Which function matches the graph?
A 2-dimensional graph with an x-axis and a y-axis is given. A parabolic curve is drawn whose axis of symmetry is parallel to y-axis and its vertex is at (1,-3); is passing through co-ordinates (3,1) and (-1,1).
A. f(x) = (x – 3)2 – 3
B. f(x) = (x + 1)2 – 6
C. f(x) = (x + 2)2 – 5
D. f(x) = (x – 1)2 – 3
Answers
vertex : (1,-3)
coordinates : (3,1) and (-1,1)
parabola formula : y = a(x -h)² + k
(x, y) - from the coordinates(h, k) - from the vertexso given,
h = 1
k = -3
x = 3
y = 1
solve for a:
1 = a(3 -1)² + (-3)1 = 4(a) - 34(a) = 4a = 1Therefore equation:
y = (x -1)² - 3
check the graph for confirmation:
Answer: Graph the parabola y=x2−7x+2 .
Compare the equation with y=ax2+bx+c to find the values of a , b , and c .
Here, a=1,b=−7 and c=2 .
Use the values of the coefficients to write the equation of axis of symmetry .
The graph of a quadratic equation in the form y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .
Substitute x=72 in the equation to find the y -coordinate of the vertex.
y=(72)2−7(72)+2 =494−492+2 =49 − 98 + 84 =−414
Therefore, the coordinates of the vertex are (72,−414) .
Now, substitute a few more x -values in the equation to get the corresponding y -values.
x y=x2−7x+2
0 2
1 −4
2 −8
3 −10
5 −8
7 2
Plot the points and join them to get the parabola
in short terms D.
Related Questions
9. A cooler contains 4.5 gallons of water and is filling up
at a rate of 0.1 gallons per second. A second cooler
contains 7 gallons of water and is draining at a rate of
0.25 gallons per second. Which could be used to
determine the number of seconds it would take for each
cooler to contain the same amount of water?
Answers
The equation that can be used to determine when each cooler would contain the same amount of water is 2.5 = 0.75t.
When the coolers would have the same amount of water?Equation that can be used to determine the amount of water in the first cooler at time t : 4.5 + 0.1t
Equation that can be used to determine the amount of water in the second cooler at time t : 7 + 0.25t
Where t represents seconds
When they have the same amount of water, the two above equations would be equal
4.5 + 0.1t = 7 + 0.25t
Combine similar terms
7 - 4.5 = 0.1t - 0.25t
2.5 = 0.75t
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Find the circumference and area of the circle to the nearest hundredth. Use 3.14 for π. Round to the nearest hundredth if necessary.
A) 452.16 cm2
B) 37.68 cm2
C) 113.04 cm2
D) 18.84 cm2
Answers
Answer:
C) 113.04
Step-by-step explanation:
A=πr2
A=3.14 · 6 ≈ 113
Find the surface area of a cylinder with radius 2 yards and height 6 yards.
Give me the answer
Answers
Anyone know this?????
Answers
Answer:
102 mm²
Step-by-step explanation:
You can split the shape into two different shapes: a trapezium and a rectangle.
Area of rectangle = length x width
= 10 x 3 = 30mm
Area of trapezium = a + b / 2 x h
h = 9 - 3 = 6mm
= 10 + 14 / 2 x 6
= 72 mm
Total area = 72 + 30 = 102 mm²
= 102 mm2
First option
3 pounds to 18 ounces
Answers
Answer:
divide the pounds to get 18 ounces
Step-by-step explanation:
i think?
A. Dilation
B. Rotation
C. Reflection
D. Translation
Answers
Answer:
Reflection
Step-by-step explanation:
Figure 1 was reflected accross the y axis :)
Have an amazing day!!
Please rate and mark brainliest!!
The following histogram shows the number of minutes that 29 students took to complete an exam.
Based on this histogram, about 10% of students took less than
minutes to complete the
exam.
Time spent taking an exam
12
10
Frency
9
.
20
Answers
Using the histogram, it is found that about 10% of students took less than 40 minutes to complete the exam.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Researching the problem on the internet, it is found that the histogram states that:
One student completed the test in less than 10 minutes.Two students took between 30 and 40 minutes to complete the test.10% of 29 is approximately 3, hence about 10% of students took less than 40 minutes to complete the exam.
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to get a free meal tom at his fav resturant, tom needs to spend $50 or more at the resturant. he has already spent 30.25$ how much more does tom need to spend to get his free meal
Answers
how much more Tom needs to spend to get the free meal.
solution:subtract the amount he has spent from the amount he needs to spend to find how much more he needs to spend.
$50 - $30.25
= $19.75
Tom needs to spend $19.75 to get his free meal.
caitlyn is on her school's softball team. so far Caitlyn has 39 hits in 75 times at bat. what is her batting average?
Answers
Answer:
0.52
Step-by-step explanation:
[tex]batting \: average \: = \frac{39}{75} \\ = 0.52[/tex]
Is the following a statistical question?
How much do new cars cost?
Answers
Select the correct answer. a cylinder has a radius of 10 inches and a height of 6 inches. about what is its volume in cubic inches? use 3.14 for π. a. 60 cu. in. b. 188.4 cu. in. c. 628 cu. in. d. 1,884 cu. in.
Answers
Answer:
Its d
Step-by-step explanation:
because you square 10 and you get 100 and you have to multiply 6 with 100 which is 600 and then you multiply the 3.14 which gives you 1,884
PLEASE MARK AS BRAINLIEST
I have a couple of questions I need help with.
This is a multiple answer question:
A) Is 120.2 + 20.03 < 120.003 + 20.20 correct?
B) Is 22 + 7.6 = 20 + 9.600 correct?
C) Is 100.002 + 8.503 > 98 + 10.5 correct?
D) Is 72.2 + 82.3 < 70.6 + 84.1 correct?
any help will be much appreciated
Answers
Answer:
b
Step-by-step explanation:
b is correct i think
2
Find the distance between (-3, -4) and (2, -4)
Answers
Answer:
[tex]\boxed{\sf{5}}[/tex]Step-by-step explanation:
Distance can be calculated using a distance formula.
⇒ (-3,-4) and (2,-4)Distance formula:
[tex]\Longrightarrow: \sf{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
The distance between (-3,-4) and (2,-4) are:
[tex]\Longrightarrow: \sf{\sqrt{\left(2-\left(-3\right)\right)^2+\left(-4-\left(-4\right)\right)^2}}[/tex]
Then, you solve.
[tex]\Longrightarrow:\sqrt{\left(2-\left(-3\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=\boxed{\sf{5}}[/tex]
Therefore, the distance between (-3,-4) and (2,-4) is 5, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Yo I need to bring up my math grade bad so
y>-x+1
(please show it graphed already :D)
Answers
Answer:
Step-by-step explanation:
A random sample of people were surveyed on their favorite sport, as shown in the table below sorted by the respondent’s age.
How many people between the ages of 35 and 54 prefer football?
Answers
Answer:
the answer is five 5 students prefer football
what is 1/4x-6=-10 please i need something by tomorrow.
Answers
Answer:
If you need what x equals its -16
x = -16
Explanation:
[tex]\rightarrow \sf \dfrac{1}{4} x - 6=-10[/tex]
collect variables
[tex]\rightarrow \sf \dfrac{1}{4} x =-10+6[/tex]
simplify
[tex]\rightarrow \sf \dfrac{1}{4} x =-4[/tex]
cross multiply
[tex]\rightarrow \sf x=-4*4[/tex]
final answer
[tex]\rightarrow \sf x=-16[/tex]
Find the length of the third side to the nearest tenth
Answers
Answer: ≈ 1.4.
Step-by-step explanation: To find the hypotenuse of a triangle (the longest side of a triangle), you need to add the legs (the two sides of the triangle that are not the hypotenuse). You need to have ^2 when adding each leg. For example, both legs are 1 so when you're adding them, the equation should look like this--> 1^2 + 1^2. Then, once you find the answer to that, you need to find the square root of the answer. The work is done below:
1^2 + 1^2 = 2.
√2 ≈ 1.41421356 or ≈ 1.4.
Therefore, your answer is ≈ 1.4.
Let me know if this is right! :)
I NEED HELP ASAP PLEAS HELP ME
Answers
Answer:
m=117
Step-by-step explanation:
So this area is 360 degrees
What you can see the 68 degrees is congruent to its opposing side so we can eliminate those. 360 - 126= 234
We can see m is congruent to U
234/2=117
m=117
NEED HELP NOW!!!!!!!
Answers
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
the baseline (where the height hits at a 90° angle) is 4 m.
the height is 3.7 m.
so, the area is
4 × 3.7 / 2 = 2 × 3.7 = 7.4 m²
find the m < VXW of the parallelogram
Answers
Answer: A
Step-by-step explanation:
I need help with some geometry workbook pages!
Answers
Answer: D
Step-by-step explanation:
1. What is the center of dilation used to dilate quadrilateral WXYZ to quadrilateral W'X'Y'Z'?
A. (-1,3)
B. (0,0)
C. (-3,4)
D. (-1,0)
Answers
Answer: I believe the answer is C. (-3,4)
Step-by-step explanation:
Jenny chose two cards randomly from a deck. What is the probability of getting an ace and then a king?
Answers
because if there is 52 cards in a deck
i know this is probably simple but ive forgotten how to do it and i cant find it in my notes help appreciated!
Answers
Answer:
This is pythagoras
A squared plus b squared equals c squared.
The unknown side is c as its the hypotenuse,
So the length of the first side is 6.4 this squared = 40.96
The other length is 12 as 6 is the radius so the diameter of the circle amd therfore the length of the triangle is 12.
12 squared is 144
144 + 40.96 = 184.96
The length of c squared is 184.96
To find the length of c alone we calculate the square root.
The square root of 184.96 = 13.6
? = 13.6
i-Ready Solve Multi-Step Equations ) Solve the equation -2y + 6 = -12. y =
Answers
Subtract 6 from both sides.
-2y equals -12 minus 6
That is -2y equals -18
Solve for y by dividing by -2
Y equals -18/-2
That is y equals 9
Answer is 9
Mark as the best!
0.4 divided by 29 equally is?
Answers
Answer:
72.5 (Not rounded)
Hope this helps!
What is the perimeter of the figure?
Answers
Answer:
68.7
Step-by-step explanation:
Lets say this triangle is represented as ABC.
AB = BC
So:
23+23+22.7 = p
p = 68.7
On January 1, Trisha put $100 into a savings account that earns interest. That same day, Mark put some money into another savings account that also earns interest. After 5 years, Trisha’s account balance is 145% of her original balance, and Mark’s is 160% of his original balance. Mark and Trisha withdraw all of their money and use it to spend $225 at the amusement park. If together they have $40 left from their withdrawals after the amusement park, how much did Mark put into his savings account?
Trisha thinks that if Mark also put $100 into his account, then they would had more than $100 left after the amusement park. Is she correct or not? Explain.
Answers
Answer:
Mark deposited $75Trisha is not correctStep-by-step explanation:
The total of their account balances is equal to the total spent plus the remaining amount. The given relations tell us ...
Trisha withdrew $100 × 145% = $145Mark withdrew d × 160% = 1.6d . . . for some initial deposit d$145 + 1.6d = $225 +40 . . . . . withdrawals = spent + change__
a.Solving this equation, we can find Mark's withdrawal and his initial deposit.
145 +1.6d = 265
1.6d = 120 . . . . . . . the amount Mark withdrew
d = 120/1.6 = 75 . . . . the amount Mark deposited
Mark put $75 into his savings account.
__
b.Had Mark put $100 into his savings account, the total of withdrawals would have been ...
Trisha + Mark = $100 × 145% +$100 ×160% = $145 +160 = $305
After spending $225 of this amount, they would have had a leftover amount of ...
$305 -225 = $80
Trisha is not correct in her thinking that there would be more than $100 left over.
Enola owns a small business selling ice-cream. She knows
customers paid cash, 76 customers used a debit card, and 10 customers used a credit
card. .
Based on these results, express the probability that the next customer will pay with
something other than a credit card as a decimal to the nearest hundredth.
Answers
the probability that the next customer will pay with something other than a credit card as a decimal to the nearest hundredth is 0.93.
To calculate the probability that the next customer will pay with something other than a credit card, we need to know the total number of customers who paid cash or used a debit card.
The total number of customers who paid cash or used a debit card is the sum of the customers who paid cash and those who used a debit card:
Total customers who paid cash or used a debit card = customers who paid cash + customers who used a debit card = 76 + 10 = 86
Therefore, the probability that the next customer will pay with something other than a credit card is:
P = Total customers who paid cash or used a debit card / Total number of customers
P = 86 / (76 + 10 + 1) (adding 1 to account for the next customer)
P = 0.93
So the probability that the next customer will pay with something other than a credit card as a decimal to the nearest hundredth is 0.93.
Learn more about probability here
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Find the length of AB
help
Answers
Answer: 9
Step-by-step explanation:
