Mathematics High School

Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands.

Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.

There is a moment when the basketballs are at the same height.



What is this height?

Enter your answer, rounded to the nearest tenth of a meter, in the box.

Answers

Answer 1

Answer:

Just took the K12 quiz, and like killdrone said in the comments, the correct answer is 9.8 m

Step-by-step explanation:

Answer 2
Final answer:

The height at which both basketballs are at the same height is approximately 16.3 meters.

Explanation:

To find the moment when the basketballs are at the same height, we need to find the common height value for both functions.

Setting the functions equal to each other, we get: -4.9x^2 + 12x + 2.5 = -4.9x^2 + 14x

Simplifying the equation, we get 2x = 2.5, which means x = 1.25.

Substituting this value back into the original function for Eli, we get f(1.25) = -4.9(1.25)^2 + 12(1.25) + 2.5 = 16.325

Therefore, the height at which both basketballs are at the same height is approximately 16.3 meters.

Related Questions

Can someone help me...?

Answers

1. (x, y) = (7, -12)

2. x = 1, x = 2 are both solutions

A machine can produce 27 inches of ribbon in 3 minutes.how much ribbon can the machine produce in 1 hour produce in 1 hour?

Answers

540 it produce in a hour

He measure of one angle of an octagon is twice that of the other seven angles. what is the measure of each angle? answer: ,

Answers

Final answer:

The measure of one angle in an octagon is 135.625 degrees.

Explanation:

Let's denote the measure of one angle as x.

Since there are eight angles in an octagon,

the sum of all the angles in the octagon is 180(x) + 7(2x) = 180x + 14x = 194x.

We know that the sum of the angles in any polygon is equal to (n-2) times 180 degrees, where n is the number of sides of the polygon.

Therefore, 194x = (8-2) × 180. Solving this equation,

we find that x = 135.625. So, the measure of each angle is 135.625 degrees.

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50 POINTS AND BRAINLIEST!!! QUICK

3. At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. The inner edge of the sidewalk is a circle with a radius of 9 m.

(a) Write and simplify an expression for the exact area of the sidewalk.
(b) Find the approximate area of the sidewalk. Use 3.14 to approximate π.

Answers

A)

R = outside radius
r = inside radius

equation: ( pi*R^2) - (pi*r^2)

B)
 3.14 x 11^2 - 3.14 x 9^2

379.94 - 254.34 = 125.6 square meters






A = pi r^2  pi 9^2 81pi  81 * 3.14 = 254.34   pi 11^2 = 121pi   121 * 3.14 =379.94
379.94 - 254.34 = 125.60 area of sidewalk

Hope it helps  

Two circle are inscribed inside squares. Write a function f in terms of the radius r that represents the area of the shaded region. Leave your answer in terms of π.

f(r)=___

Answers

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex].

The area of the shaded region is the sum of the areas of the two circles of same radius, each of them represented by the following formula:

[tex]A_{r} = \pi\cdot r^{2}[/tex] (1)

Where:

[tex]A_{r}[/tex] - Area of the circle.[tex]r[/tex] - Radius of the circle.

Then, the formula for the shaded area is:

[tex]f(r) = 2\cdot A_{r}[/tex]

[tex]f(r) = 2\pi\cdot r^{2}[/tex] (2)

The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex]. [tex]\blacksquare[/tex]

Remark

The figure is missing and the statement present mistakes. Correct statement is shown below:

Two circle are inscribed inside squares. Write a function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region. Leave your answer in terms of π.

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What is the sum of the first 7 terms of the series −8+16−32+64−

Answers

Lets Get started :)

The terms given are 
- 8 , + 16 , - 32 , + 64

The formula for finding the sum of this geometric sequence is:

Sn = [tex] \frac{a1(r^n - 1)}{r -1} [/tex]
a₁ = first term of sequence = -8
r = common ration = -2
n = term of sum we need to find = 7

Sn = [tex] \frac{-8((-2)^7 - 1)}{-2-1} [/tex]
     = -344

There is also another way, by simply adding, but you cannot perform this when they ask for a larger terms sums

Each term are multiplied by - 2, so to find the rest of the terms, we multiply by - 2 

+ 64 x - 2 = - 128
- 128 x -2 = + 256
+256 x - 2 = - 512

( - 8 ) + ( 16 ) + ( - 32 ) + ( 64 ) + ( - 128 ) + ( 256 ) + ( - 512 ) (first 7 terms)
= -344
-8 + 16 + -32 + 64 + -128 + 256 + -512 (These are the first 7 terms) The total = -344

an internet passcode consists of a digit followed by a letter, followed by another digit. Assuming the digits are 0-9, how many different passcode are possible?

Answers

There are 10 single-digits (0 through 9) and 26 letters (A through Z)

For the first slot there are 10 choices which represents selecting a single digit
For the second slot there are 26 choices because we choose a single letter here.
Finally there are another 10 choices for the third slot (assuming repeats are allowed)

Multiply the values out: 10*26*10 = 260*10 = 2600

Answer: 2600

Answer:

2600

Step-by-step explanation:

What is the solution to the equation 5x = 40?

Answers

To find X, we can divide 5 into 40.
40 divided by 5 is 8.
Now we can do 5 x 8. That is 40.

X=40

OR we can do it another way.
40 divided by 5 is 8.
Cross out 5 divided by 5.

Now we have 8. Still.
X is 8
Hello,

The answer is "x=8".

Reason

5x=40=40/5

40/5=8

x=8

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

Find the angle with a tangent ratio of 0.9325

Answers

To find the angle with a given tangent, use the inverse tangent.  
Putting tan⁻¹ (0.9325) in the calculator gives us a value of 42.9995 ≈ 43°.  Double check by using the calculator for tan(43).  You get a value of 0.9325.

Answer:

B. 43

Step-by-step explanation:

given that (-8,- 7) in on the graph of f(x), find the corresponding point for the fuction f(x -4)

Answers

The point (x1,y1) on the graph of f(x) is the point (x1-a,y1) for the function
f(x+a)

(-8,-7)=(x1,y1)→x1=-8, y1=-7
f(x-4)=f(x+a)→a=-4

(x1-a, y1)=(-8-(-4), -7)=(-8+4, -7)=(-4,-7)

The corresponding point for the fuction f(x -4) is (-4,-7)

What is general form of equation of a circle with center at (a,b) and radius of length m?

Answers

All points on a circle has the same distance (radius) to the center. Specifically, the distance from point (x,y)to center (a,b) is \sqrt((x-a)^2+(y-b^2)), which is equal to radius m. So \sqrt((x-a)^2+(y-b^2))=m. Square both sides, (x-a)^2+(y-b)^2=m^2.

The general form of the equation of a circle with centre at [tex]\((a, b)\)[/tex] and radius [tex]\(m\)[/tex] is: [tex]\[ x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \][/tex].

The general form of the equation of a circle is [tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex], where [tex]\((h, k)\)[/tex] represents the centre of the circle and [tex]\(r\)[/tex] represents the radius.

If we expand and rearrange this equation, we get [tex]\( x^2 + y^2 - 2hx - 2ky + (h^2 + k^2 - r^2) = 0 \)[/tex].

Comparing this with the given options, we see that [tex]\( h = a \), \( k = b \), and \( r = m \)[/tex].

Substituting these values into the general form, we get [tex]\( x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \)[/tex], which matches the correct option.

Complete Correct Question:

What is the general form of the equation of a circle with center at (a, b) and radius of length m?

a. x2 + y2 - 2ax - 2by + (a2 + b2 - m2) = 0.

b. x2 + y2 + 2ax + 2by + (a2 + b2 - m2) = 0.

c. x2 + y2 - 2ax - 2by + (a2 + b2 + m2) = 0.

d. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.

What power do you raise a number to to get the square root of it?

Answers

Answer:  To get the "square root" of a number,  you can raise a number to the 
  "(1/2)" exponent.

Determine whether each triangle with sides of given lengths is a right triangle. Hint: Set a2+b2=c2a2+b2=c2 If One side is equal to the other, then it's a right triangle. It sides are not equal, then it's not a right triangle. a = 6 cm b= 8 cm c = 10 cm

answers yes or no

Answers

a = 6
b = 8
c = 10 will produce a rt angle triangle.

a^2 + b^2 = c^2
6^2 + 8^2 =? 10^2
36 + 64 = ? 100
100 = 100 so the answer is yes to this part.

How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?

Answers

Cylinder Volume   =   π • r² • height
Cylinder Volume   =   3.14159 * 12 * 12 * 30
Cylinder Volume   =   13,571.67 cubic feet

 



The line through (8, 0) with slope -3/4 in slope-intercept form

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~ 8 &,& 0~) \end{array} \\\\\\ % slope = m slope = m\implies -\cfrac{3}{4} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-0=-\cfrac{3}{4}(x-8) \implies y=-\cfrac{3}{4}x+6[/tex]

please help understand this and get it done.

Answers

You have an odd number of minus signs in your problem statement. You need an odd number of minus signs in your answer.

The 1st, 3rd, and 5th selections are appropriate.

The graph illustrates a reflection of abc . What line is abc reflected across to create a'b'c'?

Answers

triangle ABC is reflected over the y axis
the answer is : y-axis

helpppppppppppppppppp

Answers

y = e ^ (4x)
 For this case what you should see are the values that the function takes when substituting any value of y.
 We have then that the function will always be greater than zero.
Therefore the rank of the function is:
 y> 0
 Answer:
 y> 0
 option 2
Answer:
y > 0

Explanation:
The range is defined as all the possible values for the y.
We know the exponential function never gives a negatives zero. It also doesn't give a zero value.
This means that whatever the value of the power of the exponent is, the answer would always be a positive value greater than zero

Hope thus helps :)

A animal shelter has 16 puppies. If the puppies are 32% of the total dogs and cats population, how many dogs and cats are in the animal shelter?

Answers

32%=16
100%=[tex] \frac{100}{32} *16=50animals[/tex]

The total number of animals in a shelter is 50 and number of cats in the shelter is 34.

Given that, a animal shelter has 16 puppies. If the puppies are 32% of the total dogs and cats population.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let x be the total number of dogs and cats are in the animal shelter.

So, 32% of x=16

⇒ 32/100 ×x=16

⇒ 0.32x=16

⇒ x=16/0.32

⇒ x=50

So, number of cats =50-16

= 34

Therefore, the total number of animals in a shelter is 50 and number of cats in the shelter is 34.

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A 3500.00 $ principal earns 3% annual interest, Compounded semiannually after 20 years, what is the balance in the account

Answers

$4,713.99

Hope this helped!

The perimeter of a rectangular outdoor patio is 60 ft. the length is 4 ft greater than the width. what are the dimensions of the patio? l w

Answers

The length of rectangular outdoor patio is 17 feet and the width is 13 feet.

Given that, the perimeter of a rectangular outdoor patio is 60 ft.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Let the width of the rectangular outdoor patio be x.

Then, the length is 4 ft greater than the width = x+4

Now, perimeter = 2(x+x+4)

⇒ 2(2x+4) = 60

⇒ 4x+8=60

⇒ 4x=52

⇒ x=13

Length = x+4 = 17

Therefore, the length of rectangular outdoor patio is 17 feet and the width is 13 feet.

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Lucy watched TV for 25 of an hour on Monday. She watched 79 of an hour on Tuesday. What day did she spend more time watching TV?

Answers

Hello there,

Lucy watched more TV on Tuesday.

This is because 1 hour = 60 minutes.

so, 25% of 60 min = 15 min on Monday

and, 79% of 60 min = 47.7 min rounded gives 48 minutes on Tuesday...

Hope this answer helps. Good luck.


A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answers

We must solve the system in order to find an answer.
Let's solve the system of equations:
[tex]x + y = 24\\ 3x + 5y = 100[/tex]
Now let us multiply the first equation by -3:
[tex]x + y = 24/\cdot(-3)\\ 3x + 5y = 100\\ --------\\ -3x-3y=-72\\ 3x + 5y = 100 [/tex]
We add those two equations together( 3x-3x will cancel out):
[tex]-3x-3y=-72\\+ 3x + 5y = 100\\ --------(+)\\ 2y=28\\ y=14 [/tex]
Now we simply plug y=14 into any of the starting equations to find x:
[tex]x + y = 24\\ x+14=24\\ x=10[/tex]
The answer is B:
The test contains 10 three-point questions and 14 five-point questions.

The answer to your question is B :)

There are 20,000 owls in the wild. Every year the population decreases by 8%. How many owls will there be after 8 years?

Answers

After 8 years, there will be approximately 10,260 owls remaining in the wild. This calculation is based on an initial population of 20,000 owls decreasing by 8% annually, yielding a final population using the formula for exponential decay.

To find out how many owls will remain after 8 years, we can use the formula for exponential decay:

[tex]\[ \text{Final population} = \text{Initial population} \times (1 - \text{Rate of decrease})^{\text{Number of years}} \][/tex]

Given:

Initial population (P) = 20,000 owls

Rate of decrease (r) = 8% = 0.08

Number of years (t) = 8

Plugging in the values:

[tex]\[ \text{Final population} = 20,000 \times (1 - 0.08)^8 \][/tex]

[tex]\[ \text{Final population} = 20,000 \times (0.92)^8 \][/tex]

[tex]\[ \text{Final population} \approx 20,000 \times 0.513 \][/tex]

[tex]\[ \text{Final population} \approx 10,260 \][/tex]

So, after 8 years, there will be approximately 10,260 owls remaining in the wild.

Find the equation for the line that passes through the point (1, 3), and that is perpendicular to the line with the equation −3x − 4y = 13.

Answers

-3x - 4y = 13
-3 - 12 = 13
-15 = 13

Pls, answer!! I will mark the 1st person to answer correctly with work as brainliest for 20 points!

Answers

Lets get started ;)
 
[tex] 8\frac{1}{3} [/tex] = [tex] \frac{25}{3} [/tex]
[tex]2 \frac{1}{3} [/tex] = [tex] \frac{7}{3} [/tex]
8.1 = [tex] \frac{81}{10} [/tex]

(When you divide by a value/fraction, you can multiply by its reciprocal)

[tex] \frac{25}{3} [/tex] × [tex] \frac{1}{x} [/tex] = [tex] \frac{7}{3} [/tex] × [tex] \frac{10}{81} [/tex]

[tex] \frac{25}{3x} [/tex] = [tex] \frac{70}{243} [/tex]

We can cross multiply :)

25 × 243 = 3x × 70
6075 = 210x

We can divide by on either side to isolate x and thus find its value

[tex] \frac{6075}{210} [/tex] = [tex] \frac{210x}{210} [/tex]

210 and 210 cancels out on the right-hand side


[tex] \frac{405}{14} [/tex]  = x


The yearly profit of a company in thousands of dollars is given by the finction P(x) =3000+1200-6x^2 where x is the amount in thousands the company spneds on advertising. Find the amount ,x, that the company has to spend to maxamize its profit

Answers

the maximum or minimum happens when x=-b/2a
x=-1200/[2*(-6)]=100


the maximum happens when x=100

Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song. King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?

Answers

Answer: 4

Explanation:

Translate the english language to mathematical (algebraic) language.

This implies to define the variables and translates the statements into equations.

1) Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song.

Cost = price of the mp3 player + price each song * number of songs

Variables:

number of songs: n
price each son: $3.25
price of the mp3 player: $ 18.00
Cost: c(n), this means that the cost is a function of n.

c(n) = 18 + 3.25n

2) King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?

Using the same procedure used for Adventure Play case:

c(n) = 23 + 2n

3) Equal cost =>

18 + 3.25n = 23 + 2n

=> 3.25n - 2n = 23 - 18
=> 1.25n = 5
=> n = 5 / 1.25
=> n = 4

Answer: the cost will be the same for 4 songs.

Answer:

4 songs

Step-by-step explanation:

What is the slope of the line 3x + 4y = -11?

answers:
3\4
-3\4
3
4

Answers

 you need to make it in the form of y=mx+b, and m will be the slope 
so... 
3x-4y=7 
subtract 3x from both sides 
-4y=-3x+7 
then divide both sides by -4 
y=(3/4)x-7/4 

so the slope is 3/4

Final answer:

To find the slope of the line given by 3x + 4y = -11, the equation is rearranged into the slope-intercept form, yielding a slope (m) of -3/4.

Explanation:

The question asks: What is the slope of the line 3x + 4y = -11?

To find the slope of the line, we first need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept. Starting with the given equation

3x + 4y = -11

We isolate y on one side by first moving 3x to the right side of the equation, and then dividing everything by 4:

4y = -3x - 11y = (-3/4)x - 11/4

Now, in the form of y = mx + b, it's clear that the slope (m) of the line is -3/4.

The coordinates of triangle DEF are Upper D left parenthesis 3 comma 3 right parenthesis​, Upper E left parenthesis 8 comma 3 right parenthesis​, and Upper F left parenthesis 5 comma 7 right parenthesis. If you translate triangle DEF 2 units right and 3 units down​, what are the coordinates of Upper E​'?

Answers

The answer would be (10 , 5)
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