A soccer ball is kicked into the air, and its path can be modeled with a quadratic function. The table shows the time, t, in seconds, and the height of the soccer ball, h, in feet. Follow the steps to write the function. 1. Identify x-intercepts: (0, 0) and (5, 0) 2. Use factored form: f(t) = a(t − 0)(t − 5) f(t) = at(t − 5) 3. Find the value of: 12 = a(3)(3 − 5) 4. Write function: f(t) = t(t −)

Answers

Answer 1

Answer:

The quadratic equation for the soccer ball kicked into the air is,

$f(t) = -2t^2+ 5t$

Given-

Given that t is the time and h is height gain by the ball after kicked.Step 1- Identify x-intercepts at (0,0) and (5,0)

Equation of quadratic function for the given question can be written as,

$y=a(x-h)^2+k$

Step 1- Identify x-intercepts at (0,0) and (5,0)

The intercepts of y are (0,0) and (5,0)

Step 2- The equation of the quadratic function

$f(t)= at (t-5)$

Step 3- Find the value of a for the given function,

$12=a(3)(3-5)$

$12=3a*(-2)$

$a=(12)/(-6)$

Step 4-Function of the equation

Put the value of a in function, we get

$f(t) = -2t(t- 5)$

$f(t) = -2t^2+ 5t$

Hence, the above equation is the required equation for the given problem.

For more about the quadratic function, follow the link below-

brainly.com/question/2279619

Answer 2

Answer: The y-intercepts are
(0,0) and (5,0)
The equation of the quadratic function is
f(t) = at(t-5)
Solving for a
12 = a(3)(3-5)
a = -2
The equation of the quadractic function is
f(t) = -2t(t -5)
f(t) = -2t² + 10t

Further Explanation

Place value and total value

Place value refers to the value represented by a digit in a number based of its position in the number. Place values can be ones, tens, hundreds, thousands, etc

For example;

In the number; 13,548, the place value of the digits in the number are;

Ones -8

Tens - 4

Hundreds - 5

Thousands - 3

Ten Thousands – 1

Total value

Total value is given as the product of the digit and its place value.
For example; in the number, 13,548.
Total value of digits 1, 3, 5, 4, and 8 in the number 13,548 will be;

1 x 10,000 = 10,000

3 x 1000 = 3,000

5 x 100 = 500

4 x 10 = 40

8 x 1 = 8

The sum of the total values of digits in a number will be equivalent to the value of that number.

In the question.

Comparing the value of 3 in 6,300 and 530

The value of 3 in 6,300 is 300 and

The value of 3 in 530 is 30

Therefore; the value of 3 in 6300 is ten times the value of 3 in 530

Keywords: Place value, total value

Learn more about;

Types of number form: brainly.com/question/10754198
Example of place value: brainly.com/question/10754198
Example of total value: brainly.com/question/10754198

Level: Middle school

Subject: Mathematics

Topic: Place value and total value

Comparing the values of 3 in each of 6,300 and 530, we will have:

3 in 6300 is 3 hundreds while 3 in 530 is 3 tens

How to solve number place value?

Place value is defined as the value of each digit in a number. For example, the 5 in 853 represents 5 tens, or 50; however, the 5 in 5,003 represents 5 thousands, or 5,000.

We want to compare the values of 3 in each of the numbers 6,300 and 530.

Thus, we can say that:

3 in 6300 is called 3 hundreds while 3 in 30 is called 3 tens or 30

Read more about Number place value at: brainly.com/question/24997908

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Decrease £1280 by 60%

Answers

Hi rainy here !!! so lets see lets set up your problem like this

X/1280 = 60%/100 so lets cross multiply

100 times X =100X

60 times 1280 = 76800

100X=76800 now lets divide each side by 100

100 divided by 100 = 0

76800 divided by 100 = 768

X=768

So now we have to subtract to get the total amount so 1280 minus 768 = 512

512 is your answer :)

Hope I helped if u have any questions on how I did your problem feel free to message me or comment on my page bye !!!

Love ~Rainy~

For this question explainition should be proper

Answers

Answer:

960m

Step-by-step explanation:

10×8×3×4×xcm

960m

Your school wants to collect at least 5,000 box tops for a fundraiser. Write and graph an inequality to describe the amount of box tops that your school hopes to collect.

Answers

The answer is: $b\geq5,000$ and the graph is attached.

The explanation is shown below:

1. You must use the information given in the problem to write the inequality.

2. $b$ represents the number of box tops for the fundraiser. Based on the information, the value of $b$ must be greater than or equal to 5,000 box tops. Therefore, you have that the inequality is:

$b\geq5,000$

3. Then, you obtain the graph attached. As you can see, you must use a closed circle for ≥.

A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of bookmark ? Use 3.14 for pie

Answers

So you know that the are of a rectangle is Length x width, so that part is simply 12x4, which =48 sq cm.
To find the area of the two ends of the bookmark, two semicircles make one circle, so you can just find the area of one circle. The formula for the area of a circle is (3.14) x r². Because the diameter of the circle is the same as the width of the rectangle, half of the 4cm is the radius (2cm).
Area of Circle= (3.14)x(2²)=12.56 cm sq.
Total area = Area of rectangle + Area of Circle
TA= 48 + 12.56
TA= 60.56 sq cm

Which is the number, which when squared and added to 12 becomes seven times its value ?

Answers

$x^(2)+12=7*x$ , where x is unknown numer

Now we are moving $7*x$ on left side to obtain quadratic equation:

$x^(2)+12-7*x=0$

Our goal is to find two roots of this equation.

First we are finding delta:

$\Delta =b^(2)-4*a*c$

$\Delta =(-7)^(2)-4*1*12=1$

First root:

$x_(1)=(-b+√(\Delta))/(2*a)$

$x_(1)=(7+√(1 ))/(2)=4$

Second root:

$x_(2)=(-b-√(\Delta))/(2*a)$

$x_(2)=(7-√(1 ))/(2)=3$