A builder wants to build a sump to store water in an apartment. The volume of the
rectangular sump will be modelled by V(x) = x3 + x2 - 4x - 4.
He planned in such a way that its length and breadth are (x + 1) and (x - 2) respectively.
How much he has to dig?
(a) (x + 1]
(b) (x - 2)
(c) (x-3)
(d) (x + 2)
(ii) If x = 4 meter, what is the storage capacity (in litres) of this sump?
(iii) A ladder is kept a point halfway from the base as shown in the figure. It just touches
the top of the sump. Find the length of the ladder, assuming x-42 (correct to 1 dp)​

Answers

Answer 1

Answer:

1) b, 2) d, 3) d

Step-by-step explanation:

The volume is the product of three dimensions

V = lwh

Given:

w = x + 1, l = x + 2 and V(x) = x³ + x² - 4x - 4

1) Let's find the height:

x³ + x² - 4x - 4 =x²(x + 1) - 4(x + 1) = (x² -4)(x + 1) = (x + 2)(x - 2)(x + 1)We got h = x - 2

2) x = 4 m

Volume is:

V = 4³ + 4² - 4*4 - 4 = 60 m³

3) x = 4 m

Dimensions are:

w = x + 1 = 5 m, l = x + 2 = 6 m, h = x - 2 = 2 m

Full surface area is:

2(lw + lh + wh) =2(5*6 + 6*2 + 5*2) = 104 m²

Related Questions

pls help..thanks,,,,​

Answers

Answer/Step-by-step explanation:

Given, y = k√x

Let's find the following:

a. To find k, using the first pair given, (64, 16), plug in the values of the ordered pair into y = k√x

Thus:

16 = k√64

16 = k*8

Divide both sides by 8

16/8 = k

k = 2

b. To find F, substitute k = 2, and x = 100 into y = k√x

Thus:

y = 2√100

y = 2*10

y = 20

F = 20

c. To find x, substitute k = 2, and y = 10√2 into y = k√x.

Thus:

10√2 = 2√x

Divide both sides by 2

(10√2)/2 = √x

5√2 = √x

Square both sides

x = (5√2)²

x = 25*2

x = 50

d = 50

can anyone PLEASE HELP ME with this question i really need help

Answers

the missing angle is 49

Answer:

x = 49°

Step-by-step explanation:

180 = 90 + 41 + x

x = 180 - 131

x = 49

Find the value of 5x - 4x^2 for x=2

Answers

Answer:

=10

Step-by-step explanation:

5x-4x². (x=2)

5(2)-4(2)²

=10-0

=10

HELP
Please don’t answer if you don’t know it.

Answers

Answer:

d=5

Step-by-step explanation:

Answer: d= 5

Step-by-step explanation:

I did this test on edgunity if you need a step by step I can leave it in the comments below. Good luck

Find C.
Round to the nearest tenth.
90 ft
55 ft
A
В
50 ft
C = [? ]°
YLaw of Cosines: c2 = a+ b2 - 2ab cos C

Answers

9514 1404 393

Answer:

  29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

  C = arccos((a^2 +b^2 -c^2)/(2ab))

  C = arccos((90^2 +55^2 -50^2)/(2·90·55))

  C = arccos(8625/9900) ≈ 29.4002°

  C ≈ 29.4°

HELP ASAP An office employee ears $600 weekly. Find the equivalent earnings if paid biweekly, semimonthly, monthly, and annually

Answers

1200~bi-weekly

1200~semimonthly

2400~monthly

31,200~annually

Which method would you choose to solve the following system?
-5x + 2y = 15
y = - 3x - 20
Equal Values Method
O Substitution Method
O Graphing Method
Elimination Method

Answers

Answer: combining like terms

Step-by-step explanation:


Solve the equation below for x.
cx- 4 = 7

A. x=11/c
B. x=c/3
C. x=3/c
D. x= c/11

Answers

Answer:

a. x = 11/c

Step-by-step explanation:

cx - 4 = 7 [add 4 to both sides of the equation]

cx = 11 [divide by c to isolate x]

x = 11/c

Four copies of the triangle shown are joined together, without gaps or overlaps, to make a parallelogram. measurements= 5cm, 13cm, 12cm What is the largest possible perimeter of the parallelogram?

Answers

Answer:

Highest Possible Perimeter = 52cm

Step-by-step explanation:

The triangle is not shown. But, the question can still be solved.

The given sides (5cm,12cm and 13cm) of the triangle shows that the triangle is a right angled triangle as proven below:.

[tex]13\² = 5\² + 12\²[/tex]

[tex]169 = 25 + 144[/tex]

[tex]169 = 169[/tex]

Having shown that;

The next step is to determine the highest possible value of the perimeter.

To get the highest possible perimeter;

The 4 triangles have to be joined at the 12cm and 5cm part of each triangle (see attachment).

From the attachment, the perimeter is then calculated as:

Perimeter = 13cm + 13cm + 13cm+ 13cm

Perimeter = 52 cm

Answer: 76

Step-by-step explanation:

if Efx=300+30p and N=10+p, find the valu of mean​

Answers

mean=30

Step-by-step explanation:

mean=Efx/n

=300+p/10+p

= 30(10+p)/10+p

=30

What is the value of x?

Answers

What is the equation?

-4n + 1/3m + 4n - 4/5m​

Answers

Answer:

[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]        

Step-by-step explanation:

Given the expression

[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}[/tex]

Group like terms

[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}=-4n+4n+\frac{1}{3m}-\frac{4}{5m}[/tex]

Adding similar elements: -4n + 4n = 0

                                      [tex]=\frac{1}{3m}-\frac{4}{5m}[/tex]          

L.C.M of 3m and 5n will be: 15m

so adjusting fractions based on the LCM

                                       [tex]=\frac{5}{15m}-\frac{12}{15m}[/tex]      

Since, the denominators are equal, combine the fractions:  [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]

                                       [tex]=\frac{5-12}{15m}[/tex]

                                       [tex]=\frac{-7}{15m}[/tex]

                                       [tex]=-\frac{7}{15m}[/tex]

Therefore, we conclude that:

[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]                    

25% of 96 is what number round to the nearest tenth of necessary

Answers

Answer:

y = .25 x 96

y = 24

This is the answer.

Step-by-step explanation:

25% is the same as 0.25

25% = 25/100 = 0.25

Multiply 0.25 with 96

0.25 x 96 = 24

24 is your answer

hope this helps

evaluate the expression when c=2. 6c/2​

Answers

Answer:

6

Step-by-step explanation:

Given the expression g(c) = 6c/2, we are to find the value when c = 2

Substitute c = 2 into the expression

g(2) = 6(2)/2

g(2) = 12/2

g(2) = 6

Hence the result when c = 2 is 6

If I buy 5 plants from the garden centre at £3.00 a plant how much do the plants cost? If I have a £20 note how much change will I get?

Answers

first: £15.00
second: £5.00

Answer:

They will cost you £5.00 total

Step-by-step explanation:

If the plants each cost £3.00

You multiply the amount of plants, in this case is 5 by the price :-

5×3.00

= £15.00

You then subtract the total from the cash

15.00 - 20.00

= £5.00

(HELP URGENT TWO VARIABLE INEQUALITIES)

(SEE ATTACHED PICTURE)

Which of the following inequalities matches the graph?

A) The correct inequality is not listed.
B) 5x + y ≥ 1
C) 5x + y ≤ 1
D) 5x − y ≥ 1

Answers

Answer:

D)

Step-by-step explanation:

Line: y = 5x - 1

The shaded space is less than or equal to the line.

So it is y [tex]\leq[/tex] 5x - 1

This is the same as D)

Multiply 2.3. (-1.2)​

Answers

Answer:

-2.76

Step-by-step explanation:

2.3x(-1.2)

= -2.76

which of the following rational function is graphed below?​

Answers

9514 1404 393

Answer:

  B.  1/((x -1)(x -2))

Step-by-step explanation:

The vertical asymptotes at x=1 and x=2 tell you the denominator will have factors such that these values make it zero: (x -1)(x -2). That is sufficient to identify choice B as the correct answer.

  [tex]f(x)=\dfrac{1}{(x-1)(x-2)}[/tex]

Suzy's kitchen measures 21 feet by 3 feet. She would like to add a small tile border around the entire room. How much should she expect to pay if the tile strip costs $0.95 per foot.

Answers

Find the area of kitchen

21×3=63

if tile costs $0.95 per foot,

then 63÷0.95=66.36

thus the cost will be $66.36

how much is 21 hundreds

Answers

21 hundreds would be 2100

Answer:

21,000

Step-by-step explanation:

Tom has already baked 4 cakes, and he can bake 1 cake with each additional stick of butter he buys. How many additional sticks of butter does Tom need in order to bake a total of 42 cakes?

Answer in the number of additional sticks of butter.

Answers

Answer:

since it takes 1 additional stick to bake a cake,then it takes 84 additional sticks to bake 42 cakes

Determine the intercept of the line.

Y-intercept : ( ) , ( )
X- intercept : ( ) ( )

Answers

Answer:

Y: (0) (0.4)

X: (0.3) (0)

Step-by-step explanation:

prove me wrong

Can I get the answer please

Answers

Answer:

C

Step-by-step explanation:

first equation is y=3/4x+2

second equation is -2x+17

Rob is saving to buy a new iPad. For every $15 he earns babysitting, he saves $6. On Saturday, Rob earned $75 babysitting. How much money did he save?

Answers

He saves $30 if He earns $75 on Saturday

He saves $6 for every $15
So $75 divided by $15= 5
So 5x$6= $30

(1, 1) and (4, 3) slope​

Answers

this needs to be 20 characters long but it’s 4/3

Answer:

[tex] \huge \boxed{ \boxed{ \frac{2}{3} }}[/tex]

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

From the question we have

[tex]m = \frac{3 - 1}{4 - 1} = \frac{2}{3} \\ [/tex]

We have the final answer as

[tex] \frac{2}{3} \\ [/tex]

Hope this helps you

How come nobody answers my questions? Like wth, I'm stuck but everyone else is getting their questions answered left and right.

Answers

Answer:

That is a good question and it might be your question you are trying to find the answer and maybe  your  question looks hard

Hope this help :)

Step-by-step explanation:

Divide. Write your answer in fraction form.

(5x+ + 18x+ 15) / (x+2)

Answers

Answer:

what? it seems like you just spammed anything from the web O_o

Step-by-step explanation:

Can i have some help plz

Answers

Answer:

a) 15 + 25x ≤ 70

b) 60 + 15x ≤ 500

Step-by-step explanation:

a) Let x represent the number of calculators that Ms. Burgos can buy. since each calculator cost $25, then the total cost of calculator = $25 * x = $25x

She bought three notebooks costing $5 each. Money spent on notebooks = 3 * $5 = $15

Hence the total money spent = $15 + $25x = 15 + 25x

She has only $70, therefore:

15 + 25x ≤ 70

b) Cayla initially has $60.

Cayla is saving $15 per week. Let us assume she saves for x weeks, hence money saved by Cayla = 15x

Therefore the total money saved = 60 + 15x

Since Cayla needs to save atleast $500, hence:

60 + 15x ≤ 500

4.7x 10^-1 as an ordinary number

Answers

0•47 as an ordinary number

ion understand this one ​

Answers

Answer:

angle 7 = angle 3 because corresponding angles r equal

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