At a competition with 8 runners, 2 medals are awarded for first and second

place.

Each medal is different. How many ways are there to award the medals?

O A. 56

O B. 28

O C. 40,320

O D. 64

Answer:

[tex]\large\boxed{y=-\dfrac{31}{5}x-8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept - (0, b)

The formula of a slope:

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

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

We have the points (0, -8) → b = -8, and (-5, 23).

Substitute:

[tex]m=\dfrac{23-(-8)}{-5-0}=\dfrac{31}{-5}=-\dfrac{31}{5}[/tex]

Put the value of the slope and of the y-intercept to the equation of a line:

[tex]y=-\dfrac{31}{5}x-8[/tex]

Answer:

The amount of money that Lexi had at the beginning was $131.25

Step-by-step explanation:

Let

x -----> amount of money that Lexi had at the beginning

y -----> amount of money that Maria had at the beginning

we know that

x+y=250 -----> equation A

(1-2/5)x=y-40

(3/5)x=y-40

y=(3/5)x+40 ----> equation B

substitute equation B in equation A and solve for x

x+(3/5)x+40=250

(8/5)x=250-40

(8/5)x=210

x=210*5/8

x=$131.25

Answer:

The correct option is A

Step-by-step explanation:

The given expression is:

√10/4√8

We have to eliminate the √ from the denominator

4√8 = (2^3)^1/4

Multiply the whole expression by (2)^1/4

=(2)^1/4 * √10/ 2^(1/4)*(2^3)^(1/4)

= 2^(1/4) · 10^(2/4)  / 2^1/4+3/4

=2^(1/4) · 10^(2/4) / 2^1+3/4

=2^(1/4) · 10^(2/4) / 2^4/4

=2^(1/4) · 10^(2/4) /2

=2^(1/4) · 100^(1/4) /2

=200^1/4 /2

= 4√200 /2

Thus the correct option is A....

Answer:

correct answer is a

Step-by-step explanation:

Answer:

Residual in this case is -4.215

Step-by-step explanation:

A residual can be defined by

Residual = Actual value - Predicted value

We are given:

Predicted value of y = 34.215

Actual value of y = 30

Putting values in the formula:

Residual = Actual value - Predicted value

Residual = 30 - 34.215

Residual = -4.215

So, residual in this case is -4.215

Answer:

[tex]\frac{1}{2}[/tex] x²

Step-by-step explanation:

let the length of the side be l

Then using Pythagoras' identity on the right triangle formed by the diagonal ( hypotenuse ) and the 2 sides

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

l² + l² = x²

2l² = x² ( divide both sides by 2 )

l² = [tex]\frac{1}{2}[/tex] x² ( since A of square = l² )

Answer:

4√3

Step-by-step explanation:

The question is to simplify √6 × √8

Applying surds

√6 can be written as √2 ×√3

and

√8 can be written as √2 × √4

but √4=2

so;

√8 is 2√2

Write the whole question as

√2×√3×2√2

This can be written as

2√2×√2×√3

But you know √2×√2 = √4 =2

So, write as

2×2×√3 = 4√3

4√3 is the simplified form

Simplified form of expression √6 × √8 is,

⇒ 4√3

We have to given that,

An expression to simplify,

⇒ √6 × √8

Simplify as,

⇒ √6 × √8

Since, √6 = √2 × √3

√8 = √2 × √2 × √2

Hence, We can write as,

⇒ √6 × √8

⇒ √2 × √3 × √2 × √2 × √2

⇒ 4√3

Therefore, Simplified form of expression √6 × √8 is,

⇒ 4√3

Learn more about the multiplication visit:

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Answer:

We have the following equation: y = 36 - x. And we need to find which of the following points belong to the graph:

If any of the points belong to the equation, then the equality will be met.

Then:

7 = 36 - (-13)

7 = 36 + 13

7 = 49 ❌

1 = 36 - (-35)

1 = 71❌

5 = 36 - 11

5 = 25 ❌

3 = 36 - 27

3 = 9 ❌

None of the points belong to the graph. Therefore, all points are NOT on the grah of p(x) = 36 - x.

Answer:

ANSWER IS (-35,1)

Step-by-step explanation:

I got it because I am looking at the answer right now

Answer:

1st and 3rd statements are true: 1) The inequality b=70<50 can be used to represent the situation and 2) The graph of the solution set will be shaded to the left.

Step-by-step explanation:

Lets look at this question step by step.

Therefore, the first statement is true; The inequality b=70<50 can be used to represent the situation.

This cannot be true because as heart rate increases, it gets lesser than 50 so in this case, 50 is greater than 70 not lesser than 70.

Moreover, if we take 50 to the right side, it will be 70 + 50 = 120 which is wrong because b is supposed to be less than 50.

This is true because b<50 and whenever there is a less than sign, the graph is shaded to the left.

These two statements cannot be true as be is supposed to be less than 50.

!!

Answer:

1 and 3

Step-by-step explanation:

pls give other person brainliest, they explained it very well:)

Answer:

D is the correct answer.

Step-by-step explanation:

Step 1: Write the data

Total number of songs = 100

Total ratio = 1

Total percentage = 100%

Ratio of jazz songs = 1/4

Percentage of jazz songs = 1/4 x 100 = 25%

Ratio of pop songs = 1 - 1/4 = 3/4

Percentage of pop songs = 3/4 x 100 = 75%

Step 2: Match the statement.

The correct statement is D; 25% are Julian's songs are jazz because 1/4 = 25/100 and 75% are pop because 3/4 = 75/100.

!!

Answer:

what graph? there is no graph?

Answer:

t=-8

Step-by-step explanation:

-2 (t- 1) = 18

Divide each side by -2

-2 (t- 1)/-2 = 18/-2

t-1 = -9

Add 1 to each side

t-1+1 = -9+1

t = -8

Answer:

t = -8

Step-by-step explanation:

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other.

First, Divide -2 from both sides:

(-2(t - 1))/-2 = (18)/-2

t - 1 = 18/-2

t - 1 = -9

Isolate the variable t. Add 1 to both sides:

t - 1 (+1) = -9 (+1)

t = -9 + 1

t = -8

t = -8 is your answer.

~

Answer:

the answer is 5(y-5x) (x-2)

Step-by-step explanation:

Answer:

[tex]5(x - 2)(y - 5x)[/tex]

Explanation

We want to factorize:

[tex]5xy - 25 {x}^{2} + 50x - 10y[/tex]

The factors have been grouped already. We now factor the GCF from each group to get:

[tex]5x(x- 5x) - 10(y - 5x)[/tex]

We factor further to obtain:

[tex](5x- 10)(y - 5x)[/tex]

We can still factor 5 to obtain:

[tex]5(x - 2)(y - 5x)[/tex]

Answer with explanation:

Both the normal distribution curves have sample mean equal to 16.

Normal distribution curve 1 is more wider than Curve 2, resulting in greater standard deviation.

So, Curve 1 has the  greatest standard deviation.

The first normal distribution curve has the greatest standard deviation.

Standard deviation describes how far from the mean the given data set spread out.

Thus, we can conclude that the first normal distribution curve has the greatest standard deviation.

Learn more about normal distribution curve here: https://brainly.com/question/14644201

Answer:

[tex](3x-4)(x+1)[/tex]

Step-by-step explanation:

This is in the form [tex]ax^2+bx+c[/tex].

If your wish is to factor by grouping, then you goal is too look for two numbers that multiply to be [tex]ac[/tex] and adds up to be [tex]b[/tex].

Then once you find those numbers you replace b with those numbers.  Then the factor by grouping can be done.

So you have [tex]a=3,b=-1,c=-4[/tex]

[tex]ac=3(-4)[/tex]

[tex]b=-1[/tex]

The numbers that we need are already present since -4+3 is -1.

So replace -1 in

[tex]3x^2-1x-4[/tex]

with (-4+3)

[tex]3x^2-4x+3x-4[/tex]

Now group the first two terms together and group the last two terms together:

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

Factor what you can from both pairs:

[tex]x(3x-4)+1(3x-4)[/tex]

Notice you have two terms: x(3x-4)  and 1(3x-4).  These terms have a common factor of (3x-4) so factor that out of our expression like so:

[tex](3x-4)(x+1)[/tex]

Check with foil if you like:

First: 3x(x)=3x^2

Outer: 3x(1)=3x

Inner: -4(x)=-4x

Last: -4(1)=-4

----------------------Add together:

3x^2-x-4

Answer: [tex]=(3x-4)(x+1)[/tex]

Step-by-step explanation:

Given the polynomial [tex]3x^2- x -4[/tex]

We can observe that it is written in this form:

[tex]ax^2+bx+c[/tex]

To factor completely, we need to follow these steps:

- Rewrite the term "b" as the sum of two terms whose product be [tex](3)(-4)=-12[/tex] and whose sum be -1:

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

- Applying Distributive property, we get:

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

- Make two groups of two terms each:

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

- Factor out "x" from the first group and 1 from the second group:

 [tex]=x(3x-4)+1(3x-4)[/tex]

- Factoring out [tex](3x-4)[/tex], we get:

 [tex]=(3x-4)(x+1)[/tex]

Answer:

a. 8g 1dg 3cg 3mg

b. 11dag 8g

c. 24kg 9hg

d. 7kg 1hg

Step-by-step explanation:

Answer:

a. 8g 1dg 3cg 3mg  

b. 11dag 8g  

c. 24kg 9hg  

d. 7kg 1hg

Step-by-step explanation:

got it from the other person

Answer:

[tex]\large\boxed{\sqrt{-36}+\sqrt{-100}+7=7+16i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\=====================\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrT{-1}=6i\\\sqrt{-100}=\sqrt{(100)(-1)}=\sqrt{100}\cdot\sqrt{-1}=10i\\\\\sqrt{-36}+\sqrt{-100}+7=6i+10i+7=7+16i[/tex]

Answer:

The answer is [tex]16i+7[/tex]

Step-by-step explanation:

In order to determine the answer, we have to know about imaginary numbers.

The imaginary numbers are different to real numbers because they use a new unit called "imaginary unit":

[tex]i=\sqrt{-1}[/tex]

i: imaginary unit

This new unit is applied like a factor when we have even roots with negative numbers inside.

In this case:

[tex]\sqrt{-36}=\sqrt{-1}*\sqrt{36}=6i\\\sqrt{-100}=\sqrt{-1}*\sqrt{100}=10i\\   \\\sqrt{-36}+\sqrt{-100}+7\\ 6i+10i+7\\16i+7[/tex]

Finally, the answer is [tex]16i+7[/tex]

Answer:

It is terminating decimal expansion.

Step-by-step explanation:

17/3125 is a terminating decimal expansion.

REASON:

If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.

Proof:

Lets have a look on the solution of the given term.

17/1325

We will break the denominator in the factors:

If we multiply 5 five times than it will give us 1325.

17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5

We know that any number with exponent zero = 1

∴ 2^0 = 1

So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.

Thus this term has a terminating decimal expansion....

Answer:

Two of the most important characteristics of seawater are temperature and salinity – together they control its density, which is the major factor governing the vertical movement of ocean waters. The temperature of seawater is fixed at the sea surface by heat exchange with the atmosphere.

Step-by-step explanation:

plz mark as brainliest..

Answer:

14

Step-by-step explanation:

20=2(x-4)

therefore, x=14

Answer:

2(x -4) = 20

2x - 8 = 20

2x = 28

x = 14

Answer:

Value of A(34) = 219

Step-by-step explanation:

A1, A2,A3,A4,45,51,57,63 are in Arithmetic sequence

Common difference in this Arithmetic sequence = 63 - 57 = 06

so, A4 = 45 - 6 = 39

     A3 = 39 - 6 = 33

     A2 = 33 - 6 = 27

     A1 = 27 - 6 = 21

First term of Arithmetic sequence  = 21

Common difference = 06

Using general term of Arithmetic sequence,

A(n) =  First term + (n - 1) common difference

A(34) = 21 + (34 - 1) 6

A(34) = 21 + 33 × 6

A(34) = 21 + 198

A(34) = 219

Value of A(34) = 219

Answer:

6m wide

14m long

Step-by-step explanation:

Let the length be represented by L.

Let the width be represented by W.

We are given we want the length to be 8 m longer than it's width.

So we want L=8+W.

The area of the rectangle is 84 m squared, this means that LW=84.

So I'm going to substitute L=8+W into LW=84.

LW=84

(8+W)W=84             (L=8W)

So we are going to solve (8+W)W=84 for W.

(8+W)W=84

Distribute:

8W+W^2=84

Rearrange left hand side using commutative property:

W^2+8W=84

Subtract 84 on both sides:

W^2+8W-84=0

Now to factor a quadratic with leading coefficient 1 (assuming it isn't prime) is to find two numbers that multiply to be c=-84 and add up to be b=8.

I'm going to play with factor pairs that multiply to be -84

c=-84=4(-21)=12(-7)=6(-14)

So the number we are looking for is -6 and 14 since -6(14)=-84 and -6+14=8.

The factored form of our equation is:

(W+14)(W-6)=0

This means we need to solve both W+14=0 and W-6=0.

W+14=0

W=-14  (I subtracted 14 on both sides)

W-6=0

W=6 (I added 6 on both sides)

The solution W=-14 makes no sense.

W=6 is the solution for the width.  That is the width is 6 m long.

Now the length is 8 more than the width so the length is 14 m long.

Answer:

6m wide  and  14m long

Step-by-step explanation:

If a rectangular flower bed is to be 8 m longer than it is wide and the flower bed will have an area of 84 m squared, its dimensions will be 6m wide  by  14m long.

L = length

W = Width

Answer: Second Option

[tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]

Step-by-step explanation:

If we have a function f(x) and its inverse function [tex]f ^ {- 1} (x) = g (x)[/tex]

Then by definition:

[tex](fog) (x) = (gof) (x) = x[/tex]

Notice that the inverse of the function [tex]f (x)=\frac{2}{x}[/tex] is [tex]f ^ {- 1}(x)=\frac{2}{x}[/tex]

then:

If [tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]

Then:

[tex](fog) (x) =\frac{2}{\frac{2}{x}}[/tex]

[tex](fog) (x) =\frac{2x}{2}[/tex]

[tex](fog) (x) =x[/tex]

The answer is the second option

[tex]((5 \times 1) - (4 \times - 1) = \\ 5 - ( - 4) = \\ 5 + 4 = \\ 9[/tex]

Answer:

Part a) The values of the function f(x) are {-1,5,11}

Part b) The value of g(5) is -4

Part c) The values of the function f(n) are {8,9,4}

Step-by-step explanation:

Part a) we have

f(x)=3x+5

Evaluate for  {-2,0,2}

1) For x=-2

substitute the value of x in the function

f(-2)=3(-2)+5=-1

2) For x=0

substitute the value of x in the function

f(0)=3(0)+5=5

3) For x=2

substitute the value of x in the function

f(2)=3(2)+5=11

Part b) we have

g(x)=x-9

Evaluate for x=5

substitute the value of x in the function

g(5)=5-9=-4

Part c) we have

f(n)=(3-n)+4

Evaluate for  {-1,-2,3}

1) For n=-1

substitute the value of n in the function

f(-1)=(3-(-1))+4=8

2) For n=-2

substitute the value of n in the function

f(-2)=(3-(-2))+4=9

3) For n=3

substitute the value of n in the function

f(3)=(3-(3))+4=4

Answer:

[tex]\large\boxed{y=\sqrt[3]{x+3}+3}[/tex]

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

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

The original graph ( y = ∛x) shifted 3 units to the left and 3 units up.

Therefore, the new equation is:

y = ∛(x + 3) + 3

Answer:

27+4x+8y

or

4x+8y+27 ( I can reorder this a few different ways. I don't know what your choices are)

Step-by-step explanation:

11+4(x+2y+4)

We can apply distributive property to the 4(x+2y+4), this will give us 4x+8y+16.

Bring down the 11+ and we have 11+4x+8y+16.

The only like terms we have is 11 and 16.  So reorder using commutative property and get 11+16+4x+8y.

I'm going to simplify the 11+16 part which gives us 27.

In the end we have 27+4x+8y.

Let me line up so it is all nice and neat:

11+4(x+2y+4)

11+4x+8y+16

11+16+4x+8y

27+4x+8y

Answer:

D

Step-by-step explanation:

This is exponential growth, and to my understanding, the format goes:

initial amount (percent growth/ decay)^time

percent growth = (decimal percent + 1)

percent decay = (1 - decimal percent)

Your equation:

1500(1.02)^t

Using the above format, 1500 appears to be the initial amount, which increases by 2% per annum.

i think

Answer:

domain of (f O g)(x) is {x|x≠0}

Step-by-step explanation:

Given:

f(x) = x + 7

g(x) = 1/x -13

Putting g(x) in f(x) i.e f(g(x))

(fog)(x)= 1/x -13 +7

          = 1/x-6

Domain of 1/x-6 is {x|x≠0} !

For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = \frac {1} {x} -13[/tex]

We must find [tex](f_ {0} g) (x).[/tex] By definition we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {0} g) (x) = \frac {1} {x} -13 + 7 = \frac {1} {x} -6[/tex]

By definition, the domain of a function is given by all the values for which the function is defined.

The function [tex](f_ {0} g) (x) = \frac {1} {x} -6[/tex] is no longer defined when x = 0.

Thus, the domain is given by all real numbers except zero.

Answer:

x nonzero

Answer:

x = -6 or x = 2

Step-by-step explanation:

The given equation is:

[tex]x^{2}+4x-4=8\\\\ x^2+4x-4-8=0\\\\ x^2+4x-12=0\\\\[/tex]

This is quadratic equation, so we can use the quadratic formula to find the roots of the equation i.e. the value of x that satisfy the given equation.

According to the quadratic formula, the two roots will be:

[tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

Here,

a = coefficient of x² = 1

b = coefficient of x = 4

c = constant term = -12

Using these values, we get:

[tex]x=\frac{-4 \pm \sqrt{(4)^2-4(1)(-12)}}{2(1)}\\\\ x=\frac{-4 \pm \sqrt{64}}{2}\\\\ x=\frac{-4 \pm 8}{2}\\\\ x = \frac{-4-8}{2} , x = \frac{-4+8}{2}\\\\ x=-6, x = 2[/tex]

Thus, the two values of x that satisfy the given equation are: -6 and 2. So 1st option gives the correct answer.

Answers:

22

9

20

17

20

35

26

32

23

9

Answer:

C

Step-by-step explanation:

your answer will be option number

(3) {(1,1),(2,9),(4,8)}

I hopes its help's u

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@Abhi.❤❤