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
Tems11 [23]
3 years ago
14

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

the width. What are the dimensions of this box?
Mathematics
1 answer:
ruslelena [56]3 years ago
8 0

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

  • A cuboid has 6 faces.
  • A cuboid contains 8 vertices.
  • A cuboid contains 12 edges .
  • The total surface area of a cuboid is

           = 2(length×breadth+breadth×height+length×height) square units

  • The dimension of a cuboid is written as length×breadth×height.
  • The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

=[x\times 2x\times (x+2)]   cubic inches

=[2x^2(x+2)]     cubic inches

=(2x^3+4x^2)     cubic inches

According to the problem,

2x^3+4x^2=192

\Rightarrow 2x^3+4x^2-192=0

\Rightarrow 2(x^3+2x^2-96)=0

\Rightarrow (x^3+2x^2-96)=0

\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0

\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0

\Rightarrow (x-4)(x^2+6x+24)=0

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

 length=(2×4) inches=8 inches

 and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

You might be interested in
The function h is defined by h(x)=4+3x over 5+x<br><br> Find h(4z)
Jobisdone [24]

Answer:

h(4z)=4+12z / 5+4z

Step-by-step explanation:

The function h is defined by h(x)=4+3x over 5+x

This can be written as

h(x)=4+3x / 5+x

The value of the function at any time depends on the value of x. x is the independent variable. The variable,x can take any value at any time.

To find h(4z), it means that x is taking the value of 4z.

We will substitute 4z in the place of x in the function. This becomes

h(4z)=4+3×4z / 5+4z

h(4z)=4+12z / 5+4z

5 0
3 years ago
Can somebody answer this question correctly
serg [7]
Your answer well be 8
5 0
3 years ago
I’m need help on these questions can any one answer them
LUCKY_DIMON [66]

Answer:

5. WAX and XAZ

6. WAZ and ZAX

7. WAX and YAU

8.  ZAY and YAU

Step-by-step explanation:

Complementary Angles always equal 90 degrees

Supplementary Angles always equal 180 degrees

Vertical angles are always congruent

Adjacent angles are always next to each other.

6 0
3 years ago
lea invests 3,466 in a savings account with a fixed annual interest rate of 7% compound continuously what will the account balan
arlik [135]
The account balance after 10 years will be 5,892.2
5 0
3 years ago
X∙5∙25∙4÷5, if x=813
Finger [1]
21,300 bc 813* 5=4,065 *25=101,625 *4=106,500 /5= 21,300
7 0
3 years ago
Other questions:
  • 5 times a number less 7 is equal to 7 times the number plus 13. Find the number
    8·2 answers
  • A school has 1,200 students. If 65% are girls, how many girls attend the school?
    11·1 answer
  • 9 and 3/4 as an improper fraction
    8·1 answer
  • PLS HELP!! 1 through 8, if you answer you don’t have to do them all just at least a few pls
    9·2 answers
  • Can someone explain how to solve this?
    13·1 answer
  • 5. Find the mZABC if<br> ZABD = 35°, ZDBC = 55º.
    12·1 answer
  • What is not a common factor for the two fractional terms 
    15·2 answers
  • Anyone know this answer please and thank you
    5·1 answer
  • Sin Z = <br><br> Cos Z = <br><br> Tan Z =
    14·1 answer
  • A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!