Find the axis of symmetry and the vertex of the graph of f (x) = x^2 - 16 + 55
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
Vertex: (0, 39)
Axis of Symmetry: x = 0
»»————- ★ ————-««
Here’s why:
I have graphed the equation on a program. When graphed, the the lowest point lies on the point (0, 39). This makes (0, 39) the vertex.⸻⸻⸻⸻
The axis of symmetry is a vertical line that intercepts the vertex. The vertical line makes the parabola seem 'symmetrical'. The 'x' value of the vertex is usually the line of symmetry as well.⸻⸻⸻⸻
The 'x' value of the vertex is '0', so the axis of symmetry is [tex]x = 0[/tex].
⸻⸻⸻⸻
See the graph that I have attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
For equation:
[tex]f(x)=x^2-16x+55[/tex]
Vertex: [tex](8,-9)[/tex]
Axis of symmetry, ([tex]x=8[/tex])
For equation,
[tex]f(x)=x^2-16+55[/tex]
Vertex:[tex](0,39)[/tex]
Axis of symmetry, ([tex]x=0[/tex])
Step-by-step explanation:
The x-coordinate of the vertex of a parabola indicates the line of symmetry of the parabola. Thus, to solve this problem, one must find the vertex of the parabola. This can be done through a process called completing the square.
Completing the square is a process that converts a quadratic equation in standard form into vertex form. The first step is to group the linear and quadratic terms. Then factor out the coefficient of the quadratic term. After doing so, add a term to make the group a perfect square trinomial, then balance the equation.
Possibility 1
If the given equation is the following,
[tex]f(x)=x^2-16x+55[/tex]
Group,
[tex]=(x^2-16x)+55[/tex]
There is no quadratic term, thus, complete the square,
[tex]=(x^2-16x+64)+55-64[/tex]
Simplify,
[tex]=(x-8)^2-9[/tex]
Vertex: [tex](8,-9)[/tex]
Axis of symmetry, ([tex]x=8[/tex])
Possibility 2
If the given equation is the following,
[tex]f(x)=x^2-16+55[/tex]
Combine like terms,
[tex]=x^2+39[/tex]
Put in vertex form,
[tex]=(x)^2+39[/tex]
Vertex:[tex](0,39)[/tex]
Axis of symmetry, ([tex]x=0[/tex])
Related Questions
simplify 6p/p-1 - p+5/p-1
Answers
Answer:
-(p+1) (p-5)/ P
Step-by-step explanation:
Identify who is correct
Describe the mistake that was made
Answers
Jack is wrong because he used the distributive property wrong. On the top equation, you see 2(4k - 3). The 2 multiplies into the (), so basically you have
2 x 4k - 2 x 3
which gives you
8k - 6
Answer:
Taniyah
Step-by-step explanation:
Taniyah is correct because you need to:
diistribute : 8k - 6 - 6k = 14
combine like terms : 2k - 6 = 14
add 6 to both sides : 2k - 6 + 6 = 14 + 6
simplify : 2k = 20
divide both sides by the same factor : 2k/2 = 20/2
simplify : k = 10
what is the value of A
Answers
I think the answer is a = 4.5
81 ÷ 6 ÷ 3 = 4.5
I hope this helps, have a wonderful day!
i guess it might be right or wrong.the answer will be x value is 20.
Math Tutor Pay: $11.44 per hour
they work 13 hours
how much do they get paid in a-
per week
per month
per year
Answers
Answer:
Per week: $1041.04Per month: $4610.32Per year: 55323.84Answer:
1041$/1W(M-Sun)
892$/1W(M-SAT)
744$/1W(M-Fri)
Step-by-step explanation:
Go to sleep stoo naughty
Please help ASAP
1.
Three times a number equals 40 more than five times the number what is the number
2.
A number equals four less than three times the number what is the number?
Answers
Answer:
Step-by-step explanation:
Expand (2+x)(2-x). If necessaty combine like terms
Answers
Answer:
Step-by-step explanation:
(2+x)(2-x)
2(2-x)+x(2-x)
4-2x+2x-x^2
4-x^2
What is the numerator called in a percent problem? What is the denominator called in a percent problem ?
PLEASE I NEED HELP NOW!!!
Answers
Answer:
A percentage or percent for short is a fraction; a fraction that always has the denominator as 100. Because the denominator of a percent is always a 100, no matter what the numerator is, we replace 100 with the percent symbol % after the number. By definition, for any number x, x% = x100.
Step-by-step explanation:
Rosa has 7 1/2 yards of material. Her new skirt will take 3 2/3 yards. How much material will she have left after the skirt is made?
Answers
Answer:
11 1/6
Step-by-step explanation:
NO LINKS the picture below shows six quarters and two pennies. If this was broken
down into two separate groups, what would be the equivalent ratio to six-
seconds?
Answers
Answer:
B i took the quiz
Step-by-step explanation:
Just trust me bro
There are eight boys and eight girls in a
class. The teacher randomly selects one
student to answer a question. Later, the
teacher randomly selects a different student
to answer another question. The first
student is a boy and the second student is a
girl.
Answers
Answer:
Independent events - Random selection of one
student - Selection of one boy to answer first question
Dependent Event - Selection of a girl student
Probability = 13.33 %
Step-by-step explanation:
The complete question is
Determine whether the scenario involves independent or dependent events. Then find the probability
There are eight boys and eight girls in a
class. The teacher randomly selects one
student to answer a question. Later, the
teacher randomly selects a different student
to answer another question. The first
student is a boy and the second student is a
girl.
Solution
Independent events - Random selection of one
student - Selection of one boy to answer first question
Dependent Event - Selection of a girl student
Probability
8C1 + 8C1/16C2
(8+8) /(8*15)
13.33 %
Solve this riddle I come in lots of colors and I can swallow a 1000 sheep what am I?
Answers
Answer:
A dragon maybe?
Step-by-step explanation:
1. What are the answer choices??
I say a dragon because a dragon comes in different colors and looks big enough to swallow 1000 sheep.
Could you be more specific???
Martin is driving to his uncle’s farm, which is 240 mi. from home. If he drives at a constant rate of 60 mph, how long will it take Martin to get to the farm? A. 2 hr. B. 4 hr. C. 5 hr. D. 6 hr.
Answers
Answer:
4 hours
Step-by-step explanation:
240 divided by 40
Answer:
4 hours
240 divided by 60
Step-by-step explanation:
Hope it helps
what is the answer to the question 5/6 * 1/4 =
I am having a hard time figuring it out
Answers
Answer:
5/24
Step-by-step explanation:
[tex]\frac{5}{6} *\frac{1}{4} =\frac{5*1}{6*4} =\frac{5}{24}[/tex]
What is the solution to the system of linear equations represented by the matrix equations below. Please help!!!!!
Answers
Explanation I did the test and got it right
The system of equations has infinite solutions.
Option D is correct.
What is matrix multiplication?Matrix multiplication is a binary operation whose output is also a matrix when two matrices are multiplied.
To multiply one matrix with another, we need to check first, if the number of columns of the first matrix is equal to the number of rows of the second matrix. Now multiply each element of the column of the first matrix with each element of rows of the second matrix and add them all.
Given
Matrix equations
[tex]\left[\begin{array}{ccc}2&4\\1&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}6\\3\end{array}\right][/tex]
L.H.S:
Using Matrix multiplication
[tex]\left[\begin{array}{ccc}2&4\\1&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}2x+4y\\x+2y\end{array}\right][/tex]
R.H.S:
[tex]\left[\begin{array}{ccc}6\\3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}2x+4y\\x+2y\end{array}\right]=\left[\begin{array}{ccc}6\\3\end{array}\right][/tex]
Writing equation from above matrix
2x + 4y = 6
x + 2y = 3
or
2x + 4y = 6
2x + 4y = 6
Because there are two unknown number, but the two equations are consistent.
So, the system of equations has infinite solutions.
Option D is correct.
Find out more information about matrix multiplication here
https://brainly.com/question/14490203
#SPJ2
a number y is 15 larger than a positive number x. if their sum is not more than 85, what are the possible values of y?
Answers
Answer:
y = x + 15 –(1)
x + y = 85
Putting (1)'s value,
x + x + 15 = 85
2x + 15 = 85
2x = 85 - 15 = 70
x = 70/2 = 35
[tex][/tex]
The value of y is 50.
Two simultaneous equations can be formed from the given question:
y - x = 15 equation 1
y + x = 85 equation 2
In order to determine the value of x, subtract equation 1 from 2
2x = 70
Dvidie both sides of the equation by 2
x = 70 / 2
x = 35
Substitute for x in equation 1
y - 35 = 15
y = 35 + 15
y = 50
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Oscar rides his skateboard 58
5
8
mile in 14
1
4
hour. How fast, in miles per hour, does he ride his skateboard?
Answers
Answer:
speed = distance ÷ time
58 ÷ 14
speed = 4.142
David is planning to attend a public university after he graduates from high school in 3 years. He is devising a plan to save money each month to help with the expenses of attending the university. The cost of attending the public university for one-year is $53,600. His family has promised to contribute $32,000 each year he is in school. What is the minimum amount of money David must contribute to his savings per month for the next 3 years to have enough money to pay for his first year of tuition?
a
$450
b
$600
c
$575
d
$725
Answers
Answer:
b. 600
Step-by-step explanation:
subtract money from parents from tuition
divide by months
Glenn has a garden that is shaped like a rectangle.
The perimeter of his garden is 7012 feet.
The length of the garden is 2434 feet.
What is the width of the garden?
21 ft o 11ft o 10 ½ ft o 45 ¾ ft
Answers
Answer:
Solution given:
The length of the garden[l] = 2434 feet.
breadth or width [b]=b
perimeter of his garden = 7012 feet.
2[l+b]=7012ft
2434+b=7012/2
b=3506-2434
b=1072
So the width of the garden is 1072ft.
10.
Complete.
y^2 + 15y + 56 = (y + 7)(y + )
A. 8
B. –7
C. –8
D. 7
Answers
Answer:
I would go with letter B. -7
Step-by-step explanation:
The two factors of a quadratic equation can be multiplied to form the original equation. Let the missing term be a:
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
...............................................................................................................................................
Step by Step Solution
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
Step by step solution :
STEP 1 :
Trying to factor by splitting the middle term
1.1 Factoring y2+14y+49
The first term is, y2 its coefficient is 1 .
The middle term is, +14y its coefficient is 14 .
The last term, "the constant", is +49
Step-1 : Multiply the coefficient of the first term by the constant 1 • 49 = 49
Step-2 : Find two factors of 49 whose sum equals the coefficient of the middle term, which is 14 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 7
y2 + 7y + 7y + 49
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y+7)
Add up the last 2 terms, pulling out common factors :
7 • (y+7)
Step-5 : Add up the four terms of step 4 :
(y+7) • (y+7)
The solution is:
y = -7
The solution is:
y = -14 / 2 = -7
Please help me to find area of semicircle
Answers
Answer:
Use a calculator and use the formula 1/2 × pi × (radius squared)
Please help ASAP thank you!
Answers
Answer:
y < 3
Step-by-step explanation:
If you put the equation on a graphing calculator it shows that.
Please give me BRAINLIEST and THANKS <(￣︶￣)>
Carlos bought 6.5 pounds of bananas for $5.20.
● What is the price per pound of the bananas that Carlos bought?
What quantity of bananas would one dollar buy?
Answers
Each banana cost $0.80.
Step-by-step explanation:
5.20 divided by 6.5 is 0.80
Find the measure of angle b. PLZ HELP AND SHOW WORK
Answers
Answer:
1) A because of vertical angle theorem (VAT), which means that b=37 degrees
2) C because a right angle is= to 90 degrees. Take away 23, you get 67 degrees
3) B because the image shows a full angle, which is equal to 360 degrees. Take away 207 and 58, you get 95 degrees
4) D because a right angle is= to 90 degrees. Take away 44, you get 46 degrees
5) A because a right angle is=to 90 degrees. Take away 58, you get 32 degrees
help me please!!!! asap Tia
Answers
Answer:
All of them should be marked sicne they are all less than 12.
Step-by-step explanation:
Answer:
m = 6, m = 1, m = 5, m = 7
Step-by-step explanation:
All the options are solutions of m < 12.
plz help me understand this question thankyou
Answers
Answer:
The mistakes were on points C and D
Step-by-step explanation:
Point C was graphed on (5,8) when it's supposed to be plotted on (5,7). Point D was on (-3,-4) but was supposed to be on (-4,-3?
Answer:
The mistakes are Point C and D
Select each true statement about this.
A cylinder has a diameter of 18cm and a height of 4cm.
The radius is 12cm
The volume of the cylinder is324 п cm
The volume of the cylinder is1296 п cm
The area of the base of the cylinder is 81 п cm?
Answers
Answer:
The volume of the cylinder is324 п cm
The area of the base of the cylinder is 81 п cm
Step-by-step explanation:
volume of a cylinder = nr^2h
n = 22/7
r = radius = 18/2 = 9
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
n x (9^2) x 4 = 324n
Area of the base of the cylinder : Area of a circle = πr² = π x 9^2 = 81 π
Which of the expressions below are equivalent? 8x - 4 4x 4(2x - 1)
Answers
4(2x-1) the four needs to be distributed in the parentheses.
4*2x=8x
4*(-1)=(-4)
8x-4=8x-4
HELP ASAPPPP, FIRST PERSON TO HAVE THE CORRECT ANSWER WILL HAVE BRAINLIEST
What is the distance between points (8,3) and (3, 1) on the coordinate plane?
OA. 3 units
OB. 21 units
OC.29 units
OD. 7 units
Answers
Answer:
√29
Step-by-step explanation:
You would use the distance formula in this case to solve the problem:
(8-3)^2+(1-3)^2=29
Now square root 29, leaving you with √29.
Answer:
5.39
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(3 - 8)² + (1 - 3)²
√(-5)² + (-2)²
√25 + 4
√29
= 5.39
Jacob rode his bicycle at an average rate of 15 kilometers per hour.
Which statement about Jacob's bike race could be true?
Answers
Answer:b
Step-by-step explanation:
help please!!!! thank you in advance. asap too
Answers
C=4
C=5
C=11