How many students play a team sport but do not take dance lessons​

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:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

Step-by-step explanation:

internet.

Answer:

(-3, -1)

(-4, -6)

Step-by-step explanation:

The third quadrant is the bottom left quarter of the coordinate grid, so points with a negative x and a negative y would be in it.

Answer:

What's that in the parentheses.

Step-by-step explanation:

anyways, if the parentheses aren't there, its 10. X=10

If there were parentheses, the answer would be ???????????????????????????????

Answer:

14

Step-by-step explanation:

so it means the opposite of negative 14 which is postive 14

Answer:

I corrected my mistakes.

The discount percentage when the marked price of an article , which is brought it for Rs 1280 is 25% above the cost price should be 12.5%.

Since the cost price is 1280

Now the market price be like

= 1280 + 25% of 1280

= 1600

Now the selling price is

[tex]= 1540\div 1.1[/tex]

= 1400

Now the discount percentage should be

[tex]= (1600 - 1400) \div 1600[/tex]

= 12.5%

hence, The discount percentage when the marked price of an article , which is brought it for Rs 1280 is 25% above the cost price should be 12.5%.

Learn more about discount here: https://brainly.com/question/22227795

Answer:

21/4 or 5 and 1/4 hours

Step-by-step explanation:

3/4 times 7 or 7/1

Hey there! As far as I understand the problem, she made $2,200 in profit. Take 1,375 and multiply it by 1.6.

Answer:

1. 10d + 26

Step-by-step explanation:

Given.

8(2d+3) + 2(-3d+1)

= 16d + 24 - 6d + 2

= 10d + 26

Hope it will help :)

Answer:

the answer to this question is 120km/hr

Answer:

120 km per hour

Step-by-step explanation:

150 / 1.25 = 120 km per hour

Answer:

y = 44°

Step-by-step explanation:

= 180 - 88

= 92°

y + y + 92° = 180°

2y = 180° - 92°

2y = 88°

y = 88/2

y = 44°

Answer: y=0.25

Step-by-step explanation: 1.2 / 4.8 = 0.25

Answer:

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-6*x-(84)=0

Step by step solution :

STEP 1: Pulling out like terms

1.1     Pull out like factors :

  -6x - 84  =   -6 • (x + 14)

Equation at the end of step 1:

STEP 2: Equations which are never true

2.1      Solve :    -6   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    x+14 = 0

Subtract  14  from both sides of the equation :

                     x = -14

One solution was found :

x = -14

Answer: i think u should divide 84 by 6 to keep x alone the answer is x=14

but the answer depends on the sign of the variable .

Step-by-step explanation:

Answer: 10 pounds

Step-by-step explanation:

16      ?  

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

20     12.50

Step 1: 16x12.50= 200

Step 2: 200/20= 10

Answer:

1. 25

2. 9

Step-by-step explanation:

If I'm correct, to complete the square you need to use [tex](\frac{b}{2} )^{2}[/tex]

So, for #1, b is 10. [tex]\frac{10}{2}[/tex] = 5. [tex]5^{2}[/tex] = 25.

For #2, b is -6. [tex]\frac{-6}{2}[/tex] = -3. [tex]-3^{2}[/tex] = 9.

Answer:

20c

Step-by-step explanation:

C represent the chocolate Mason brought. Cameron brought 20 times as many chocolates. This means that however many chocolates Mason brought, Cameron has 20 times more than what Mason brought. So meaning we can this equation as

[tex]20c[/tex]

Answer:

1198

Step-by-step explanation:

241+89+802+66

330+802+66

1132+66

1198

Answer:

2,000

Step-by-step explanation:

6f+21=-15

6f+21-21=-15-21

6f=-36

6f/6=-36/6

f=-6

Answer: f=-6

Step-by-step explanation:

Answer:

Is there a question?

Step-by-step explanation:

Answer:

To calculate [tex]r[/tex], calculate the quotient of two consecutive terms.

[tex]r = \frac{\frac{2(n+1)!}{2^{2(n+1)}}}{\frac{2n!}{2^{2n}}}= \frac{n+1}{4}[/tex]

For all [tex]n \ge 4[/tex], [tex]r>1[/tex], so the series converges, as the series grows (even more than) exponentially.

Answer:

[tex]Factor = 220 \%[/tex]

Step-by-step explanation:

Given

[tex]Initial = 2\frac{1}{2}[/tex]

[tex]Final = 5\frac{1}{2}[/tex]

Required

Determine the factor of increment

First, we calculate the percentage increment

[tex]\% Increment = \frac{Final - Initial}{Initial} * 100\%[/tex]

Substitute values for Final and Initial

[tex]\% Increment = \frac{5\frac{1}{2} - 2\frac{1}{2}}{2\frac{1}{2}} * 100\%[/tex]

Express fractions as decimals

[tex]\% Increment = \frac{5.5 - 2.5}{2.5} * 100\%[/tex]

[tex]\% Increment = \frac{3}{2.5} * 100\%[/tex]

[tex]\% Increment = \frac{3* 100}{2.5} \%[/tex]

[tex]\% Increment = \frac{300}{2.5} \%[/tex]

[tex]\% Increment = 120 \%[/tex]

So, the factor of increment is:

[tex]Factor = 100\% + Increment[/tex]

[tex]Factor = 100\% + 120 \%[/tex]

[tex]Factor = 220 \%[/tex]

Answer:

5 over 4,

5(numerator)

4(denominator)  

and you can not reduce 5:4 to lowest terms because it is already at it's lowest.

Step-by-step explanation:

can i get brainiest?

Step-by-step explanation:

-4x+5>-5

    -5   -5

-4x>-10

/-4   /-4

x<2/5

You switch the sign whenever you divide a negative. In this case, we did, so instead of it being x>2/5, the answer is x<2/5.

hope it helps! :3

Answer:

x<5/2

Step-by-step explanation:

Answer:

[tex]volume = 927,587.2ft^3[/tex]

Step-by-step explanation:

The equation to find the volume of a sphere is as follows:

[tex]volume = \frac{4}{3}\pi r^3[/tex]

We have a radius of 60.5ft, let's plug this into the equation and solve:

[tex]volume = \frac{4}{3} \pi (60.5)^3 \\volume = 927,587.17\\volume = 927,587.2[/tex]

Therefore, the volume of a sphere with a radius of 60.5ft is 927,587.2ft^3.

Hope this helps!!

- Kay :)

Volume of the sphere is 927587.2 cubic feet (nearest tenth).

"A sphere is a set of points in space that are a given distance r from the center. The volume of a 3 -dimensional solid is the amount of space it occupies."

Formula to find the volume of a sphere

Volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

V = [tex]\frac{4}{3} \pi (60.5)^{3}[/tex]

V = 927,587.167

Using calculator, we get

V ≅ 927587.2 cubic feet

Hence, Volume of the sphere is 927587.2 cubic feet (nearest tenth).

Learn more about volume of a sphere here

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