HELPP (ESPECIALLY PART B) Answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose. part a Inspect the equation for the type of conic section you chose. What attributes are necessary to graph it? Be sure to include specific points or equations to complete your answer. part b Explain how, if you have the attributes given below for the conic you chose, you can derive its equation in standard form.
Answers
The conic section chosen is a parabola, and the attributes for graphing of
a parabola as well as the standard form of the equation are as follows;
Part A: The attribute necessary to graph the equation of the parabola are three points, including, the vertex, the y-intercept and the image of the reflection of the y-intercept across the axis of symmetry.Part B: The equation in standard form is x = -0.25·y² + y + 3Reasons:
Part A:
The equation of the conic section of a parabola is; (x - 3)² = 12·(y - 2)
The vertex form of the equation of a parabola is; y = a·(x - h)² + k
Where (h, k) = The vertex
Rearranging the given equation gives;
(x - 3)² = 12·y - 24
12·y - 24 = (x - 3)²
12·y = (x - 3)² + 24
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + \frac{24}{12} = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
[tex]\displaystyle y = \frac{1}{12} \cdot \left(x - 3\right)^2 + 2[/tex]
Therefore, the vertex of the parabola, (h, k) = (3, 2)
At the y-intercept, x = 0, which gives;
[tex]\displaystyle y = \frac{1}{12} \cdot \left(0 - 3\right)^2 + 2 = \frac{9}{12} + 2 = 2+\frac{3}{4}[/tex]
[tex]\displaystyle y = 2+\frac{3}{4} = 2.75[/tex]
The y-intercept = (0, 2.75)
The x-intercept is given at the point where y = 0, which gives;
(x - 3)² = 12·(0 - 2) = -24
x - 3 = √(-24) = An imaginary number
Therefore, the graph has no x-intercept
Given that a parabola is symmetrical about the vertex, we have a third
point on the parabola at the image of the y-intercept reflected across the
axis of symmetry as follows;
The y-intercept (0, 2.75) is 3 units to the left of the axis of symmetry, x = 3,
therefore, the third point will be 3 units to the right of the axis of symmetry
at the point (3 + 3, 2.75) = (6, 2.75)
Therefore, using the three points, (0, 2.75), (3, 2), and (6, 2.75), the curve
representing the parabola, (x - 3)² = 12·(y - 2), can be drawn.
Please find attached the graph of the parabola created with MS Excel
Part B; Given the attributes of the parabola; Vertex: (4, 2) and focus: (3, 2), we have;
The focus of a parabola is the point (h + p, k)
Where, (h, k) = The vertex
Therefore, by comparison, we have;
(h, k) = (4, 2)
h + p = 3
Therefore;
4 + p = 3
p = 3 - 4 = -1
The vertex form of the equation of the parabola is; (y - k)² = 4·p·(x - h)
Therefore, we get;
(y - 2)² = 4 × (-1) × (x - 4) = -4·(x - 4)
y² - 4·y + 4 = 16 - 4·x
4·x = 16 - (y² - 4·y + 4) = -y² + 4·y + 12
Which gives, the standard form as follows;
[tex]\displaystyle x = -\frac{y^2}{4} + y + 3 = -0.25 \cdot y^2 + y + 3[/tex]
Standard form of the the equation of the parabola; x = -0.25·y² + y + 3Learn more about the graph of a parabola here:
https://brainly.com/question/2489929
Related Questions
complete the table of values for y=-x^2+2x+1
Answers
Answer:
-1=-2
4=-7
Step-by-step explanation:
for x=-1
y=(-1^2)+(2*-1)+1
y=-1-2+1
y=-2
for x=1
y= (-1^2)+(2*1)+1
y= -1+2+1
y=2
for x=4
y=(-4^2)+(2*4)+1
y=-16+8+1
y=-7
attachment help for question c no explanation only answer thank you
Answers
Answer:
Tablets.
Step-by-step explanation:
You didn't want an explanation so....here you go....no explanation.
Hope that helps and maybe earns a brainliest.
Have a great day!
tablets
How would I answer this using a number line to find what the sum of
-2 + 2 =
Answers
Solution: in the picture
hope it helps^°^
|5x + 1 over 2y2| What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit.
Answers
Answer:
2
Step-by-step explanation:
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The expression is given below.
⇒ |5x + 1 / 2y²|
The value of the expression at x = 3 and y = 2, then we have
⇒ |5(3) + 1 / 2(2)²|
⇒ |15 + 1 / 2(4)|
⇒ |16 / 8|
⇒ 2
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ3
Need help with this asap.
Answers
PLEASE ANSWER!!!!!!
Which of the following is true? a) |−4| < 3 b) |−4| < |3| c) |−3| < −4 | d) −3| < |−4|
Answers
Answer:
The answer is D
Step-by-step explanation:
the first one is equal to the equation 4 < 3 because of absolute value, second 4 < 3, third 3 < -4, fourth -3 < 4
Can someone help me with this math problem
Answers
Answer:
B. (m-1)(m-8)
Step-by-step explanation:
The factors of 8 (constant term) are
{(1,8), (2,4)}, from which we see that 1+8 = 9, the absolute value of the coefficient of the second term.
Therefore we can group the expression as
m^2 - 9m + 8
= m^2-m - (8m -8)
then factor each group
= m(m-1) - 8(m-1)
and factor out (m-1)
= (m-1)(m-8)
(3x-10) (2x-5) =? A. 6x^2 - 35x + 50 B. 6x^2 + 35x + 50 C. 6x^2 - 5x - 50 D. 6x^2 - 35x - 50
Answers
Answer:
[tex]\large \boxed{\sf \bf \ \ 6x^2-35x+50 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex](3x-10)(2x-5)\\\\=3x(2x-5)-10(2x-5)\\\\=6x^2-15x-20x+50\\\\=\boxed{6x^2-35x+50}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A is the correct answer
Albert has 40 toy cars. Brad has 15 fewer toy cars than Albert, but 7 more than Chris. How many toy cars do they have all together?
Answers
Answer:
83
Step-by-step explanation:
40 - 15 = 25
25 - 7 = 18
40 + 25 + 18 =
83
We know that Albert has 40 toy cars.
If Brad has 15 fewer cars than Albert, Brad has 40 - 15 or 25 cars.
Now, we know that Chris has 7 fewer cars than Brad.
So Chris would have 18 cars.
Altogether, they would have 40 + 25 + 18 cars or 83 cars.
HELP HELP HELP HELP HELP HELP!!! What symbol is needed between –2 ? |–3| to make a true statement?
Answers
Answer:
[tex]\boxed{<}[/tex]
Step-by-step explanation:
[tex]-2 \ ? \ |-3|[/tex]
[tex]\sf Solve \ absolute \ value.[/tex]
[tex]|-3|=3[/tex]
[tex]-2 < 3[/tex]
[tex]\sf -2 \ is \ less \ than \ 3.[/tex]
Answer:
<
Step-by-step explanation:
|-3| = 3
-2 < 3
A gallon of paint covers 825 square
feet. How much paint is needed to
paint a house with a surface area of
6600 square feet?
Answers
Answer:
8 gallons
Step-by-step explanation:
1 gallon → 825 sq. feets
X Gallons → 6600 sq. feets
X=6600÷825= 8
Answer: 8 gallons
Step-by-step explanation:
If 1 gallon of paint covers 825 square feet, divide 6600 square feet by 825 square feet to determine the amount of paint needed to paint the house which would be 8 gallons.
PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!! PLEASE HELP ME!!!!!!!!!!!!
Answers
Answer:
hope this is ok...
1. a) f(h) = -4
b) f(h) = 4
c) f(h) = -6
d) f(h) = -8
2. a) f(h) = 5
b) f(h) = 11
c) f(h) = 3
d) f(h) = -1
3. a) f(x) = 11
b) f(x) = -5
c) f(x) = -245
d) f(x) = -89
4. f(56) = -29.35 or -29.346046
5. f(200) = 10√2 - 56 or -41.857864 (if u want u can round off the decimal to -41.86)
Step-by-step explanation:
1. f(h) = | h - 10 |
a) f(h) = | 6 - 10 | = -4
b) f(h) = | 14 - 10 | = 4
c) f(h) = | 4 - 10 | = -6
d) f(h) = | 2 - 10 | = -8
2. f(h) = | h - 2 |
a) f(h) = | 7 - 2 | = 5
b) f(h) = | 13 - 2 | = 11
c) f(h) = | 5 - 2 | = 3
d) f(h) = | 1 - 2 | = -1
3. f(x) = x² + 11
a) f(x) = -0² + 11 = 11
b) f(x) = -4² + 11 = -5
c) f(x) = -16² + 11 = -245
d) f(x) = -10² + 11 = -89
4. f(x) = 8√x - 31
a) f(56) = 8√56 - 31 = -29.35
5. f(x) = 2√x - 56
a) f(200) = 2√200 -56 = -41.86
Please mark Brainliest....
Answer:
The other person answer is beyond correct PLEASE mark them brainliest they REALLY deserve that o-o
Write the geometric sequence in function notation.
7, 14, 28, 56, 112, ...
3
Ax) = (7). ()x-1
f(x) = (7) · (2)X-1
O AX) = (7) . (3)X-1
Rx) = (2) (+)*-1
Answers
Answer:
a(n) = 7*2^(n - 1)
Step-by-step explanation:
The first term of the given geometric sequence, 7, 14, 28, 56, 112, ... , is 7, and the common ratio is 2. Each new term is twice the previous term.
Thus the general formula for the geometric sequence becomes
a(n) = 7*2^(n - 1).
As a check, let's see whether this formula correctly predicts the fourth term (56): Here n = 4, and so a(4) = 7*2^(4 - 1) = 7*2^3 = 7*8 = 56. Yes.
Answer:
f(x) = (7) ∙ (2)x–1
Step-by-step explanation:
The first term in the sequence is 7, and the common ratio is 2. Using the explicit formula and writing it in function notation results in f(x) = (7) ∙ (2)x–1.
when the equation is graphed is it linear or nonlinear ??
Answers
Answer:
Nonlinear
Step-by-step explanation:
This is nonlinear because its parent function is y = [tex]x^{2}[/tex]. The parent function of a linear equation is y = x.
I hope this helps :))
08.01) Which of the following statements shows a characteristic of a statistical question? (4 points) Select one: a. The question is focused. b. The distribution can be broken into categories. c. The question asks for a quantitative response. d. The question allows for surveys to be conducted
Answers
Answer:
the distribution can be broken into categories
Statement c shows a characteristic of a statistical question.
What is statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
So, based on the definition of statistics we can say.
1)Statistical data can be analysed.
2)Statistical data can be used to interpret many things.
3)Statistical data can forecast the results.
Out of the given statements, only statement c falls under the category of statistical statement.
Hence, statement c shows a characteristic of a statistical question.
To get more about statistics visit:
https://brainly.com/question/15525560
Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
x + y < 45
x + y > 45
x + y ≤ 45
x + y ≥ 45
Answers
Answer:
x + y ≥ 45
Step-by-step explanation:
This is because the total amount of minutes could be equal to 45, meaning your inequality sign has to have a line underneath it.
Additionally, x + y is greater than or equal to because the amount could be more than 45... therefore, 45 is not greater than x + y
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
If the total time he spent on both is 45 minutes or more, the answer is:
x + y ≥ 45.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hints for next time
(≥ Means greater than or equal to.)
(≤ Means less than or equal to)
(> Greater than)
(< Less than)
5. Find the measures of the following. Round to the nearest whole number
Answers
Answer:
a - HT = 17
b - ∠T = 62
c - ∠H = 28
a-17
b-62
c-28
help me please real quick
Answers
Volume of cuboid = L x b x h = 8 x 5 x 9 = 360.
Answer:
D) [tex]360 m^{3}[/tex]
Step-by-step explanation:
Let's review the formula for finding the volume of a cube or rectangular prism.
[tex]V = (l)(h)(w)[/tex] - Basically saying "Volume = length × height × width".
In this case, you can consider 9 meters as the length, 5 meters as the height, and 8 meters as the width (but it doesn't really matter which dimensions are which since you are just multiplying them all together).
Now, let's multiply our dimensions together.
[tex]9 * 5 * 8 = 360[/tex]
That's your answer! Make sure to not forget your units (in this case, meters) cubed.
Hope that helps and maybe earns a brainliest!
Have a splendid day! <3
Find the value of x.
Answers
Answer:
D. 15
Step-by-step explanation:
Both equations need the same end result because this is a square:
3x - 15 = 45 - x =
3x - 3x = 45 - x - 3x
0 = 45 - 4x
4x = 60
4x/4 = 60/4 =
X = 15
Check:
3(15) - 15 = 45 - 15
45 - 15 = 45 - 15
30 = 30
What is h decreased by 20
Answers
Answer:
h minus 20
Step-by-step explanation:
This is because decreased means or signifies “-“
plz help urgent ,plz have step by step explanation find a and b
Answers
Answer:
but i didn't understand the root 5 with b on the question
What is the range of possible sizes for side x?
8.0
2.5
Please helpp!!
Answers
Triangle inequality theorem:
In any triangle, the length of any side must be:
less than the sum of the lengths of the other two sides.greater than the difference of the lengths of the other two sides.For the problem you have:
x must be greater than 8.0 - 2.5 and less than 8.0 + 2.5
5.5 < x < 10.5
Answer:
5.5<x<10.5
Step-by-step explanation:
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
A. 14
B. 91
C. 21
D. 127
Answers
Answer:
D. 127°
Step-by-step explanation:
The exterior angle (x) is the sum of the remote interior angles (y, z).
Setupx = y +z
(197 -5n) = (6n +22) +(n +7) . . . . . substituting the given expressions
SolutionEliminating parentheses and collecting terms, we have ...
197 -5n = 7n +29
168 = 12n . . . . . . . . . add 5n-29
14 = n . . . . . . . . . . divide by 12
Then the measure of remote exterior angle x is ...
m∠x = (197 -5(14))° = (197 -70)°
m∠x = 127°
Solve. 4x - 2 ——— = -7 2
Answers
Answer:
x = -3
Step-by-step explanation:
Dividing by 2 is the same as multiplying by 1/2. The distributive property applies.
[tex]\dfrac{4x-2}{2}=-7\\\\2x-1=-7\quad\text{simplify}\\\\2x=-6\quad\text{add 1}\\\\\boxed{x=-3}\quad\text{divide by 2}[/tex]
x=-3
A graph is shown. The x-axis is labeled from 0 to 9 and the y-axis is labeled from 0 to 10. The four points shown on the graph are ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6. These points are joined by a line. The label on the x-axis is Bags of candy. The title on the y-axis is Total cost in dollars. What is the constant of proportionality?
Answers
Answer:
Heres the graph:
Step-by-step explanation:
Constant is $2 dollars per bag od candy or just 2.
Answer:
2
Step-by-step explanation:
from (0,0) ⇒ (1,2) ⇒ (2,4) ⇒ (3,6)
∴ 2
Carly is traveling to visit family. She drives x miles on the first day and y miles on the second day for a total of 800 miles. What are the domain and range of this relationship?
Answers
Answer:
The domain and range of this relationship is (-∞,∞) and (-∞,∞) respectively.
Step-by-step explanation:
We are given that Carly is traveling to visit family.
She drive distance on first day = x
She drive distance on second day = y
We are also given that Carly is travelling a total of 800 miles.
So,x+y=800
We are supposed to find domain and range of this relationship.
y=800-x
Domain : (-∞,∞)
Range:(-∞,∞)
Hence the domain and range of this relationship is (-∞,∞) and (-∞,∞) respectively.
Answer:
domain: 0 ≤ x ≤ 800
range: 0 ≤ y ≤ 800
Step-by-step explanation:
Sally’s house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at
the midpoint of Sally’s house and school. What coordinate represents Molly’s house?
A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answers
Answer:
B. (−2, 3)
Step-by-step explanation:
To find the midpoint of a segment, add the x-coordinates of the endpoints and divide by 2. Add the y-coordinates of the segments and divide by 2.
x: (5 + (-9))/2 = -2
y: (-1 + 7)/2 = 3
Midpoint: (-2, 3)
Answer: B. (−2, 3)
Answer:
b
Step-by-step explanation:
-9+5=-4÷2=-2
-1+7=6÷2=3
What is the reference angle for 4560 degrees?
Answers
Answer:
30 degrees
Step-by-step explanation:
Answer:
30°
Step-by-step explanation:
4560° ÷360°= 12.667 (5 s.f.)
This means that the angle 4560° goes around from quadrant I to quadrant IV 12 times, before coming back to quadrant I. The 13th round does not reach quadrant IV.
So, let's find the angle covered after the 12 full rounds.
12 ×360°= 4320°
remaining angle left
= 4560° -4320°
= 240°
See the attached picture to see where 240° will lie in the quadrants. It lies in quadrant III and its reference angle is the red coloured angle in the picture.
Reference angle
= 270° -240°
= 30°
4 cm, 5 cm, 20 cm
can the side lengths
form a triangle ?
Answers
Answer: No
Step-by-step explanation:
Because 4^2=16
5^2=25
25+16=41
41 squared =6.4031.....
6.4031 does not = 20
Answer: No, a triangle is not possible
The two smaller sides add to 4+5 = 9 which is not larger than 20. For a triangle to be possible, we need to be able to add 2 sides to make them longer than the third side. This is an application of the triangle inequality theorem.
If 6 • 3 = 18, then 4 + 8 = 20. T F → F T T → T F T → T F F → T
Answers
Answer:
False.
Step-by-step explanation:
For the statement: "If 6 • 3 = 18, then 4 + 8 = 20.":
6 * 3 = 18
If you added two after multiplying 6 and 3, you would get 20.
(6*3) + 2 = 20
8 + 4 does not equal 20.
8 + 4 = 20
12 ≠ 20
