find the volume of this figure

Answer:

[tex]4x^2 - 8x + 15 - \frac{78}{4x+5}[/tex]

Step-by-step explanation:

To solve polynomial long division problems like these, it's helpful to build a long division table. Getting used to building these can make problems like this much simpler to solve.

Begin by looking at the first term of the cubic polynomial.

What would we have to multiply [tex]4x + 5[/tex] by to get an expression containing [tex]16x^3[/tex]? The answer is [tex]4x^2[/tex], since [tex](4x + 5) \times 4x^2 = 16x^2 + 20x[/tex].

This is the first step of our long division, and we write out the start of our long division table like this:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,16x^3 + 20x^2\\[/tex]

On the left is the divisor. On top is [tex]4x^2[/tex]. In the middle is the polynomial we are dividing, and on the bottom is the result of multiplying our divisor by

The next step is to subtract the bottom expression from the middle one, like so:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,0x^3 - 32x^2\\[/tex]

We are left with [tex]-32x^2[/tex]. The next thing to do is to add the next term of the polynomial we are dividing to the bottom line, like this:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\[/tex]

Now we return to the beginning of the instructions, and repeat the process: namely, what would we have to multiply [tex]4x + 5[/tex] by to get an expression containing [tex]-32x^2[/tex]? The answer is [tex]-8x[/tex], and we fill out our long division table like so:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2 - \,\,\,\,8x\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 - 40x\\[/tex]

Once again, we subtract the bottom expression from the one above it, and include the next term of the divisor, like so:

[tex]{ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+ 15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\[/tex]

And repeat. What do we multiply [tex]4x + 5[/tex] by to get an expression containing [tex]60x[/tex]? The answer is 15. Our completed long division table looks like this:[tex]{ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\{ }\qquad{ }\hspace{3cm}\,\,\underline{60x + 75}\\{ }\hspace{4.3cm}\,\,-78[/tex]

Now, the expression at the top,

[tex]4x^2 - 8x + 20x + 15[/tex]

is our quotient, and the last number, [tex]-78[/tex], is our remainder.

Hence we arrive at the solution of

[tex]\frac{16x^3-12x^2+20x-3}{4x+5} =4x^2 - 8x + 15 - \frac{78}{4x+5}.[/tex]

Answer:

800 students failed

Step-by-step explanation:

Since 60% passed the class, 40% failed

This means that 40% of the 2,000 students are failures

[tex]\frac{40}{100} (2,000)= 800[/tex]

Answer:

105.7143%

Step-by-step explanation:

pls make me brainliest

Answer:

$13,160

Step-by-step explanation:

5,600*.03=168

168*45= 7,560

5,600+7,560= 13,160

The amount of money in the account of Tom after 3 years with simple interest of 9.5 % is $6135.

Calculating the amount of interest that will be charged on a loan can be done quickly and easily using the simple interest formula. To calculate the simple interest, we need to multiply the principle amount, the number of days between payments (in years), and the interest rate (in decimals).

The formula to calculate Simple Interest is:

SI  = P*I*T

Here, P = Principal amount,

I = interest rate (in  decimals),

T = time duration (in years).

putting the values from question:

SI = 5600 * 0.095*3

Simple Interest = 535

The money in the account will be the sum of principal amount and the simple interest.

Final amount = Principal amount + Simple Interest.

A = 5600 + 535

A = 6135

Therefore, the money in the account after 3 years is $6135 .

To know more about simple interest, go to link

brainly.com/question/2294792

#SPJ2

complete question;

Tom deposits $5,600 into a savings account.  The simple interest rate for the account is 9.5%.  If Tom does not withdraw any money from the account, how much money will be in the account after 3 years?

Answer:

y + 3x = 64

y - 3x = 32

(8,40) is the solution to the system

(Basically A & D)

Step-by-step explanation:

1 large + 3 small = 64 y+3x=64

1 large - 1 small = 32 y-x=32

(12,10) cannot be a solution because the small box (x) holds more than the large box (y).

Substitute (8,40): 40 + 3(8) = 64 and 40 - 8 =32

2.4 x 1/3 = 0.8 liters more.

2.4 + 0.8 = 3.2 liters

Stephen drinks 3.2 liters which is 3,200 milliliters

Answer:

Explanation:

Length: (6x - 7)

Width: (5x + 2)

(6x - 7) (5x + 2)

= (6x + −7)(5x + 2)

(6x)(5x) + (6x)(2) + (−7)(5x) + (−7)(2)

= 30x² + 12x − 35x − 14

- PNW

Answer: 2.2876792e+13

Step-by-step explanation: calculator

Answer:

k/10

Step-by-step explanation:

Quotient of k and 10 simplified to k/10

Answer:

B

Step-by-step explanation:

We see that the line intersects the y-axis at -1.  As a result, we need to choose an equation with -1, either B or C.  We see that the different is the slope.  For choice B, the slope is [tex]\frac{1}{3}[/tex], meaning that every unit up equates to 3 blocks to the right.  Counting along the line, we see that this is correct.

Answer:

1:4

Step-by-step explanation:

Convert 8 pints into cups which we can do this by 8x2=16 we can do this because 1 pint=2 cups. So know we have 4:16 which we can simplify to 1:4

Hope this helps :)

Answer:

11943.31 mg

Step-by-step explanation:

460mg a day per kilo of weight, 4 doses for that total amount

460/4=115mg per kilo per dose

1 kilo = 2.205 pounds

115/2.205=52.15 approx mg per pound per dose

52.15*229=11943.31 approx, which is how much per dose

uwu

Answer:B

Step-by-step explanation:m is the slope and m=-3

Answer:

Your answer is "C"

Step-by-step explanation:

Dont ask me how I know, I just know

No clue why but brainly said I had inappropriate words in my answer so here's a picture

Answer:

-8(3x-8)

Step-by-step explanation:

factor -8 out of -24x+64

Answer:

-8(3x-8)

Step-by-step explanation:

Answer:

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Step-by-step explanation:

r = rate of boat (speed of boat)

t = time

d = distance.

c = rate of current (speed of current)

with the current, the formula becomes (r + c) * t = d

against the current, the formula becomes (r - c) * t = d

going with the current, the boat takes 1 hour to travel 12 miles.

therefore:

(r + c) * t = d becomes (r + c) * 1 = 12

going against the current, the boat takes 1.5 hour to travel the same 12 miles.

therefore:

(r - c) * t = d becomes (r - c) * 1.5 = 12.

your two equations that need to be solved simultancously are:

(r + c) * 1 = 12

(r - c) * 1.5 = 12

divide both sides of the second equation by 1.5 and leave the first equaion as is to get:

r + c = 12

r - c = 8

add the equations together to get:

2 * r = 20

solve for r to get:

r = 20 / 2 = 10

(r + c) * 1 = 12 becomes (10 + c) * 1 = 12

simplify to get 10 + c = 12

solve for c to get c = 12 - 10 = 2

(r - c) * 1 = 8 becomes (10 - c) * 1 = 8

simplify to get 10 - c = 8

solve for c to get c = 10 - 8 = 2

you have:

r = 10

c = 2

that's your solution.

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Answer:

i think it is y=15x-6

Step-by-step explanation:

if it is correct plz plz mark as brainliest

thank you

19NBoli

Answer:

y = 2x-6

Step-by-step explanation:

Slope intercept form:

y = mx+b

m = slope

b = The point where the line crosses the y-axis

So if you put it all together you get the answer of:

y = 2x-6

I hope this helped!

P.S. I am so sorry I couldn't respond earlier :(

Sincerely,

Rekifromsk8theinfinity

:D

Answer:

Step-by-step explanation:

No solution. Lines M and P have the same slope but different y-intercepts., so they are parallel lines.

Parallel lines don’t intersect each other, so there is no solution.

Answer:

2.5

Step-by-step explanation:

Answer:

substitute 11 into the equation:

[tex]\frac{11+44}{2(11)}[/tex] = [tex]\frac{55}{22}[/tex] or 2.5

Answer:

253

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

x + 44/2x

x = 11

Step 2: Evaluate

Step-by-step explanation:

50 * 25 = 1250 square meters

3000 / 1250 = 2.4 meters deep

Answer:

$17.50

Step-by-step explanation:

$18.37=x+5%

18.37=1.05x

18.37/1.05=x

x=$17.50

Slope = change in Y / change in x:

Slope = (5- 5) / (-1 - -9)

Slope = 0/8

Because the change in Y = 0, the slope = 0

Slope = 0

Answer:

0

Step-by-step explanation:

(-9,5) and (-1,5)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(5 - 5) / (-1 - 9)

Simplify the parentheses.

= (0 ) / (-10)

Simplify the fraction.

0/-10

= 0

This is your slope.

This is also a horizontal line, which will have a slope of 0.

Answer:

19 beads

Step-by-step explanation:

If Jennifer has 34$ she automatically loses 5$ because that's the fee for the necklace. So, you subtract 34 from 5 and you get 29. After that you divide 29 by 1.50 and you get 19.333333. But, since you can't get 1/3 of a bead Jennifer can only buy 19 beads.

Answer:

Yeppers Peppers. (That means yes)

Step-by-step explanation:

You did a good job on that. Good work!