The vertex of the given quadratic function is (-3, 0).
What is vertex form of a quadratic equation?The vertex form of a quadratic equation or function is [tex]f(x)=a(x-h)^{2} +k[/tex].
Where,
(h, k ) is the vertex
And, a is constant.
According to the given question
We have a quadratic function
[tex]f(x) = x^{2} + 6x + 9[/tex]
The above function can be written as
[tex]f(x) = x^{2} +2(3x) +9[/tex]
⇒[tex]f(x) = x^{2} + 2(3x) + (3^{2}) -(3)^{2} + 9[/tex]
⇒[tex]f(x) = (x+3)^{2} -9+9[/tex]
⇒[tex]f(x) = (x+3)^{2} + 0[/tex]
Comparing the above equation with the standard vertex form of quadratic function we get
h = -3 and k = 0
Hence, the vertex of the given quadratic function is (-3, 0).
Thus, option A is correct.
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Veronica takes of an hour to write of a page of calligraphy.
How long will it take Veronica to write one page of calligraphy?
Using proportions, it is found that it will take Veronica 4/3 of an hour to write one page of calligraphy.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, it is found that she takes 1/3 of an hour to write 1/4 of a page of calligraphy. How long it takes her to write a page?
The rule of three is:
1/3 hour - 1/4 page
x hours - 1 page
Applying cross multiplication:
[tex]\frac{x}{4} = \frac{1}{3}[/tex]
[tex]x = \frac{4}{3}[/tex]
It will take Veronica 4/3 of an hour to write one page of calligraphy.
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What is the final price of a $125 jacket that is on sale for 35% off?
Answer:
$81.25
Step-by-step explanation:
first change the percent into a decimal by moving the point 2 spaces to the left. then multiply that decimal by the asnwer to see how muhc money she's getting off. Finally subtract the total by that number.
A line with a slope of -1/4 passes through the point (8,7). What is it's equation in slope- interception form?
Answer:
y= -1/4x + 9
Step-by-step explanation:
When given the point (8,7) and the slope -1/4, you have to convert this into a formula called point slope form. This is the formula:
y - y1 = m(x - x1)
First, label the given information.
-1/4= m (slope)
8= x1 (the first x given)
7= y1 (the first y given)
Then, plug in the values into the equation
y - 7 = -1/4(x - 8)
After, do the property of distribution by multiplying the -1/4 with whatever is in the bracket
-1/4 multiplyed by x= -1/4x
-1/4 multiplyed by -8= 2
Next, bring the 7 to the other side of the equal sign by adding the 7 from one side to the 2. Then combine like terms
y - 7 = -1/4x +2
+7 +7
This gets you your answer:
y = -1/4x +9
Bruh I’m dumb pleaseeeee help
Answer:
m is the slope
x is the variable
b is the y-intercept
In July, the average temperature in one US city was 29 degrees by December, the average temperature had fallen by 29 degrees. Explain why the average temperature in December was 0 degrees.
Step-by-step explanation:
In July, it was positive 29 degrees, but in December it was negative 29 degrees. When you have 29-29 you get 0. Hope that helped
Answer:
Sample Response: The temperature went up 29°C, which represents a positive 29. Then the temperature fell 29°C, which represents a negative 29. The average temperature rose and fell the same amount. The absolute values are the same, so the difference is 0.
Step-by-step explanation:
A baseball stadium holds 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper level. The middle level has 40 more than twice as many seats as the upper level.
x + (2x + 40) + (3x – 50) = 15,002
The upper level has how many seats
Answer:
The equation x + (2 x + 40) + (3 x - 50) = 15,002 represents this scenario suitable.
Step-by-step explanation:
Hope it helps :)
I know I'm answering all your questions it's just bc I'm bored
HELP ASAP PLEASE!!!
what is the equation of the line that passes through the points (11, - 4) and (13,- 7) in slope-intercept form?
answer choices shown in picture
Answer:
E. None of these
Step-by-step explanation:
Points: (11, -4), (13, -7)
slope = m = (y2 - y1)/(x2 - x1) = (-7 - (-4))/(13 - 11) = (-7 + 4)/2 = -3/2
y - y1 = m(x - x1)
y - (-4) = (-3/2)(x - 11)
y + 4 = (-3/2)x + 33/2
y + 8/2 = (-3/2)x + 33/2
y = (-3/2)x + 25/2
Answer: E. None of these
Step-by-step explanation:
A(11,-4) B(13,-7)
x1 y1 x2 y2
y=mx+c
-4=11m+c -(i) -7=13m+c -(ii)
Subtract equation (ii) from (i)
-7=13m+c
-4=11m+c
+ - -
-3=2m
2m=-3
m=-3/2
put m=-3/2 in equation (ii)
-7=13*(-3/2)+c
c=-7+39/2
c=(-14+39)/2
c=15/2
y=mx+c
y=-3/2x+15/2
y=(-3x+15)/2
2y=-3x+15
2y+3x-15=0
What is the difference between the function's values on Day 1?
0
35
70
105
The square root of 15 is in between what 2 whole numbers?
The square root of 15 is between 3 and 4.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
Given that the square root is 15. The value of the square root of 15 is calculated as,
The square root of 15 is 3.872.
Therefore, the square root of 15 is between 3 and 4.
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Use your answers above to find the total length of the part of the track that is made up of sides of the square.
Hadley earned 8 more points on her test than Adam earned. Their points add up to 162. How many points did each student earn ?
Answer:
Adam - 77 / Holly - 85
Step-by-step explanation:
x + (x + 8) = 162
2x + 8 = 162
2x = 154
x = 77
x = Adam
x + 8 = Holly
Therefore, Adam - 77 / Holly - 85.
-5X - 8y = 3
6x + 3y =3
Solve using elimination ?
Answer:
for the first one its x=30
for the second one its x=6
Step-by-step explanation:
its x=30 because at the end if you do the problem yourself, you would have to multiply 5×6 which is 30.
im not sure why its x=6 on that one i might be wrong but i did it but im also confused on it but i tried so yeah maybe it is.
Determine the range from the set of ordered pairs
Answer:
2nd option
Step-by-step explanation:
range is all the outputs
Your student class council needs $600 for the Winter Dance. With only $210 in their treasury, the council decided to raise the rest by selling donut coupons for a profit of $1.50 per dozen. Write and solve an equation to find how many donut coupons they will need to sell
Answer:
$390
Step-by-step explanation:
Need: 600
Have: 210 600-210=390
Can someone help me please, thanks.
Answer:
138
Step-by-step explanation:
my teacher told me to answer this it got complicated for me
Answer:
SOLUTION FOR A:
YOU NEED TO MULTIPLY THE VARIABLE FROM THE DENOMINATOR
SOLUTION FOR B:
MULTIPLY TO REMOVE THE VARIABLE FROM THE DENOMINATOR
THE ANSWERS FOR SOLVING FOR B AND A ARE IN THE SCREENSHOTS
yk i just rlly wanted to type in caps-
1.(03.01 LC)
Which of the following sets represents the range of the function shown? (5 points)
{(-3, 4), (5, 11), (9, -1), (10, 13)}
{-3, 5, 9, 10}
O {-1, 4, 11, 13}
{(4, -3), (11, 5), (-1, 9), (13, 10)}
{-3, -1, 4, 5, 9, 10, 11, 13}
HELP ME
Answer:
-1, 4, 11, 13
Step-by-step explanation:
the range of the function is the y values in this scenario, which are the second numbers of the original points given
Find the slope of a line parallel to the given line.
Which point lies on the line that passes through the
point (9,-5) and has a slope of -6?
Answer:
y=5
Step-by-step explanation:
I am pretty sure that is the answer but dont rely completely on me
The formula t=√h/4 represents the time t in seconds that it takes an object to fall from a height of h feet. If a rock falls from a height of 125 feet, estimate how long it will take to reach the ground
Answer:
it would take 14mph
Step-by-step explanation:
A function assigns the values. The time it will take for the rock to reach the ground from a height of 125 feet is 2.795 seconds.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the formula t=√h/4 represents the time t in seconds that it takes an object to fall from a height of h feet.
Now, in order to calculate the time, it will take for the rock to fall from the height of 125 feet, simply substitute the height of the rock from which it is dropped in the formula given.
Therefore, the time it will take for the rock to reach the ground from a height of 125 feet is,
t = √h / 4
t = (√125) / 4
t = (5√5) / 4
t = 2.795 seconds
Hence, the time it will take for the rock to reach the ground from a height of 125 feet is 2.795 seconds.
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Choose a linear function for the line represented by the point-slope equation y-5= 3(x - 2).
O f(x) = 3r+1
O f(x) = 3x - 1
O f(x) = &r + 10
O flac) = 8x - 10
Answer:
y = 3x - 1
Step-by-step explanation: All you have to do here is solve the equation for y. When you add 5 to both sides, you are left with 3(x-2) + 5. Now, you just have to open the parentheses, giving you 3x-6+5, or 3x-1.
Solve inequality 5-3(4x-5)<32
Answer: x > -1
Step-by-step explanation:
1) Subtract 5 from both sides
-3(4x - 5) < 27
2) Divide both sides by -3 (Remember to change the inequality sign to face the other way, because you have multiplied/divided by a negative number)
4x - 5 > -9
3) Add 5 to both sides
4x > -4
4) Divide by 4 on both sides
x > -1
find the value of X for which m is parallel to n .
Answer:
x = 42
Step-by-step explanation:
the angles are considered congruent so the equation would be 4x-27 = 3x+15
add 27 to both sides: 4x= 3x +42
subtract 3x from both sides: x= 42
bruh someone helpp ffs
Answer:
Step-by-step explanation:
B ruh????????
Eve Marie used the table to describe a list of numbers. How should she fix the table?
Number
Rational
Integers
Whole
Counting
0.258
х
0
X
x
X
х
-45
X
X
4
15
Х
F 0.258 is also an integer, and should have an X placed in that column as well.
GO is not a counting number, and should not have an X in counting number column.
H-45 is also a counting number and should also have an X in the counting number
column.
3 The table is correct, theſe is no need to change it.
Answer:
your answer would be g
Step-by-step explanation:
NEED HELP ASAP!! convert 287 cm to inches
287 centimeters is 112.992 inches
Answer:
112.992
Step-by-step explanation:
divide the length value by 2.54.
if length of the square is 7-x and width is 19-3x then what is the value of x
11. Given: 17 - 3(w + 5) = 6(w + 5) - 2w;
Prove: w = -4
Statements
Reasons
11.17-3(3+5)=6(W+5)-2W
2.17-30-15= 60 +30 -2W
3.-3W +2 = 4W+30
4. -7W +2=30
5. -W=28
1. W= -4
Answer:
Step-by-step explanation:
Statements Reasons
1). 17 - 3(w + 5) = 6(w + 5) - 2w 1). Given
2). 17 - 3w - 15 = 6w + 30 - 2w 2). Distributive property
3). -3w + 2 = 4w + 30 3). Addition property of equality
4). -7w + 2 = 30 4). Subtraction property of equality
5). -7w = 28 5). Subtraction property of equality
6). w = -4 6). Division property of equality
Which point is a point where the graph of y = (x − 5)(x2 − 7x + 12) crosses the x-axis?
A. (-5,0)
B. (-3,0)
C. (4,0)
D. (12,0)
Answer:
answer is c (plato users)
Step-by-step explanation:
The point is a point where the graph of y = (x − 5)(x2 − 7x + 12) crosses the x-axis is (4,0).
The answer is option C (4,0)
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the line
slope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
solving the equation:-
⇒y = (x − 5)(x2 − 7x + 12)
⇒y= 2x²-7x²+12x-10x+35x-60
⇒y=-5x²+37x-60
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Help me pls. Show the working for the following questions in the picture