an outfielder throws a ball to home plate. the balls path is modeled by the graph of y=x/5-x^2/1000 where x represents the horizontal distance of the ball from the outfield and y represents the balls vertical distance above the ground. what are the coordinates of vertex of the ball's path?

Answer:

C.) 70

Step-by-step explanation:

The line PN is made up of PK and KN (PN = PK + KN). We also know that PK must equal KN (definition of a parallelogram). Therefore, you can set the value of both lines equal to each other, solve for x, then add them together to find PN.

PN = ?    
PK = 5x    
KN = n² - 14

PK = KN                                  <----- Both lines must equal one another

5x = n² - 14                             <----- Substitute values in

0 = n² - 5x - 14                        <----- Subtract 5x from both sides

0 = (x - 7)(x + 2)                      <----- Factor

x = 7    x = -2                          <----- Set both parentheses equal to 0

The value for "x" can be 7 and -2. However, it does not make sense to use a negative value in this situation. If we were to plug -2 into the equations, it would result in lines with a negative value. Therefore,  "x" must be 7. Next, plug this value in for "x" to find the numerical value of PK and KN.

PK = 5x  ----->  5(7) = 35

KN = n² - 14  ----->  (7)² - 14 = 35

The fact that these are equal makes sense. Now, add these two numbers to find the value of the overall line.

PK + KN = PN

35 + 35 = 70

Therefore, C.) 70 is the value of PN.

[tex]\boxed{\sf (-3, -1)}\boxed[/tex]

Answer:

C. 1/4

Step-by-step explanation:

Step 1

Make the fraction denominators the same!

1/2 will become 4/8 over here, and 2/8 is already good!

Step 2

Subtract the new fractions!

4/8 - 2/8 is easy! It's 2/8

Step 3

Simplify the answer (2/8)

2/8 will become 1/4 when simplified

or C

Answer:

h > 24

Step-by-step explanation:

h/3 > 8

so basially you move the number three from the left side to the right side

so from division to multiplication

h > 8 x 3
h > 24
Solved !

Hope it helped ! Have a nice day !

Answer: 2

Step-by-step explanation:

3x² + 4

3.-3.-3 + 4

27 + 4

31

hope it helps...!!!

Answer:

31

EXPLANATION

[tex] = 3 \times { - 3}^{2} + 4 \\ = 3 \times 9 + 4 \\ = 27 + 4 \\ = 31[/tex]

Answer:

1

Step-by-step explanation:

m/8n > 4/8(1/2) ( since its 1/2 all you need to do is change the fraction to whole number which is 1/2 = 0.5)

The given will become 4/4 then simplest form is 1

Answer: x > 6

Step-by-step explanation:  -4(2x+2) < -40

-8x - 8 < -40

      +8     +8

-8x < 48

/-8x   /-8x

x  > 6              *The less than sign got flipped to a greater than sign because we divided by a negative.

Answer:

$12 is the sale price of shirt.

Explanation:

Calculate the percentage of sale

[tex]\sf \rightarrow \sf \dfrac{15}{20} *100[/tex]

[tex]\sf \rightarrow \sf 75 \%[/tex]

Then find the sale price of shirt

original price * percentage of sale

$16 * 75%

$12

Answer:

$12

Step-by-step explanation:

First, calculate the sale discount as a percentage using the given information about the pants.

[tex]\sf percent\:change=\dfrac{|final\:value-initial\:value|}{initial\:value} \times 100[/tex]

[tex]\implies \sf percent\:change=\dfrac{|15-20|}{20} \times 100=25\%[/tex]

Therefore, the clothes are on sale with a 25% discount.

This means they are 75% of the original sale price, as 100% - 25% = 75%

To find the sale price of the shirt, we simply need to find 75% of the original selling price of the shirt:

  75% of $16

= 0.75 × $16

= $12

Using ratios of original price : sale price, where x is the sale price of the shirt:

pants → 20 : 15

shirt → 16 : x

Therefore, as the ratios are the same:

   20 : 15 = 16 : x

⇒ 20/15 = 16/x

⇒ 20x = 16 · 15

⇒ 20x = 240

⇒ x = 240 ÷ 20

⇒ x = 12

Answer:

  a. dimpled: 4 < 7 < 2·4

  b. not symmetrical about θ = π/2

  c. r2: smaller, cardioid

Step-by-step explanation:

The general form of the equation for a limaçon can be written ...

  r = a·cos(θ) +b

This equation gives rise to 4 types of limaçon based on the relationship between a and b:

__

We have a=4, b=7, so a < b < 2a. The limaçon is dimpled.

The equation is not the same if θ is replaced by π/2 -θ. The curve is not symmetrical about θ = π/2.

The equation for r2 ...

Answer:

x = -13/5

Step-by-step explanation:

8+3(2x-7) = 11x

8 + 6x - 21 = 11x
     8 - 21   = 11x - 6x
     -13        = 5x
      -13/5    = x

Answer:

Step-by-step explanation:

3x^2 - x + 4 and 2x- 4x^2 - 7

3x^2 - x + 4 = no solution

2x- 4x^2 - 7 = no solution

Answer:

(a) sector

(b) chord

(c) tangent

Step-by-step explanation:

Answer:

BELOW

Step-by-step explanation:

DO I HEAR 100 POINTS? Yes.

For the first image, that answer is A.

For the second image, I'm a bit confused on which problems you want me to do, so I'll do number 10, 11, and 14.

10) Yeah, you're correct, it is J.

11) (1,-6), (-2,-5), (8,2) (4,0) and I can't see the last point so..

14)  Can't see the question :(

#1

Put (0,0)

Shading will be away from origin.

y inetercept

Check the direction of line by taking 4 and -4

The graph should bend down on left side while rise up in right side

Option A

#2

Putting origin in it

Shading away from origin

And

Putting origin

Shading towards origin

[tex]\log_6 6^3\\\\=3 \log_6 (6)~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=3 \cdot 1~~~~~~~~~~~~~~~~~~~~~~;[\log_a a=1]\\\\=3[/tex]

Answer:

351.68 m²

Step-by-step explanation:

surface area of cylinder = 2πrh + 2πr²

r = 4m

h = 10m

2πrh + 2πr² = 2*π*4m*10m + 2*π*(4m)² = 2*3.14*4m*10m + 2*3.14*4m*4m = 351.68 m²

[tex]\text{L.H.S}\\\\=\dfrac{\cos^2 t +4\cos t +4}{\cos t +2 }\\\\\\=\dfrac{(\cos t)^2 + 2\cdot 2\cos t+2^2}{\cos t +2}\\\\\\=\dfrac{(\cos t +2)^2 }{\cos t +2}\\\\\\=\cos t +2\\\\\\=\dfrac 1{\sec t} +2\\\\\\=\dfrac{2\sec t +1}{\sec t}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Step-by-step explanation:

fgx= x+6

g(f(x)=√x²+6

am not sure about the rest

Answer:

64 in²

Step-by-step explanation:

I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.

Remember,

A = [tex]\pi r^2[/tex]

And if we have 4 circles that means the area of one circle is 1/4th the total

So,

[tex]A=\frac{\pi r^2}{4}[/tex]

Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.

[tex]A=\frac{16\pi }{4}=\frac{4\pi }{1}=4\pi[/tex]

Now lets get it back to  by square rooting the 4

[tex]A=\sqrt4\pi =2\pi[/tex]

The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.

This gives us a final radius of the bigger circle of 8

Therefore, the area of the bigger circle is 8² which simplifies to 64

And a final answer of

64[tex]\pi[/tex] in²

Hope this helps :)

Attached images. :)

-

Comment if it's confusing, I would love to explain. <3

Answer:

A. The initial amount of medicine.

Step-by-step explanation:

Same explanation as the one I answered before. The 250 is the original value.

Answer:

Step-by-step explanation:

   8) AC = DC              Given

       BC  = EC              Given

      ∠ACB ≅ ∠DCB    Vertically opposite angles are congruent

9)  RS = TS                              Given

     SU =SU                              Reflexive property

     ∠RSU = ∠TSU                    Given

15 males and 20 females would maximize the total number of animals

The table is given as:

                           Males      Females    Time available

Environment a    20 min      25 min       800 min

Environment b    20 min      15 min       600 min

Represent the male with x and the female with y.

The time available is limited i.e. ≤

So, the constraints are:

20x + 25y ≤ 800

20x + 15y ≤ 600

Solve the above system of inequalities graphically (see attachment)

(x, y) = (15,20)

Hence, 15 males and 20 females would maximize the total number of animals

Read more about maximizing functions at:

https://brainly.com/question/16826001

#SPJ1

Answer:

Below in bold.

Step-by-step explanation:

The 3 angles of a triangle sum to 180 degrees, so:

if one angle is x degrres the other id 2x, and:

x + 2x + 60 = 180

3x = 180 - 60 = 120

x = 120/3 = 40

So m<B = 40 and m < A = 80 degrees.

Answer:

The sample space S for a probability model is the set of all possible outcomes.

Answer:

 [tex]-x^{3} -9x^{2}[/tex]

Step-by-step explanation:

I think.

Pls give Brainliest.

Answer:

Equation: 2x + x = 180

x = 60

∠GFH = 120

∠CBD = 60

Step by step:

Use 2x + x = 180 because the angles are on a straight line meaning they have a sum of 180:

2x + x = 180

3x = 180

3x/3 = 180/3

x = 60

Now just substitute:

∠CBD = x = 60

∠GFH = 2x = 120

Step-by-step explanation:

u didn't showed me but I will help u

here is your answer