Answers
Answer:
(3, 8)
Step-by-step explanation:
x² - 6x - y + 17 = 0
x² - 6x = y - 17
x² - 6x + 9 = y - 17 + 9
(x - 3)² = y - 8
The vertex is (3, 8)
The vertex of the parabola given by the equation x² - 6x - y + 17 = 0 is (3, 8).
To complete the square and find the vertex of the parabola given by the equation x² - 6x - y + 17 = 0, we can follow these steps:
1. Rearrange the equation: Move the constant term (17) to the other side of the equation by subtracting it from both sides. This gives us x² - 6x - y = -17.
2. Group the x-terms together: Rearrange the equation so that the x-terms are next to each other. This gives us x² - 6x = y - 17.
3. Complete the square: Take half of the coefficient of x (-6) and square it. Add this value to both sides of the equation. Half of -6 is -3, and (-3)² is 9. So we add 9 to both sides: x² - 6x + 9 = y - 17 + 9.
4. Simplify the equation: On the left side, the expression x² - 6x + 9 can be factored as (x - 3)². On the right side, -17 + 9 simplifies to -8. So the equation becomes (x - 3)² = y - 8.
5. Rewrite the equation in vertex form: The vertex form of a parabola is (x - h)² = 4p(y - k), where (h, k) represents the vertex of the parabola. Comparing this with our equation, we have (x - 3)² = y - 8, which matches the vertex form.
6. Identify the vertex: By comparing the equations, we can see that the vertex of the parabola is at the point (h, k) = (3, 8).
Therefore, by completing the square, we have found that the vertex of the parabola given by the equation x² - 6x - y + 17 = 0 is (3, 8).
To learn more about parabolas;
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Related Questions
SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation was =σ120. A random sample of 20 students who took the test in 2010 had a mean score of 515. Following is a dotplot of the 20 scores. (a) Are the assumptions for a hypothesis test satisfied? Explain. (b) If appropriate, perform a hypothesis test to investigate whether the mean score in 2010 differs from the mean score in 2009. Assume the population standard deviation is =σ120. What can you conclude? Use the =α0.10 level of significance and the critical value method.
Answers
Answer:
we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
Step-by-step explanation:
H0 : μ = 582
H1 : μ < 582
Test statistic :
T = (xbar - μ) ÷ σ/√n
Xbar = 515 ; n = 20 ; σ = 120
T = (515 - 582) ÷ 120/√20
T = -67 / 26.832815
T = 2.50
Pvalue at t score = 2.50 ; df = 19 is 0.0187
At α = 0.0187
Pvalue > α ; Hence, we fail to reject the Null
Hence, we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.
what is the shape identify in the image
Answers
Answer:
it is a triangular prism
Pam and her grandma are planning to make a quilt together. The quilt will be made out of fabric squares that measure 6 inches on each side. The quilt will have 3 more squares along its longer edge than it will have along its shorter edge.
If there are x fabric squares along the quilt's shorter edge, find an expression for f(x), the length of the quilt's shorter edge in inches.
f(x)=
6x
Next, find an expression for g(x), the length of the quilt's longer edge in inches.
g(x)=
Which function can you use to find the area of the quilt in square inches?
Answers
Answer:
There are x squares on the shorter side, each square measures 6 inches.
The length of the shorter side is:
f(x) = x*6 = 6xThe length of the longer side is:
g(x) = (x + 3)*6 = 6x + 18The area of the quilt is:
A = 6x(6x + 18) = 36x² + 108xIf Mike loses $5 per week, how much does he lose in 4 weeks?
Answers
Answer:
$ 20Step-by-step explanation:
[tex]1week \: = 5 \\ 4 \: weeks = x \\ \\ x = 20[/tex]
hope this helps you.
Can I have the brainliest please?
Have a nice day!
A LOT OF POINTS!!
Suppose you borrow $40,000 at 13% APR for a 12-year term to be paid monthly. Your monthly payment is $450.00.
How much of your first payment goes toward interest?
Make sure you show your work to earn full credit.
Answers
Answer:
You get $45,200 first with interest with the 5400 you made in 1 year that dedeucts
Step-by-step explanation:
8% of $796.25 is how much?
Answers
8/100*796.25
=63.7%
Answer:63.7%
Answer: Hello, there! your Answer is below
63.7 would Be the correct answer
Step-by-step explanation: Below Is Info About How to Calculate Precentage UwU
how to calculate percentage of a number. Use the percentage formula: P% * X = Y
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
The side lengths of a rectangle are all multiplied by 5. What happens to its perimeter?
Answers
Answer:
The perimeter is multiplied by 5.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with sides l and w is given by:
[tex]P = 2(l + w)[/tex]
The side lengths of a rectangle are all multiplied by 5.
This means that [tex]l = 5l, w = 5w[/tex]. So
[tex]P_M = 2(5l + 5w) = 2*5(l+w) = 10(l + w)[/tex]
What happens to its perimeter?
The rate is:
[tex]\frac{P_M}{P} = \frac{10(l+w)}{2(l+w)} = 5[/tex]
The perimeter is multiplied by 5.
I need so much help help me please UwU
Answers
Answer:
Line A: y = 3x + 3
Line B: y = -1/3x + 3
Step-by-step explanation:
Line A points: (0, 3) and (1, 6)
Slope:
m=(y2-y1)/(x2-x1)
m=(6-3)/(1-0)
m= 3
y - y1 = m(x - x1)
y - 3 = 3(x - 0)
y - 3 = 3x
y = 3x + 3
Line B points: (0, 3) and (9, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-3)/(9-0)
m= -1/3
y - y1 = m(x - x1)
y - 3 = -1/3(x - 0)
y - 3 = -1/3x
y = -1/3x + 3
find the gradient of the line
with the equation 3x+4y=10
Answers
7n - 4 (8n+4) = 159
Answers
Answer:
n = -7
Step-by-step explanation:
Use distributive property:
7n - 32n - 16 = 159
Combine like terms
-25n - 16 = 159
Add 16 to both sides to isolate variable n
-25n = 175
Divide both sides by -25 to isolate variable n
n = -7
Check your work:
7(-7) - 32(-7) - 16 = 159
-49 + 224 - 16 = 159
159 = 159
what is the area of the shaded region? use 3.14 for pi
Answers
Answer:
13.8
Step-by-step explanation:
Area of square = πr²
=22/7 × 4²
=50.2
Area of square = l²
=8²
= 64
Area of shape is 64 - 50.2 = 13.8
Answer:
The answer is 13.8
Step-by-step explanation:
Yes
Can someone give me a fake band name???
Answers
Answer:
loaded diper
Step-by-step explanation:
There are 4 roses for every 7 carnations in a bouqeuet. Mr rodriguez buys a bouqeuet with 12 roses in it. How many total flowers are in the bouqeuet Mr rodriguez bought?
Please explain step by step I dont get it.
Answers
Answer:
33 total flowers are in the bouquet Mr Rodriguez bough
Step-by-step explanation:
So for every 4 roses there are 7 carnations meaning the ratio is 4:7
4 times x = 12
x=3
So we do the same for carnations
7 x 3 = 21
Now we add to find the total
21+12=33
33 total flowers
sin(30°)cos(45°) + cos(30°)sin(45°)
Answers
Step-by-step explanation:
sin(30°)cos(45°) + cos(30°)sin(45°)=1+√3/2√2
cos45 = √2/2
cos30 = √3/2
sin45 = √2/2
answer: √2 + √6
—————
4
Calculate the mass of NaOH in 0.2 moles of NaOH
Answers
Answer:
0.2M i.e
Step-by-step explanation:
Which number has the least absolute value?
Answers
Explanation: The bigger the negative number, the lower the number actually is.
what is the area of a right triangle with sides 7ft 24ft and 25ft?
Answers
Answer:
84 ft^2
Step-by-step explanation:
[tex] \frac{7 + 24 + 25}{2} = 28[/tex]
The area is:
[tex] \sqrt{28 \times (28 - 7) \times (28 - 24) \times (28 - 25)} [/tex]
[tex] = 84 \: {ft}^{2} [/tex]
please help meeeee i will give brainlyest
Answers
Answer:
answer is 63 min
Step-by-step explanation:
math+calculator like and subscribe to yourmom.com31
Tinisha is planning a birthday party. She can buy:
10 balloons, 8 cupcakes, and 8 hats for $50
5 balloons, 9 cupcakes, and 7 hats for $46, or
12 balloons, 7 cupcakes, and 9 hats for $51
Using b for the number of balloons, c for the number of cupcakes, and h for
the number of hats, write a system of equations to represent this situation.
Answers
Answer:
b+c+h=50
Step-by-step explanation:
Its the first one because you need to have the same amount of hats as cupcakes cause the hat really stands for people.
brainiest exchange give me and I will give you 2+2
Answers
Answer:
4
Step-by-step explanation:
and sure
Answer:
4
Step-by-step explanation:
Do 5 yd 12 yd 13 yd make a right angle?
Answers
What is the theoretical probability that the spinner below will land on 6 if someone spins it 48 times?
Answers
Answer:
1/4 or 12*
Step-by-step explanation:
There are 8 possibilities. 2 of them are 6.
2/8=1/4
1/4 of 48 is 12
*The theoretical probability doesn’t change no matter how many times you spin the spinner. It will always be 1/4. (Or 0.25, or 25%). That could be what they’re asking. If you spun it 48 times, it would probably land on a six 12 times. That could also be what they’re asking for. 12:48 = 1:4.
In sixteen years Paul will be 48 years old.
How old is he now?
Answers
Answer:
32 years old
Step-by-step explanation:
48-16=32
Answer:
Paul is 32 years old
Step-by-step explanation:
48 - 16 = 32
how to solve by factoring
x^2 + x = 0
Answers
Answer:
x=0 and x=-1
Step-by-step explanation:
Given: x^2+x=0
Factor: x(x+1)=0
Use Zero Product Property: x=0 and x+1=0
Therefore, x=0 and x=-1
50 pts please help asap (:
Answers
Answer:
d. 8 units
Step-by-step explanation:
If AC = 16 units then the length of CB is 8 units because DB is perpendicular bisector from the centre of circle.
Answer: B
Step-by-step explanation: I took the quiz
Hope this helps
A bicycle is originally priced at $60. The online retailer gives a discount and the bicycle is now priced at $42. Enter the percentage discount for the cost of the bicycle.
Answers
Answer:
30% ywww
Step-by-step explanation:
If x=3 and y=7, evaluate the following expression: 100 − 3 ( 3 − 4x )
Answers
Answer:
[tex]100 - 3(3 - 4x) \\ = 100 - 3(3 - 4 \times 3) \\ = 100 -27 \\ = 73[/tex]
Answer:
873
Step-by-step explanation:
100 - 3 ( 3- 4x ) 97 ( 3 - 4×3 )97 (3 - 12 ) 97 × 9 873PLEASE GIVE ME AN ANSWER!!!!ILL MARK BRAINLIEST ANSWER
Answers
Answer:
3 3/4
Step-by-step explanation:
3.75 square ft per hr.
5/8 x 6 = 3.75
I got this question
Kristin charges $30 to train a small dog, and $50 to train a big dog. If Kristin trains 15 small dogs and 6 big dogs, how much money will she make?
Answers
Answer:
$750
Step-by-step explanation:
We can set up the equation 30x + 50y = z where x = the amount of small dogs, y = the amount of big dogs, and z = the total.
After plugging in the x and y values to solve for z, we are left with the following equation:
30(15) + 50(6) = 750
-A sequence is a list of numbers or obje
What is a pattern?
-A pattern is a repetitive sequence and
numbers and almost everywhere you ca
What's More
A. Directions: Give the pattern rule of t
Rul
1. 1, 4, 7, 10, 13
2.2, 8, 32, 128, 512
Rul
Answers
Answer:
1. Add 3
2. Multiply 4
Step-by-step explanation:
Given
[tex](1)\ 1, 4, 7, 10, 13[/tex]
[tex](2)\ 2, 8, 32, 128, 512[/tex]
Required
The rule
[tex](1)\ 1, 4, 7, 10, 13[/tex]
This is a linear function because successive terms have a common difference
The common difference between each term is:
[tex]d = 4 - 1 = 3[/tex]
[tex]d = 7 - 4 = 3[/tex]
[tex]d = 10 - 7 = 3[/tex]
[tex]d = 13 - 10 = 3[/tex]
The above shows that 3 is [tex]added\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Add 3
[tex](2)\ 2, 8, 32, 128, 512[/tex]
This is a geometric function because successive terms have a common ratio
The common ratio between each term is:
[tex]r = 8/2 = 4[/tex]
[tex]r = 32/8 = 4[/tex]
[tex]r = 128/32 = 4[/tex]
[tex]r = 512/128 = 4[/tex]
The above shows that 4 [tex]is\ multiplied\ to\ each\ term[/tex] to get the next term.
Hence, the rule is: Multiply 4