Last year, 3,270 athletes finished a marathon in Lancaster. This year, there were 2,616 athletes finishing. What is the percent of decrease in the number of finishers? %

A parabola is a mirror-symmetrical U-shape.

From the question, we have:

[tex]\mathbf{Vertex: (h,k) = (80,10)}[/tex]

[tex]\mathbf{Origin: (x,y) = (0,0)}[/tex]

The equation of a parabola is:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Substitute the values of origin and vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{0 = a(0 - 80)^2 + 10}[/tex]

[tex]\mathbf{0 = a(- 80)^2 + 10}[/tex]

[tex]\mathbf{0 = 6400a + 10}[/tex]

Collect like terms

[tex]\mathbf{6400a =- 10}[/tex]

Solve for a

[tex]\mathbf{a =- \frac{1}{640}}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

The focus of a parabola is:

[tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

Substitute the values of a and the vertex in [tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]

[tex]\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}[/tex]

[tex]\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}[/tex]

[tex]\mathbf{Focus = (80, -11\times 160)}[/tex]

[tex]\mathbf{Focus = (80, -1760)}[/tex]

The equation of the directrix is:

[tex]\mathbf{y = -a}[/tex]

So, we have:

[tex]\mathbf{y = \frac{1}{640}}[/tex] ----- the directrix

The axis of symmetry is:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

We have:

[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}[/tex]

Expand

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}[/tex]

[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }[/tex]

A quadratic function is represented as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

So, we have:

[tex]\mathbf{a = -\frac{1}{640}}[/tex]

[tex]\mathbf{b = \frac{1}{4}}[/tex]

Recall that:

[tex]\mathbf{x = -\frac{b}{2a}}[/tex]

So, we have:

[tex]\mathbf{x = -\frac{1/4}{2 \times -1/640}}[/tex]

[tex]\mathbf{x = \frac{1/4}{1/320}}[/tex]

This gives

[tex]\mathbf{x = \frac{320}{4}}[/tex]

[tex]\mathbf{x = 80}[/tex]

Hence, the axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]

Read more about parabola at:

https://brainly.com/question/21685473

Answer:

Step-by-step explanation:

Step-by-step explanation:

= [tex](a\sqrt{a} + 2a)+(\sqrt{a}+2 )[/tex]

= [tex]a(\sqrt{a} + 2a)+(\sqrt{a}+2 )[/tex]

= [tex](a+1)(\sqrt{a} +2)[/tex]

please give me a brainliest answer

Answer:

B

Step-by-step explanation:

Answer:

y= [tex]\frac{2}{5}[/tex](x)+2

Step-by-step explanation:

First take two points from the line (x-int (-5,0) and y-int (0,2)). Once you get that you want to find the slope using the formula [tex]\frac{Y_{2} -Y_{1} }{X_{2}- x_{1} }[/tex]. Substitute the values and find the slope. Once you find the slope (m) to be [tex]\frac{2}{5}[/tex], take any of the two points and apply it to the slope intercept formula (y=mx+b) to find b. I took the point (0,2) and applied it to the formula. It should look like 2= [tex]\frac{2}{5}[/tex](0)+b. Solve for b by multiplying 2/5 by zero and your left with 2=b. Plugin the missing varibles for the equation and it should come out to be y= [tex]\frac{2}{5}[/tex](x)+2.

Answer:

Coefficients!!!

Step-by-step explanation:

They're numbers that are multiplied by a variable.

Answer:

Step-by-step explanation:

I believe the answer would be coefficients. Coefficients are the number that is being multiplied by the variable.

Answer:

[tex]x > 8[/tex]

Step-by-step explanation:

1. Simplify the expression

Expand the parentheses:

[tex]-2*2x-2*-3<-26[/tex]

Simplify the arithmetic:

[tex]-4x+6<-26[/tex]

2. Group all constants on the right side of the inequality

Subtract 6 from both sides:

[tex]-4x+6-6<-26-6[/tex]

Simplify the arithmetic:

[tex]-4x<-26-6[/tex]

Simplify the arithmetic:

[tex]-4x<-32[/tex]

3. Isolate the x

Divide both sides by-4:

When dividing or multiplying by a negative number, always flip the inequality sign:

[tex]\frac{-4x}{-4} >\frac{-32}{-4}[/tex]

Cancel out the negatives:

[tex]\frac{4x}{4} >\frac{-32}{-4}[/tex]

Simplify the fraction:

[tex]x>\frac{-32}{-4}[/tex]

Cancel out the negatives:

[tex]x>\frac{32}{4}[/tex]

Find the greatest common factor of the numerator and denominator:

[tex]x>\frac{8*4}{1*4}[/tex]

Factor out and cancel the greatest common factor:

[tex]x>8[/tex]

4. Solution on a coordinate plane

Solution:

[tex]x>8[/tex]

Interval notation:

[tex](8, { \infty} )[/tex]    

Answer:

m^2/n

Step-by-step explanation:

The following laws of exponent are useful to this problem:

[tex] \displaystyle \large{ {(mn)}^{b} = {m}^{b} {n}^{b} } \\ \displaystyle \large{ {n}^{ - b} = \frac{1}{ {n}^{b} } }[/tex]

We are given the expression:

[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } }[/tex]

Use the first law of exponent above.

[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{(8)( \frac{1}{4}) } {n}^{ ( - 4)( \frac{1}{4}) } } \\ \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } {n}^{ - 1} }[/tex]

Make sure to recall the important necesscary fundamental math such as operation with negative numbers/integers, basic division, fraction, etc.

From the expression, apply the second law of exponent to n^-1.

[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } ( \frac{1}{ {n}^{1} } )} \\ \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = {m}^{2 } ( \frac{1}{ {n} } )} \\ [/tex]

Multiply m in.

[tex] \displaystyle \large{( {m}^{8} {n}^{ - 4} )^{ \frac{1}{4} } = \frac{ {m}^{2} }{ {n} } }[/tex]

Thus the answer is m^2/n.

Step-by-step explanation:

let tye number Ahmed thinks be x.

so, a/q

the equation is,

→ 2x/5 = 4

→ 2x = 4×5 = 20

→ x = 20/2

→ x = 10

therefore, he thinks the number 10.

hope this answer helps you dear!

Answer:

10

Step-by-step explanation:

I'm doing it from the end.

if the answer is 4, you have to multiple it by 5 and then divide it by 2

4 x 5 ÷ 2 = 10

10 multiple by 2 is 20 and 20 divided by 5 is 4 so

10 is correct answer

mean; 147

median; 147

mode; 152

Answer:

27m^6 n^12

Step-by-step explanation:

Answer:

27m^6n^12

Step-by-step explanation:

3^3 = 27

m^2^3 = m^6

n^4^3 = n^12

Hence, it is

27m^6n^12 (the last option)

Hope this helps and be sure to have a wonderful time at Brainly! :D

Answer:

1/4

Step-by-step explanation:

Answer:

3 or 5 cause there is  2 eights 2 fours 3 ones 2 six's  2 two's 2 sevens

Step-by-step explanation:

the answer must be because i don't know 6

Answer:

8912

Step-by-step explanation:

don't use awnser plz

Answer:

36 since they are similer triangles

Longer process:

24/24 = 36/x

solve this and you get 36

Answer:180 is what it need to be

Step-by-step explanation:

Answer:

(a+6)²

by identity (a+b)²=a²+2ab+b²

(a+6)²= a²+ 2×a×6 + 6²

= a²+ 12a + 36

(2a)²+5a = 4a²+5a

Answer:

x < 1 and x > -2

Step-by-step explanation:

5x - 1 < 4 and 3x + 5 > x + 1

Step 1.) Transfer the -1 over by the 4 by adding it because you use the opposite symple when its transfered.

5x < 5 and 3x + 5 > x + 1

Step 2.) Divide 5 by 5 to get the variable alone

x < 1 and 3x + 5 > x + 1

Step 3.) Subtract x from 3x which gives 2x and subtract 5 from 1 which gives -4

x < 1 and 2x > -4

Srep 5.) Divide -4 by 2 to get the variable alone and you get -2

x < 1 and x > -2

Answer:

[tex]3^{3}[/tex]= 3*3*3 or 27

[tex]4^{3}[/tex]= 4*4*4 or 64

[tex]3^{4}[/tex]= 3*3*3*3 or 81

Step-by-step explanation:

Hope this helps! :)

Answer:

[tex]X^{3}[/tex] = [tex]3^{3}[/tex] = 3*3*3 = 27    ( Because X is equal to 3 )

[tex]4^{X}[/tex] = [tex]4^{3[/tex] = 4*4*4 = 64

[tex]X^{4}[/tex] = [tex]3^{4}[/tex] = 3*3*3*3 = 81

Step-by-step explanation:

Hope this helps!

Answer:

Variable- an unknown number

Each shirt is 25$

Step-by-step explanation:

P (Price)

S (Shirt)

F) p=40+3s

S) 115=40+3s, 115-40=3s, 75=3s

E) s=25

Answer:

x = -4

Step-by-step explanation:

2x + 34 = 6 - 5x

Subtract 34 from both sides.

2x = -28 - 5x

Add 5x to both sides.

7x = -28

Divide both sides by 7.

x = -4

Proof:

2x + 34 = 6 - 5x

Substitute variable.

2(-4) + 34 = 6 - 5(-4)

Multiply.

-8 + 34 = 6 + 20

Add.

26 = 26

Answer:

x = -4

Step-by-step explanation:

2x+34=6-5x

+5x +34 = 6+5x

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

7x +34 = 6

7x -34 = -34

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

7x = -28

---    ------

7       7

x = -4

Answer:

yes, since 513 has more than two factors

have a spook-tastic day

Step-by-step explanation:

Answer:

25 degrees

Step-by-step explanation:

trust :)

Answer:

The answer would be 25 degrees

Step-by-step explanation:

Fill in 25

Answer:

40 comic books

Step-by-step explanation:

36-16=20

20×2=40

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The two corresponding angles of the Triangles are equal and the the side between them is common between them (so equal).

So, the stated triangles are congruent by :

Answer:

p = -1

Step-by-step explanation:

3(2p - 1) - 2*(3p+ 4) = 11p

Use distributive property: a(b +c) =a*b +a*c

3*2p -3*1 -2*3p + (-2)*4 = 11p

6p - 3  - 6p - 8 = 11p

6p - 6p - 3 - 8 = 11p

          - 11 = 11 p

Divide both sides by 11

     -11/11 = p

p = -1