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:
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Related Questions
Using the GCF and distributive property, which expressions is equivalent (equal) to 12y + 16
A 2(6y + 80)
B 4(3y + 4)
C 28y
D 16 + 12y
Answers
Answer:
4(3y+4)
Step-by-step explanation:
12y + 16
4*3*y +4*4
Factor out 4
4(3y+4)
Answer:
2(6y+80) = 12y+160
4(3y+4) = 12y+16
28y = 28y
16+12y = 12y+16 (did not use distributive property)
So, B is correct.
Let me know if this helps!
(07.05 LC)
Which statement is true for the equation 4n − 3 = 4n − 2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answers
Answer:
The answer is (A); there is no solution.
Step-by-step explanation:
It doesn't require any calculations, really, just logic. Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value. However, if you subtract both values by different numbers, you won't get the same number:
Let's say n = 5
4n = 4n
= 4(5) = 4(5)
= 20 = 20
Now,
4n - 3 = 4n - 2
= 4(5) - 3 = 4(5) - 2
= 20 - 3 = 20 -2
= 17 ≠ 18
Hope this helps! Tell me if I was wrong!
Answer:
It has no solution.
Step-by-step explanation:
If we try and solve it we end up with nonsense, so it has no solutions:
4n - 3 = 4n - 2
4n - 4n = - 2 + 3
0 = 1
- which is, of course, absurd.
Also, just by looking at the equation we can see that the term 4n -3 cannot in any way be equal to 4n - 2.
write the formula used to find length when the breadth height and volume are known........breadth when the length height and volume are known............ height when the breadth length and volume are known ..............Please answer this as fast as possible my homework is due tommorow
Answers
Answer: L = V/bh
b= V/Lh and h= V/Lb
Step-by-step explanation: V = Lbh or V= lwh is also used for the Basic form for the Volume of a cube or rectangular prism is
Volume = Length × breadth × height
The volume will be expressed as cubic units such as cubic meters cubic feet. Sometimes abbreviations are used like cm^3 for cubic centimeters.
When you know the Volume, and you need to find a missing dimension, just make a fraction with the V in the numerator and the dimensions you know in the denominator. This means you are dividing the Volume by the area of the dimensions you have been given to find the missing dimension.
PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!
Find the output, y, when the input, x, is -5.
Answers
Answer:
[tex]\boxed{y = -2}[/tex]
Step-by-step explanation:
Hey there!
To find y when x is -5 we go to -5 on the x-axis.
When at -5 find where the blue line is vertical to -5,
which is -2.
Hope this helps :)
y = - 2
I don't understand this question, somebody help
Answers
Answer:
H. 50 sq cm
Step-by-step explanation:
Triangle PSU is an equilateral triangle because each side of it is a radius of semicircle TRP. Also, the radius of semicircle TRP is the short side of the rectangle. So, if the total perimeter of the triangle is 15, each side is 5 cm. So, the short side of the rectangle is 5cm and the long side is 5*2 = 10 cm.
5 * 10 = 50 sq cm
Use the graph to determine the vertex point of the quadratic function. Is the vertex a
maximum or a minimum?
Vertex (1,3),maximum
Vertex (3,1) minimum
Vertex (1,3),minimum
Vertex (3,1) maximum
Answers
It is a minimum because it is at the bottom, whereas a maximum would be at the top. The coordinates are read off the graph to find the point.
Answer:
Vertex (3,1) minimum
Step-by-step explanation:
Hello, I attached a graph with two examples where you can see the Vertex and when this is a minimum vs maximum.
You can see in your graph that the vertex is the point (3,1) and this is a minimum.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
If g(x) = 1 - ¾ x
find: g(0)
Answers
[tex] \sf \: g(x) = 1 - \frac{3}{4} x \\ \sf \:g(0) = \: ? \\ \\ \sf \: Substitute\: the \: value \: of \: x \: as \: 0 \\ \\ \sf \:1 - \frac{3}{4} (0) \\ \sf \: = 1 - \frac{3}{4} \times 0 \\ \sf \: = 1 - 0 \\ \sf \: = \underline{\bf \: 1}[/tex]
Hope it helps.
RainbowSalt2222
Plz I need the answer ASAP.
Answers
Answer:
-10
Step-by-step explanation:
The reason why I believe the answer to your question is -10 is because inequality represents the difference in size, degree, circumstances, etc.; lack of equality. So I had to find the difference between -5 and 5, and -5 minus 5 is -10.
Also if this helps, it would be nice if you gave brainlest :)
The five-number summary for the number of touchdowns thrown by each quarterback in the British Football League is shown in the following table. About what per cent of quarterbacks in the British Football League threw more than 13 touchdowns?
Answers
Answer:
❁ 25% ❁
Explanation:
❁ The answer would be 25% ❁
Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of equations? 2x+3y=25 -3x+=22 first equation can be multiplied by –3 and the second equation by 2. The first equation can be multiplied by –4 and the second equation by 2. The first equation can be multiplied by 3 and the second equation by 2. The first equation can be multiplied by 4 and the second equation by –3.
Answers
Answer:
The first equation can be multiplied by 3 and the second equation by 2.
Step-by-step explanation:
Given
[tex]2x+3y=25[/tex]
[tex]-3x + y=22[/tex]
Required
How to eliminate x
To eliminate x using addition, we have to do the following;
1. Take the coefficient of x in equation 1; Coefficient = 2
2. Take the coefficient of x in equation 2; Coefficient = -3
3. Multiply equation 1 by 3
[tex]3(2x + 3y = 25)[/tex]
[tex]6x +9y = 75[/tex]
4. Multiply equation 2 by 2
[tex]2(-3x + y = 22)[/tex]
[tex]-6x + 2y = 44[/tex]
5. Add both resulting equations
[tex]6x +9y = 75[/tex] + [tex]-6x + 2y = 44[/tex]
[tex]6x - 6x + 9y + 2y = 75 + 44[/tex]
[tex]11y = 75 + 44[/tex]
Notice that x has been eliminated;
2 equation x by 2
Determine whether each sequence is a geometric sequence. If yes, then state the common ratio.
5, 10, 15, 20,...
Answers
Answer:
Step-by-step explanation:
it is not a geometric sequence
Answer:
no
Step-by-step explanation:
Take the second term and divide it by the first term
10/5 = 2
Take the third term and divide it by the second term
15/10 = 3/2
The ratio is not the same so it is not a geometric sequence
solve for m. √m-7 = n+3 It is worth like 40 points
Answers
Answer:
sqrt of (m-7) = n+3
m = (n+3)^2 + 7 or m= n^2 + 6n + 16
sqrt of (m)-7 = n+3
m = (n+10)^2 or m =n^2 + 20n + 100
Step-by-step explanation:
(2) move the constants to the other side, and square
or (1) square and move constants
then you can solve for m
Answer:
[tex]n^2+6n+16[/tex]
Step-by-step explanation:
I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not [tex]\sqrt{m} - 7 = n+3[/tex].
[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]
Hope this helped!
5. The cost of movie tickets at the
Cinema Verite is 9 dollars for adults
and five dollars for children under 12.
During the Saturday and Sunday
matinees, adults are charged 8 dollars
for admission and children under 12
are charged 4 dollars. At any time at
all, there is a group discount for groups
of 15 or more adults at a cost of 6
dollars per ticket. What is the cost for 2
adults and 3 children during the
Saturday matinee?
a. 27
b. 28
C. 14
d. 32
Answers
Answer:
its 28 dude, because it says that adults and children are played more on saturday.(adults on Saturday=$8 and children under 12 are $4
Help me pleaseeeeeee
Answers
Answer:
B
it's a recurring number therefore it's irrational
A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi. A.21.2 B.24.7 C.7.9 D.31.8
Answers
Answer:
A = 56.5cm²
Step-by-step explanation:
r = 1.5cm
h = 4.5cm
A=2πrh+2πr2
A = 2πr(h+r)
A = 2 x 3.14 x 1.5 x ( 4.5 + 1.5 )
A = 56.62cm²
[tex] \large{ \underline{ \underline{ \bf{ \red{Given}}}}}[/tex]
Height of the cylinder = 4.5 cmDiameter of the cylinder = 1.5 cmConsider π = 3.14[tex] \large{ \underline{ \underline{ \bf{ \purple{To \: find}}}}}[/tex]
Surface area of the cylinder in cm²?[tex] \large{ \underline{ \underline{ \bf{ \green{Now, \: What \: to \: do?}}}}}[/tex]
For solving this question, we should know how to calculate the surface area of cylinder i.e Total surface are of cylinder = 2πr(r + h)
Where, r = radius of the cylinder and h is the height of the cylinder.
[tex] \large{ \bf{ \underline{ \underline{ \blue{Solution}}}}}[/tex]
We are provided with,
h = 4.5 cmd = 1.5 cmThen, Radius = 1.5 cm / 2
By using formula,
⇛ 2πr(r + h)
⇛ 2 × 3.14 × 1.5/2 (1.5/2 + 4.5) cm²
⇛ 2 × 3.14 × 3/4( 5.25) cm²
⇛ 24.7275 cm²
❇ Option B
✤ TSA of the cylinder = 24.7275 cm²
━━━━━━━━━━━━━━━━━━━━
9x^3-16x^2=0. Solve and show all steps.
Answers
Answer Step one x=16/9 =1.778
Last step is x²=0
Hope I helped you
Answer:
the roots are {0, 0, 16/9}
Step-by-step explanation:
The trick to solving this is to factor out x^2 from both terms on the left:
x^2*9*x - 16x^2=0, or
x^2(9x - 16) = 0
Then, either x^2 = 0 or (9x - 16) = 0.
Thus, the roots are {0, 0, 16/9}
Solve the equation 14=7(2x-4) using two different methods. Show your work. Which method do you prefer? Explain. need help thanks
Answers
Answer:
x=3
Step-by-step explanation:
14=7(2x-4)
14/7=2x-4
2=2x-4
2x=2+4
2x=6
x=6/2
x=3
------------
14=7(2x-4)
14=14x-28
14x=14+28
14x=42
x=42/14
x=3
The equation 14 = 7(2x - 4) can be solved using two different methods: the distributive property method and the inverse operations method. Both methods yield the same solution, which is x = 3. The preference between the two methods depends on personal preference and the specific equation being solved.
Distributive Property Method:
We'll distribute the 7 to the terms inside the parentheses:
14 = 7(2x - 4)
14 = 14x - 28
Next, we'll isolate the variable term:
14x = 14 + 28
14x = 42
Finally, we'll solve for x by dividing both sides of the equation by 14:
x = 42/14
x = 3
So the solution to the equation is x = 3.
Inverse Operations Method:
We'll use inverse operations to solve the equation step by step:
14 = 7(2x - 4)
Divide both sides of the equation by 7 to isolate the term in parentheses:
14/7 = 7(2x - 4)/7
2 = 2x - 4
Add 4 to both sides of the equation to isolate the variable term:
2 + 4 = 2x - 4 + 4
6 = 2x
Divide both sides of the equation by 2 to solve for x:
6/2 = 2x/2
3 = x
To learn more on Equation:
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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
What are the coordinates of the vertices of the polygon in the graph that are on one of the axes? A) (0,2), (5,0), (0,–2) B) (–4,–4), (–3,4), (4,3), (4,–3) C) (–5,0), (0,2), (0,–2) D) (–5,0), (0,2), (5,0), (0,–2)
Answers
Answer:
D) (–5,0), (0,2), (5,0), (0,–2)
Step-by-step explanation:
The vertices are basically the x and y intercepts.
Hope this helped :)
You can choose from the following 15, 16, 24, -88, 75, -62, 151, 88, 1, 30, -5 Also thank you in advance I don't know why I don't get this one so please explain if possible!
Answers
Answer:
-88
Step-by-step explanation:
whoever deleted my answer thanks a lot
This is for my math class
Answers
Answer:
-25 feet
Step-by-step explanation:
We know that the change in altitude for the air balloon is -1500 feet, all within a span of 60 minutes, which then we are asked what is the rate of change.
To find the rate of change, we have to be able to divide a number by both sides that will not give us a decimal or very odd number. To avoid getting a decimal, divide both sides by 60.
-1500/60 = -25
60/60 = 1
So the rate of change would be -25 feet
Find f-1.
f(x)=4 log2 (x – 7)
Answers
Answer:
f(1) = 10.33985 + 18.1294406 i
Step-by-step explanation:
f(1) = 4log2(1-7)
f(1) = 10.33985 + 18.1294406 i
i think
cqn someone answer this?
Answers
Answer:
-3Step-by-step explanation:
-11/2+27/4+(-17/4)(-22+27-17)/4(-12)/4-3A, B, C and D lie on the circumierence of the circle.
Lengths AB and AD are equal.
Lengths BC and BD are equal.
Work out CBD.
Answers
Answer:
Step-by-step explanation:goofy
Which of the following are exterior angles? Check all that apply.
6
52
3
O A. 21
O B. 25
O c. 24
O D. 23
E. 22
O F. 26
Answers
Using it's concept, it is found that the exterior angles of the triangle are given as follows:
B. <5
C. <4
What are the exterior angles of a triangle?The exterior angles of a triangle are the angles that are outside the triangle.
In this problem, the angles are 4 and 5, which means that options B and C are correct.
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what is EG and EF ( can you do number 9 too thank you
Answers
Answer:
EF = 32 in (Approx)
EG = 16 in (Approx)
Step-by-step explanation:
Given:
Side FG = 28 in
∠ E = 60°
Find:
EG = ?
EF = ?
Computation:
Using trigonometry application.
Sin 60° = FG / EF
√3/2 = 28 / EF
0.866 = 28 / EF
EF = 32.33
EF = 32 in (Approx)
Tan 60° = FG / EG
1.732 = 28 / EG
EG = 16.16
EG = 16 in (Approx)
TELL ME THE FORMULA FOR VOLUME AND SURFACE AREA OF PRISMS
Answers
Answer:
surfacevolume = 1/2 (bh) l
surfacearea = bh + pl
PLS HELP ME WITH THIS QUESTION I NEED IT QUICK! anything helps..
Answers
Answer:
Graph A
Step-by-step explanation:
if you look at the numbers on the top row they correspond with the left side of the graph and the bottom row of numbers correspond with the bottom of the Graph.
Answer:
Graph A)
Step-by-step explanation:
The first points 20,70 and 30,70 are both plotted correctly on this graph, same with the other points. :)
What is the best estimate of the sum of $14.30, $143.08, and $19.74
Answers
Answer:
Step-by-step explanation:
ok so you start off by adding
14.30
143.08
19.74
177.12
177.12 is close to 180 if u estimate in tens, 177 if ones
The addition of the numbers $14.30, $143.08, and $19.74 will be $177.12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
All real numerals and 0 are included in the category of whole numbers.
The process of adding up the different or more sums or figures.
The sum means plus sing is present between the terms.
The whole numbers are given below,
$14.30, $143.08, and $19.74
Then the summation of the whole numbers is given below.
⇒ $14.30 + $143.08 + $19.74
⇒ $177.12
Thus, the addition of the numbers $14.30, $143.08, and $19.74 will be $177.12.
More about the Algebra link is given below.
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A basin is filled by two pipes in 12 minutes and 16 minutes respectively. Due to the obstruction of water flow after the two pipes have been running together for some time, the 1st pipe carries 7/8 of the carrying capacity and the 2nd pipe carries 5/6 of the carrying capacity. After removing the water barrier, the tank is full in 3 minutes. How long after the flow of water in the two pipes became normal?
Answers
Answer:
The time duration of the two pipes restricted flow before the flow became normal is 4.5 minutes
Step-by-step explanation:
The given information are;
The time duration for the volume, V, of the basin to be filled by one of the pipe, A, = 12 minutes
The time duration for the volume, V, of the basin to be filled by the other pipe, B, = 16 minutes
Therefore, the flow rate of pipe A = V/12
The flow rate of pipe B = V/16
Due to the restriction, we have;
The proportion of its carrying capacity the first pipe, A, carries = 7/8 of the carrying capacity
The proportion of its carrying capacity the second pipe, B, carries = 5/6 of the carrying capacity
Whereby the tank is filled 3 minutes after the restriction is removed, we have;
[tex]\dfrac{7}{8} \times \dfrac{V}{12} \times t + \dfrac{5}{6} \times \dfrac{V}{16} \times t + \dfrac{V}{12} \times 3 + \dfrac{V}{16} \times 3 = V[/tex]
Simplifying gives;
[tex]\dfrac{(2\cdot t +7) \cdot V}{16} = V[/tex]
2·t + 7 = 16
t = (16 - 7)/2 = 4.5 minutes
Therefore, it took 4.5 seconds of the restricted flow before the the flow of water in the two pipes became normal