the volume of a swimming pool is 4x^3 - 20x^2 + 3x - 15 . what is one of the dimensions of the pool

Answers

Answer 1

Answer:

[tex]Height = x - 5[/tex] --- one of the dimension

Step-by-step explanation:

Given

[tex]Volume = 4x^3 - 20x^2 + 3x - 15[/tex]

Required

The side dimension

Factorize the given expression

[tex]Volume = 4x^2 (x- 5) + 3(x - 5)[/tex]

Factor out x - 5

[tex]Volume = (4x^2 + 3)(x - 5)[/tex]

Volume is the product of base area and height'

Hence:

[tex]Area = 4x^2 + 3[/tex]

[tex]Height = x - 5[/tex]


Related Questions

Chase took a taxi from his house to the airport. The taxi company charged a pick-up fee of $1.20 plus $4.75 per mile. The total fare was $48.70, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride. write the equation

Answers

48.70=1.20+4.75x is the equation for this problem

8. If a prism is 15cm high with its base a triangle having sides 6cm, 8cm and 10cm. Find its volume. (a) 350cm (b) 30cm (c)460cm3 (d)90cm3

Answers

Answer:

360cm³

Step-by-step explanation:

Volume of a triangular prism = Base area * Height of prism

Height of prism = 15cm

Base area = 1/2 * 6 * 8

Base area = 24cm²

Volume of the prism = 15 * 24

Volume of the prism = 360cm³

Can someone help me with this question? Will give brainliest.

Answers

Answer:

5.2561

step by step explanation:

using BODMAS, multiplication comes before addition.

Therefore,

[tex] \sqrt{1.13 + (2.84 \times 9.33)} [/tex]

[tex] \sqrt{1.13 + 26.4971} [/tex]

[tex] \sqrt{27.6272} [/tex]

Therefore the answer is

5.2561

3. A straight line passes through two points with
coordinates (6,8) and (0,5).
Work out the equation of the line.

Answers

Answer:

Step-by-step explanation:

Find the slope of the line

(x₁ , y₁) = (6 , 8)   & (x₂ , y₂) = (0 , 5)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{5-8}{0-6}\\\\=\frac{-3}{-6}\\\\=\frac{1}{2}[/tex]

m = 1/2  ;(x₁ , y₁) = (6 , 8)

y - y₁ = m(x - x₁)

[tex]y - 8 = \frac{1}{2}(x - 6)\\\\y - 8 =\frac{1}{2}x -\frac{1}{2}*6\\\\y - 8 =\frac{1}{2}x- 3\\\\y = \frac{1}{2}x - 3 + 8\\\\y = \frac{1}{2}x + 5[/tex]

Please help explanation if possible

Answers

Answer: x = 2 and y = -4

x + 2y = -6

x = -6-2y

Putting this in value of x in

6x + 2y = 4

6(-6-2y) + 2y = 4

-36-12y+2y = 4

-10y = 4+36

y = 40/(-10)

y = -4

Now putting this value of y in

x + 2y = -6

x + 2(-4) = -6

x -8 = -6

x = -6+8

x = 2

Therefore x = 2 and y = -4

If we put these values we can check this

x + 2y = -6

2 + 2(-4) = -6

2 -8 = -6

-6 = -6

please click thanks and mark brainliest if you like :)

find x:
x+2y= -6 => 2y= -6-x
so substitute 2y into the equation 6x+2y=4
=> 6x-6x-x=4
x=2
find y:
6(2) + 2y= 4
y= -4

-there u go! :)

Tính giá trị của I = [tex]\lim_{x \to \infty}[/tex] ([tex]\frac{4^{n} - 5.3^{n} + 1}{2.4^{n} + 2}[/tex])

Answers

I assume you're supposed to find the limit as n approaches infinity, not x.

You have

[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5.3^n+1}{2.4^n+2} = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-\left(\dfrac{5.3}{5.3}\right)^n+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}} \\\\ = \lim_{n\to\infty}\frac{\left(\dfrac4{5.3}\right)^n-1+\dfrac1{5.3^n}}{\left(\dfrac{2.4}{5.3}\right)^n+\dfrac2{5.3^n}}[/tex]

For |x| < 1, we have lim |x|ⁿ = 0 as n goes to infinity. Then each exponential term converges to 0, which leaves us with -1/0. This means the limit is negative infinity.

On the other hand, perhaps you meant to write

[tex]\displaystyle \lim_{n\to\infty}\frac{4^n-5\times3^n+1}{2\times4^n+2}[/tex]

The same algebraic manipulation gives us

[tex]\displaystyle\lim_{n\to\infty}\frac{\left(\dfrac44\right)^n-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2\left(\dfrac44\right)^n+\dfrac2{4^n}} = \lim_{n\to\infty}\frac{1-5\left(\dfrac34\right)^n+\dfrac1{4^n}}{2+\dfrac2{4^n}}[/tex]

Again the exponential terms converge to 0, but this time we're left with the limit 1/2.

Xochitl went to the store to buy some cherries. The price per pound of the cherries is $4 per pound and she has a coupon for $3.50 off the final amount. With the coupon, how much would Xochitl have to pay to buy 3 pounds of cherries? Also, write an expression for the cost to buy pp pounds of cherries, assuming at least one pound is purchased

Answers

Answer: Xochitl pay 8.5$ for 3 pound of cherries

Explanation:

4$ per pound
3.5$ coupon

If he buy 3 pound he would need to pay 12$ but since he a 3.5$ coupon thus 12 - 3.5 = 8.5$

Can also written as an expression:

4x - 3.5 = x

Where x determine the amount of pound that is bought.


Xochitl needs to pay $8.50 to buy 3 pounds of cherries.

The expression for the cost to buy p pounds of cherries would be

$(4p - 3.50)

What is an equation?

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, The price per pound of the cherries is $4 per pound and she has a coupon for $3.50 off the final amount.

Therefore, The cost of 3 pounds of cherries before the discount would be,

= $(3×4).

= $12.

And after the discount, it would be $(12 - 3.50).

= $8.50.

An expression for the cost to buy p pounds of cherries would be,

= $(4p - 3.50)

learn more about equations here :

https://brainly.com/question/29657992

#SPJ2

Help me pleaseeeeeee

Answers

Answer:

Step-by-step explanation:

6. Yes: these two angles are opposite 2 equal line.

7. No: We don't know that AC bisects <JAD

8. No: We don't know that JCA or DCA are right angles.

9. Yes. Both angles have AC in common. JD is a straight line which has 180 degrees. AC intersects a JD and creates 2 angles. We know their total but not their equality.

10. Yes. They are given as equal.

Not everything you see is true just because it looks that way.

I need help!!! Need it asap!!!!!

Answers

Answer:

Not enough infomation, you need to provide #12

Step-by-step explanation:

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER

Answers

The answer would be 66km³

Answer:

V=l×w×h

so the answer is 66km

11×2×3=66

Determine what type of model best fits the given situation: A retirement account that is expected to

grow by $1,000 per year.

Answers

Answer:

Step-by-step explanation:

If the account grows steadily, this is a linear representation, where the constant, steady growth translates to the slope of a line.

Write an equation of the graph (shown below) in slope intercept form.

Answers

This is not a valid question and, therefore, cannot be answered. (Reason: No graph is attached.) Try revising it or giving more information. Hope this helps! ❤️

hello could you please help me with this math problem with full explanation which I am unable to solve? Thanks a lot.

Answers

Area of a square is side^2

Diagonal of a square is sqrt(2) x side

Using this rewrite the area formula as :

1/2 x diagonal^2

Area = 1/2 x 40^2 = 800

Area = 800 m^2

Answer = b) 800m^2

A triangle can have at most___ right angle
О
2
4
1

Answers

a right angle can have at least 2

What is a simplified form of 1 − sin^2 θ?

Answers

Answer:

cos^2(θ)

Step-by-step explanation:

Ayuda plis..
5 (2x+3) - 4x= - 4 +3 (x-4)

Answers

Answer:

x=- 31/3

Step-by-step explanation:

distribute 5(2x+3)-4x=-4+3x(x-4)

10x+15-4x=-4+3(x-4)

combine like terms

distribute

Click on the graphic to select the figure that would make the following "a reflection in line k."

Answers

Answer: Choice A (both are smiley faces)

This is because the reflection doesn't flip the faces upside down or anything (instead it does a left-right swap in a way). This is why both faces are smiley faces.

Algebraic math question

Answers

Answer:

[tex] 7 \: {ft}^{2} [/tex]

Step-by-step explanation:

Area of the trapezoidal table

[tex] =\frac{1}{\cancel 2}(4 + 3)\times \cancel 2[/tex]

[tex] = 7 \: {ft}^{2} [/tex]

Answer:

7 ft squared

Step-by-step explanation:

Area of the trapezoidal table

Find derivative of 3x^2+4 using limits

Answers

The derivative of a function f(x) is defined as

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h[/tex]

For f(x) = 3x ² + 4, we have

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{(3(x+h)^2+4) - (3x^2+4)}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{(3(x^2+2xh+h^2) - 3x^2}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}\frac{6xh+3h^2}h[/tex]

[tex]f'(x)=\displaystyle\lim_{h\to0}(6x+3h) = \boxed{6x}[/tex]

Find the slope of the line that passes through the points (-12,10) and (-18,14).


PLEASE HELP ASAP

Answers

Answer:

-2/3

Step-by-step explanation:

The slope is -2/3 because the slope formula, y2-y1/x2-x1

[tex]\huge\text{Hey there!}[/tex]

[tex]\boxed{\huge\boxed{\mathsf{Formula: m = \dfrac{y_2- y_1}{x_2- x_1}}}}[/tex]

[tex]\boxed{\huge\boxed{\mathsf{m = \dfrac{14 -10}{-18 - (-12)}}}}\\\\\\\huge\textsf{14 - 10 = \bf \boxed{\bf 4}}\\\\\\\huge\textsf{-18 - (-12)}\\\huge\textsf{= -18 + 12}\\\huge\textsf{= \bf -6}\\\\\boxed{\huge\boxed{\mathsf{m = \dfrac{4}{-6}}}}[/tex]

[tex]\boxed{\huge{\boxed{\mathsf{m = \dfrac{4\div2}{-6\div2}}}}}\\\\\huge\boxed{\mathsf{4\div2 = \bf 2}}\\\huge\boxed{\mathsf{-6\div2 = \bf -3}}\\\\\\\boxed{\boxed{\huge\boxed{\mathsf{\star m = \bf \dfrac{2}{-3}\star}}}}[/tex]

[tex]\boxed{\boxed{\huge \boxed{\mathsf{Answer: }\frak{\dfrac{2}{-3}}}}}\huge\checkmark[/tex]

[tex]\huge\boxed{\frak{Good\ luck\ on\ your\ assignment\ \& \ enjoy \your \ day!}}[/tex]

~[tex]\rm{Amphitrite1040:)}[/tex]

Help anyone can help me do this question,I will mark brainlest.​

Answers

Answer:

Question 3: 220 centimeters

Question 4: 31.4 millimeters

Step-by-step explanation:

Question 3:

Formula for circumference: 2πr

2πr

Exchange π for 22/7

2 · (22/7) · r

Exchange r (radius) for 35

2 · (22/7) · 35

Simplify:

2 · (22/7) · 35

44/7 · 35

220; 220 centimeters

Question 4:

Formula for circumference: 2πr

2πr

Exchange π for 3.14

2 · 3.14 · r

Exchange r (radius) for 5

2 · 3.14 · 5

Simplify:

2 · 3.14 · 5

6.28 · 5

31.4; 31.4 millimeters

Answer:

220 cm31.4 mm

Step-by-step explanation:

Concept:

Here, we need to know the idea of circumference.

The circumference is the perimeter of a circle. The perimeter is the curve length around any closed figure.

Circumference = 2πr

Solve:

Question # 1

r = 35 cm

π = 22/7

Circumference = 2πr

Circumference = 2 (22/7) (35)

Circumference = 2 (110)

Circumference = 220 cm

Question # 2

r = 5 mm

π = 3.14

Circumference = 2πr

Circumference = 2 (3.14) (5)

Circumference = 10 (3.14)

Circumference = 31.4 mm

Hope this helps!! :)

Please let me know if you have any questions

what is the relation that represents the relation

Answers

Answer:

what can i help u with

Step-by-step explanation:

I really can't help u with that sorry i am bad at math

Help pleaseeeee:)))))))

Answers

5 by 3

3rd one

there we have to find hypotenuse.

Answer:

+- 5/3

Step-by-step explanation:

When we construct a right triangle with legs with length 3 and 4. The hypoteneuse must 5. Since tan(x) = opp/adj = 4/3 and sec(x) = hyp/adj,

We get the answer to be 5/3. Now there is a +- there because if we use the unit circle, if we take the point (-3, -4), we get tan(x) = (-4/-3) = 4/3. However, the hypoteneuse for sec(x) is always positive so sec(x) = 5/-3 = -5/3.

That is why there are two solutions, one with the terminal arm in Q3 and one in Q1. But that's the explanation using the unit circle.

ASAP!!!!!!!!!!
What is the line of symmetry for the graph of y = -3x^2 + 12x - 11?
wrong= reported
ty<3

Answers

Answer:

line of symmetry is : x=2

Step-by-step explanation:

Answer:

Thus, the required line of symmetry is x = 2.

Step-by-step explanation:

The length of a rectangular field is 6 metres longer than its width. If the area of the field is 72 square metres, What are the width and the length of the field?​

Answers

Answer:

Let's call the length of the field "l", and the width of the field "w".

If the area of the field is 72 square meters, then we have:

l x w = 72

And if the length is 6 meters longer than the width, we have:

l = w+6

So looking at the first equation (l x w = 72), we can substitute the l for a w+6.

And we obtain:

(w+6) x (w) = 72

Which simplifies to w^2 + 6w = 72.

This quadratic equation is pretty easy to solve, you just need to factor it.

w^2 + 6w - 72 = 0

(w-6)(w+12)

This leaves the roots of the  quadratic equation to be 6 and -12, but in this case, a width of -12 wouldn't make sense.

So, the width of the rectangular field is 6, and the length of the field is 12.

Let me know if this helps!

Answer:

we assume one side is x and other side must be x+6 and when we multiple it together we can find x²+6x =72

Step-by-step explanation:

one side is 6 and. other is 12 so the lenght= 12 the width=6

15x + 14 = 149


Plz solve for x

Answers

Answer:

x = 9

Step-by-step explanation:

When doing these types of problems, the main goal is to get the variable by itself. Its kind of hard to explain with words so I will just use numbers.

15x + 14 = 149

(Subtract 14 on both sides. Remember, when you do something (Like subtracting, adding, etc.) on one side you have to do it to the other.)

15x + 14 = 149

       -14 =  -14

---------------------------

15x = 135

(Divide 15 on both sides. Since we need to use inverse operation to cancel the 15 out, we would divide 15 on both sides.)

15x/15 = 135/15

x = 9

Hope this helps :)

Answer:

x=9

Step-by-step explanation:

[tex]\sf 15x + 14 = 149[/tex]

[tex]\sf 15x+14-14=149-14[/tex]

[tex]\sf 15x=135[/tex]

[tex]\sf \cfrac{15x}{15}=\cfrac{135}{15}[/tex]

[tex]\sf x=9[/tex]

What is the equation of the line that passes through (-1, 5) and (3, -7)?

Answers

Answer:

[tex] 3x + y = 2 [/tex]

Step-by-step explanation:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 5 = \dfrac{-7 - 5}{3 - (-1)}(x - (-1)) [/tex]

[tex] y - 5 = \dfrac{-12}{4}(x + 1) [/tex]

[tex] y - 5 = -3(x + 1) [/tex]

[tex] y - 5 = -3x - 3 [/tex]

[tex] 3x + y = 2 [/tex]

The topic= Direct and Inverse Proportions
It is given that y is directly proportional to x and y=36 and when x=12
(a)
An equation connecting to x and y

(b)
That value of y when x=5

(c)
The value of x when y=12

Please help me answer my hw, thank you!

Answers

Answer:

A) 3

B)60

C)4

Step-by-step explanation:

y = kx

36 = 12k

A)k=3

~~~~~~~~~~

b) 60

12*5

c) 4  

12/3

Can somebody help me PLEASE IM BEGGING YOU !!

Answers

Answer:

37

Step-by-step explanation:

360 -(110+110+66) = 74

74/2 = 37

A fruit stand has to decide what to charge for their produce. They decide to charge \$5.30$5.30dollar sign, 5, point, 30 for 111 apple and 111 orange. They also plan to charge \$14$14dollar sign, 14 for 222 apples and 222 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

Answers

Answer:

a + b = 5.30

a + b = 7

No

Step-by-step explanation:

Expressing the information as system of linear equation :

Let apples = a, oranges = b

If $5.30 is charged for one apple and one orange, then we have ;

a + b = 5.30 - - - (1)

If $14 is charged for 2 apples and 2 oranges, then we have ;

2a + 2b = 14 - - - - (2)

a + b = 7

Since both equations gives varying combined cost for equal amount of the fruit, then a unique cost cannot be obtained for each fruit from the systems of equation using simultaneous equation process.

From (1)

a = 5.30 - b

Put a = 5.30 - b in (2)

2(5.30 - b) + 2b = 14

10.6 - 2b + 2b = 14

10.6 = 14 - - - - - (variables cancels out).

Answer:No the System has no solution

Step-by-step explanation:

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