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.

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Related Questions

In a parking lot 30% of the cars are white write this as a decimal

Answers

Answer:

0.3

Step-by-step explanation:

Answer:

[tex]{ \tt{30\% = 0.3}} \\ [/tex]

Using the table find then relative frequency of each color, to 3 decimal places

Answers

Answer:  The table is shown below.

Explanation:

For each row, divide the color counts over the total. For example, we have 9 red in bag one out of 61 total. This leads to a relative frequency of 9/61 = 0.1475 which rounds to 0.148; so approximately 14.8% of the items in bag one are red. This represents the top left corner of the table.

As another example, we have 5 brown out of 60 total in bag ten. That leads to a relative frequency of 5/60 = 0.0833 = 0.083 (see the bottom right corner of the table).

Take note that for any given row, adding up the relative frequencies will yield the value of 1 (though there might be some slight rounding error along the way).

Solve 3-x/2<18.
A. X>-42
B. x > -30
C. X< -30
D. X<42

Answers

The solution of the given equation will be C -x< 30

What does it mean to solve an equation?

An equation represents the equality of two or more mathematical expressions.

A Solutions to an equation are those values of the variables, involved in that equation for which the equation is true.

We have been given the equation as 3-x/2<18.

Now solving for x

3-x/2<18.

Eliminate 3

-x/2 < 18 - 3

-x/2 < 15

Multiply by 2 on both sides;

-x/2 < 15 (2)

-x< 30

Therefore, the solution of the given equation will be C -x< 30

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David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $4.45 per pound, and type B coffee costs $5.85 per pound. This month, David made 123 pounds of the blend, for a total cost of $643.95. How many pounds of type B coffee did he use?

Answers

Step-by-step explanation:

x = pounds A

y = pounds B

x + y = 123

4.45x + 5.85y = $643.95

from the first equation we get

x = 123 - y

and we use that in the second equation :

4.45×(123 - y) + 5.85y = 643.95

547.35 - 4.45y + 5.85y = 643.95

1.4y = 96.6

y = 69

x = 123 - y = 123 - 69 = 54

so, he used 69 pounds of B coffee.

7362*637 help please

Answers

Answer:

4689594

Step-by-step explanation:

please help I am so lost rn
(please put step by step if you can)
thanks!​

Answers

Answer:

x=-5 and y= 4

Step-by-step explanation:

To eliminate x, add up both equations

9y= 36

divide both sides by 9

y=36/9

y= 8

To eliminate y, multiply the first equation by 8

-16x + 8y = 112

2x+ 8y= 22

Subtract equation 2 from equation 1

-18x = 90

Divide both sides by -18

x= 90/-18

x= -5

Rewrite in simplest terms: (-9x + 7y) - (-9x + 5y)

Answers

Answer:

3y

Step-by-step explanation:

(-9x+7y)-(-9x+5y)

Distribute the negative(-)

-9x+7y+9x-5y

-9 and 9 cancel each other

3y

The simplest terms of the given expression  (-9x + 7y) - (-9x + 5y) will be 2y.

What is an expression?

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

(-9x + 7y) - (-9x + 5y)

Open the bracket

-9x + 7y + 9x - 5y

Combined likely terms together

-9x + 9x + 7y - 5y

0 + 2y = 2y

Hence "The formula (-9x + 7y) - (-9x + 5y) will have 2y as its simplest terms".

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I thought of a number. This number double is 7 less than 29. What is my number? hurry please

Answers

Answer:

11

Step-by-step explanation:

11*2=22

29-7 =22

Answer:

11

Step-by-step explanation:

Let x be your number

Is means equals

2x = 29-7

2x= 22

2x/2 = 22/2

x =11

Which story represents the equation six-sevenths times one-fourth?

A: Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more milk. How much milk did she drink in all?
B: Mike walked one-fourth mile and then he took the bus for six-sevenths miles to school. How many miles did he travel in total?
C: Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
D: Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left?

Answers

Answer:

C I think.

Step-by-step explanation:

I don't know for sure, but A, B and D all talk about adding or subtracting the answers together, while C tells us to find the fraction of a fraction so I'm pretty sure you multiply. Hope this helps!

A rectangular cube of iron is a side 8 cm. What is it volume.​

Answers

A rectangular cube of iron is a side 8 cm.Given, side (a) = 8 cm.We know, volume of a cube [tex] = {a}^{3} [/tex]Therefore, the volume

[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]

Answer:

The volume is 512 cube centimetres.

Hope you could get an idea from here.

Doubt clarification - use comment section.

QUESTION 21 PLEASE HELPPP

Answers

Answer:

one solution

Step-by-step explanation:

Since both are y-isolated equation, we can write as:

[tex]\displaystyle \large{6x-2=4x-2}[/tex]

Solve for x, first move 4x to subtract with 6x and -2 to add with -2

[tex]\displaystyle \large{6x-4x=-2+2}\\\displaystyle \large{2x=0}\\\displaystyle \large{x=0}[/tex]

Then substitute x = 0 in any of these equations which we receive y = -2.

And the solution is (0,-2) which only has one solution.

HELPPPP PLEASEEEEE ​

Answers

I’m not rly sure what it means by flipping the card …. I’m assuming there’s more to this question but if it’s what I think it is the only way this equation will be true is by switching the + Symbol to - (subtraction) which would be 1-2= 3-4 since it would 1=1 making the equation true

ST
16. (26)
A bag contains 3 green marbles and
7 yellow marbles. Find the probability of
drawing a green marble, keeping it, and
drawing another green marble. Write the
probability as a fraction in simplest form.
17.

Answers

Answer:

the probability would be 30% but as a fraction it would be 3/10

Step-by-step explanation:

Answer:

7/15

Step-by-step explanation:

The probability of the first one is 7/10 and the second one is 6/9. Multiply them together and you get 42/90, which simplifies to 7/15.

Help with this please?

Answers

A and b good luck (:(:
the answers are A and B

Express the following surds in the simplest form

a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]

Answers

[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]

[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]

[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]

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

Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
that is 64% acid?

Answers

Step-by-step explanation:

Solution A is 40% acid and solution B is 80% acid. How many

liters of each should be used in order to make 100 L of a solution

is 64% acid

There should be 40 L of solution A and 60 L of solution B should be added in order to make 100 L of a solution that is 64% acidic.

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, solution A is 40% acidic and solution B is 80% acidic, they are mixed to get a 100 L solution which is 64% acidic.

Establishing the equations,

A+B = 100

A = 100-B.......(i)

40% of A + 80% of B = 64% of 100

0.4A + 0.8B = 64......(ii)

Solving the equations,

0.4(100-B) + 0.8B = 64

40 - 0.4B + 0.8B = 64

0.4B = 24

B = 24/0.4

B = 60

Putting, B = 60 in Eq(i)

A = 100-60

A = 40

Hence, The amount of solutions needed is A = 40 L and B = 60 L.

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Mrs Ang bought k apples at 50% each from a supermarket. How much
change did she receive if she paid $10 to the cashier? Express your answer
in cents.

Answers

Answer:

The apples may have costed 0.50 cents each, and she may have bought 10, which would result in her paying 10 dollars, and receiving 5 dollars in change.

Step-by-step explanation:

Multiply 10 (the amount she gave to the cashier) by 0.50%, it equals 5, so that's how much she paid, and since she gave a 10 dollar bill, she should get 5 dollars in change.

T^T

find three solutions for 9x - 2y = 18​

Answers

Answer:

[tex](x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)[/tex]

Step-by-step explanation:

Ben currently has $70 in his trip fund. He makes $45 per week doing yard work for his neighbors. He keeps $18 of the $45 for weekly expenses. The remaining amount goes into his trip fund. Which function can be used to determine the amount of money (y), in dollars, that Ben has in his trip fund at the end of xx weeks?

y=70+27x

Answers

Answer:

he starts with 70 and $45-18=27 so he makes $27 to add to those $70

Step-by-step explanation:

Need answer to the question

Answers

Answer:

B) Symmetric property of congruence

Step-by-step explanation:

The angles 1 and 2 are marked as congruent

If a ≅ b, then b ≅ a, this is called the symmetric property of congruence:

The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first.

Correct choice is B

Answer:

Symmetric property of similarity

Step-by-step explanation:

If a=a then that's reflexive propertyIf a=b and b=c then a=c, transitive property

What is the percent decrease from 16 to 0

Answers

The percentage that decreases is 1


What is the value of x in the equation 4
.
+
2

Answers

Answer:

x=-3

Step-by-step explanation:

In a group of workers, 16 belonged to a lottery syndicate and 4 did not.

What fraction of the workers did not belong to the syndicate?

1: 4/16

2: 1/5

3: 1/4

4: 3/4

Answers

Answer:

HI THERE

the answer is number 1 !!

correct me if I'm wrong

rewrite in simplest terms -6(-7u+6)+2u

Answers

Answer:

44u-36

Step-by-step explanation:

42u-36+2u

44u-36

help plsssssssssssssss

Answers

Answer:

Last answer, height is 150 ft

Step-by-step explanation:

from the graph, you can clearly see, when T=3, H=150

Which means The firework is at a height of 150 feet

Answer:

D

Step-by-step explanation:

At 3 seconds, the firework is at a height of 150 feet

Answer is D. third option

The firework is at a height of 150 feet

"When I started here, there were 500 employees. Since then, we have
added 35% more employees, so we now have a total of employees."

Answers

Answer:

Assuming that the question is asking how many employees there are, your answer would be 675.

Step-by-step explanation:

First, to find 35% of 500, you can use this equation (35 x 500) / 100 Second, solve the equation (The answer is 175) Third, you add 500 + 175 to get 675

Find the intersection point for the following linear functions.
Rx) = 2x + 3
8(x) = -4x - 27

Answers

Answer:

(-5, -7)

Step-by-step explanation:

Answer:

[tex](-5,-7)[/tex]

Step-by-step explanation:

[tex]f(x)=2x+3[/tex]

[tex]g(x)=-4x-27[/tex]

[tex]2x+3=-4x-27[/tex]

[tex]6x+3=-27[/tex]

[tex]6x=-30[/tex]

[tex]x=-5[/tex]

[tex]f(-5)=2(-5)+3[/tex]

[tex]f(-5)=-10+3[/tex]

[tex]f(-5)=-7[/tex]

Therefore, the point of intersection is [tex](-5,-7)[/tex]

Help help help math math

Answers

Answer:

Function

Step-by-step explanation:

Hope it help !!

What is the prime factorization of 32?
A. 32 = 2 x 4x4
B. 32 = 2x2x2x2x2
C. 32 = 2x2x2x2
D. 32 = 2 * 2 * 2 * 4

Answers

Answer:

2nd option

Step-by-step explanation:

Repeatedly divide by 2 until the value 1 is reached

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1 ← finish here

Then

32 = 2 × 2 × 2 × 2 × 2

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