Answers
Answer:
(x−2)^2=16(y+1)
Step-by-step explanation:
The equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
The vertex of the parabola = (2, -1)
The focus of the parabola = (2, 3)
As we know, the vertex form of the parabola is given by:
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
(x - 2)² = 4a(y - (-1))
(x - 2)² = 4a(y + 1)
The value of a can be found using the formula:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
(c, d) = (2, 3)
a = √[(2-2)² + (3-(-1))²]
a = √ (3+1)²]
a = 4
(x - 2)² = 4(4)(y + 1)
(x - 2)² = 16(y + 1)
Thus, the equation for the parabola is (x - 2)² = 16(y + 1) if the vertex of the parabola is (2, -1) and focus of the parabola is (2, 3) option (D) is correct.
Learn more about the parabola here:
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Related Questions
11. Find the volume and the surface area of the solid.
Answers
Answer:
Part A
The surface area of the solid is 408 cm²
Part B
The volume of the solid is 312 cm³
Step-by-step explanation:
Part A
The surface area of the figure is found by finding the sum of the surface area of the individual rectangles that make up the figure as follows;
The areas of the rectangles are;
A₁ = 6 cm × 2 cm = 12 cm²
A₂ = 6 cm × 4 cm = 24 cm²
A₃ = 6 cm × 6 cm = 36 cm²
A₄ = 12 cm × 6 cm = 72 cm²
A₅ = 2 × 6 cm × 2 cm = 24 cm²
A₆ = 2 × 8 cm × 2 cm = 32 cm²
A₇ = 8 cm × 2 cm = 16 cm²
A₈ = 10 cm × 6 cm = 60 cm²
A₉ = 2 × 12 cm × 2 cm = 48 cm²
A₁₀ = 6 cm × 2 cm = 12 cm²
A₁₁ = 12 cm × 6 cm = 72 cm²
The area, A = A₁ + A₂ + A₃ + A₄ + A₅ + A₆ + A₇ + A₈ + A₉ + A₁₀ + A₁₁
Therefore, A = (12 + 24 + 36 + 72 + 24 + 32 + 16 + 60 + 48 + 12 + 72) cm² = 408 cm²
The surface area of the solid, A = 408 cm²
Part B
The volume is found similarly as follows;
V₁ = 6 cm × 6 cm × 2 cm = 72 cm³
V₂ = 8 cm × 6 cm × 2 cm = 96 cm³
V₃ = 12 cm × 6 cm × 2 cm = 144 cm³
The volume of the solid figure, V = V₁ + V₂ + V₃
∴ V = (72 + 96 + 144) cm³ = 312 cm³
The volume of the solid figure, V = 312 cm³.
You buy a new wheel for your bicycle. The diameter of the bicycle wheel is 22 inches. What is the radius of the bicycle wheel? What is the circumference of the bicycle wheel? What is the area of the bicycle wheel?
Answers
Answer is in a photo. I can only upload it to a file hosting service. link below!
bit.[tex]^{}[/tex]ly/3a8Nt8n
420 student 25 times 3 times the number of girls 2 times the number of boys how many girls amd how many boys
Answers
Complete Question
We have a total of 420 students. 2 times 3 times the number of girls is equal to 2 times the number of boys how many girls and how many boys
Answer:
The number of boys = x = 315 boys
The number of girls = y = 105 girls
Step-by-step explanation:
Let
The number of boys = x
The number of girls = y
We have 420 students
2 times 3 times the number of girls is equal to 2 times the number of boys
x + y = 420..... Equation 1
2 × 3y = 2x
6y => 2x
x => 6y/2 = 3y
We substitute 3y for x in Equation 1
3y + y = 420
4y = 420
y =>420/4
y => 105
Solving for x
x = 3y
x = 3 × 105
x = 315
Therefore,
The number of boys = x = 315 boys
The number of girls = y = 105 girls
If 3cm represents 4m what is 6cm • 3cm?
Answers
Answer:
18cm duh
Step-by-step explanation:
Find the surface area of the come in terms of pi
Answers
Answer:
1157.91 or rounded 1157.9 or 1158
Step-by-step explanation:
π • r^2 • (h/3)
π • 10^2 • 11/3
Find the area of the polygon.
A. 336 feet squared
B. 13,824 feet squared
C. 288 feet squared
D. 384 feet squared
Answers
Answer:
12 x 24 = 288
32 - 24 = 8
8 x 12 = 96
96 divided by 2 = 48
288 + 48 = 336 ft2 is your answer.
24. Solve the system of equations below: 2x - 6y = - 12 x+2y = 14
how do I do this I don't get it please help
Answers
Answer:
(x,y) (28/19, -35/19)
hope this helps
Answer:
x = 6, y = 4
Step-by-step explanation:
multiply the equation x + 2y = 14 by two then subtract the equation 2x - 6y = - 12 to eliminate x and solve for y:
×2 => 2x + 4y = 28
-) 2x - 6y = -12
_________________
10y = 40
=> y = 4
substitute y = 4 to either of the equation 2x - 6y = - 12 OR x + 2y = 14 to solve for x:
=> 2x - 6(4) = -12
=> 2x = 12
=> x = 6
Classify this triangle by its sides and angles.
Answers
Answer:
right and isosceles but not equilateral
After graduating from college, Herbert decided to join a new
company. He agreed to a salary which will increase by 4.5% each
year and he will earn $63,417 for his tenth year of work.
Answers
Answer:
500
Step-by-step explanation:
please help me with this i will give brainliest
Answers
4(1)^3 = 4
4(2)^3 = 4(8) = 32
4(1/2)^3 = 4(1/9) = 4/9
Hopefully this helps and you can mark me as brainliest
What is the sum of the two expressions? (2/7x + 5) + (4/7x - 3)
Answers
Answer:
= 6/7x+2
Step-by-step explanation:
just remove the parenthesis and combine like terms.
i hope this helps :)
Answer:
Step-by-step explanation:
Combine like terms.
2/7x and 4/7x are like terms
5 and -3 are like terms
[tex](\frac{2}{7}x + 5) + (\frac{4}{7}x - 3) = \frac{2}{7}x+ \frac{4}{7}x + 5 - 3\\\\\\ = \frac{2+4}{7}x+ 2 \\\\= \frac{6}{7}x+2[/tex]
Part A: The graph of which equation below is a
horizontal line?
1.) 2+y=3
2.) y=3
3.) 2 = 3
Part B: Explain in 3- 4 sentences why your equation in Part A is a horizontal line. Your answer should include at least 4 of the following words:
x-coordinate
y-coordinate
ordered pair
slope
y-intercept
slope-intercept form
Answers
Answer:
part A (2)
Step-by-step explanation:
because when x-coordinate equals zero we will have a one value for y
what ia 4(t-5) FAST !!!!!!
Answers
Answer:
4t-20
Step-by-step explanation:
Answer:
4t-20
or
unknown
Step-by-step explanation:
if there is a value for t then i,d,k the answer if there isnt then 4t-20 is the answer
What fraction is equal to 40% ?
Answers
Your Answer is:
4/10
Step-by-step explanation:
because 4 out of 10=40%...
i have been on this test like- forever trying to figure this out im horrible at math someone please help me-
Answers
Answer:
Step-by-step explanation:
total cost = c
students = s
cost = 7
c = s*7
independent is s
dependent is c
Question 2: What is the volume of this prism?
Answers
Answer:
42 cubic units
Step-by-step explanation:
2x3x7
i need help please hurrrrry
Answers
Answer:
the meaning of ha
Step-by-step explanation:
jshaisnakanjnds
AYO CAN YALL HELP Me PLZZZZz IF U HELP WIT ALLL U GET BRAINLES
Answers
Answer:
The first one is B
Step-by-step explanation:
if you count how many faces or sides it has its 5
Answer:
1. B
2. D
3. D
4. A
5. C
REMEMBER TO DOUBLE-CHECK JUST IN CASE.
What is the factored form of the expression x^2 - 16?
Answers
Answer:
(x + 4)(x - 4)
Step-by-step explanation:
Answer:
( − 4 ) ( + 4 )
Step-by-step explanation:
x^2 - 16
x^2 + 4x - 4x = 16
x^2 + 4x - 4x - 16
( + 4 ) − 4 ( + 4 )
( − 4 ) ( + 4 )
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
A.45
B.30
C.90
D.180
E.40
F.55
G.130
H.50
Answers
Answer:
If you were to make a 360 degree circle and minus the 50 thats already there you get 310 the right angle on angle 5 is 90 degrees because its a right angle so then the 310-90=220 the obtuse angle on angle 2 is 180 so 220-180=40 lastly you share those forty between angles 3 and 4 and the solution is your answer.
Glab to help!
solve for x show all work
Answers
Answer:
x=4
Step-by-step explanation:
we know the ratio of left to right is 2:1 because 6:3=2:1
the horizontal lines are parallel, so the other set of numbers follows the same proportions
[tex]x^{2} +2x+11=2(x+13.5)\\x^{2} +2x+11=2x+27\\x^{2} +2x-2x=27-11\\x^{2} =16\\x=\sqrt{16} \\x=4[/tex]
A function g models a relationship in which the dependent variable doubles for every 3 units the independent variable increases.
Answers
Answer:
x-intercept = 3
y-intercept = -2
Step-by-step explanation:
P.S - The exact question is -
Given - A function g models a relationship in which the dependent variable doubles for every 3 units the independent variable increases.
To find - Graph g when g(0) = -2. Identify the y-intercept and x-intercept.
Proof -
By using the given information , we get
g(x) = [tex]\frac{2}{3} x - 2[/tex]
g(0) = 0 - 2 = -2
It also satisfy the condition g(0) = -2
Here,
by comparing with general form of slope-intercept form y = mx + c
where m = slope, c = y-intercept
Slope, m = [tex]\frac{2}{3}[/tex]
For x-intercept,
Put y = 0
⇒[tex]\frac{2}{3} x - 2[/tex] = 0
⇒[tex]\frac{2}{3}x = 2[/tex]
⇒x = 3
So,
x-intercept = 3
For y-intercept,
Put x = 0
⇒y = 0 - 2
⇒y = 2
∴
y-intercept = -2
A red light flashes every 14 minutes. A blue light flashes every 24 minutes. When will the two lights flash together again if they last flashed together at 8 AM
Answers
Answer:
It happened in 168 minutes
Step-by-step explanation:
24: 48, 72, 96, 120, 144, 168
14: 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168
The common LCM is 168. It happened in seven 24's and in twelve 14's
40 POINTS AND BRAINLIEST FOR THE BEST ANSWER!!!!
PLS ANSWER QUICK !!!!!!!!!!!!
A candle burns down at the rate of 0.75 inches per hour. The original height of the candle was 9 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 9) would represent a height of 9 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.5 inches per hour instead of 0.75 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
Answers
Answer:
15
Step-by-step explanation:Welcome for the answer. This answer is for good intentions only dont flag me please.Step-by-step explanation:
Ordered Pairs
9 inches after 0 hours
8.15 inches after an hour
7.40 inches after 2 hours
6.65 inches after 3 hours
5.90 inches after 4 hours
4.15 inches after 5 hours
3.40 inches after 6 hours
Function
I don't believe it is a function but I could be wrong
Heya!
[tex] \underline{ \underline{ \bf{Question}}}: [/tex] In the given figure , ABC is a triangle in which AB = AC. Also a circle passing through B and C intersects the sides AB and AC at the points D and E respectively. Prove that AD = AE.
~Thanks in advance! :)
Answers
Answer:
See Below.
Step-by-step explanation:
We are given that ABC is a triangle in which AB = AC.
A circle passing through B and C also intersects the sides AB and AC at points D and E respectively.
And we want to prove that AD = AE.
By the secant-secant theorem (shown below), we know that:
[tex]AD(AB)=AE(AC)[/tex]
We are given that AB = AC. So, by substitution:
[tex]AD(AB)=AE(AB)[/tex]
And by dividing both sides by AB (AB ≠ 0), we acquire:
[tex]AD=AE[/tex]
Q.E.D.
Roger is building a frame for a flower bed. He is using left-over scraps of wood from his garage. He needs a total of 12 feet of wood. The pieces he has in his garage are 314 feet, 412 feet, and 4 feet. Does he have enough wood to build the frame?
A. Yes, because 12 > 1134
B. Yes, because 1234 > 12
C. No, because 1134< 12
D. No, because 1116 < 12
Answers
Answer:
C. No, because 11.34 < 12
Step-by-step explanation:
3.14 + 4.12 + 4 has to be greater than or equal to 12
solve the equation
3.14 + 4.12 + 4 >= 12
7.26 + 4 >= 12
11.26 >= 12 is false
I don't know why it says 11.34 because the numbers don't add up, so I'll assume that there is a typo somewhere.
Can someone tell me if this adjacent,vertical or linear
Answers
Answer:
vertical
Step-by-step explanation:
its going straight up
In what way is a debit card similar to a check? a. You must always provide a signature to use either. b. Both always take a few days to clear, so there is some float time until the payment goes through. c. Both pull money directly from a checking or savings account. d. Both charge interest on the purchases you make with them.
Answers
Answer:
both pull money directly from a checking or savings account.
Answer:
c
Step-by-step explanation:
Please Help! I’m not really sure about anything at this point.
Answers
Answer:
sorry bro im d.u.m.b
Step-by-step explanation:
:_ )
Solve 16 = 2x − 2. 2 4 6 8
Answers
Answer:
The answer to this question is 6.
Step-by-step explanation:
To find the value of x we must find what minus 2 gets us 16. To find this we pretty much just see what 2 to the power gives us 16, therefore we find that 2^4 is 16. We now must solve for x. We take all of our possible solutions and find what minus 2 gets us 4. We then can see that 6-2 is 4 and that 2^4 is 16. Therefore, we can conclude that x is equal to 6.
If the linear equation with a single variable is 2x - 2 = 16. Then the value of the variable x is 9.
What is linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear equation with a single variable is given below.
16 = 2x - 2
Then the value of x will be given as
18 = 2x
x = 9
Then the value of the variable x is 9.
More about the linear system link is given below.
https://brainly.com/question/20379472
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