A cuboid with a volume of 925cm^3 has dimensions.
4cm, (x + 1) cm and (x + 11) cm.
Show clearly that x^2 + 12x - 220 = 0
Solve the equation by factorising, making sure you show the factorisation.
State both values of x on the same line.
Finally, find the dimensions of the cuboid, writing all three on one line.

Answers

Answer 1

Answer:

Step-by-step explanation:

Volume of the cuboid = Length * Width * Height

Given

Length = 4cm

Width = (x+1)cm

Height = (x-11)cm

Volume of the cuboid = 4(x+1)(x+11)

Volume of the cuboid = 4(x^2+11x+x+11)

Volume of the cuboid = 4(x^2+12x+11)

Volume of the cuboid = 4x*2+48x+44

925 = 4x*2+48x+44

4x*2+48x+44-925 = 0

4x*2+48x-881 = 0

Divide through by 4

x^2 + 12x - 220.25 = 0

Factorize using the general formula;

x = -12±√12²-4(-220.25)/2

x = -12±√144+881/2

x = -12±√1025/2

x = -12±32/2

x = 12+32/2

x = 20/2

x = 10

Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm

Dimension is 4cm by 11cm by 21cm


Related Questions

A carpenter use 65 shelves to make 13 bookcases. She uses the same number of shelves for each bookcase. Are 32 shelves enough to build 6 more bookcases?

Answers

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

what does 28-8 represent?

Answers

Step-by-step explanation:

subtraction if that wut u askim

Which of the following finds T given I, P and R

Answers

Answer:

D. T= I/PR

Step-by-step explanation:

PRT are multiplyed so you divide PR to get T by itself.

Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8.
need asap

Answers

Answer:

y + (-3) = -8

Step-by-step explanation:

i just know

pls mark branliest

Find the slope and the y-intercept of the graph of y
-4/5x - 2

Answers

Answer:

slope - (-4/5)

y- intercept - (0,-2)

Step-by-step explanation:

Answer:

the slope is -4/5 and the y intercept is -2

Step-by-step explanation:

In triangleABC, a = 1.4 cm, b = 1.5 cm and c=1.5 cm. Find the measure of angleA to the nearest 10th of a degree.​

Answers

Answer:55.6

Step-by-step explanation:

Answer:

55.6

Step-by-step explanation:

Find the slope of the following graph and Identify the type of
Slope:

Answers

Answer:

undefined

Step-by-step explanation:

Horizontal lines have no slope. The line on the graph is vertical, so we can't really tell what slope it is. But there isn't any run and only rise, therefore the slope is "undefined."

Explain in your own words why you would use division to change a smaller unit to a bigger one . What would happen if you multiplied instead ? TOPIC IS MEASUREMENT

Answers

Answer:

you would use division to change bigger units into smaller ones as a form of cancellation

PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help

Answers

Answer:

22 units

Step-by-step explanation:

Known Quantities:

AB = CD and AC = BD

Calculations:

AB = 8AC = 3CD = 8BD = 3

Final Calculations:

perimeter = 2 x (3+8)perimeter = 22

7 + 5x = 2x + 25
step by step pls:(

Answers

Answer:

x = 6

Step-by-step explanation:

7 + 5x = 2x + 25

first subtract 7 from both sides to isolate 5x on the left

5x = 2x + 18

then subtract 2x from both sides to isolate all of the x terms to one side

3x = 18

then divide 18 by 3 to solve for x

x = 6

hope this helped!! :)

Answer:

i got you, i wrote it out and all gimme brilliantness

Step-by-step explanation:

Evaluate 1/6t+1/12 when t=1/2

Answers

Answer:

1/6

Step-by-step explanation:

You're welcome :)

A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?

Answers

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

success (reaching 4 before 0) and failure (reaching 0 before 4).

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Learn more probability about here:

https://brainly.com/question/23846068

#SPJ4

Simplify the expression by combining like terms.
t + 8 + 3t
SHOW YOUR WORK: Use different colors to circle your like terms then use addition/subtraction to combine
them.
*Remember: Variable term goes FIRST!

Answers

Answer:

4t + 8

Step-by-step explanation:

t + 3t = 4t

4t + 8

Answer:

4t+8

Step-by-step explanation:

If you look at your equation t+8+3t you will notice how you have two t parts

part 1: t

part 2: 3t

Since they have the same variable or letter you are able to combine them. When you add them together you get 4t.

Then you just put your 8 back on to the equation! 4t+8

Is the relation in the mapping below a function? Explain.
Domain
1,3,5,7
Range
2,4,6

Answers

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

Please help me hahahhahahhahahhhhhhshshs can

Answers

Answer:

The slope of this line is -2/3x.

Step-by-step explanation:

The slope can be found by getting x1 and y1 (0,3) and x2 and y2 (3,1). Once you have these you would do y2 - y1 / x2 - x1.

And the equation then is

1 - 3 / 3 - 0.  After simplifying this you get -2/3.

HELP ME PLEASEEEEEEEEEEEEEEEEE YOU CAN GET BRAINEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

its red okay? i hop help

Answer:3:1. Yellow

Step-by-step explanation:

The nth term of a sequence is 3−2n

Work out the 8th term of the sequence

Answers

Answer:

-13

Step-by-step explanation:

3-2n

3-2×8

3-16

-13

Quadratic functions 2. Did I do it right

Answers

Yea you did, good job

Describe the products made by the process of cellular respiration.

Answers

Step-by-step explanation:

The product is carbon dioxide and water

NEED ASAP . Plz help

Answers

It’s 4 and what they said

i need help on this please​

Answers

-6 answer to -4+(-2)

3 answer to 7+(-4)

In triangle ABC, the measure of angle A is 48° and the measure of angle C is 24°. What type of triangle is triangle ABC?

Answers

Answer:108 degrees

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

24+48= 72

180-72=108

All three angles are different meaning that the triangle must be a scalene triangle.

Date
Page
A rectangular meadow has an area of 28 square
meter and perimeter 22 m, find the length and breadth.​

Answers

Answer:

perimeter =22m

area=28square meter

perimeter of rectangle=4l

22m=4l

22÷4=l

5.5=l

l=5.5m

area of rectangle =l×b

28=5.5×b

28÷5.5=b

5.09=b

b=5.09m

length =5.5m and breadth =5.09m answer !!!!

y-2 = -3(x + 6), write the equation of the line in slope intercept form.

Answers

Answer:

y = -3x - 16

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Given: y - 2 = -3(x + 6)

Slope-intercept form: y = mx + b

To write the equation in slope-intercept form, we need to know the slope(m) and the y-intercept(b). By looking at the given equation, we can see that the slope is -3. We are also given the value of one point: (-6, 2).

To find the y-intercept, input the given values of the slope and the point into the equation format and solve for b:

y = mx + b

2 = -3(-6) + b

2 = 18 + b

Subtract 18 from both sides of the equation to isolate b:

2 - 18 = 18 - 18 + b

-16 = b

The y-intercept is -16.

Now that we know the slope and the y-intercept, we can write the equation:

y = -3x - 16

7a(3b - 2c + 4)


Help?

Answers

Answer:

21ab-14ac+28a

Step-by-step explanation:

[tex]7a(3b - 2c + 4)\\\\\mathrm{Distribute\:parentheses}\\\\=7a\times \:3b+7a\left(-2c\right)+7a\times\:4\\\\\mathrm{Apply\:minus-plus\:rules}\\\\+\left(-a\right)=-a\\\\=7\times\:3ab-7\times\:2ac+7\times\:4a\\\\Simplify\\\\21ab-14ac+28a[/tex]

1. To graph any linear equation in the calculator it needs to be in the slope
y intercept form. What is the slope y-intercept form for the equation
4y – 20x = -8

Answers

Answer:

y=mx+b no judgement i think this is right but i coukldbe completely off

Step-by-step explanation:

A rectangular lawn 4m by 10m has a garden of uniform width added to one end. Then, along the combined side length of the lawn and garden , another garden is added, whose width is twice that of garden . The total area of the lawn and both gardens is 72 m2

Answers

Answer and explanation:

A rectangle's width is longer than the length

And so given a rectangular lawn 4m by 10m,

the width of the lawn= 10m

the length of the lawn= 4m

If a garden of uniform width is added, then garden's width = 10m

The garden of uniform width is added to the width side of the rectangular lawn( since along the combined side length of the lawn and garden, another garden is added)

The garden added to the combined side length of the lawn and garden has width twice that of the garden = 2*10= 20m

Given that total area of the lawn and two gardens = 72m²

Total area of lawn and 2 gardens(Area of rectangle(lawn+2 garden's)) is length * width

= 4*10+ 10*x+ 20*y=72

Therefore equation for total area of lawn and both gardens is 40+10x+20y=72

Where x is length of second garden attached to the width side of the lawn and y is length of the garden attached to the combined length side of the lawn and first garden

x can be solved

40+10x+20y=72

10x+20y=72-40

10x+20y=32

10x=32-20y

x=32-20y/10

Y can be solved

40+10x+20y=72

10x+20y=72-40

10x+20y=32

20y=32-10x

y=32-10x/20

What is the ratio of 3:6

Answers

Answer:

1:2

Step-by-step explanation:

You didn't really specify, but I'm going to assume you meant as simplified as possible. If you write it as a fraction, it will be ½ or as a decimal it will be 0.5.

Answer:

1:2

Step-by-step explanation:

Simplifying a ratio is like simplifying a fraction.

Simply put the number to the left as the numerator, and the number to the right as the denominator.

In this case, 3/6 = 1/2.

Hence, plug the numbers right back in and you get 1:2.

Hope this helped!

The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?

Answers

Answer:

France's GDP is 50 000 times larger than Tuvalu's GDP.

Step-by-step explanation:

Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]

            Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]

To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.

[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]

           = [tex]\frac{200000}{4}[/tex]

           = 50000

Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.

Evaluate -9x-2 when x =-4

Answers

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

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