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

Answer:

[tex]2(6 + 4) - 3(5) \\ 12 + 8 - 15 \\ = 5[/tex]

Answer:

1

Step-by-step explanation:

2*6+4-3*5

12+4-15

16-15

1

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to simplify:

[tex]\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}[/tex]

First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:

[tex]\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}[/tex]

Now, create a common denominator. To do this, we can multiply the first term by (a + 1) and the second term by (a + 2). Hence:

[tex]\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}[/tex]

Add the fractions:

[tex]\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}[/tex]

Factor:

[tex]\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}[/tex]

Simplify:

[tex]\displaystyle =\frac{a+4}{(a-1)(a+1)}[/tex]

We can expand. Therefore:

[tex]\displaystyle =\frac{a+4}{a^2-1}[/tex]

Problem 2)

We want to simplify:

[tex]\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}[/tex]

Again, let's create a common denominator. First, let's factor out a negative from the second term:

[tex]\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}[/tex]

Now to create a common denominator, we can multiply the first term by (a - c) and the second term by (a - b). Hence:

[tex]\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}[/tex]

Subtract the fractions:

[tex]\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}[/tex]

Distribute and simplify:

[tex]\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}[/tex]

Cancel. Hence:

[tex]\displaystyle =\frac{1}{(a-b)(a-c)}[/tex]

Please find attached photograph for your answer.

Hope it helps

Do comment if you have any query

Answer:

24

Step-by-step explanation:

The greatest number of trays the caterer can split the 72 ham sandwiches  and 48 pimento cheese sandwiches into can be determined by calculating the highest common factor and 48 and 72

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.

the highest common factor is 48 ad 72 is 24

Answer:

B: Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.

D: Jorge will not move any point that lies on the line of reflection.

E: Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.

Step-by

i just took the test lol

Answer:

BDE are the answeres

Step-by-step explanation:

took the quiz

Answer:

1026

Step-by-step explanation:

Common difference = d = 2nd term  - first term

 d = -3 - (-11) = -3 +11 = 8

First term = a = -11

First we need to find the number of terms in this series

[tex]a_{n} = 125\\\\a + (n- 1)d = a_{n}\\\\[/tex]

-11 + (n- 1) * 8 = 125

 (n-1)*8 = 125 + 11

 (n-1) * 8 = 136

n -1 = 136/8

n -1 = 17

  n = 17+1

 n = 18

[tex]S_{n} =\frac{n}{2}(a+a_{n})\\\\S_{18} =\frac{18}{2}(-11+125)\\\\[/tex]

   = 9 * 114

   = 1026

Answer:

C

Step-by-step explanation:

They are the same without rotation and translation

Step-by-step explanation:

The second equation

[tex]2.4x = 1.2x + 15[/tex]

is the answer for the 1st picture.

2nd, solve for x.

[tex]1.2x = 15[/tex]

[tex]x = 12.5[/tex]

You cant create half a page so let lower it down to 12.

12 is the answer for the second answer.

Answer:

24

Step-by-step explanation:

p/2 = 12.

To leave the p alone, multiply 2 from both sides.

p = 24

Answer:

c

Step-by-step explanation:

Answer:

6) [tex]x^2 -4x+1[/tex]

7)   26x-1y +4z

Step-by-step explanation:

long division

      ____[tex]x^{2}[/tex]__-4x__+1____

x-2 | [tex]x^3-6x^2+9x-2[/tex]

  -    [tex]x^3-2x^2[/tex]

       -----------

             [tex]-4x^2+9x[/tex]

             [tex]-4x^2+8x[/tex]

        ----------------

                x-2

                x-2  

Answer:

speed=distance / time

speed=(4/3) / (1/10)

speed=13.33miles per hour

Answer:

the fourth option

Step-by-step explanation:

1/2x - 2y > -6

1/2x + 6 > y

or

y < 1/2x + 6

so, the solution is all the y values smaller (= below) the line function.

and because it is "<" and not "<=" the line itself is not included

Answer:

y = 7x and y = 28

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 56 when x = 8 , then

56 = 8k ( divide both sides by 8 )

7 = k

y = 7x ← equation of variation

When x = 4

y = 7 × 4 = 28

Answer:

hey mate

plz mark it as brainliest

Answer:

hope this will help you more

Step-by-step explanation:

hope it is helpful to you

stay safe healthy and happy

Answer:

y = 2x - 7

Step-by-step explanation:

(1,-5) (2,-3)

y2 - y1 / x2 - x1        -3 - (-5) / 2 - 1     2/1       = 2

y = 2x + b

-3 = 2(2) + b

-3 = 4 + b

-7 = b

Answer:

hope that is helpful

Step-by-step explanation:

W= VI

W= VI

I. I

V= W

I

Answer:

V = [tex]\frac{W}{I}[/tex]

Step-by-step explanation:

Given

W = VI ( isolate V by dividing both sides by I )

[tex]\frac{W}{I}[/tex] = V

Answer:

I believe it would be A 3^2(2-sqr2)

Step-by-step explanation:

x+35+25=180

x+60 =180

x = 120.

y+x =18

Answer:

A 2,3,6 :)

Step-by-step explanation:

thats answer corect me if im wrong hope it help

Answer: Using the formula

V=πr2h

3

Solving for h;

h=3V

πr2=3·308

π·72≈6.00241cm

Step-by-step explanation:

Answer:

last one

y = [tex]\frac{1}{5}[/tex]x

Step-by-step explanation:

slope = [tex]\frac{3-0}{15-0}[/tex] = [tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]

y- intercept is 0

A is the correct answer since x=15

Answer:

A≈102.79

Step-by-step explanation:

The formula for area of a circle is πr² so we need to substitute the r by 5.72.

π×5.7² = 102.79 m²

Answer:

Approximately 102.79 meters squared

Step-by-step explanation:

pi times 5.72 meters squared

Hope this helps!

Answer:there’s needs to be an image

Step-by-step explanation:

Answer:No

Step-by-step explanation:

To check:put value of m and n in both equations

Answer: n=2 and m=1

Step-by-step explanation:

m+3n=7 , 5m-n=3

m=7-3n => 5(7-3n)-n=3

=> 35-15n-n=3

=> -16n=-32

=> n=2

n=2 => 5m-2=3

=> m=1

9514 1404 393

Answer:

  A. subtraction

  B. division

  C. multiplication

  D. addition

Step-by-step explanation:

Observe what is done to the variable. Choose the operation that turns the unwanted value into the appropriate identity element.

A. 3.75 is added. To make that value be 0, we subtract 3.75.

B. -3 is multiplied. To make that value be 1, we divide by -3.

C. m is divided by 5. To make that 1/5 multiplier be 1, we multiply by 5.

D. 4 is subtracted. To make that value be zero, we add 4.

_____

Additional comment

Since subtraction is the same as addition of the opposite, and division is the same as multiplication by the reciprocal, the only two properties we really need are the addition property and multiplication property. Your grader may disagree.

Answer:

Other dude is right.

Step-by-step explanation:

Be safe, have an amazing day. :)

Answer:

[tex]896 \pi~m^3[/tex]

Step-by-step explanation:

[tex] V_{cylinder} = \pi r^2 h [/tex]

[tex] V_{cylinder} = \pi (8~m)^2 \times (14~m) [/tex]

[tex]V_{cylinder} = 896 \pi~m^3[/tex]

Answer:

A, B, D, E

Step-by-step explanation:

[tex]\sqrt{81}[/tex] = ± 9 → D and E

Since 9 × 9 = 81 and - 9 × - 9 = 81

[tex]81^{\frac{1}{2} }[/tex] = [tex]\sqrt{81}[/tex] = 9 → B

- [tex]81^{\frac{1}{2} }[/tex] = - [tex]\sqrt{81}[/tex] = - 9 → A