when the height of a rectangular prism was halved, the volume was 168 cubic cm. if the original prism had a length, width, and height of consecutive integers, increasing in that order,

(a) write and equation to solve for the length, x, of the original figure,
(b) solve length, x,
(c) show that the equation is unique
show all work.​

Answers

Answer 1

a) The equation is therefore; x³ + 3x² + 2x = 336

b) Solving for the length, we get the length to be; x = 6.

c) All workings are as shown below;

According to the question;

When the height of a rectangular prism was halved, the volume was 168 cubic cm.

In essence, the volume of the original prism is;

Volume = 168 × 2.

Volume = 336cm³

Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.

Therefore, length = x

width = (x +1)

height = (x +2)

Volume = x (x+1) (x+2) = 336

a) The equation is therefore;

x³ + 3x² + 2x = 336

b) Solving for the length, x is as follows;

(x-6) (x² + 9x + 56) = 0

By testing values and checking;

Upon solving the polynomial, x = 6.

c) All workings are as shown above.

Read more on cubic equation:

https://brainly.com/question/8878887


Related Questions

G(x)=4.8x -5

I needed help finding the slope

Answers

Answer:

Slope is 4.8

Step-by-step explanation:

[tex]{ \tt{G(x) = 4.8x - 5}} \\ [/tex]

Answer: The Answer is 4.8

57846*3746 help please

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Answer:216691116

Step-by-step explanation:

Answer:

216,691,116

Step-by-step explanation:

Simplify (2x + 5y) + (3x - 2y) ​

Answers

Answer:

5x + 3y

Step-by-step explanation:

Combine Like terms: 2x + 3x = 5x

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

                                    Ans: 5x + 3y

                                   

How to find domain of (1/x-3)(x^2-x-12)

Answers

Set denominator to zero and solve for x.

x^2 - x - 12 = 0

Factor.

(x - 4)(x + 3) = 0

Solve each factor for x.

x - 4 = 0

x = 4

x + 3 = 0

x = -3

Answer:

The domain is ALL REAL NUMBERS except for x = 4 and x = -3.

At a certain shirt factory, 6 buttons are used on each shirt. If a box containing 120 buttons costs $7, determine the cost for the number of buttons needed for 680 shirts​

Answers

Answer: $238

Step-by-step explanation:

120/6 = 20 shirts for $7

680 / 20 = 34 lots of shirts costing $7

the cost = 34 x 7 = $238

Answer:

238$

Step-by-step explanation:

680*6=4080

this is how many buttons used

4080/120=34

this is how many boxes of buttons

34*7=238

this is the amount


A line passes through the point (-4, 7) and has a slope of -5/4
Write an equation in slope-intercept form for this line.

Answers

Answer:

[tex]y=-\frac{5}{4} x+2.[/tex]

Step-by-step explanation:

1) slope-interception form is: y=s*x+i, where 's' and 'i' are slope and interception;

2) according to the condition s= -5/4, then the required equation is: y= -5/4 *x +i, where i - interception;

3) if to substitute (-4;7) into the required equation y= -5/4 *x +i, it is possible to calculate 'i':

7= -5/4*(-4)+i; ⇒i=2, then

[tex]4) \ finally, \ y=-\frac{5}{4}x+2.[/tex]

Factor the expression to fill in the blank. 25 + 45 = ? (5 + 9)

Answers

Answer:

25 + 45 = 5 (5 + 9)

Step-by-step explanation:

25 + 45 = ? (5 + 9)

Step 1: 25 ÷ 5 = 5

Step 2: 25 ÷ 9 = 5

? = 5

ANSWER: ? = 5
Ok done. Thank to me :>

What are the odds of not selecting a black 2 in cards

Answers

the odds of not selecting a black are 1/2 or 50/50

-10-9-8-7 -6 -5 -4 -3
-2.1
0
1 2 3 4 5
6
7 8 9 10
3) Which inequality matches the graph?
A) X > .2
B) X <-2
C) x = -2
D) 3.2

Answers

Answer:

I think its D

Step-by-step explanation:

The dot starts on -2 and decreases so the answer would = -2 or be less than -2 :)

Someone please help me with this

Answers

Answer:

135.5-8.50=127

127/31.75=4

4 friends or your self and 3 friends

Hope This Helps!!!

Answer:

Equation:

31.75x + 8.50 = 135.50

Answer:

x = 4

Step-by-step explanation:

31.75x + 8.5 = 135.5

31.75x = 135.5 - 8.5

31.75x = 127

x = 127/31.75

x = 4

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $70. For one performance, 25 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was $2050. What was the price of each kind of ticket?

Answers

Answer:

You can use the method of substitution.

Let the advance and same-day tickets be x and y respectively.

x + y = $70 ---> (1)

25x + 35y = $2050 ---> (2)

From Statement (1):

Let (1) × 25

25x + 25y = $1750

10y = $2050 - $1750

      = $300

y = $300 ÷ 10

  = $30 ---> (3)

From Statement (3):

Substitute (3) into (1)

x + $30 = $70

x = $70 - $30

  = $40

Advance ticket: $40

Same-day ticket: $30

Find the value of n




Plz help me fast and send the answer​

Answers

Answer:

n is 113

Step-by-step explanation:

Is an isosceles triangle so the base angles are equal

therefor angles sum up to 180

46 + x + x = 180

46 + 2x = 180

2x = 180 - 46

2x = 134

x = 67

now to find n

the sum of angles on a straight line equals 180

n + x = 180

n + 67 = 180

n = 180 - 67

n= 113

Answer:

the base angle of an isosceles triangle are equal

let the base angle be y°

46° + y° + y° = 180°(sum of angles in a ∆)

46° + 2y° = 180°

2y° = 180° - 46°

2y° = 134°

y° = 134/2

y°=67°

n+y=180°[sum of angles on a straight line]

n+67=180°

n=180-67

n=113°

MSRP (Manufacturer's Suggested Retail Price) = $18.99 retailer's price = $14.99 discount = ?%

Answers

Discount=$ 4

Discount percent :21.06%

solution given:

Marked price: $18.99

selling price: $14.99

Now

discount : Marked price - selling price

:$18.99- $14.99

:$4

Now

discount percent:[tex] \frac {discount}{marked \:price} *100\percent [/tex]

=[tex]\frac {4}{18.99}*100 [/tex]%

=21.06%

Step-by-step explanation:

Hope it will help you a lot.


Please help with this!

Answers

Answer:

I think this is the answer

Step-by-step explanation:

p= x+2+x+9+2x

Simplified

4xin+11in

Please help I need the answer quick this assignment is almost due!

Answers

the correct answer is x= -3

Answer:

x = -3

Step-by-step explanation:

The two angles shown are corresponding angles, meaning that they have the same value. Because of this, we can create an equation to solve for the value of x.

2x + 9 = 7x + 24

Remember, those two angles are similar, and that's why we can make the two values equal to each other. First, let's remove 7x from both sides.

2x - 7x + 9 = 7x - 7x + 24

-5x + 9 = 24

Then, we'll remove 9 from both sides.

-5x + 9 - 9 = 24 - 9

-5x = 15

Finally, we'll divide both sides by -5 to isolate x and figure out what it is equivalent to.

-5x/-5 = 15/-5

x = -3

And there it is... the value of x. Hopefully that's helpful! :)

21
4x + 5
E
חו
What is the value of x?

Answers

Answer:

don't know

Step-by-step explanation:

On Tuesday morning a school cafeteria served 18 gallons of orange juice during breakfast. How many cups are in 18 gallons?

A.288 cups
B.64 cups
C.2,048
D.128 cups

Answers

Answer:

A

Step-by-step explanation:

288 cups did this before

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (What is the circumference of the circle?)

Answers

Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to plug in a = 8 and b = 6. You should find that the hypotenuse is c = 10. The diameter of the circle is 10 units, which leads to the circumference of [tex]C = 10\pi[/tex]

Answer:  [tex]\boldsymbol{10\pi}[/tex]

The larger I grow, the less you can see!
What am I??

Answers

Answer: The darkness is the correct answer

Step-by-step explanation:

As you know that if the darkness becomes bigger you are unable to see it. Hope you like the answer do let me know in the about your thoughts.

Devon has $900 in a savings account. The interest rate is 7% per year and is not
compounded. How much interest will she earn in 2 years?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and t is the time in years.
=

Answers

Answer:

$ 12600

Step-by-step explanation:

According to the question, you have to find the simple interest that Devon earn after 2 years,

You can use this formula to find that.

I = P r t

Here,

P = principal ( $ 900)

r = rate ( 7%)

t = time ( 2 years)

Let us solve now.

I = p × r × t

 = $ 900 × 7% × 2 years

 = 6300 × 2

 = $ 12600

Hope this helps you.

Let me know if you have any other questions :-)

PLEASE HELP WILL GIVE BRAINLIEST

Answers

Answer:

Variable = 4 (1/4x) 1/Variable - 12 - 12

(Hope this helps.)

11) Which shows another way to write 6%?
A) 6
B) -6
C) 0.06
D) six tenths

Answers

Answer:

i think C. 0.06 is answer

Step-by-step explanation:

6% = 6/100 = 0.06

[tex]6\% \\ = \frac{6}{100} \\ = 0.06[/tex]

Answer:

C) 0.06

Hope you could get an idea from here.

Doubt clarification - use comment section.

you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is your total bill

Answers

Answer:

$4.32

Step-by-step explanation:

If you are splitting it evenly, just divide 12.96 by 3

12.96 / 3 = $4.32

At Cheesecake Factory, the cost of your meal before the tip is $77.23. You leave a 15% tip. How much
money did you leave for tip? What is the total cost of your meal?

Answers

Answer:

$88.81

Step-by-step explanation:

to find tip, multiply 77.23 and .15 to get $11.58

total cost = meal + tip

total cost = 77.23 + 11.58 which equals $88.81

The population of Fantasy City doubles each month. When will the city be half populated if it will be fully populated in 10 months.

Answers

Using an exponential function, it is found that the city will be half populated in 9 months.

The population of Fantasy City doubles each month, hence, after t months, the population is given by:

[tex]P(t) = P(0)2^{t}[/tex]

In which P(0) is the initial population.

Fully populated in 10 months, hence, the full population is:

[tex]P(10) = P(0)2^{10} = 1024P(0)[/tex]

Hence, half populated is [tex]P(t) = \frac{1024P(0)}{2} = 512P(0)[/tex], hence:

[tex]P(t) = P(0)2^{t}[/tex]

[tex]512P(0) = P(0)2^{t}[/tex]

[tex]2^t = 512[/tex]

[tex]2^t = 2^9[/tex]

[tex]t = 9[/tex]

The city will be half populated in 9 months.

To learn more about exponential functions, you can take a look at https://brainly.com/question/25537936

Dose anyone know questions 2 and 3?

Answers

Answer:

Step-by-step explanation:

1.6 / 0.2 = 8 x 10⁽⁵⁻²⁾ = 8 x 10³

The cost increases by $1.50 for each additional toothbrush made.

what is -6 - 2=
A. 8
B. -4
C. -8
D. 4

Answers

a negative subtract negative will still be negative, the answer is C. -8

14. Provide a written description of the complement of the given event.
of ten adults, at least one of them has high blood pressure.


None of the adults have high blood pressure.
At most one of the adults has high blood pressure.
All of the adults have high blood pressure.
Nine of the adults have high blood pressure

Answers

Answer:

At most one of the adults has high blood pressure.

Step-by-step explanation:

The triangle and rectangle have the same perimeter.find the value of x.

Answers

Answer:

X=2

Step-by-step explanation:

Triangle

3x+18

Rectangle

6x+12

Same perimeter:

3x+18=6x+12             //-12

3x+6=6x                   //-3x

6=3x                         //:3

2=x

Answer:

x = 2

Step-by-step explanation:

Perimeter of triangle = a + b + c

Perimeter of rectangle = 2(l + b)

=> x + 5 + x + 6 + x + 7 = 2(2x - 1 + x + 7)

=> 3x + 18 = 2(3x + 6)

=> 3x + 18 = 6x + 12

=> 3x - 6x = 12 - 18

=> -3x = -6

=> x = -6/-3

=> x = 2

Please answer the file question.

Answers

Answer:48 16 = ?

27 9 = 9

60 20 - 10

Step-by-step explanation:

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