step 1: 8(m + 2) = 3(12 - 4m) remove the parentheses

step 2: 8 m + 2 = 3 12 - 4m move the terms

step 3: 8m+ 12m= 36 - 16 collect like terms and calulate

step 4: 20m=20 divide both sides

solution: m=1

3 0
3 years ago
Read 2 more answers
When is x - y = 4x - 4y
Setler79 [48]
The answer is
When x = 4
Y = 4
Maybe the answer is correct
3 0
3 years ago
Please help me, I will give brainliest! :D
solong [7]

Answer:

Sorry i dont know but need the points

Step-by-step explanation:

3 0
2 years ago
Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much al
UNO [17]
After 12 hours the pound would have 720 pounds of algae.
4 0
3 years ago
Other questions:
  • Help ASAP!!!<br> Please and thank you
    15·1 answer
  • PLZZ ANSWER THE QUESTION ​
    13·2 answers
  • I need help now is due today!!!! : An animal shelter houses only cats and dogs, and there are 25% more cats than dogs. If there
    7·1 answer
  • Does anybody know the awnser to -12x+8+5x=36
    9·1 answer
  • 3 3/5 x (-8 1/3) please answer this question
    15·1 answer
  • Why is 1 + (−5) equal to −4? (1 point)
    11·1 answer
  • what is -172826183618261820172728 + 1526142625615177272827183862782937370282002993030300283883838376266201983837373662. plz i ne
    7·1 answer
  • Find the value of x.<br> X + 11<br> X-1<br> B<br> 8<br> 10<br> E<br> x=
    12·1 answer
  • Solve this inequality for n.<br> 14.&lt; n - 22
    9·2 answers
  • Subtract the following polynomials.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!