There are 30 runners in a cross country race. How many different groups of runners can finish in the top 3 positions

 The greatest common factor is the biggest number that divides evenly into each one of the numbers without a remainder...the only thing that's different about our situation is that we have variables in addition to regular number (but the same logic applies...we need to find the biggest variable that goes into k^4 , k^3 , and k^2 ).

The biggest number that goes into 15, 35 and 20 is the number 5. The biggest variable that goes into k^4 , k^3 , and k^2 is k^2

Combining the number and the variable, we get that the greatest common monomial factor is 5k^2

Since area is length x width, and we just figured out that width is 5k2 , all we have to do to find length is divide 15k4+35k3+20k2 by 5k2 , and we get that the length is 3k^2+7k+4

So the width is 5k^2 and the length is 3k2+7k+4

:))

-Eli

Answer:

A

Step-by-step explanation:

vol of a cylinder = pie* r^2×h

r= 5

h= 9

......vol= 9×5^2 pie= 225pie units ^3

Answer:

21u-16v+18w

Step-by-step explanation:

(7u-4v+4w) 14u-12v+14w

21u-16v+18w

Answer:

= 21u−16v+18w

Step-by-step explanation:

Let's simplify step-by-step.

7u−4v+4w−2(−7u+6v−7w)

Distribute:

=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)

=7u+−4v+4w+14u+−12v+14w

Combine Like Terms:

=7u+−4v+4w+14u+−12v+14w

=(7u+14u)+(−4v+−12v)+(4w+14w)

=21u+−16v+18w

Answer:

=21u−16v+18w

Answer:

120

Step-by-step explanation:

90→75%

X→100%

⇒X=(90×100)÷75=120

Before the price reduction, the cost was 120 dollar.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that shop advertises 25% off its prices in a sale a dress is 90% .

Here 90 percent is equivalent to 75%

Let X = 100%

So,X=(90×100)÷75

x =120

The price was 120 dollar.

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Answer:

The point-slope form of an equation of the line through the points (-7, 7) and (4,1):

(y - 7) = m(x + 7)

or

(y - 1) = m(x - 4)

with

m = (1 - 7)/(4+7) = -6/11

Answer:

y=-6/11 x +35/11

Step-by-step explanation:

(-7, 7) and (4,1)

m=y2-y1/x2-x1

m=1-7/4-(-7)

m=-6/11

y=mx+b     take one point(4,1) to find b

1=-6/11(4)+b

1=-24/11 +b

b=1+24/11

b=(11+24)/11

b=35/11

y=-6/11 x +35/11

==================================================

Explanation:

The weird or fancy looking E symbol is the greek uppercase letter sigma. It is effectively the english version of S to represent summation. So we add up all the [tex](x-\overline{x})^2[/tex] terms to get this. Luckily this has already been done for us in the table where they wrote "sum = 34", so [tex]\sum(x-\overline{x})^2 = 34[/tex]

From here, we substitute this into the formula, along with n = 5 since there are 5 items in the original list

So,

[tex]s = \sqrt{\frac{1}{n-1}\sum(x-\overline{x})^2} \\\\s = \sqrt{\frac{1}{5-1}*34} \\\\s = \sqrt{\frac{1}{4}*34} \\\\s = \sqrt{0.25*34} \\\\s = \sqrt{8.5} \\\\s \approx 2.91547594742266 \\\\s \approx 2.9 \\\\[/tex]

This computes the sample standard deviation. To get the population standard deviation, you'd basically change the "n-1" to simply "n", and the rest of the formula is identical.

Answer:

You could approximate pi to be 3.14, and divide that by 6.

Step-by-step explanation:

Answer:

30 degrees

Step-by-step explanation:

If π/6 is an angle in radians

So, Converting it into degrees will make :

=> π/6 * 180 => 30 degrees

Answer:

y=2 is the correct ans.

here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.

we have, equn of st line parallel to y xaus is y= b

so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).

Answer:

The rate of change is -0.75

Step-by-step explanation:

For each unit of t the volume of water is decreasing by 0.75.

At t=13.333 the volume of water is 0. at t=0 the volume of water is 10

Hope this helps

Answer:

Step-by-step explanation:

Given the following;

cosθ=8/17 and sinθ=−15/17

In trigonometry identity, tanθ = sinθ/cosθ

Substituting the given values in the equation;

tan θ = (−15/17)/(8/17)

tanθ = −15 /17 * 17/8

tanθ = -15/8

Answer:

D. -15/8

Step-by-step Explanation

Answer:

Option (A)

Step-by-step explanation:

Parent function (in red) graph is represented by,

f(x) = x²

If this function is translated by 'a' units to the right, rule to be followed,

f(x) → f(x - a)

If the parent function is shifted by 4 units to the right (blue graph), the new function will be,

g(x) = f(x - 4)

g(x) = (x - 4)²

Therefore, Option (A) will be the correct option.

Answer:

The area of the sector is 21.39 cm^2

Step-by-step explanation:

Mathematically, to calculate the area of a sector, the formula to use is;

A = Theta/360 * pi * r^2

where Theta is the angle subtended at the center of the circle = 50 degrees

r is the radius of the circle = 7cm

pi = 22/7

Substituting these values into the area of sector equation, we have;

A = 50/360 * 22/7 * 7 * 7 = (5 * 22*7 )/36 = 21.39 cm^2

Answer:

A.) 2000N

B.) 0

C.) 1414.2 N

Step-by-step explanation:

Given that the force on the rope = 1000N

A.) If the two students pull in the same direction, the resultant force will be addition of the two forces. That is

1000 + 1000 = 2000 N

B.) If the two students pull in the opposite direction, the resultant force will be sum of the two forces equal to zero. That is,

F1 + F2 = 0

F1 = positive 1000N

F2 = negative 1000N

Therefore, 1000 - 1000 = 0

The resultant force of the two forces is zero.

C.) If the two forces are at right angles, south and east to each other, the resultant force R will be achieved by using pythagorean theorem.

R = sqrt( 1000^2 + 1000^2 )

R = sqrt( 2000000 )

R = 1414.2 N

The resultant force of the two forces will be 1414.2N

Answer:

The 18th term of the sequence is -117.

Step-by-step explanation:

The given sequence is 2,-5,-12,-19

From this AP,

First term, a = 2

Common difference, d = -5-2 = -7

It is required to find the 18th term of the sequence. The nth term of an AP is given by :

[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]

So, the 18th term of the sequence is -117.

Answer:

-8

Step-by-step explanation:

Hope it helps you.

Can you mark my answer as a Brainliest Please

Answer:

The answer is option A. 2x - 3

The expression 3x - 4 is subtracted from

5x - 7 is written as

5x - 7 - (3x - 4)

= 5x - 7 - 3x + 4

= 2x - 7 + 4

= 2x - 3

Hope this helps

Answer:

C)you must be no older than 13 to play the game.

Step-by-step explanation:

≤this means equal to or less than which in this case is 13

The situation represented by the inequality g ≤ 13 will be option C. You must be no older than 13 to play the game.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the inequality is g ≤ 13.

The inequality can be represented by the situation you must be no older than 13 to play a game.

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Answer:

£14.29

Step-by-step explanation:

0.98x=14

x=14.29

Answer:

14.28

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

The inequality states that the amount that Yvonne drives is more than 540 miles.  Since h represents the number of hours, we know that 69 probably means the number of miles Yvonne can drive per hour.  Finally, 126 shows the amount of miles that Yvonne has already driven.

Answer:

[tex] \sqrt{ {2}^{5} } [/tex]

Step-by-step explanation:

[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]

Answer: false

Step-by-step explanation: A line segment may not have more than one midpoint.

Answer:

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

Answer:

Range = [5, ∞)

Step-by-step explanation:

The initial  number of snakes is 5 and it is increasing at a high rate so the maximum number is infinite. The population is increasing exponentially according to the equation  P = 5(2)^t  where t = the number of years.

solution,

X=5

[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]

hope this helps...

Good luck on your assignment..

Answer:

When x=5

Y=(5+9)÷(5-3)

= 14 ÷2

= 7

Answer: a simple interest rate of 3.2% will be the better deal.

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:  

A = P (1 + r/n) nt  

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r = Nominal Interest Rate (decimal form, 3/100= 0.03)  

n= number of compounding periods in each year (1)  

Replacing with the values given  

A = 7000 (1+0.03/1)^(1x5)

A = 7000( 1.03)^5 = $8,114.92

For simple interest:

I = p x r x t  

Where:  

I = interest  

Replacing with the values given:

I = 7000 x (3.2/100) x 5 = $1,120

Adding the principal amount: 7000+1120 = $8,120

Since 8,120 (simple) >8,114.92(compound)

a simple interest rate of 3.2% will be the better deal.

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

Answer:

[tex]\boxed{\sf \ \ \ 3x^2-7x+2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

There are a lot of polynomials which have 2 and 1/3 as zeroes,

I can show you one below

[tex]3(x-2)(x-\dfrac{1}{3})=(x-2)(3x-1)=3x^2-x-6x+2=3x^2-7x+2[/tex]

hope this helps

Answer:

The equation above represents the total time the play director spent preparing for a play.

Step-by-step explanation:

The time spent by the play director for preparing for a play is, 190 hours.

Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.

Let the varying amounts of time be denoted by, x.

The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.

The equation provided is:

[tex]35x+\frac{3}{4}=190[/tex]

The equation above represents the total time the play director spent preparing for a play.

Answer:

One

Step-by-step explanation:

Through any 2 points, there is exactly one line.

Answer:

ONE

Step-by-step explanation:

Through any 2 points there is exaclty ONE line.