Answers
The equation of the quadratic function is y = -1/4(x + 2)² + 4
How to determine the quadratic equation?A quadratic equation is represented as:
y = ax² +bx + c
When x = 0 and y = 3, we have:
3 = a(0)² +b(0) + c
This gives
c = 3
So, we have:
y = ax² +bx + 3
When x = 1 and y = 1.75, we have:
1.75 = a(1)² +b(1) + 3
This gives
a + b = -1.25
Make b the subject
b = -1.25 - a
When x = -2 and y = 4, we have:
4 = a(-2)² +b(-2) + 3
This gives
4a - 2b = 1
Substitute b = -1.25 - a in 4a - 2b = 1
4a - 2(-1.25 - a) = 1
Expand
4a + 2.5 + 2a = 1
Evaluate the like terms
6a = -1.5
Divide both sides by 6
a = -1/4
Substitute a = -1/4 in b = -1.25 - a
b = -1.25 + 1/4
Evaluate
b = -1
So, we have:
y = -1/4x² - x + 3
Factor out -1/4
y = -1/4(x² + 4x) + 3
-------------------------------------------------
Take the coefficient of x
k = 4
Divide by 2
k/2 = 2
Square both sides
(k/2)² = 4
-------------------------------------------------
Add and subtract 4 inside the bracket of y = -1/4(x² + 4x) + 3
y = -1/4(x² + 4x + 4 - 4) + 3
Expand
y = -1/4(x² + 4x + 4) + 1 + 3
Evaluate the sum
y = -1/4(x² + 4x + 4) + 4
Express the bracket as a perfect square
y = -1/4(x + 2)² + 4
Hence, the equation of the quadratic function is y = -1/4(x + 2)² + 4
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Related Questions
can someone help me please I'm exhausted can someone find the quotient of 36.8 divided by 2.3
Answers
Answer:
16
Step-by-step explanation:
36.8÷2.3=16 with no remainders
Answer:
16
Step-by-step explanation:
36.8 divided by 2.3 is 16
Mr. Smith works 26 hours and earns $468. If Mr. Smith works for 16 hours, how much does he earn?
I got $ 288 but I just want to make sure
Answers
Answer:
$288
Step-by-step explanation:
468 ÷ 26 = 18
so $18 per hour times 16 hours would give you $288, your right
Write each decimal as a fraction in simplest terms
Answers
Answer:
A. 25/33
B. 1/3
C. 1/33
D. 25/9
Answer:
Step-by-step explanation:
solve fast pls i am mark you
Answers
Answer:
[tex] \bold{ x = - \frac{5}{6} }[/tex]
Step-by-step explanation:
⠀
⠀
⠀⠀⠀⠀■ Question[tex] \large \sf{ \frac{4x + 9}{3x + 11} = \frac{4x + 3}{3x + 2} }[/tex]
Solve for x.
⠀
⠀
⠀⠀⠀⠀□ Solution⠀
⠀
We will cross multiply the above equation⠀
[tex] \sf (4x + 9)(3x + 2) = (4x + 3)(3x + 11) \\ \\ \sf 4x(3x + 2) + 9(3x + 2) = 4x(3x + 11) + 3(3x + 11) \\ \\ \sf 12 {x}^{2} + 8x + 27x + 18 = 12 {x}^{2} + 44x + 9x + 33 \\ \\ \sf 12 {x}^{2} + 35x + 18 = 12 {x}^{2} + 53x + 33[/tex]
⠀
⠀
Now we will take the values of RHS(right hand side) to LHS(left hand side) of the equation. During this, the values of RHS will get opposite sign while going to LHS.⠀
[tex] \sf 0 = 12 {x}^{2} + 53x + 33 - 12 {x}^{2} - 35x - 18 \\ \\ \sf 0 = 18x + 15[/tex]
⠀
⠀
Taking 15 to LHS⠀
[tex] \sf - 15 = 18x[/tex]
⠀
⠀
Dividing both RHS and LHS of the equation by 18⠀
[tex] \large{ \sf \frac{ - \cancel{15} \tiny {5}}{ \cancel {18} \tiny6 } = x} \\ \\ \boxed{ x = - \frac{5}{6} }[/tex]
Answer:
[tex]\textsf{$x=-\dfrac{5}{6}$}[/tex]
Step-by-step explanation:
Given: [tex]\textsf{$\dfrac{4x+9}{3x+11}=\dfrac{4x+3}{3x+2}$}[/tex]
1. Cross-multiply
(4x + 9)(3x + 2) = (4x + 3)(3x + 11)
2. Distribute
⟶ (4x + 9)(3x + 2) = (4x + 3)(3x + 11)
⟶ 4x(3x) + 4x(2) + 9(3x) + 9(2) = 4x(3x) + 4x(11) + 3(3x) + 3(11)
⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33
3. Combine like terms
⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33
⟶ 12x² + 35x + 18 = 12x² + 53x + 33
4. Subtract 12x² from both sides
⟶ 12x² - 12x² + 35x + 18 = 12x² - 12x² + 53x +33
⟶ 35x + 18 = 53x + 33
5. Subtract 35x from both sides
⟶ 35x - 35x + 18 = 53x - 35x + 33
⟶ 18 = 18x + 33
6. Subtract 33 from both sides
⟶ 18 = 18x + 33
⟶ 18 - 33 = 18x + 33 - 33
⟶ -15 = 18x
7. Divide both sides by 18 to isolate the variable
[tex]\longrightarrow\textsf{$\dfrac{-15}{18}=\dfrac{18x}{18}$}\\\\\\\longrightarrow\textsf{$\dfrac{-15}{18}=x$}\\\\[/tex]
8. Reduce
[tex]\longrightarrow\textsf{$\dfrac{-15\div 3}{18\div 3}=x$}\\\\\\\longrightarrow\textsf{$-\dfrac{5}{6}=x$}[/tex]
Mickey tosses a coin 50 times and records 27 heads. Based on these results, what is the probability if
Mickey tosses the same coin three more times, she will get three tails?
a) 112,833: 125,000
b) 23:50
c) 69:50
d) 12,167: 125,000
Answers
The probability of getting three tails in three tosses When Mickey tosses a coin 50 times and records 27 heads is 12,167:125,000.
What is probability of an event?It is the ratio in an event of the number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus, he probability of failure of a event is equal to the difference of the 1 to the success of the event.
Mickey tosses a coin 50 times and records 27 heads. Thus, the probability of getting a head is,
[tex]P=\dfrac{27}{50}\\[/tex]
The probability of not getting a head or getting a tail is,
[tex]P^{-1}=1-\dfrac{27}{50}\\P^{-1}=\dfrac{50-27}{50}\\P^{-1}=\dfrac{23}{50}[/tex]
Now, Mickey tosses the same coin three more times. The probability of getting three tails in these tosses are,
[tex]P_{3t}=\dfrac{23}{50}\times\dfrac{23}{50}\times\dfrac{23}{50}\\P_{3t}=\dfrac{12167}{125000}[/tex]
Thus, the probability of getting three tails in three tosses When Mickey tosses a coin 50 times and records 27 heads is 12,167:125,000.
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5. Graph the hyperbola ya
16
What are the equations of the asymptotes?
Answers
Answer: y = ± [tex]\frac{4}{3}x[/tex]
Step-by-step explanation:
Just believe it, it's the right one. I don't know how to explain it.
Find the slope on the table
Answers
Answer:
1
Step-by-step explanation:
x = +2 you add 2 every time
y = +2 you add 2 every time
2/2 = 1
D = {x:x is an integer -3
Answers
Answer:
yes , because -3 is the whole number
12. Select all the numbers that are greater than 1.
a.
23
b.
0.63
7
C.
1
-
5
5
d.
7
N
2
e.
w
Im
2.
f.
Answers
Answer:
its 23, (0.63 maybe), 7 ,5,5 that’s it
Step-by-step explanation:
The neighborhood movie store rents a game machine for $12.50 plus $1.50 per day. the downtown store rents the same machine for $4 per day with no initial fee. after how many days will the total rental charge be the same for each store?
Answers
In 5 days the total rental charge is the same for each store.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
A movie store rents a game machine for $12.50 plus $1.50 per day. The downtown store rents the same machine for $4 per day with no initial fee.Let x be the days. The two-equation will be formed as:-
Total amount = 1.5x + 12.5
Total amount = 4x
For the same total amount, we will equate the two equations.
1.5x + 12.5 = 4x
12.5 = 4x - 1.5x
12.5 = 2.5x
x = 12.5 / 2.5
x = 5 days
Therefore In 5 days, the total rental charge is the same for each store.
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Which statements are true regarding this scenario? check all that apply. the sample space is {1, 2, 3, 4, 5, 6}. the expected value for the game is 0. the expected value for the game is one-half. the game is fair because the expected value is equal to 0. the game is unfair because the expected value does not equal 0.
Answers
Based on the game involving rolling a number cube, the applicable statements are:
The sample space is {1, 2, 3, 4, 5, 6}. The expected value for the game is 0. The game is fair because the expected value is equal to 0.What happens in a game involving rolling a number cube?There are six sides of a number cube which means that the sample space is all the sides the cube can land on which are 1,2,3,4,5, and 6.
Because there are 3 odd numbers which can give you a negative point, and 3 even numbers which can give a point, the expected value is 0 as these cancel each other out.
This makes the game fair because situations that have an expected value of 0 are considered fair because there are no expected losses or profits.
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Answer:
A,C,D
Step-by-step explanation:
short and simple for you ;)
A graph of f(x) = 6x2 + 7x – 3 is shown on the grid.
What are the zeros of f ?
Answers
Answer:
Option d
Step-by-step explanation:
The zeroes of given function can be obtained from graph when the graph intersects at x axis
Can you work out what the
next number in the pattern
should be? 4 – 6-9-6-14 - 6
-
Answers
Look the left side as right is constant (6).
9-4=514-9=5So common difference is 5..
next no=14+5=19
Next term
19-6Find the length of z. Round your answer to the nearest tenth.
Answers
SOMEONE HELP ME PLEASEE
Answers
Answer:
area: 165yd^2 perimeter:26yd or 33yd
Step-by-step explanation:
11ydx15yd= 165yd^2
11yd+15yd=26yd
Answer:
56.1, 36.2
Step-by-step explanation:
For this we need to use the Pythagorean Theorem, which is a^2+b^2=c^2. We have our a and c values, so we can make the equation 11^2+b^2=15^2, or 121+b^2=225. Next, we isolate b.
121+b^2=225
-121 -121
___ ___
0 104
b^2=104
Now, we have to find the square roots of both sides. If we do this, we get b= 10.2.
Now, we can find our perimeter:
11+15+10.2= 36.2
For area, the formula is 1/2(b)h (1/2 times the base and height), so:
1/210.2=5.1
5.1*11=56.1
Hope this helps!
Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) -3, -23, -43, -63, ...
Answers
Answer:
1) Arithmetic since it decreases by 3 so, -3n + 38.
2) Arithmetic since it decreases by 20 each time, so -20n+17
Step-by-step explanation:
Choose the histogram that has the smallest variance.
Answers
The histogram first represents the smallest variance option first is correct.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have four histograms shown in the picture.
As we know in a histogram, the curves that resemble hills show groupings of statistics that are close collectively, leading to low variation.
Whenever the taller bars are farther away from the mean in a histogram, the variability is greater, and when the taller bars are closer to the mean, the variability is less.
In the histogram first, there is very less variability.
Thus, the histogram first represents the smallest variance option first is correct.
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7.
Quadrilateral PQRS is inscribed in a
circle. The ratio of m/P to m/R is 2: 4.
What is mZR?
F 30°
H 120°
G 60°
Not here
Answers
Answer: Ha
Step-by-step explanation:
please awnser quickly
Answers
Answer:
B': (-8,2)
C':(-8,9)
D':(-5,4)
Step-by-step explanation:
If im wrong pls tell me!
What is the length of the hypotenuse of the triangle?
what is the length of the hypotenuse of the triangle?
what is the length of the hypotenuse of the triangle?
triangle a b c. side a c is 7 feet and side c b is 4 feet. hypotenuse a b is unknown.
startroot 22 endroot ft
startroot 33 endroot ft
startroot 57 endroot ft
startroot 65 endroot ft
Answers
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}[/tex]
all i know is the answer isn’t 10. pls help
Answers
Answer:
X is 72 i think
Step-by-step explanation:
all triangle equal 180, triangle formula bxh/2, so i did that and got 72.
NEED HELP QUICK - State the reference angle and what quadrant the terminal side of the angle is in.
Answers
Answer:
the answer is 225
Step-by-step explanation:
y+135=360
y=360-135
y=225
During a sale the regular price of an item is reduced by 20 percent if the sale price is $600 what is the regular price
Answers
please please please help me this is for my brother.
Answers
Answer:
below
Step-by-step explanation:
it was the first thing I saw
A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. what is the probability that a student chooses drama as an elective?
Answers
The probability that a student chooses drama as an elective is 7%.
What is the concept of probability?Probability is the study of the odds of obtaining each outcome of a random experiment. These odds are assigned the real numbers in the range between 0 and 1. Results closer to 1 are more likely to occur.
In this case, we can call:
A represents ArtD represents Drama.So, the information given was:
P(A) = 15%P(A or D) = 20%P(A and B) = 2%The formula will be:
P(A or D) = P(A) + P(D) - P(A and D)
So:
[tex]20\% = 15\% + P(D) - 2\%\\P(D) = 20\% - 15\% + 2\%\\P(D) = 7\%[/tex]
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Ms. lewis has 20 students in her p.e. class.
she puts each student's name in a hat and will select
the names of 2 students at random as team leaders for
a volleyball game. how many different pairs of team
leaders could she choose?
Answers
Considering the definition of combination, she could choose 190 different pairs of team.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following formula is applied:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.
Different pairs of team leadersMs. lewis has 20 students in her p.e. class. She puts each student's name in a hat and will select the names of 2 students at random as team leaders for a volleyball game.
So, you know that:
m= 20n= 2Replacing in the definition of combination:
[tex]C=\frac{20!}{2!(20-2)!}[/tex]
Solving:
[tex]C=\frac{20!}{2!18!}[/tex]
C= 190
Finally, she could choose 190 different pairs of team.
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What is the solution to the equation
m - 8 = 12
Answers
Answer:
m= 20
Step-by-step explanation:
add 8 to both sides,
12+8=20
Identify the slope and y-intercept of the function y = -8x + 1. OA. The slope is 1. The y-intercept is (0, -8). OB. The slope is 8. The y-intercept is (0, 1). O C. The slope is 1. The y-intercept is (0,8). O D. The slope is -8. The y-intercept is (0, 1).
Answers
Answer:
d is the answer
Step-by-step explanation:
y=mx+b
m being the slope and b being the y intercept
11. Find the equation for the circle with center (−2,−3) and passing through (1,5).
Answers
Answer:
(x +2)² + (y+3)² = 73
Use the distance formula to find radius:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf \sqrt{(-2-1)^2+(-3-5)^2}[/tex]
[tex]\rightarrow \sf \sqrt{73}[/tex]
Eqaution of circle:
(x-h)² + (y-k)² = r²
(x-(-2))² + (y-(-3))² = (√73)²
(x +2)² + (y+3)² = 73
The Simple intrest on $765,000 invested for 3 years at 3% is?
Answers
Answer: 68850
Step-by-step explanation:
interest = 765000(3/100x3)
= 68850
if your finding total cost add 765000 + 68850 = 833850