Johnny kicks a ball into the air. Assume the path of the ball can be modeled with a quadratic function. The ball reaches a height of 10 feet and lands on the ground 3 seconds later. Draw and label a graph that models the path of the ball. Write an equation that models the path of Johnny’s ball.
Answers
An equation that models the path of Johnny’s ball is [tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
The maximum height is given as:
[tex]h_{max}= 10ft[/tex]
And the time spent is:
[tex]t = 3s[/tex]
So, the vertex of the ball would be:
[tex]Vertex = (t/2,h_{max})[/tex]
This gives
[tex]Vertex = (3/2,10)[/tex]
[tex]Vertex = (1.5,10)[/tex]
Rewrite properly as:
[tex](h,k) = (1.5,10)[/tex]
The ball is on the floor after 3 seconds.
So, another point on the graph is:
[tex](x,y) = (3,0)[/tex]
A quadratic equation is represented as:
[tex]y=a(x - h)^2 + k[/tex]
Substitute [tex](x,y) = (3,0)[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]0=a(3 - 1.5)^2 + 10[/tex]
[tex]0=a(1.5)^2 + 10[/tex]
Evaluate the exponent
[tex]0=2.25a + 10[/tex]
Subtract 10 from both sides
[tex]2.25a =- 10[/tex]
Divide both sides by 2.25
[tex]a = -\frac{10}{2.25}[/tex]
Multiply by 4/4
[tex]a = -\frac{40}{9}[/tex]
Substitute [tex]a = -\frac{40}{9}[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
See attachment for the graph that models the path
Read more about quadratic functions at:
https://brainly.com/question/11441586
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D={1, 2, 3, 4}
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convert 3x-y=-5 to slope intercept form
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Answer:
y=3x+5
Step-by-step explanation:
y=mx+b
-y=-5-3x
divide each term
y=5+3x
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marlene is painting square tiles for a project.each tile has a perimeter of 16 in.what is the length of each side.
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Answer:
64 i hope im right
Step-by-step explanation:
Answer: 4 in.
Step-by-step explanation:
A square has 4 equal sides for its perimeter.
Perimeter = 4x
16 = 4x
x = 4 in.
After the first four games of a professional football season, three players scored a total of 80 touchdowns.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns.
Andre Roberts scored the remaining touchdowns.
How many touchdowns did Andre Roberts score?
A.20 touchdowns
B.28 touchdowns
C.32 touchdowns
D.52 touchdowns
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Find the slope of a line perpendicular to the given line. x = - 1
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What is the correct classification of the system of equations below?
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y+ 7x=-5
A.
parallel
B.
coincident
C.
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Answer:
parallel
B.
coincident
C.
intersecting
Answer:
I think it's parallel, because they have the same gradient. parallel lines always have the same gradient
Given the function f(x) = √x. If the function is shifted right 2 units, then shifted down 1.5 units and reflected about the x-axis, what is the equation of the new function?
Answers
Answer:
f(x) = -√(x-2) + 1.5.
Step-by-step explanation:
y = √x
2 units to right:
y = √(x-2)
1.5 down:
y = √(x-2) - 1.5
Reflect about x-axis
y = -(√(x-2) - 1.5)
y = -√(x-2) + 1.5.
Bonjour à tous, pouvez vous m'aider à trouver la réponse pour cette "question ouverte" svp?
Parmi les rectangles de périmètre 100cm, quelles sont les dimensions du rectangle d'aire maximale?
Merci d'avance, Joudy :))
Answers
La solution:
625 cm^2.
Explication étape par étape:
Si la forme est rectangulaire, elle aura la plus grande superficie possible quand la longueur équivaut à la largeur. Pour avoir un périmètre de 100 cm, cela signifie que chaque côté doit faire 25 cm.
La superficie serait alors de 25 cm x 25 cm = 625 cm^2.
A sports teacher had 1025 sweets. After distributing these equally amongst all the participants in a sports meet, he had just 1 sweet left with him. Which of these could be the number of sweets given away to each participant?
Answers
Step-by-step explanation:
Since it remains only 1 sweet, we can subtract it from the total and get the amount of sweets distributed (=1024).
As all the sweets are distributed equally, we must divide the number of distributed sweets by all its dividers (excluding 1024 and 1, we'll see later why):
1) 512 => 2 partecipants
2) 256 => 4 partecipants
3) 128 => 8 partecipants
4) 64 => 16 partecipants
5) 32 => 32 partecipants
6) 16 => 64 partecipants
7) 8 => 128 partecipants
9) 4 => 256 partecipants
10) 2 => 512 partecipants
The number on the left represents the number of sweets given to the partecipants, and on the right we have the number of the partecipants. Note that all the numbers on the left are dividers of 1024.
Why excluding 1 and 1024? Because the problem tells us that there remains 1 sweet. If there was 1 sweet for every partecipant, the number of partecipants would be 1025, but that's not possible as there remains 1 sweet. If it was 1024, it wouldn't work as well because the sweets are 1025 and if 1 is not distributed it goes again against the problem that says all sweets are equally distributed.
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[tex]\text{Given that,}\\\\ (x_1,y_1) = (-7,-4) ~~ \text{and slope}~ m = 3\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +4 = 3(x+7)~~~~~;[\text{Point-slope form.}]\\\\\implies y = 3x +21 -4\\\\\implies y = 3x +17~~~~~~~~~~~;[\text{Slope-intercept form.}]\\\\\text{Hence the answers are A and F.}[/tex]
what's 1+1 ???
enjoy!
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hope it helps
1. What translation is made from f(x) → -f(x)?
Answers
Answer: this is a reflection across the x-axis
PLEASE HELP ME, I NEED HELP ASAP!!!! :(
ty ty
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Answer:
y=10/3
Step-by-step explanation:
Answer:
y = - [tex]\frac{24}{7}[/tex]
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 6 when x = - 7
6 = - 7k ( divide both sides by - 7 )
- [tex]\frac{6}{7}[/tex] = k
y = - [tex]\frac{6}{7}[/tex] x ← equation of variation
When x = 4 , then
y = - [tex]\frac{6}{7}[/tex] × 4 = - [tex]\frac{24}{7}[/tex]
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Answer:
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Step-by-step explanation:
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Answers
Answer:
60°
Step-by-step explanation:
180° in a triangle.
180° ÷ 3 = 60°
The measure of each of the given angles of a triangle is 60°.
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Consider a triangle ΔABC. Since the angles of the triangle are congruent, we can say that -
∠A = ∠B = ∠C = X°
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X° + X° + X° = 180°
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Answer:
Step-by-step explanation:
1. 15/50 = 3/10
2. 8/24 = 1/3
3. 14/49 = 2/7
4. 6/63 = 2/21
5. 18/81 = 2/9
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Answers
Answer:
1/12
Step-by-step explanation:
1/4 divide by three= 1/4*1/3=1/12
Answer: 1/4 ÷ 3 = 1/12
Explanation: In order to divide fractions, you must follow these 3 simple steps:
Step 1. Turn the second fraction (the one you want to divide by) upside down
(this is now a reciprocal).
Step 2. Multiply the first fraction by that reciprocal.
Step 3. Simplify the fraction (if needed).
Simplify this question
Answers
[tex]4 + \sqrt{ - 16} \\ = 4 + \sqrt{ - 2 \times 2 \times 2 \times 2} \\ = 4 + 2\sqrt{ - 4} \\ = 2(2 + \sqrt{ - 4} )[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\\ \sf\longmapsto 4+√-16[/tex]
[tex]\\ \sf\longmapsto 4+√16i[/tex]
[tex]\\ \sf\longmapsto 4+4i[/tex]
Take 4common[tex]\\ \sf\longmapsto 4(1+i)[/tex]
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If the circumference of a circle is changed from 9am to 3 cm, how will the diameter change?
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Francesca is painting a picture of the purple flowers in her garden. She mixes paint to make the perfect color for each type of flower. For the daisies, she mixes 2 ounces of white paint and 5 ounces of purple paint. For the tulips, she mixes 3 ounces of white paint and 6 ounces of purple paint. Which flower is a darker shade of purple?
Answers
Find total ounces mixed for each flower:
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Tulips = 3 +6 = 9 ounces
Now find the ratio of purple to white for each one:
Daisies = 5/7 = 0.714
Tulips = 6/9 = 0.666
Daisies have more purple so would be the darker ones.
Answer:
Daisies
Step-by-step explanation:
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Answer:
Step-by-step explanation:
2:33pm
Answer:
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If 10 plus 2 equals 12 the what does 10 times 8 times 12 times 1 mean
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Answer:
960
Step-by-step explanation:
(10 + 2) = 12
"10 times 8 times 12 times 1"
what does 10 times 8 times 12 times 1 mean
10 * 8 * 12 * 1 = (10)(8)(12)(1)
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What additional information can be used to prove AZDX = AXYZ by SSS?
XZ=ZD
DX=YZ
DZ=YX
XZ=XY
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Answer:
B. DX = YZ
Step-by-step explanation:
you roll a die 100 times and a six shows up 74 times out of 100. based on these outcomes, what is the estimated probability that the next roll shows up as a six?
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In which situation below would you want to use the Explicit Formula instead of the Recursive Formula?
a. Find the 100th term when the first term is -3 and the common difference is 4.
b. Find the 3rd term when the first term is 2 and the common difference is 5.
c. Find the 7th term when the first term is -1 and the common difference is 10.
d. Find the 5th term when the first term is 7 and the common difference is -2.
Answers
Answer:
Find the 100th term when the first term is -3 and the common difference is 4.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Find the 100th term when the first term is -3 and the common difference is 4. I took the test and got 100 percent.
Solve the following quadratic equation for all values of x in simplest form.
2(5x + 9)2 + 10 = 28
Answers
Step-by-step explanation:
x = 2/5 or x = 0 Hope that will help
How do I find the percentage of two column data table?
Answers
Answer:
a) 47.7%
b) 87.2%
Step-by-step explanation:
Find the ratio of interest, and convert it to a percentage.
a)(messy right-handed writers)/(right-handed writers)
= 31/65 = 31/65 × 100% ≈ 47.7%
__
b)(neat right-handed writers)/(neat writers)
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Isaiah is ordering a sub sandwich for lunch. He can have turkey, ham, chicken, roast beef, or tuna. His bun choices are wheat, honey oat, and white. How many different sub combinations can Isaiah order?
Answers
Answer:
45 different sandwiches
Step-by-step explanation: