Answer:
what is the question asking?
Algebra 2 - Standard form of a quadratic function
1. A field goal kicker discussed his performance with this coach. Based on the coach’s data, the kicker usually kicks the ball so it reaches a maximum height of 50 yards
after it has traveled 25 yards down the field. What is the equation, in standard form, of the kick? Round your answer to the nearest hundredth
2. If the goal posts are 10 yards high, what is the minimum and maximum distance that his kick will make it over the goalpost? Round your answer to the nearest hundredth
Using quadratic function concepts, it is found that:
1) The equation is [tex]y = -0.08x^2 + 4x[/tex]
2) The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
In this problem:
The ball was kicked from the ground, thus [tex]y(0) = 0[/tex], which means that c = 0.Item 1:
The vertex is: [tex]V(x_v,y_v)[/tex], in which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, it is (25,50). Thus:
[tex]-\frac{b}{2a} = 25[/tex]
[tex]-b = 50a[/tex]
[tex]b = -50a[/tex]
[tex]-\frac{b^2 - 4ac}{4a} = 50[/tex]
[tex]-b^2 = 200a[/tex]
[tex]-(50a)^2 = 200a[/tex]
[tex]-2500a^2 - 200a = 0[/tex]
[tex]200a(-12.5a - 1) = 0[/tex]
Then, as [tex]a \neq 0[/tex]
[tex]a = -\frac{1}{12.5} = -0.08[/tex]
[tex]b = -50a = -50(-0.08) = 4[/tex]
Thus, the equation, in standard form, is:
[tex]y = -0.08x^2 + 4x[/tex]
Item 2:
The distances are the values of x for which:
[tex]y = 10[/tex]
Then
[tex]-0.08x^2 + 4x = 10[/tex]
[tex]-0.08x^2 + 4x - 10 = 0[/tex]
Which is a quadratic equation with [tex]a = -0.08, b = 4, c = -10[/tex]. Then:
[tex]\Delta = 4^2 - 4(-0.08)(-10) = 12.8[/tex]
[tex]x_{1} = \frac{-4 + \sqrt{12.8}}{2(-0.08)} = 2.64[/tex]
[tex]x_{2} = \frac{-4 - \sqrt{12.8}}{2(-0.08)} = 47.36[/tex]
The minimum distance is of 2.64 yards, and the maximum is of 47.36 yards.
A similar problem is given at https://brainly.com/question/24713268
Each year the local country club sponsors a tennis tournament. Plays starts with 128 participants. During each round, half of the players are eliminated. How many players remain after five rounds?
Answer:
128 divided by 2 for 5 times is your answer enjoy my.kiddo
4.5 kg equals times one gram
Answer:
4500 gr
Step-by-step explanation:
4.5 kg equals some number (n) times one gram. Solve this for n:
4.5 kg = n(1 gr)
Recall that 1 kg = 1000 gr. Because of this, the equation above becomes
4.5 kg (4.5)(1000 gr)
n = --------------- or ------------------- or 4500 gr
1000 gr 1 gr
Find (f +g)(x) where f(x) = x+ 3 and g(x) = x + 4.
Answer:
Correct answer is A
Step-by-step explanation:
In pic
Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
help please because I feel like my brain is gonna rot from this (please look at the image)
Answer:
124.3
Step-by-step explanation:
42.15+20.00=1/2x
62.15=1/2x
62.15*2
124.3 is the total of her paycheck.
42.1<20.00+x
Liam is a tyre fitter question
Answer:
a) 168
b) 3
Step-by-step explanation:
a) 56÷4=14 14×12=168
b) 56÷4=14 56-14=42 42÷14=3
HELP!! Please!! Complete the equation describing how
x and y are related.
Answer please
Can someone give me the answer
Answer:
sorry I don't know pls ask someone else
Jennifer has 84.5 yards of fabric to make. She makes 6 identical curtains and has 19.7 yards of fabric remaining. How many FEET of fabric does Jennifer use per curtain?
Answer: 118.2
Step-by-step explanation:
Shaq painted 600 portraits in 8 hours at that rate how many portraits would he paint in 4 minutes?
Answer: In 4 minutes he will make 5 portraits
Step-by-step explanation:
[tex]\large \boldsymbol{} 600p-8h=480 min \\\\ x \ p-4 min \\\\ x=\dfrac{600\cdot 4}{480} =\dfrac{2400}{480} =5 \ portraits \\\\ \rm Answer : 5[/tex]
Simplify
2^4 x 2^3/
2^5 x 2^4
leaving your answer in index form.
Answer:
2^-2
Step-by-step explanation:
When multiplying indices or exponents with the same base number, you can add the powers:
2^4 x 2³ = 2^7 (4 + 3 = 7)
2^5 x 2^4 = 2^9 (5 + 4 = 9)
When dividing indices or exponents with the same base number, you can subtract the powers:
2^7 ÷ 2^9 = 2^-2 (7 - 9 = -2)
Three out of nine cats weigh less than 15 pounds.
What is the decimal equivalent for the number of cats weighing less than 15 pounds?
Answer:
0.333...
Step-by-step explanation:
3 out of 9 can be written as 3/9 which reduces to 1/3.
1/3 = 0.333...
The value of
[tex]2 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + ... \infin} } } \: is \\ [/tex]
Given answer with step by step explanation.
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to find out the value of the fraction.
Let us assume that:
[tex] \sf \longmapsto x =2 + \dfrac{1}{2 + \dfrac{1}{2 + \dfrac{1}{2 + ... \infty} } } [/tex]
We can also write it as:
[tex] \sf \longmapsto x =2 + \dfrac{1}{x} [/tex]
[tex] \sf \longmapsto x =\dfrac{2x + 1}{x} [/tex]
[tex] \sf \longmapsto {x}^{2} =2x + 1[/tex]
[tex] \sf \longmapsto {x}^{2} - 2x - 1 = 0[/tex]
Comparing the given equation with ax² + bx + c = 0, we get:
[tex] \sf \longmapsto\begin{cases} \sf a =1 \\ \sf b = - 2 \\ \sf c = - 1 \end{cases}[/tex]
By quadratic formula:
[tex] \sf \longmapsto x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm \sqrt{8} }{2} [/tex]
[tex] \sf \longmapsto x = \dfrac{2 \pm2 \sqrt{2} }{2} [/tex]
[tex] \sf \longmapsto x = 1 \pm\sqrt{2}[/tex]
[tex] \sf \longmapsto x = \begin{cases} \sf 1 + \sqrt{2} \\ \sf 1 - \sqrt{2} \end{cases}[/tex]
But "x" cannot be negative. Therefore:
[tex] \sf :\implies x = 1 + \sqrt{2}[/tex]
So, the value of the fraction is 1 + √2.
How to solve for j -10=║j-7║
Answer:
No solutions.
Step-by-step explanation:
-10 = 7
No solutions
can someone please help me with this question including a full explnation?
Given :-
Diameter of table = 2.3m Length of cloth to be hanged = 10cm .To find :-
The area of tablecloth required .Solution :-
According to Question ,
r = 2.3/2 + 10/100 m r = 1.15 + 0.1m r = 1.25mAs we know that ,
Area = πr²Area = 3.14 * 1.25 * 1.25 m² Area = 4.90 m² ≈ 5m²what is the slope of this line?
a) -1/3
b)1/3
c) -2/3
d) 2/3
Answer:
look at the picture i have sent
Eighth grade Y.14 Solve equations with the distributive property SRP Solve for u. -9.6u - 6.96 = -3(2.4u – 4.72) – = U = Submit
Answer:
2.93 repeating
Step-by-step explanation:
help please I need help
Answer:
a is 16 yards hope this helps
Step-by-step explanation:
15. A 12.5 oz bag of Doritos for $3.79 or a 3 oz bag for $1.00.
☆
Which is the better buy
Answer: $3.79 for 12.5 oz. is cheaper per ounce than $1.00 for 3oz.
Step-by-step explanation: Without much effort we can see that $ 1.00 for 3 oz $4.00 for 12 oz. but you can get more (12.5 oz.) for less than $4.00 (for $3.79) if you buy 12.5 oz. for $3.79
What is the axis of symmetry of the quadratic function y = 2(x + 3)2 + 5?
Answer:
I would answer it correctly but only 5 points -_-
Step-by-step explanation:
A water tank currently contains 275 gallons of water. The amount of water in the tank will decrease at a constant rate of 15 gallons per week.
Which function can be used to find t, the total number of gallons of water in the tank after w weeks?
F t = 15w - 275
G t = -15w + 275
H t = 275w - 15
J t = -275w + 15
The function that can be used to find t, the total number of gallons of water in the tank after w weeks will be t = -15w + 275
The initial volume of water in the tank is 275 gallons
The amount of water in the tank decreases at a constant rate of 15 gallons per week.
t = total number of gallons water in the tank after weeks
w = number of weeks
Therefore, the following equation/theory can be establish
The initial gallon of water in the tank is 275 gallons that means we should have positive value of 275 in the equationThe gallon of water reduces by 15 gallons each week which means 15 gallons will be subtracted from the initial gallons of water each week. This means we have to find the product of -15 and w(number of weeks).The equation will be
t = 275 - 15w
or
t = -15w + 275
Check here for more details on how to find linear equations: https://brainly.com/question/17846793?referrer=searchResults
Complete the following statement.
The ratio of adults to children at a family reunion is 16 to 10. If there are 91 people at the family reunion, there are
adults and
children.
Answer:
56 adults and 35 children
Step-by-step explanation:
sum the parts of the ratio 16 + 10 = 26
Divide 91 by 26 to find one part of the ratio
91/26 = 3.5 ← 1 part of the ratio
16 parts = 16 × 3.5 = 56 ← number of adults
10 parts = 10 × 3.5 = 35 ← number of children
Therefore it 56 adults and 35 children.
To Check the Answer: 56 + 35 = 91
Which equations describes a line that has a y-intercept of 4 and a slope of 3?
Hello there!
If a line has a slope of 3 and a y-intercept of 4, its equation looks like this:
[tex]y=3x+4[/tex]
Hope this helps you! Mark Brainliest, please! :)
~Just a joyful teen
[tex]SilentNature[/tex]
Answer:
y = 3x + 4
Step-by-step explanation:
The diagram shows triangle QRS with side SR on ray ST.
Part A. What is the measure of ∠QRS?
Part B. What is the measure of ∠Q?\
PLEASE HELP WITH ALL SERIOUSNESS AND A PROPER EXPLANATION
Enter the correct answers in the boxes.
The measure of angle QRS is 35 degrees and the measure of angle Q is 116 degrees.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know in the triangle the sum of the two interior angles is equal to the exterior angle.
Angle RQS + Angle RSQ = Angle TRQ
4y + y = 145
5y = 145
y = 29
The measure of angle QRS = 180 - Angle RQS - Angle RSQ
= 180 - 4(29) - 29
Angle QRS = 35 degree
The measure of angle Q = 4y = 4(29) = 116 degree
Thus, the measure of angle QRS is 35 degrees and the measure of angle Q is 116 degrees.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ1
Help plz I need help plz
Step-by-step explanation:
the third option is the correct one
Pablo owes his sister $9. His sister Nina owes their mother three times that amount. What number on the number line represents Nina’s debt?
Answer:
Step-by-step explanation:
Nina's debt = 3 * 9 = $ 27
Debt is represented using negative sign.This represents (-27) on the number line.
Answer:(-27)
Step-by-step explanation:
i got it right on edge 2022
can someone please help me with this? i don’t understand it at all
Answer: I’m pretty sure they are similar because they have the same interior degree.
Step-by-step explanation:
please help ill gjve u brainliest.
Answer: (Read Explanation)
Step-by-step explanation:
I have attached a picture of the matching plot.
I NEED HELPPP WHEN THESE!!! please can someone help
Answer:
a: 36
b: 10
c: 3.2
d: a
Step-by-step explanation:
Answer:
A = 36
B = 10
C = 3.2
D = a
Step-by-step explanation:
The square roots and power of 2s zero each other out.
What’s the perimeter of 4 feet long and 4 feet wide
4 times 4 so your awnser is 12
Hope that helps :)
Answer:
16
Step-by-step explanation:
4+4+4+4