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The equation [tex]y = x^2 - 8x + 3[/tex] is an illustration of a quadratic equation
The vertex of the quadratic equation [tex]y = x^2 - 8x + 3[/tex] is (4,-13)
How to determine the vertex?The equation is given as:-
[tex]y = x^2 - 8x + 3[/tex]
A quadratic equation is represented as:
[tex]y = ax^2 + bx + c[/tex]
By comparison, we have:
a = 1; b = -8; c = 3
The x-coordinate of the vertex is:
[tex]x = -\frac b{2a}[/tex]
So, we have:
[tex]x = \frac 8{2*1}[/tex]
[tex]x = 4[/tex]
Substitute 4 for y in [tex]y = x^2 - 8x + 3[/tex]
[tex]y = 4^2 - 8 * 4 + 3[/tex]
[tex]y = -13[/tex]
When x = 2 and 3, we have:
[tex]y = 2^2 - 8 * 2 + 3 = -9[/tex]
[tex]y = 3^2 - 8 * 3 + 3 = -12[/tex]
When x = 5 and 6, we have:
[tex]y = 5^2 - 8 * 5 + 3 = -12[/tex]
[tex]y = 6^2 - 8 * 6 + 3 = -9[/tex]
So, the table of values is:
x y
2 -9
3 -12
4 -13
5 -12
6 -9
Read more about quadratic functions at:
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Related Questions
PLS HELP ME I WILL MARK THE BRAINIEST 50 POINTS!!!!!!
Answers
Answer:
Done. Check comments
Step-by-step explanation:
Inscribed angles are half the measure of the intercepted arcs. This example shows major arc BEA being intercepted by the supplement of 74, which is 106. If you double that, you get the arc, 212.
The next example shows 80 and 154 are intersected by two chords. The angle created by that intersection is the average of the two intercepted arcs. 117.
When two secant lines intersect, they form an angle that is half the measure of the DIFFERENCE of the intercepted arcs. 145 - 53 = 92/2 = 46.
This is similar to the previous one. Except the difference is between 263 and 97. ACTUALLY, I MADE AN ERROR on the comment about this one.
263-97 = 166/2 = 83***
Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle? 82° 92° 102° 112°.
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the sum of all interior angles in a polygon is
180( n - 2), n = number of sideswe know this one is a PENTAgon, so it has 5 sides, so the total for the interior angles will be
180( 5 - 2) = 540 degrees.
540° - 88° - 118° - 132° - 100° = 102° <- fifth angle.
The final interior angle of the pentagon measures 102°.
What is the measure of the fifth interior angle?We know that for a figure of n sides, the sum of its interior angles is equal to:
S = (n - 2)*180°
Then for a pentagon, 5 sides, we have:
S = (5 - 2)*180° = 3*180° = 540°
Then if X is the missing interior angle, we must have:
88° + 118° + 132° + 100° + X = 540°
438° + X = 540°
X = 540° - 438° = 102°
So the measure of the last interior angle is 102°.
If you want to learn more about interior angles:
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#SPJ2
choose the name of the highlighted part.
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Answer:
B.edge it is the correct answer!
SOMEONE PLS HELP ME !!!!
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HELP PLEASE!!!!!!!!!
James left a bin outside in his garden to collect rainwater. He notices that 1/4 gallon of water fills 2/3 of the bin. Write and solve an expression to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words
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Answer:
3 pints of water will fill up the bin
Step-by-step explanation:
1 gallon = 4 quarts
1/4 gallon = 1 quart
1 quart = 2 pints
That means that Two pints filled 2/3 of the bin meaning that one more pint will fill it up completely
look at pic please and answer
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What is the slope of the line containing the points (-1, -2) and (3, -5)? A. B. C. D.
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Answer:
-7/4
Step-by-step explanation:
(-1,2) (3,-5)
x1 y1 x2 y2
-5-2=-7
3-(-1)=4
-7/4
Describe what happens to a figure when the given sequence of transformations is applied
to it: (x, y) → (-x, y); (x, y) → (0.5x, 0.5y); (x, y) → (x - 2, y + 2)
(If you answer this you will get 100 points for answering in brainly)
Answers
Answer:
After the sequencing of transformations, reflection over the y-axis.
dilation with a scale factor of 0.5
translation 2 units left and 2 units up
Step-by-step explanation:
what steps are used to solve this equation x/2=7 complete each statement
Answers
Answer:
x=14
Step-by-step explanation: Multiply all terms by the same value to remove denominators from fractions,Cancel the multiplied terms that are in the denominator, Multiplica los números
A yogurt machine makes
gallon of yogurt
every minute. The total amount y that the
machine makes in x minutes is given by
the equation y
]×. Determine whether the
relationship between x and y is linear and, if
so, if it is proportional,
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Step-by-step explanation:
the relationship between x and y is defined by a constant factor.
you can "go" from x to y and from y to x consistently and without any interruptions by applying that constant factor.
that makes it a linear relationship (a line on a chart, hence the name).
proportional relationships are relationships between two variables where their ratios are equivalent. another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
so, yes, it is proportional.
and the table is then
x y
0 0
3 3×2/3 = 2
6 6×2/3 = 4
9 9×2/3 = 6
calculate the arithmetic mean of -121 and 49
Answers
Answer:
i dont rlly know
Step-by-step explanation:
-121+49 then divide by 2
Answer:
-36
Step-by-step explanation:
The arithmetic mean of n numbers is their sum, divided by n.
The arithmetic mean of your 2 numbers is ...
(-121 +49)/2 = -72/2 = -36
The arithmetic mean of -121 and 49 is -36.
__
Many calculators and spreadsheets have an arithmetic mean function built in.
Multiply. Write your answer in simplest form. 2 5/6x2/5
Answers
Answer:
17/15
Step-by-step explanation:
2 5/6 x 2/5
convert 2 5/6 into improper fraction
17/6 x 2/5
cancel out the greatest common factor which would be the 6 and the 2
17/3 x 1/5
multiply straight across
17/15
could also be written as 1 2/15 or 1.13
Can some please explain and solve how to do these unit rate equations?
Answers
(2) 6:3=2:1. 10:5 It will take 5 hours because she’s walking 2km per hour, so it would take 5 hours to walk 10km.
(3) 1:20 4:80 It will take 80 minutes because 20x4=80
(4) 1:1 20:20 it will take her 20 days since she makes one craft a day and she’s making 20.
(5) 12:1 84:7 84 cakes since there is 7 days in a week. 12x7=84
If you still need help, here’s the answers
complete the proof, word bank at the bottom HELP PLEASE LOL
Given: ∠VYZ≅∠YWX, m∠VZY+m∠ZYX=180°
Prove: △ZVY∼△XYW
Answers
Answer:
Step-by-step explanation:
3) Definition of supplementary angles
4) Consecutive interior angles converse
5) Alternate interior angles
6) AA similarity
Helpppppp!!!
(Show work)
Answers
Answer:
Step-by-step explanation:
Part B: A"C
Jennifer is looking to lease a car. bob’s auto has a car available with a money factor of 0.00344. aaa auto has the exact same car available with a money factor of 0.00313. which of the following statements is true? a. the lower money factor with bob’s auto will give jennifer the lowest monthly payment. b. the lower money factor with aaa auto will give jennifer the lowest monthly payment. c. the higher money factor with bob’s auto will give jennifer the lowest monthly payment. d. the higher money factor with aaa auto will give jennifer the lowest monthly payment.
Answers
Answer:
B. The lower money factor with AAA Auto will give Jennifer the lowest monthly payment
You have just inherited $150,261 from a trust that has matured. You would like to invest the total amount into an account that pays you an annual compounded interest rate of 9. 1%, and you would like to make annual withdrawals over the next 20 years such that by the end of this 20 year period, the amount remaining in the account will be zero dollars. Determine, from the given information, the amount of the annual withdrawals. Round to the nearest cent. A. $16,578. 03 c. $15,978. 10 b. $162,851. 31 d. $15,575. 98.
Answers
Answer:
C
Step-by-step
The amount of the annual withdrawals will be $16,574.24.
The given data in the problem is;
P = annual payment
PV= present value = $150,261
r= rate of intreast = 9.1% =9.1/100= 0.091
n = time period= 20
What is the formula for the annual payment ?[tex]P=\frac{r\times PV}{1-(1+r)^{-n}}[/tex]
[tex]P=\frac{0.091\times 150261}{1-(1+0.091)^{-20}}[/tex]
[tex]P=16754.24[/tex]
Therefore, the amount of the annual withdrawals will be $16,574.24.
To learn more about the amount visit:
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This figure represents the base of an aquarium that is 9 inches high.
What is the volume of the aquarium?
558 in³
612 in³
702 in³
810 in³
Answers
Answer:
Step-by-step explanation:
Answer:
558 in³ for K12
Please help me with this math question. I will give brainliest!! :D
Answers
Answer:
C
Step-by-step explanation:
A kite string is 100 feet long from the kite to the ground. The string makes a 45° angle with the ground
About how high off the ground is the kite? Leave your answer as a simplified radical
Answers
Answer:
It's not very high
Step-by-step explanation:
The angle that the string and the ground maje, is acute, because it's smaller than a right angle. So, since it is an acute angle, it's not very high. It is about 30cm high.
Nathan is going to invest in an account paying an interest rate of 4. 9% compounded continuously. How much would Nathan need to invest, , for the value of the account to reach $34,000 in 9 years?
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$34000\\ P=\textit{original amount deposited}\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ t=years\dotfill &9 \end{cases} \\\\\\ 34000=Pe^{0.049\cdot 9}\implies 34000=Pe^{0.441}\implies \cfrac{34000}{e^{0.441}}=P\implies 21875.35\approx P[/tex]
Ten tubs of dried cranberries cost $40 how many runs can u buy for $20
Answers
Answer:
5 tubs
Step-by-step explanation:
This because if we divided 10 in half we get 5 and if we divide 40 in half we get 20
I hope this helps :)!!
George bought a 3-pound bag of potatoes and a 32-ounce bag of carrots. How many pounds of vegetables did George buy?
A) 3 pounds
B) 5 pounds
C) 6 pounds
D) 8 pounds
Answers
Answer:
5
Step-by-step explanation:
1 pound = 16 ounces
32/16 = 2
2 + 3 = 5
So therefore he bought 5 pounds of vegetables.
A large grocery store chain pays all workers time and a half on Saturdays and double time on Sundays. If an employee's regular pay is $10.75 per hour, use the expression 10.75(1.5)(x) + 10.75(2)(y) to find their gross income if they worked 4.5 hours on Saturday and 5 hours on Sunday. (4 points)
$156.72
$177.38
$180.06
$257.44
Answers
Answer:
180.06
Step-by-step explanation:
We first need to sustitue x and y for the time workd on saturday and sunday :)
10.75(1.5)(4.5) + 10.75(2)(5)
Now we multpily in order!!
10.75(1.5)(4.5) + 10.75(2)(5)
72.56 + 10.75(2)(5)
72.56 + 107.50
Now we add!!
72.56 + 107.50
180.06
Your answer is 180.06 :)
Have an amazing day!!
Please rate and mark brainliest!!
At what point does the line given by the following equation cross the y-axis? y = (6/9)X + 9
A. (9,0)
B. (0,6/9)
C. (0,9/6)
D. (0,9)
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{6}{9}[/tex] x + 9 ← is in slope- intercept form
with y- intercept c = 9
then the line crosses the y- axis at (0, 9 )
I NEED THE ANSWER |(-2+1)*3)|
Answers
Answer:
The answer is 3
Step-by-step explanation:
add -2+1 first equal -1 flip -1 to positive equal 1. Multiply 3*1 and that equals 3
What is the number halfway between 8516 and 8586?
Answers
Answer:
8551
Step-by-step explanation:
The midpoint of two numbers can be found by finding the mean of the two numbersMidpoint = 8516 + 8586 / 2We clearly see both numbers start with the digits '85' therefore their midpoint will also start with '85'The remaining two digits on those two numbers should be added and divided by 2⇒ 16 + 86 / 2 = 102/2 = 51Midpoint = 8551how to solve 3x - y = -1 and -3x - y= 5
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a shopkeeper selling an article at discount of 20% looses rs 400 if he allow 10% discount he gains rs 200 find the marked price and the cost price of the article
Answers
Answer:700
Step-by-step explanation:
Let the M.P of the article be x .
A discount of 20% was given on the M.P .
So the selling price of the article ( S.P ) will be M.P - Discount .
Discount = 20 % of x
⇒ Discount = 20/100 of x
⇒ Discount = 1/5 × x
⇒ Discount = x/5
Now S.P = M.P - Discount .
⇒ S.P = x - x/5
⇒ S.P = ( 5 x - x ) / 5
⇒ S.P = 4 x / 5
The shopkeeper loses Rs 200 .
Loss = C.P - S.P
⇒ C.P = Loss + S.P
⇒ C.P = 200 + 4 x / 5
⇒ C.P = ( 1000 + 4 x )/5
Now if he allows 10 % discount then the gain is Rs 150 .
Gain = S.P - C.P
⇒ S.P = Gain + C.P
⇒ S.P = 150 + ( 1000 + 4 x )/5
⇒ S.P = ( 750 + 1000 + 4 x )/5
⇒ S.P = ( 1750 + 4 x )/5
Discount = 10 % of x .
⇒ Discount = 10/100 × x
⇒ Discount = x/10
S.P = M.P - Discount
⇒ ( 1750 + 4 x )/5 = x - x/10
⇒ ( 1750 + 4 x )/5 = 9 x / 10
⇒ 1750 + 4 x = 9 x / 2
⇒ 3500 + 4 x = 9 x
⇒ 9 x - 4 x = 3500
⇒ 5 x = 3500
⇒ x = 3500/5
⇒ x = 700
Evaluate the expression 10 + (8 - 4)2 ÷ 2.
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Answer:
10 + (8 - 4)2÷2
10 + (4)2 ÷2
10 + 8 ÷ 2
10 + 4
= 14