Four friends participated in a free throw contest. Sean made twice as many
points as Emily. Katle made 7 more points than Sean. Kevin scored 4 points
less than Emily. Together the four friends scored 75 points.

Problem 8

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Work Shown:

h(t) = -16t^2+48t+100 is the same as y = -16x^2+48x+100, just with different variables.

Compare this to y = ax^2+bx+c to find that a = -16, b = 48, c = 100

Then compute the x coordinate of the vertex -b/(2a) getting

h = -b/(2a)

h = -48/(2*(-16))

h = 1.5

It takes 1.5 seconds for the ball to reach its peak height. The vertex represents the max height since the parabola opens downward.

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Problem 9

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Work Shown:

Plug the result from problem 8 into the function

y = -16x^2 + 48x + 100

y = -16(1.5)^2 + 48(1.5) + 100

y = 136

The vertex is (1.5, 136)

This means at 1.5 seconds, the ball is 136 feet off the ground at its highest point.

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Problem 10

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Work Shown:

Plug in y = 0 and solve for x

y = -16x^2 + 48x + 100

0 = -16x^2 + 48x + 100

-16x^2 + 48x + 100 = 0

Apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(48)\pm\sqrt{(48)^2-4(-16)(100)}}{2(-16)}\\\\x = \frac{-48\pm\sqrt{8704}}{-32}\\\\x \approx \frac{-48\pm93.29523032}{-32}\\\\x \approx \frac{-48+93.29523032}{-32}\ \text{ or } \ x \approx \frac{-48-93.29523032}{-32}\\\\x \approx \frac{45.29523032}{-32}\ \text{ or } \ x \approx \frac{-141.2952303}{-32}\\\\x \approx -1.41547593\ \text{ or } \ x \approx 4.41547595\\\\[/tex]

A negative x value makes no sense because time cannot be negative, so we ignore the first solution. The only practical solution is roughly x = 4.415

It takes approximately 4.415 seconds for the ball to reach the ground.

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Problem 11

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Work Shown:

Use the same idea as problem 10. Instead of y = 0, use y = 120

y = -16x^2 + 48x + 100

120 = -16x^2 + 48x + 100

-16x^2 + 48x + 100 = 120

-16x^2 + 48x + 100-120 = 0

-16x^2 + 48x - 20 = 0

-4(4x^2 - 12x + 5) = 0

4x^2 - 12x + 5 = 0

Now apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-12)\pm\sqrt{(-12)^2-4(4)(5)}}{2(4)}\\\\x = \frac{12\pm\sqrt{64}}{8}\\\\x = \frac{12\pm8}{8}\\\\x = \frac{12+8}{8}\ \text{ or } \ x = \frac{12-8}{8}\\\\x = \frac{20}{8}\ \text{ or } \ x = \frac{4}{8}\\\\x = 2.5\ \text{ or } \ x = 0.5\\\\[/tex]

There are two moments in time when the ball is 120 feet in the air. Those two moments are at x = 0.5 seconds and at x = 2.5 seconds.

At x = 0.5, the ball is going upward. At x = 2.5, the ball is coming back down.

Answer:

(I'm not sure if your teacher is nit-picky about significant figures, but here I go...)

8) 1.5 seconds

9) 136 feet

10) 4.415 seconds

11) 2.5 seconds (also 0.5 seconds)

Step-by-step explanation:

See attached screenshot of Desmos graph showing y(t) = -16t² + 48t + 100, y = 120 and respective points.

Answer:

The ratio of centimeters to inches is 3 centimeters to 1.18 inches.

Step-by-step explanation:

Answer:

The ratio of centimeters to inches is 3 centimeters to 1.18 inches.

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

0.73

Step-by-step explanation:

29098 / 39598 = 0.73

I do not see the options so just compare it to your answer

Answer

p=5. I believe

Answer:

70

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

3(2)+2=8

3(3)+2=11

3(4)+2=14

3(5)+2=17

3(6)+2=20

Sum=70

Answer:

2

Step-by-step explanation:

18-4^2=2

Answer:

18-k^2

18-4^2

18-16

2

Answer:

slope of HI is -2

Step-by-step explanation:

so the line looks straight to me so just solve for the slope of D(8,32) E(12,24) which you solve with the equation y2 - y1/x2 - x1

so... 24 - 32 = -8 and 12 - 8 = 4

-8/4 = -2

I hope I helped you ;)

Answer:

[tex]v = -\frac{w}{x}[/tex]

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)

Answer:

(5,-8)

Step-by-step explanation:

if it is reflected across the X axis and this is in quadrant 3 that means if it was reflected it would fall in quadrant 2

Answer:

5/6 and 0.833

Do you mind putting Brainliest plz

Answer:

Number of sides of the polygon

Step-by-step explanation:

The formula [tex]S=(n-2)180[/tex] is the sum of the measures of interior angles. So that's what S stands for. The only other variable remaining is n which is the number of sides of the polygon.

There's nothing I can do to help you understand this, you just have to memorize it.

Answer:

Just input sin(9), sin(30), sin(81), etc.

For this set, you need a scientific calculator or else, you won't be able to answer that. There is a way but that is already obsolete now.

9514 1404 393

Answer:

  8 ft

Step-by-step explanation:

Consider the attached diagram.

The rule for secants and tangents tells us ...

  (AC)(AB) = (AT)²

  AC = AT²/AB = 15²/9 = 25

Then the diameter is ...

  BC = AB - AC = 25 -9 = 16

The pond has a diameter of 16 ft, so a radius of 8 feet.

__

Additional comment

Since point C is the nearest point on the edge of the pond to point A, it must lie on line AO. Hence BC must be a diameter.

Answer:

The first question's answer is 6 + 5 = 11

since 7 is the greatest common factor divide it into both numbers to get 6 + 5 = 11

Step-by-step explanation:

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x=0

Step-by-step explanation:

Four points are always coplanar if they: lie in same plane.

Firstly understanding the coplanar points. Coplanar points are refers to the points if they are present in same plane. Further defining the word "plane". Plane is the surface, which is flat and two dimensional in nature. The surface is infinite. Plane can also be referred as the analogue of 3 dimensional space, you we can also interpret the plane as extension of point or line.

So, the points that lie on different planes will not be coplanar. Now, understanding the points on lines. Two or more lines may or may not be in same plane. Subsequently, points may or may not be coplanar, depending upon the lines they are placed on. Thus, we can not definitely say that points lying on the same line are coplanar.

Learn more about coplanar points -

https://brainly.com/question/24430176

#SPJ4

Answer:

the answer is

A

Step-by-step explanation:

Answer:

1. 7

2. 9

3. 9

4. 6

5. 10

I believe

Answer: It is still the same thing since there are no like terms for this equation. So 5w-8x+20y+6z is the answer. Hope this helps!

Step-by-step explanation:

160 adult tickets were sold

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Set up equations to represent the problem.

Let the A and S represent the number of adult and student ticket respectively. So we can write:

12A + 6S = 3,240 --- (1)

A + S = 380  --- (2)

From (2):

S = 380 - A ---- (3)

Put (3) in (1):

12A + 6S = 3,240

12A + 6 (380 - A) = 3,240

12A + 2280 -6A = 3,240

6A = 3,240 - 2280

6A = 960

A = 960/6

A = 160 tickets

Thus, the number of adult ticket sold is 160

Learn more about word problems on:

brainly.com/question/13818690

#SPJ1

Answer:

1 1/5

Step-by-step explanation:

Answer:

1 1/5

Step-by-step explanation:

5/5 is 1 whole and you got 1 extra so it would be 1/5

Answer:

22

Step-by-step explanation:

40 degrees

Step-by-step explanation:

hour hand = 5 and 1/3 hours

minute hand = 20 minutes = 4 hours on the clock

the different = 1 and 1/3 hours

each hour = 360 / 12 = 30 degrees

therefore the answer = 4/3 x 30 = 40 degrees

Answer:

l = 20 m

Step-by-step explanation:

600/30 = 20

Answer:

Felipa is correct

Step-by-step explanation:

carl

[tex]6-4(4-6x)+12x\\\\2(4-6x)+12x[/tex] this is incorrect by PEMDAS  he should have multiplied the 4 by 4-6x and then add with 6

so Felipa is correct

Answer:

ΔV = 24*π   inches

Step-by-step explanation:

Amy Tube volume   =  V₁    the 6 inches sides will shape the circumference of area   A₁ = π*r²  

A₁ = π*(3)²    and

V₁ =  π*r²*h₁

V₁ = π*(3)²*8

V₁ = 72*π

In the case of Belinda, r will be 4 inches and h₂ = 6  and V₂

V₂ = A₂*h₂

V₂ =  π*(4)²*6

V₂ = 96* π

Then differences of the volumes is

V₂  -  V₁  =  ΔV = 96*π - 72*π

ΔV = 24*π   inches

Answer:

c

Step-by-step explanation:

Answer:

ima say c since the other person did.

but it already takes points from u when u make this question btw.

Step-by-step explanation:

Answer:

Here

Step-by-step explanation:

Make each one fraction like 5 red will be a 1/20 chance. After you make them all fractions, multiply the right ones(green or black).