Answer:
Step-by-step explanation:
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
Subtract the linear expressions. (−2.6x+4.2)−(3.9x+2.5) What is the difference? Enter your answer in the box.
Answer:
-13x/2+1.7
Step-by-step explanation:
The difference of the given expression is - 6.5 x + 1.7.
Given that, (−2.6x+4.2)−(3.9x+2.5).
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Now, (−2.6x+4.2)−(3.9x+2.5)
= (-2.6x-3.9x)+4.2-2.5
= - 6.5 x + 1.7
Therefore, the difference of the given expression is - 6.5 x + 1.7.
To learn more about the subtraction of expression visit:
brainly.com/question/12959016.
#SPJ2
I need some help with this plz
Answer: acute angle
Step-by-step explanation:
In a church, the ratio of adults to children is 10 to 5. If there are 135 people in the church, how many children are there?
Answer:
45
Step-by-step explanation:
That means in every group of 15, there are 5 children
135 / 15 = 9. So Nine groups of 15. 9 x 5 = 45
guys pls help me!!!!!!
Answer:
56 degrees
Step-by-step explanation:
Answer:
X 56 Y 56
Step-by-step explanation:
because 180-124=56
What is
5
90
in decimal form?
Answer:
590 decimal form is 5.9
Step-by-step explanation:
Answer:
0.05555555555Step-by-step explanation:
it is only a division
5/90 =
5 : 90 =
0.05555555555
Which angle in the isosceles triangles is the biggest?
Answer:
Since the two base angles are congruent (same measure), they are each 70°. If we are given a base angle of say 45°, we know the base angles are congruent (same measure) and the interior angles of any triangle always add to 180°.
Answer:
degrees
Step-by-step explanation:
49000000 -8373448588766
answer:
-8.3733995^12
can someone please help me fill in the answer in the bottom.
Answer:
Step-by-step explanation:
1) Initial water level = 30 feet
2) Rate of change = (30 - 25) / (0 - 1) = 5/(-1) = -5
5ft per hour
3) y-intercept = 30
Find the slope of the line that contains the following pair of
points:
(-3,-4) and (3,-2).
Answer:
1/3
Step-by-step explanation:
gradient or slope = m
m = change in y ÷ change in x
= (-4 - -2) ÷ (-3 - 3)
= (-4 + 2) ÷ (-3 - 3)
= -2 ÷ -6
= 1/3
If < is the angle sign
What is the value of z?
Answer:19
Step-by-step explanation:
8 kg of potatoes and 5 kg of carrots cost $28 whereas 2 kg of potatoes and 3 kg of carrots cost $11.20. Find the cost of 1 kg of each item.
also give the explanation.
Answer:
Step-by-step explanation:
Cost of 1 kg of Potatoes = $ 2
Cost of 1 kg of Carrots = $ 2.40
Let the cost of 1 kg of Potatoes = x
Let the cost of 1 kg of Carrots = y
ATQ , 8x + 5y = 28 - 1)
2x + 3y = 11.20 - 2)
Multiplying 2) by 4
8x + 12y = 44.80 - 3)
Applying Elimination method in 1) and 3)
8x + 5y = 28.00
8x + 12y = 44.80
0 + -7y = - 16.80
y = 16.8/7
y = 2.4
Putting the value of "y" in 1)
8x + 5(2.4) = 28
8x + 12 = 28
8x = 16
x = 16/8
x = 2
A college student takes out a $7 500 loan from a bank. Assuming the student has not started paying back the money, how much does the student owe . . .
1.1 . . . after 1 year, if the bank charges 3.8% interest each year?
easy one - giving brainly if correct!
Answer:
option 4 is the right answer
Answer:
The last option is right
HELP WILL GIVE BRAINLIEST ASAP
Answer:
I believe it's also 74°
Step-by-step explanation:
Because AGF and CGE are congruent,so the angle measurement should stay the same
Answer:
CGE is 74°
Step-by-step explanation:
AGF = FGD
FGD = CGE
AGF = EGB
AGF = 74°
FGD = 74°
CGE = 74°
EGB = 74°
360° is a circle and CGA = BGD
74 + 74 + 74 + 74 + x + x = 360
296 + 2x = 360
2x = 360 - 296
2x = 64
2x/2 = 64/2
x = 32
CGA and BGD are 32
CGE is 74°
Hope This Helps! •v•
I'll give brainliest if correct.
File included down below
No solution. The first two equations would need to equal each other, but they don't, so it is mathematically impossible.
Answer: k=0
Step-by-step explanation:
[tex]kx+z=3\\\\-z -z[/tex]
[tex]kx=3-z[/tex]
[tex]\frac{kx}{k} =\frac{3}{k}-\frac{z}{k}[/tex]
[tex]x=\frac{3-z}{k}[/tex]
Feel free to let me know if it's wrong
HELP!
Find f(-1) for f(x) = -3x + 2x”.
Answer:
f(-1) = 1
Step-by-step explanation:
f(-1) just means you plug -1 into the equation:
-3x + 2x
-3(-1) + 2(-1)
3 - 2
1
Hopefully this helps!
Brainliest please?
An ant moves at 14 cm a min. How many minutes will it take him to travel 10 points
364 cm? What is the time ? (Write your answer in "t=" form)
Answer:
26 minutes/ t=26
Step-by-step explanation:
F) c=14t
S) 364=14t
E) t=26
Yo can y'all help me with this I already did it on another paper. It would be very helpful if it was a step by step explanation take 100 points brother
Answer:
there is no question if you provide one in comments I will edit my answer to answer the question
Step-by-step explanation:
Write the expression 44(4-7)(4) using a single
exponent.
O
4-28
044
X
4-3
O 4-2
RETRY
___________
[tex] \: [/tex]
[tex] {4}^{4} ( {4}^{ - 7} )(4) = ...[/tex]
[tex] = {4}^{4 + ( - 7) + 1} [/tex]
[tex] = {4}^{ - 3 + 1} [/tex]
[tex] = \bold{{4}^{ - 2} } \to({ \sf{d.}})[/tex]
*
-12 -10 8 6 4 2 0 2 4 6 8 10 12
Which division problem is modeled on the number line?
012-3
-12 - 3
0-12 =-4
124
the correct answer is b :)
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.
Step-by-step explanation:
y coordinate
m = slope
x = x coordinate
b = y intercept
Please solve the math problem for me... I will mark you brainliest
Answer:
x = 5
Step-by-step explanation:
3x + 1 should equal 16
Answer:
X=5
Step-by-step explanation:
3x+1=16
move the 1 over to the 16 so it is 16 - 1 = 15
3x=15
Move the 3 over to where the 15 is in order to get x by itself
3/3 = x
3/15 = 5
so X should = 5
hoose the statement that describes its
solution.
3(x + 8) - 9x = 6(4- x)
O There is no solution.
оо
There is only one solution.
ws
о
All real numbers are solutions.
Answer:
3rd option
Step-by-step explanation:
3(x + 8) - 9x = 6(4 - x) ← distribute parenthesis on both sides
3x + 24 - 9x = 24 - 6x , collect like terms on left side )
24 - 6x = 24 - 6x
Since both sides are the same then any value of x will make the equation true.
That is all real numbers are solutions
Answer: C g(x) is a function because f(x) is one-to-one.
Step-by-step explanation:
What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y=-4/3x -1
Answer:
[tex]y=\displaystyle-\frac{4}{3}x+22[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-interceptParallel lines always have the same slope (m)Determine the slope (m):
[tex]y=\displaystyle-\frac{4}{3}x -1[/tex]
The slope of the given line is [tex]\displaystyle-\frac{4}{3}[/tex], since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be [tex]\displaystyle-\frac{4}{3}[/tex]. Plug this into y=mx+b:
[tex]y=\displaystyle-\frac{4}{3}x+b[/tex]
Determine the y-intercept (b):
[tex]y=\displaystyle-\frac{4}{3}x+b[/tex]
To find the y-intercept, plug in the given point (6,14) and solve for b:
[tex]14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22[/tex]
Therefore, the y-intercept of the line is 22. Plug this back into [tex]y=\displaystyle-\frac{4}{3}x+b[/tex]:
[tex]y=\displaystyle-\frac{4}{3}x+22[/tex]
I hope this helps!
Help!!!! I have a math assignment due this WEDNESDAY!!! I don’t understand what I’m supposed-to do. I started writing but I feel like whatever I wrote is incorrect! Just someone PLEASE help!
Eight people are competing in an art contest for 1st, 2nd, and 3rd place awards. How many
different combinations of awards are there?
Answer:
24 Combinations
Step-by-step explanation:
There are 8 people and there is a possibility that each can be either 1st, 2nd, 3rd. You would multiply 8 x 3 to get 24 or add 3 eight times
A cube has an edge length of 21 cm. What is the volume?
o 212 cm3
o 6 x 21 cm
o 213 cm
o 3x21 cm3
Answer:
Step-by-step explanation:
Volume = 21^3 cm^3.
WILL CHOOSE BRAINLIEST:Directions: From the graph, write the linear equation in slope-intercept form
Answer:
y = -2/3x - 2
Step-by-step explanation:
Picking two points on the line: (0,-2) & (-3,0)
Using the slope formula:
[tex]\frac{x2-x1}{y2-y1}[/tex]
= (0-(-2))/(-3-0)
= 2/-3
= -2/3
y = -2/3x + c
Subsituting (0,-2) into 'y = -2/3x+c':
-2 = 0 + c
c= -2
Hence,
y = -2/3x -2
Hope this helps, and be sure to have a wonderful time ahead at Brainly! :D
Feel free to mark this as brainliest :D
