The graph of function g is a parabola with the vertex located at (5,9). The parabola also passes through the point (3, 1). Which of the following is an
equation in vertex form for this function?
Answers
I just did this the answer is C. g(x) = –2(x – 5)2 + 9
The required function is [tex]g(x)=-2(x-5)^2+9[/tex].
Important information:
Vertex of parabola is at (5,9).Parabola passes through the point (3,1).We need to find the equation in vertex form for the function g.
Parabola:The vertex form of a parabola is:
[tex]g(x)=a(x-h)^2+k[/tex] ...(i)
Where, [tex]a[/tex] is a constant and [tex](h,k)[/tex] is the vertex.
Substitute [tex]h=5,k=9[/tex] in (i).
[tex]g(x)=a(x-5)^2+9[/tex] ...(ii)
Parabola passes through the point (3,1). So, substitute [tex]x=3,g(x)=1[/tex] in (ii).
[tex]1=a(3-5)^2+9[/tex]
[tex]1-9=a(-2)^2[/tex]
[tex]-8=4a[/tex]
[tex]-2=a[/tex]
Substitute [tex]a=-2[/tex] in (ii).
[tex]g(x)=-2(x-5)^2+9[/tex]
Thus, the required function is [tex]g(x)=-2(x-5)^2+9[/tex].
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Related Questions
Esther had five times as many cards as Richard. Esther gave 1/4 of her cards to Richard. Then, Richard gave 1/6 of his cards to Esther in return. In the end, Esther had 90 more than Richard. How many cards did Esther have at first?
Answers
Answer:
Esther has 200, Richard has 40
Esther gives Richard 50 cards. Now they have
Esther: 150, Richard: 90
Richard gives Esther 15, so they now have
Esther: 165, Richard 75
Step-by-step explanation:
Answer:
Esther had 200 cards at first
Step-by-step explanation:
Variables:
Esther: 5r
Richard: r
Equalities:
e = 5r
e - e/4 + 1/6 (r + e/4) = 5/6 (r + e/4) + 90
Solve:
Replace e with 5r and solve for r:
e - e/4 + 1/6 (r + e/4) = 5/6 (r + e/4) + 90
5r - 5r/4 + 1/6 (r + 5r/4) = 5/6 (r + 5r/4) + 90
5r - 5r/4 + 1/6 (2.25r) = 5/6 (2.25r) + 90
5r - 1.25r + 0.375r = 1.875r + 90
5r - 1.25r + 0.375r - 1.875r = 90
2.25r = 90
r = 40
Esther: 5r = 5(40) = 200
Richard: r = 40
NEED HELP ASAP!!!!Instructions: Using the following image, solve for the trigonometry ratios of
Answers
Answer:
17
8/17
Step-by-step explanation:
x=[tex]\sqrt{8^{2} +15^{2} } =17[/tex]
sin∠D = [tex]\frac{8}{17}[/tex]
Complete this item.
Identify _1 and 22. Select all that apply of the following terms: acute, right, obtuse, adjacent, vertical,
complementary, supplementary.
Answers
Answer:
Angle 1 is obtuse, and adjacent. Angle 2 is obtuse, and is also adjacent.
Step-by-step explanation:
Both seem to be obtuse since they're not right triangles, and they're both adjacent because they have two angles that share the same vertex. Hope this helped :)
What’s 1/4 +2/3 or 3/4+2/3
Answers
Answer:
1/4+2/3=11/12
3/4+2/3=17/12
Step-by-step explanation:
Please explain to me how to do this question with right answer
Answers
Answer:
[tex]\boxed {\boxed {\sf b=8}}[/tex]
Step-by-step explanation:
The Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this triangle, 6 and b are the legs, because they form the right angle.
10 is the hypotenuse, because it is opposite the right angle. Plus, it's the longest side.
[tex]a=6 \\b=b\\c=10[/tex]
Substitute the values into the Theorem.
[tex]6^2+b^2=10^2[/tex]
Evaluate the exponents.
6²= 6*6= 36[tex]36+b^2=10^2[/tex]
10²= 10*10= 100[tex]36+b^2=100[/tex]
Subtract 36 from both sides of the equation to isolate the variable (b).
[tex]36-36+b^2=100-36[/tex]
[tex]b^2=100-36[/tex]
[tex]b^2=64[/tex]
b is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.
[tex]\sqrt{b^2}=\sqrt{64[/tex]
[tex]b=\sqrt{64}[/tex]
[tex]b=8[/tex]
In this triangle, b (the other leg) is equal to 8
PLS HELP BRAINLIST and 100 POINTS
The diagram below shows a boat and a scuba diver that is approximately 40 feet below the boat. The top of the flagpole on the boat is 15 feet above the surface of the water. The elevation of the surface of the water is 0 feet. Which number represents the elevation of the scuba diver?
A. –55 ft
B. –40 ft
C. 40 ft
D. 55 ft
Answers
Answer:
B, He is -40 due to it asking which number is his point. If he was positive 40 then he would be on an island or flying in the sky. Your answer is -40
100
3
80
6
60
9
40
20
0
100
web and Windows
BE
a
02 AM
NETT Dann
Answers
Answer:
Uhhhh what?
Step-by-step explanation:
I am confused...
The graph below shows the relationship between the number of dollars a worker earns and the number of hours worked.
Which statement best describes the rate of change for this situation?
A. The worker earns $40 per hour.
B. The worker earns $8 per hour.
C. The worker earns $10 per hour.
D. The worker earns $320 per hour.
Answers
Option B - The worker earns $8 per hour is the correct alternative.
We have a graph that shows the relationship between the number of dollars a worker earns and the number of hours worked.
We have to select the statement which best describes the rate of change for this situation.
How do you calculate the Slope of Line ?The slope of a line can be calculated using -
[tex]$m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
According to the question, we have two coordinate points marked on the graph -
P(20, 60)
Q(40, 320)
Using the formula to calculate the slope of a line, we get -
[tex]$m = \frac{320-160 }{40 -20 }[/tex]
m = 8
We know that the slope of the line represents the rate of change of y with respect to x. Therefore, the worker earns $8 per hour.
Hence, Option B is correct.
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What is the next term in this arithmetic sequence?
11, 8, 5, 2,...
0-3
06
05
Answers
Answer: the next term is -1
WILL GIVE POINTS!! Must answer!
What is the range in interval notation?
Answers
Answer:I think it’s option 2, light blue
Step-by-step explanation:
someone help me out please
Answers
Answer:
The answer would be B :)
Step-by-step explanation:
explanation: the line of symmetry is NOT equal to zero.
mark me brainliest! :)
Suppose the sample space for a continuous random variable is 0 to 8. If the area under the density curve for the variable from 0 to 5 is 0.625, what is the area under the density curve from 5 to 8?
Answers
========================================================
Explanation:
The portion from x = 0 to x = 5 has area 0.625, so 62.5% of the total area is accounted for. The remaining 100% - 62.5% = 37.5% of the total area must be in the remaining portion from x = 5 to x = 8. Convert 37.5% to decimal form to get the answer 0.375
-----------------
Another approach
We have two disjoint areas under a curve. The two areas must add to 1. Let A be the unknown area
So,
0.625+A = 1
A = 1-0.625
A = 0.375
The area under the curve from x = 5 to x = 8 is 0.375
Given the side lengths of 20,23 and 41, determine whether the triangle is acute, right, obtuse, or not a triangle.
Answers
=====================================================
Explanation:
In this case, a triangle is possible since adding any two sides leads to a sum larger than the third side
20+23 = 43 is larger than 4120+41 = 61 is larger than 2323+41 = 64 is larger than 20I'm using the triangle inequality theorem here.
----------------------------
To determine what kind of triangle we have, we'll use the converse of the Pythagorean theorem. Specifically, we'll use a corollary of it.
Consider a triangle with sides a,b,c. Let c be the longest side.
We have three possible cases:
If a^2+b^2 = c^2, then we have a right triangleIf a^2+b^2 > c^2, then the triangle is acute.If a^2+b^2 < c^2, then the triangle is obtuse.For this problem, we have a = 20, b = 23, c = 41.
We see that a^2+b^2 = 20^2+23^2 = 929 and c^2 = 41^2 = 1681.
In short, a^2+b^2 = 929 and c^2 = 1681.
Since 929 < 1681, this means a^2+b^2 < c^2.
Therefore, this triangle is obtuse.
Slope for (5,-5) (3,5)
Answers
Answer:
-5
Step-by-step explanation:
5-(-5)/3-5=10/-2=-5
(can I get brainliest please)
A textbook store sold a combined total of 392 physics and psychology textbooks in a week. The number of physics textbooks sold was three times the number of psychology textbooks sold. How many textbooks of each type were sold?
Answers
Answer:
Psychology textbooks = 98 and physics textbooks = 294
Step-by-step explanation:
Let there are x psychology textbooks sold.
No of physics textbooks sold = 3x
ATQ,
A textbook store sold a combined total of 392 physics and psychology textbooks in a week.
x + 3x = 392
4x = 392
x = 98
It means there are 98 psychology textbooks sold and 3x = 3(98) = 294 physics textbooks sold.
whoever knows what 9+10 is i will reward them
Answers
Answer:
19
Step-by-step explanation:
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77.
How much was the tip in dollars?
Answers
Answer;
7.77
Step-by-step explanation:
An Olympic-sized swimming pool holds 2,500,000 liters of water. How many gallons of water does an Olympic-sized swimming pool hold? Round your answer to the nearest tenth.
Answers
Answer:
The Olympic sized swimming pool hold 660501.9 gallons of water.
Step-by-step explanation:
Given that:
Water hold by an Olympic sized swimming pool = 2500000 liters
We know that;
1 gallon = 3.785 liters
Therefore,
We will divide the total number of water in liters by 3.785 to find the number of gallons.
Gallons of water in pool = [tex]\frac{2500000}{3.785}[/tex]
Gallons of water in pool = [tex]660501.9[/tex] gallons
Hence,
The Olympic sized swimming pool hold 660501.9 gallons of water.
Johnny divided 3 1/2 x 4 what number did he get
Answers
Answer:
14
Step-by-step explanation:
3 1/2= 3.5
so...
3.5*4=14
Answer:
14
Step-by-step explanation:
7 / 2 × 4
7 × 2
14
hope it helps!
6. A ball is selected at random from a bag containing
3 red balls, 4 black balls and 5 green balls. The
first ball is replaced and a second is selected. Find
the probability of obtaining:
(a) two red balls,
(b) two green balls.
Answers
Answer:
two green balls
Step-by-step explanation:
because of many reasons boy
Answer:
a. 1/16 b. 25/144
Step-by-step explanation:
Since the bag does not change each time, the probability stays the same. To get the desired outcome both times, we must square the probability.
Which expression would the model be most helpful in solving?
An area model has 5 shaded parts and 1 unshaded part.
Answers
This question is awfully vague without any images of the equation to back it up, sorry
Is this true or false ??
Answers
If the equation 5(3x + 7) – 1 = 3(52 + k) + 4 has infinitely many solutions, what is the value of k?
Answers
Answer:
k = 5x - 42
Step-by-step explanation:
Which of the following is a solution of x^2 -10x = -36?
-5 - i √10
5 + i √61
-5 - i √11
5 + i √11
Answers
god loves you!!!!!!!!!
Answers
Answer:
He loves you too!!
Step-by-step explanation:
HELP!!!!!!!!!!
The perimeter of a rectangle is 44 inches. If the width of the rectangle is 10 inches, what is the length?
A.
12 inches
B.
22 inches
C.
34 inches
D.
24 inches
Answers
P .= 2L + 2W at W= 10, P= 44
44 = 2L + 2 (10)
44 = 2L + 20
44-20 = 2L
24 = 2L
L= 24/2
L= 12cm
What is 4 2/5 times 2 2/3
Answers
MY HRW ‼️ Solve the equation. You may find using algebra tiles helpful in solving this problem.
X +6=-X-6
Answers
Answer:
x=-6
Step-by-step explanation:
x+6=-x-6
(-6)+6=(6)-6
0=0
Answer:
Solve the equation. You may find using algebra tiles helpful in solving this problem. X +6=-X-6 X= -6
please help!! i need someone to write me an equation for this please!
Answers
A local insurance agent visits the high school and tells the students that his insurance company will give students a 7% discount on liability insurance, PIP. comprehensive insurance, and collision insurance for three years if they take a defensive driving course. Maria spends $1,437.00 on her auto insurance annually.
Answers
The question is vague, but I'll try and help.
Answer:
She saves $100.59 a year.
Step-by-step explanation:
Saving 7% of $1,437.00 each year.
7% of $1,437.00 (0.07 x $1,437.00) = $100.59
If it asks how much she saves over a certain number of years, just multiply 100.59 times how many years it asks for. Hope this helps.
The required, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.
What is the investment?Investment is defined as when an individual spends money on something that returns him or her higher money than the money they invested.
Here,
If Maria spends $1,437.00 on her auto insurance annually and she takes the defensive driving course, she will get a 7% discount on her liability insurance, PIP, comprehensive insurance, and collision insurance for three years.
To calculate the amount of the discount, we first need to find 7% of $1,437.00:
Discount = 0.07 × $1,437.00 = $100.59
So, the amount of the discount that Maria will receive annually is $100.59.
To find the total savings over three years, we multiply the annual discount by three:
Total savings = $100.59 × 3 = $301.77
Therefore, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.
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