what is the vertex of y=-x^2+12x-31?????
[tex]h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} [/tex]
Vertex Form[tex]y = a{(x - h)}^{2} + k [/tex]
Where the a-term determines how wide, narrow, upward or downward the graph is.
The h-term determines the horizontal shift of graph. (x-axis)
The k-term determines the vertical shift of graph. (y-axis)
The vertex of graph is at (h,k). We can find the vertex by using the given formulas.
Find the vertexFrom the equation, the coefficients are:
[tex] \begin{cases} a = - 1 \\ b = 12 \\ c = - 31 \end{cases}[/tex]
Substitute these values in the formulas.
Find the value of h
[tex]h = - \frac{12}{2( - 1)} \\ h = - \frac{12}{ - 2} \\ h = - \frac{ - 6}{1} \longrightarrow - ( - 6) = 6 \\ h = 6[/tex]
Hence, the value of h is 6.
Find the value of k
[tex]k = \frac{4( - 1)( - 31) - {(12)}^{2} }{4( - 1)} \\ k = \frac{124 - 144}{ - 4} \\ k = \frac{ - 20}{ - 4} \longrightarrow \frac{5}{1} = 5 \\ k = 5[/tex]
Hence, the value of k is 5. Then we substitute both value of h and k in the vertex form
Rewrite the equation of vertex form by substituting the value of h and k[tex]y = a {(x - h)}^{2} + k \\ y = - 1 {(x - 6)}^{2} + 5 \\ y = - {(x - 6)}^{2} + 5[/tex]
AnswerSince the vertex is at (h,k). Therefore the value of h is 6 and k is 5. Therefore:
[tex] \large{(h, k)=(6, 5)}[/tex]
(6,5) is the vertex.
please help last question 50 X 2 - 10
the answer is 90
50 ×2 = 100
100 - 10 = 90
Could someone help me with this im so confused
Jonas is buying a fence for his garden if his garden has a perimiter of 36 feet and fencing cost 10.00 a yard
Answer:
120
Step-by-step explanation:
3 feet in a yard
36÷3=12
12×10=120
Which pair of angles are alternate exterior angles ?
8 and 1 are alternate exterior angles.
Answer:
<8 and <1
Step-by-step explanation:
<8 and <1 are both outside of the parallel so they are exterior and opposite to each other which is alternative exterior.
Hope this helps, thank you !!
What is the solution to this equation? -6x + 3 = 21 A. X= 4 B. X = -8 C. X = 3 D. X= -4
Answer:x+-3
Step-by-step explanation:
-6x+21-3
-6x=18
(0,5), (1,6), (2,9), and (3,14) are points on the graph of a function. Which of the following equations represents that function?
O A. g(x)= x2 + 5
O B. g(x)=522 +5
O C. g(x)= 3x2 +5
o D. g(x)= x + 5
Answer:
Step-by-step explanation:
It's with c or d I am confused with those two
2000:$5.00 2015:6.50 what is the change in the cost of the cheeseburger
can someone please help with this? will give brainliest
Answer:
0.004
Step-by-step explanation:
Just mutiply and divide by 2
Please can you help me on this equation.I just cant seem to solve this though i mostly don't need help.Thank you [tex]\frac{1}{x^2+1} -\frac{x^4}{x^2+1}+\frac{x^4}{x^2-1} -\frac{1}{x^2-1}[/tex]
Answer:
2
Step-by-step explanation:
combine like denominators:
(1-x^4)/(x^2+1)+(x^4-1)/(x^2-1)
factor:
(1-x^2)(1+x^2)/(x^2+1)+(x^2+1)(x^2-1)/(x^2-1)
reduce:
(1-x^2)+(x^2+1)
1+1=2
Charlotte has a piece of yarn in her craft kit. She uses 3/8
of the length of the yarn to make a bookmark. What part of the yarn is left?
Answer:
5/8
Step-by-step explanation:
8/8-3/8=5/8
can you help me please
Choose the correct inequality symbol for the following statement.
-4 - (-2) _____ -6
options:
>
<
=
Please... I just gave out 70 points and no one helped me. They just took the points and left
7. A computer software manufacturer wanted to know if its customers were satisfied with
the graphics in a new game program called Zinger they released six months ago. The
company randomly polled 1000 of the 50,000 people who had purchased the program.
Here is part of the results of the poll:
Zinger Program Graphics Percent
Satisfied with Graphics 42%
Not Satisfied with Graphics
No Opinion 13%
a. What percent of the 1000 game users surveyed were not satisfied with the graphics
of Zinger? (2 points)
b. Based on the survey findings, how many of the current 50,000 game users would the
company expect to not be satisfied with the graphics or to have no opinion? (3
points)
c. Based on the survey findings, the software manufacturer has decided to create a new
version of the game program with improved graphics. Why did they make this
decision? (2 points)
Please I don't have any more points
Answer:
A)
45% of customers were not satisfied with the graphics.
B)
22,500 people are expected to not be satisfied with the graphics.
6,500 people are expected to have no opinion.
C)
The majority of people are unsatisfied with the graphics.
Step-by-step explanation:
The company polled 1,000 out of the 50,000 people who had purchased the program.
42% was satisfied with the graphics.
And 13% had no opinion.
Part A)
When totaled, those satisfied, unsatisfied, and with no opinion should be 100%.
Since 42% are satisfied and 13% have no opinion, this leaves 100 - 42 - 13 or 45%.
So, 45% of customers were not satisfied with the graphics.
Part B)
Since 45% of the polled were unsatisfied with the graphics, 45% of the total 50,000 can also be expected to not be satisfied.
45% of 50,000 is 0.45(50000) = 22500.
So, 22,500 people are expected to not be satisfied with the graphics.
Likewise, 13% had no opinion.
So, 13% of 50,000 is 0.13(50000) = 6500.
6,500 out of the current 50,000 customers are expected to have no opinion with the graphics.
Part C)
Since the majority of people are unsatisfied with the graphics (45% > 42%), it is reasonable to create a new version with improved graphics.
The answers are in the photo. Hope this helps! ;)
1 2x3 4x + 7x²+7
x² + 2x-1
DIVIDE
Answer:I think its 2×-3
Step-by-step explanation:Hope it helps kiddo
John ordered three lobsters.the fist o e weighed 3.2 pounds,the second weighted 1.75 pounds,the third 1.9 pounds what is the total weight of the three lobsters
Answer:
6.85 pounds
Step-by-step explanation:
3.2+1.75+1.9=6.85
A culture started with 2,000 bacteria. After 8 hours, it grew to 2,400 bacteria. Predict how many bacteria will be present after 19 hours. Round your answer to the nearest whole number.
Answer:
2950 [Starting from 2,000 bacteria.]
Step-by-step explanation:
400/8 = 50
Bacteria grown/time = bacteria per hour
19x50 = 950
time x bacteria per hour = bacteria grown
2000 + 950
bacteria started + bacteria grown
someone plz help this is due today
3x+5x+1=17
x=2
y=5•2+1
y=1
(x, y)=(2, 11)
3x+2(4x+5)=43
x=3
y=4•3+5
y=17
(x, y)=(3, 17)
I think I did it right and I hope I helped you
This is the list of points that Maurice scored in the last 10 games.
13, 30, 25, 17, 16, 28, 31, 22, 68, 17, 12
What is the outlier?
68
Outliers are numbers that don't fit in with the rest of them..
The sun of two numbers is 10. The difference between the two numbers is 4.
Answer:
7 and 3
Step-by-step explanation:
Graph the line y = x + 6.
To graph a line, plot any two points on the line.
Your Graph would look like this
Step-by-step explanation:
what is the square root of 8
Answer:
2.82842712475
Step-by-step explanation:
√8 = 2.82842712475
How do I find volume of the cylinder?
Please help it's due today. Also please don't help if you don't know.
w = 24
work=
1000⁸=10w
write the expression in exponential form with the base of 10
10²⁴=10w
since the bases are the same, set the exponents equal
w=24
What is the slope the line?
Answer:
the slope is 3/4x
Step-by-step explanation:
if you need it in slope intercept form too its y=3/4x-1
in the diagram below, de is parallel to xy. what is the value of y
15 POINTS & BRINILY IF RIght!
Solve for r.
r + 12 / 5 = 5
R =?
help pls
The quantities I and y are proportional.
y
12
36
18.
54.
25
75
Find the constant of proportionality (7") in the equation y = rx.
cevap:y=5 inşallah faydalı cevaptır
y'all I need help asap
Answer:
Let's solve for x.
4x+5y=7
Step 1: Add -5y to both sides.
4x+5y+−5y=7+−5y
4x=−5y+7
Step 2: Divide both sides by 4.
4x/4=−5y+7/4
x=−5/4 y+ 7/4
Answer: for the first one x=−5/4 y+ 7/4
3x−2y=−12
Step 1: Add 2y to both sides.
3x−2y+2y=−12+2y
3x=2y−12
Step 2: Divide both sides by 3.
3x/3=2y−12/3
x=2/3y−4
Answer:
x=2/3y−4
Step-by-step explanation:
What is the ratio of the number
of sides of a square to the number
of edges of a cube.
Answer:
1:2
Step-by-step explanation:
The ratio of the number of sides of a square to the number of edges of a cube is- A)1:2.