A quadratic function has an axis of symmetry at x=4 and contains the points (2, -6) and (7, -11). Find the equation in standard form (y=ax2+bx+c). Then state the "a" value in the equation.
Answers
Answer:
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Step-by-step explanation:
A quadratic function is the standard form of the parabola. We can take advantage of the symmetry property of the parabola by using the following formula from the Analytical Geometry:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]C[/tex] - Parabola constant, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Depedent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex of the parabola, dimensionless.
If we know that [tex](x_{1},y_{1})=(2,-6)[/tex], [tex](x_{2},y_{2})=(7,-11)[/tex] and [tex]h = 4[/tex], then we have the following system of linear equations:
[tex](x_{1},y_{1})=(2,-6)[/tex]
[tex]-6-k = C\cdot (2-4)^{2}[/tex]
[tex]4\cdot C +k = -6[/tex] (2)
[tex](x_{2},y_{2})=(7,-11)[/tex]
[tex]-11-k =C\cdot (7-4)^{2}[/tex]
[tex]9\cdot C + k = -11[/tex] (3)
By clearing [tex]k[/tex] in (2) and (3) and equalizing each other, we get that:
[tex]-6-4\cdot C = -11-9\cdot C[/tex]
[tex]5\cdot C = -5[/tex]
[tex]C = -1[/tex]
And the remaining variable is calculated by substituting directly on (3):
[tex]k = -11-9\cdot C[/tex]
[tex]k = -11-9\cdot (-1)[/tex]
[tex]k = -2[/tex]
Then, the equation of the parabola is:
[tex]y+2 = -(x-4)^{2}[/tex]
And the standard form of the equation is obtained by algebraic handling:
[tex]y+2 = -(x^{2}-8\cdot x + 16)[/tex]
[tex]y + 2 = -x^{2}+8\cdot x -16[/tex]
[tex]y = -x^{2}+8\cdot x -18[/tex] (4)
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Related Questions
Your school band is performing a concert. Tickets cost $3 for students and $5 for adults. A total of 125 people attended the concert for a total ticket sales of $475. Write and solve a system of equations to find the number of students and adults that attended the concert. Make sure to write your answer in a complete sentence.
Answers
Given :
Tickets cost $3 for students and $5 for adults.
A total of 125 people attended the concert for a total ticket sales of $475.
To Find :
The number of students and adults that attended the concert.
Solution :
Let, number of students and adults that attended the concert is x and y.
Mathematical equation of given conditions :
x + y = 125 ....1)
3x + 5y = 425 ....2)
Putting value of x from 1 to equation 2 is :
3( 125 - y ) + 5y = 425
375 - 3y + 5y = 425
2y = 50
y = 25
x = 125 - 25
x = 100
Therefore, number of students and adults that attended the concert is 100 ans 25 respectively.
Hence, this is the required solution.
A circuit overloads at 1800 watts of electricity you plug in a toaster that uses 800 watts of electricity write and solve an inequality that represents how many watts you can add to the circuit without overloading it.
Answers
Answer:
x ≤ 1000 W
Step-by-step explanation:
Since the circuit becomes overloaded when the load exceeds 1800W and the toaster uses 800 W.
Let the additional watts be x
Therefore;
800 + x ≤ 1800
x ≤ 1800 -800
x ≤ 1000 W
______ terms are also expressions. (fill in the blank)
A. No
B. All
C. Some
Answers
c. some
please help meee i’m abt to failllllllllllll
Answers
Answer:
stop cheating boi
Step-by-step explanation:
Noa was paid a 25 percent commission for selling a used car.
Percents
Total
100%
If she was paid $1,631.24, what was the selling price of the car?
$4,078.10
$6,524.96
$8,156.20
$40,781.00
Answers
Answer:
$6,524.96
Step-by-step explanation:
His quarter commission times four is the awnser
Answer:
BHOPE THIS HELPSJordie's curtain company is making curtains for a local hotel. He wants each curtain to be 36 inches long. At the fabric store, fabric is sold by the foot. If Jordie's curtain company wants to make 67 curtains, how many feet of fabric will he need?
Answers
Answer: 201 feet
Step-by-step explanation:
It should be noted that 1 foot = 12 inches. Therefore, 36 inches = 36/12 = 3 feets.
Each cotton uses 3 feets in length. Therefore, 67 curtains will use:
= 67 × 3 feets
= 201 feets
The table list the profits of some of the worlds largest corporations in 2013. List the companies in order from greatest to least amount of profit
Answers
Answer:
C
Step-by-step explanation:
can someone help me answer this question please?
Answers
Answer:
A
Step-by-step explanation:
f(x) = (x + 3)(x + 2)(x - 3)
The three roots are going to give - 18 so only A and D can be correct. Why minus? because at some point 3 and 2 and - 3 will all be multiplied together. When they are, the result is - 18
So why did I write x + 2 rather than x - 2? Because the roots turn an equation into 0. You are looking for a way to make x + 2 = 0. It will do that when x = - 2
which is what you were given.
Now to get the answer
(x - 3)(x + 3) = x^2 - 9
(x^2 - 9)(x + 2) = x^3 + 2x^2 - 9x - 18 = f(x)
Find the area of a square with side length x when x is equal to the given value. Are the area of a square and the length of its side directly proportional? Justify your answer. x=10 in.
Answers
Step-by-step explanation:
The formula for calculating the area of a square is expressed as;
A = x² where;
x is the length of one side of the square
Given
x = 10in
A = 10²
A = 10 * 10
A = 100in²
Area of the square with side length 10in is 100in²
From the equation A = x², we can see that as the value of x increases, the value of the area also increases and vice versa. This means that the area of the square is directky proportional to its length. Hence we can say YES, the area of a square and the length of its side directly proportional
Answer:
100 sq in
Step-by-step explanation:
No, not proportional
Write an equation that could be used to find three consecutive odd integers whose sum is -3
Answers
Answer:
2x+1 + 2x+3 + 2x+5 = -3Step-by-step explanation:
2x+1 - the first odd integer
2 x+1 + 2 = 2x+3 - the next odd integer consecutive to 2x+1
2x+3+2 = 2x+5 - the odd integer consecutive to 2x+3 (the third consecutive odd integer)
2x+1 + 2x+3 + 2x+5 - the sum of three consecutive odd integers
therefore the equation:
2x+1 + 2x+3 + 2x+5 = -3
6x + 9 = -3
6x = -12
x = -2
2x+1=2(-2)+1=-3
2x+3=2(-2)+3=-1
2x+5=2(-2)+5=1
the three consecutive odd integers whose sum is -3 are: -3,-1,1
using the same application you used in part f, reflect the line segment across the x-axis. then, rotate it 90° clockwise. Finally. translate it down 2 units. what is the relationship between the original line segment and the transformed segment ? if you transform a line segment with a seweurnce of reflections, to stations, or translations, is it still a line segment ?
Answers
Answer:
non
Step-by-step explanation:
There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
Answers
Answer:
The maximum area is therefore is 93750 ft²
Step-by-step explanation:
The given parameter are;
The a]length of fencing available = 1500 ft.
The perimeter of the figure = 9·x + 4·y
Therefore, 9·x + 4·y = 1500 ft.
The area of the figure = 6 × (x × y) = 3·x × 2·y
From the equation for the perimeter, we have;
9·x + 4·y = 1500
y = 1500/4 - 9/4·x = 375 - 9/4·x
y = 375 - 9/4·x
Substituting the value of y in the equation for the area gives;
Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²
Area = 2250·x - 27/2·x²
The maximum area is found by taking the derivative and equating to zero as follows;
d(2250·x - 27/2·x²)/dx = 0
2250 - 27·x = 0
x = 2250/27 = 250/3
x = 250/3
y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5
The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²
The maximum area is therefore = 93750 ft.²
Help plz:))) I’ll mark u brainliest
Answers
Emie read that the movie made 25,992,412.50 in its third week he also read that the average ticket price for this week was 8.35how many people saw the movie this week
Answers
Given :
Collection in third week, C = $25,992,412.50 .
Average ticket price, T = $8.35 .
To Find :
Number of people who saw movie in week.
Solution :
Let, number of people are x.
[tex]\text{Number of people }=\dfrac{\text{Total amount }}{\text{Average price}}\\\\= \dfrac{25,992,412.50 }{8.35}\\\\[/tex]
≈ 3112864
Therefore, around 3112864 people saw the movie this week.
Hence, this is the required solution.
At a farming supply store 7 pounds of seed cost $153.37. If a farmer needed 4 pounds of seeds, how much would it cost him?
Answers
$613.48 / 7 = $87.64
i believe $87.64 is your answer
What value of x is in the solution set of 9(2x + 1) < 9x – 18?
Answers
Answer:
-3 > x
Step-by-step explanation:
Multiply 2x and 1 by 9. You have 18x + 9 < 9x - 18.Add 18 to 9. You are adding because it is the opposite of subtraction, so it cancels out. You now have 18x + 27 < 9x.Subtract 18x from 9. There is no addition sign in front of the 18x, but it's basically implied. You now have 27 < -9x.Divide both sides by -9. When you divide by a negative, the inequality sign flips. You now have -3 > x.Nadia charges $5.50 an hour for babysitting. She babysits 19.50 hours the first week of the month and 19 hours the second week of the month. Suppose Nadia raises her rate by $0.55 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month? Complete the explanation and give your answer. Nadia's new hourly rate is $ . She would need to work hours in the next two weeks to make the same amount she made in the first two weeks.
Answers
Answer:
Step-by-step explanation:
ind her earnings for the first two weeks of the month at the $5.50 an hour rate.
5.50 × (18 + 20.50) = 5.50 × 38.5
= 211.75
She earned $211.75 the first two weeks of the month.
Find her new hourly rate, if she raises her rate by $0.55.
5.50 + 0.55 = 6.05
Her new hourly rate is $6.05.
Find how many hours she would need to work at $6.05 an hour in order to earn $211.75.
211.75 ÷ 6.05 = 35
She would need to work 35 hours.
How do you solve this problem?
9=-y it is equations and inequalities
PLEASE HELP
Answers
Find the product: a) (5 – 2h) (3 + h) b)4p ^2 q ^2 (p ^2 – q ^2)
Answers
Answer:
A.) -8h
Step-by-step explanation:
a.) . (5 – 2h) (3 + h)
a.) (5 – 2h) (3 + h)
(5+3) (h-2h)
8(-h)
-8h
Help!
What is one and sixty-seven hundredths added to fifteen and nine tenths?
Answers
What is the definition of scale factor
Answers
Answer:
The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Example: Here, XYUV=123=4 . So, the scale factor is 4 .
Step-by-step explanation:
:D
24. Seven tenths of a number plus 14 is less than forty-nine.
Answers
Answer:
50. ☺️☺️
Step-by-step explanation:
I'm going to assume you need this inequality solved.
First, write it as numbers, not words.
7/10n + 14 < 49
where "n" is the unknown number.
Second, if I were you, I'd change that fraction into a decimal, as it'll make life easier later on.
7/10 = 0.7
Now, solve it like you would any other equation.
0.7n + 14 < 49
0.7n +14 - 14 < 49 - 14
0.7n < 35
0.7n ÷ 0.7 < 35 ÷ 0.7
n < 50
The answer is n < 50
Answer: 50
Step-by-step explanation:
49 - 14 = 35
35/7 = 5
10 x 5 = 50
Since, 35 is Seven tenths of a number, One tenth is 5 and there are ten tenths, One tenth which is 5 times ten since there are ten tenths equals to 50 (5 x 10 = 50).
I have something to say- Brainly your users are very rude like im failing bEcAuSe YoU pEoPlE! but like yu history people r like saving my life-
Sincerely - Miha~
Answers
Answer:
thank you. someone had to say it
Step-by-step explanation:
Answer:
Omg ik what you mean i feel you
Step-by-step explanation:
The maximum speed possible on a length of railroad track is directly proportional to the cube root of the amount of money spent ob maintaining the track. Suppose that a maximum speed of 25 km/hr is possible on a stretch for which 450,000 was spend on maintence, find the maximum speed if the amount spent on maintence is increased to $1,750,000 Pls help me show steps please
Answers
Answer:
[tex]39.29\ \text{km/h}[/tex]
Step-by-step explanation:
s = Speed of the train
m = Money spent on maintanence
[tex]s\propto m^{\dfrac{1}{3}}[/tex]
Let k be the constant of proportionality so
[tex]s=k (m)^{\dfrac{1}{3}}[/tex]
Now a case is given where 25 km/hr is possible on a stretch for which 450,000 is spent so
s = 25
m = 450000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow k=\dfrac{s}{m^{\dfrac{1}{3}}}\\\Rightarrow k=\dfrac{25}{450000^{\dfrac{1}{3}}}\\\Rightarrow k=0.326[/tex]
Now when m = 1750000
[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow s=0.326\times 1750000^{\dfrac{1}{3}}\\\Rightarrow s=39.29\ \text{km/h}[/tex]
The maximum speed of the train would be [tex]39.29\ \text{km/h}[/tex].
What is the slope of this graph?
O
5
3
o
3
O
-3
Answers
Answer:
where is the graph?
Step-by-step explanation:
A cleaning mixture requires 5 cups of water for every 2 cups of solution which ratio of cups of water to cups of solution will make the same cleaning mixture?
a. 15:6
b. 8 :20
c. 60;18
d. 20:14
Answers
Answer:
a.15.6
Step-by-step explanation:
simplify all the ratios to their simplest forms.
15/3:6/3
5:2
Solve the equation for y , (REDUCE IF POSSIBLE, AND WRITE YOUR ANSWER IN THIS FORM; y=mx+b).
−6x+y=18
Answers
Answer:
y=6x+18
Step-by-step explanation:
add the -6x to the other side to get y alone
Answer:
-6x + y = 18 reduced is -2x + y = 2
Step-by-step explanation:
it is called the Hamber Pickering Formula according to STUIPDPEDIA LOL!
solve 5x + 20=75
What is x
Answers
Answer:
x = 11
Step-by-step explanation:
this answer can be solved by simple operations
5x + 20 = 75
5x = 55 (subtracted the 20 from 75)
x = 11 (divided the 5 by 55)
hope this helps !!
- emily
What figure models 6 divided by 3/2?
(6 divided by 3/2 equals 4)
NEEDS HELP NOW!
BRAINLIEST!
Answers
Pls mark brainliest
Will give brainliest if correct.
Answers
Answer:
The equation is y = 3x + 15.
The second equation is y = 3 * 50 + 15
If you have a value of 50 berries picked, you would make 165 dollars.