Answers
Answer:
Step-by-step explanation:
Before we begin this, there are a few things that need to be said and a few formulas you need to know. First is that we need to use the work form of a parabola, which is
[tex]y=a(x-h)^2+k[/tex]
All of the parabolas listed in blue highlight open either up or down, and this work form represents those 2 options. The only thing we need to know is that if there is a negative sign in front of the a, the parabola opens upside down like a mountain instead of up like a cup.
Another thing we need to know is how to find the focus of the parabola. The formula to find the focus for an "up" parabola is (h, k + p) and the formula to find the focus for an upside down parabola is (h, k - p). Then of course is the issue on how to find the p. p is found from the a in the above work form parabola, where
[tex]p=\frac{1}{4|a|}[/tex] .
In order to accomplish what we need to accomplish, we need to put each of those parabolas into work form (as previously stated) by completing the square. I'm hoping that since you are in pre-calculus you have already learned how to complete the square on a polynomial in order to factor it. Starting with the first one, we will complete the square. I'll go through each step one at a time, but will provide no explanation as to how I got there (again, assuming you know how to complete the square).
[tex]y=-x^2+4x+8[/tex] and, completing the square one step at a time:
[tex]-x^2+4x=-8[/tex] and
[tex]-(x^2-4x+4)=-8-4[/tex] and
[tex]-(x-2)^2=-12[/tex] and
[tex]-(x-2)^2+12=y[/tex]
From this we can see that the h and k values for the vertex are h = 2 and k = 12. Now to find p.
[tex]|a|=1[/tex], ∴
[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]
Using the correct focus formula (h, k - p), we get that the focus is
[tex](2, 12-\frac{1}{4})[/tex] which simplifies to (2, 11.75) which is choice 2 in your options.
Now for the second one (yes, this takes forever...)
[tex]y=2x^2+16x+18[/tex] and completing the square one step at a time:
[tex]2x^2+16x=-18[/tex] and
[tex]2(x^2+8x+16)=-18+32[/tex] and
[tex]2(x+4)^2=14[/tex] and
[tex]2(x+4)^2-14=y[/tex]
From this we can see that the vertex is h = -4 and k = -14. Now to find p from a.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex] .
Using the correct focus formula for an upwards opening parabola (h, k + p),
[tex](-4, -14+\frac{1}{8})[/tex] which simplifies down to (-4, -13.875) which is choice 3 in your options.
Now for the third one...
[tex]y=-2x^2+5x+14[/tex] and completing the square step by step:
[tex]-2x^2+5x=-14[/tex] and
[tex]-2(x^2-\frac{5}{2}x+\frac{25}{16})=-14-\frac{50}{16}[/tex] and
[tex]-2(x-\frac{5}{4})^2=-\frac{137}{8}[/tex] and
[tex]-2(x-\frac{5}{4})^2+\frac{137}{8}=y[/tex]
From that we can see the vertex values h and k. h = 1.25 and k = 17.125. Now to find p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the correct focus formula for an upside down parabola (h, k - p),
[tex](1.25, 17.125-\frac{1}{8})[/tex] which simplifies down to (1.25, 17) which is choice 4 in your options.
Now for the fourth one...
[tex]y=-x^2+17x+7[/tex] and completing the square step by step:
[tex]-x^2+17x=-7[/tex] and
[tex]-(x^2-17x)=-7[/tex] and
[tex]-(x^2-17x+72.25)=-7-72.25[/tex] and
[tex]-(x-8.5)^2=-79.25[/tex] and
[tex]-(x-8.5)^2+79.25=y[/tex]
From that we see that the vertex is h = 8.5 and k = 79.25. Now to find p.
[tex]|a|=1[/tex], ∴
[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]
Using the correct formula for an upside down parabola (h, k - p),
[tex](8.5, 79.25-\frac{1}{4})[/tex] which simplifies down to (8.5, 79) and I don't see a choice from your available options there.
On to the fifth one...
[tex]y=2x^2+11x+5[/tex] and again step by step:
[tex]2x^2+11x=-5[/tex] and
[tex]2(x^2+\frac{11}{2}x+\frac{121}{16})=-5+\frac{242}{16}[/tex] and
[tex]2(x+\frac{11}{4})^2=\frac{81}{8}[/tex] and
[tex]2(x+\frac{11}{4})^2-\frac{81}{8}=y[/tex]
from which we see that h = -2.75 and k = -10.125. Now for p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the correct focus formula for an upwards opening parabola (h, k + p),
[tex](-2.75, -10.125+\frac{1}{8})[/tex] which simplifies down to (-2.75, -10) which is choice 1 from your options.
Now for the last one (almost there!):
[tex]y=-2x^2+6x+5[/tex] and
[tex]-2x^2+6x=-5[/tex] and
[tex]-2(x^2-3x+2.25)=-5-4.5[/tex] and
[tex]-2(x-1.5)^2=-9.5[/tex] and
[tex]-2(x-1.5)^2+9.5=y[/tex]
from which we see that h = 1.5 and k = 9.5. Now for p.
[tex]|a|=2[/tex], ∴
[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]
Using the formula for the focus of an upside down parabola (h, k - p),
[tex](1.5, 9.5-\frac{1}{8})[/tex] which simplifies down to (1.5, 9.375) which is another one I do not see in your choices.
Good luck with your conic sections!!!
Related Questions
Solve for a side in a right triangle
Answers
Answer:
1.88 = ?
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent / hypotenuse
cos 20 = ?/ 2
Multiply each side by 2
2 cos 20 = ?
1.879385242 = ?
To the nearest hundredth
1.88 = ?
without actually calculating the cubes, find the value of (16)^3+(-7)^3+(-9)^3
Answers
Answer:
(16)^3 = (7 + 9)^3 = 7^3 + 9^3 + 3 x 7^2 x 9 + 3 x 9^2 x 7
=>(16)^3 + (-7)^3 + (-9)^3 = (-7)^3 + (-9)^3 + 7^3 + 9^3 + 3 x 7^2 x 9 + 3 x 9^2 x 7
= [(-7)^3 + 7^3] + [9^3 + (-9)^3] + 3 x 7^2 x 9 + 3x9^2x7
= 0 + 0 + 3 x 7^2 x 9 + 3 x 9^2 x 7
= 3 x 7^2 x 9 + 3 x 9^2 x 7
= 3 x 9 x 7 x (7 + 9)
= 3 x 7 x 9 x 16
= 3 x 7 x 9 x 8 x 2
= 6 x 7 x 8 x 9
= 3024
Hope this helps!
:)
Three less than twice a number is seventeen. What is the number?
Answers
The temperature was 54° at 7:00 a.M. At 3:00 p.M. On the same day, the temperature was 82°. What is the rate of change in temperature during this time?
Answers
Answer:
3.5°/hour
Step-by-step explanation:
Rate of change of temperature=change in temperature/Change in time
Change in temperature
=82° - 54°
=28°
Change in time=3:00pm - 7:00am
=8:00 hours
Rate of change of temperature=28°/8 hours
=3.5°/hour
Answer:
The rate of temperature change is 3.5 degree celcius per hour
Step-by-step explanation:
Here, we want to calculate the rate of change of temperature
Firstly, we calculate the number of hours it took the temperature to change
that mathematically = 15:00(3pm) - 7:00(7 am) = 8 hours
now let’s calculate the temperature rise = 82-54 = 28
The rate of temperature change is thus = change in temperature/ number of hours taken
= 28/8 = 3.5 degree celcius per hour
Tobias made a fruit salad with a blueberry to raspberry ratio of 8:6. Tobias' container of blueberries contains 72 blueberries. If he keeps to the same ratio, how many raspberries will Tobias use?
Answers
Answer:
54.
Step-by-step explanation:
8/6 = 72/ x where x is the number of raspberries.
8x = 6*72
8x = 432
x = 54.
If $5000 earns $6000 simple interest in 12 years, find the interest rate.
Answers
Answer:
2.2% interest
Step-by-step explanation:
You can compute the slope of a line by using the slope ___
Answers
You can compute the slope of a line by using the slope formula. This is given by:
slope,m=(change in y-axis)/(change in x-axis)
=(Δ y-axis)/(Δ x-axis)
Given the points (x1,y1) and (x,y) from a linear graph, then:
slope m will be:
m=(y-y1)/(x-x1)
You can compute the slope of a line by using the slope formula.
a : 27=6:18, find a
Answers
Answer: 9
Step-by-step explanation:
The reason for this answer, is because when you decide 18 by 6 it gives you 3. Which means that when you devide 27 by 3 it will give you your answer. 9. You can make sure it’s correct when you do the math. 27/9=3. 18/6=3.
This way, your answers are equivalent to each other.
If you found this answer helpful, give it a five-star rating and a thanks! It would really mean a lot!
(Even a brainliest if you want ;D)
Answer:
a=9
Step-by-step explanation:cross multiply
There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 reds?
Answers
Answer:
here
Step-by-step explanation:
The probability of getting 1 red is 4/7. The probability of getting 2 reds in a row is (4/7)^2 = 16/49.
What is the value of 3 in 731.8?
Answers
Answer:
Tens
Step-by-step explanation:
the three is in the tens value
Answer:
value = 30
place = tens
Step-by-step explanation:
( attached for reference)
the digit "3" is in the tens place.
Hence the value is "3-tens" or 3 x 10 = 30
Find the remainder when p(x)= x^5 + x^4 + x^3 + x^2 + 2x + 2 is divided by q(x) = x + 1
Answers
Answer:
0
Step-by-step explanation:
Given a polynomial p(x) divided by (x + h), then the remainder is
p(- h)
Here divisor is (x + 1), so evaluate p(- 1) for remainder
p(- 1) = [tex](-1)^{5}[/tex] + [tex](-1)^{4}[/tex] + (- 1)³ + (- 1)² + 2(- 1) + 2
= - 1 + 1 - 1 + 1 - 2 + 2
= 0
This means that (x + 1) is a factor of p(x)
Given ΔADC and ΔAEB, What is AE?
Answers
Answer:
AE = 43.2 units
Step-by-step explanation:
As per the given question image, it can be seen that in the [tex]\triangle ADC \text { and }\triangle AEB :[/tex]
1. [tex]\angle B = \angle C = 90^\circ[/tex]
2. [tex]\angle A[/tex] is common to both the triangles.
3. Two angles are common, so the third angle [tex]\angle E[/tex] is also equal to [tex]\angle D[/tex].
All the three angles in the [tex]\triangle ADC \text { and }\triangle AEB[/tex] are equal to each other, hence the triangles are similar.
As per the property of similar triangles, the ratio of their sides will be equal.
AB : AC = AE : AD
AC = 88 units
BC = 55 units
AB = AC - AB = 33 units
Let side AE = [tex]x[/tex] units
Side AD = AE + ED
So, AD = [tex]x + 72[/tex]
Using the ratio:
[tex]\dfrac{AB}{AC} = \dfrac{AE}{AD}\\\Rightarrow \dfrac{33}{55} = \dfrac{x}{x+72}\\\Rightarrow 55x = 33 \times 72\\\Rightarrow x = \dfrac{3\times 72}{5}\\\Rightarrow x = 43.2\ units[/tex]
So, AE = 43.2 units
Carlton and Will went fishing together. Carlton caught 21 bass and 7 walleye. Will caught 13 bass and 8 walleye. How many more fish did Carlton catch than Will?
Answers
Answer:
7
Step-by-step explanation:
Fish caught by Carlton= 21+7=28
Fish caught by Will= 13+8=21
Therefore, Carlton caught more fish
By how much=28-21=7
PLEASE HELPPPPPPPPP
MARKING BRANLIEST
Answers
Answer:
A
A
5
Step-by-step explanation:
Rectangular Prism A
volume = length * width * height = 7 cm * 7 cm * 5 cm = 245 cm^3
Rectangular Prism B
volume = length * width * height = 8 cm * 6 cm * 5 cm = 240 cm^3
Answers:
A
A
5
A mechanic cuts 14 pieces of copper
tubing from a coil. Each piece is 3 1/2
inches long. What is the total length
used?
Answers
Answer:
49
Step-by-step explanation:
14*3.5
Because 49/3.5 = 49
Thats how I got it
Hope it helps
Help please! What are the first 4 terms of the arithmetic sequence in the graph?
Answers
Answer:
2, -2, -6, -10
Step-by-step explanation:
In this graph, the x value represents the count of the terms, while the y represents the value of each term. This means that the value of the first one is 2, the value of the second one is -2, the third one -6, and the fourth one -10. Hope this helps!
The value of k, for which the system of equations x-3y+6=0, 4x-6y+.15=0 represent parallel lines, is:
A)1
B)2
C)3
D)4
Answers
Given circle B, what is its diameter if its area is 56 square units?
Answers
Answer:
Diameter of the circle is 8.4 units
Step-by-step explanation:
To find the diameter of a circle with area of 56 square units, we will follow the steps below:
write the formula for calculating the area of a circle
area of a circle = πr²
from the question area= 56 units .
π is a constant which is ≈ 3.14
we can now proceed to substitute the values into the formula and solve for r
area of a circle = πr²
56 = 3.14×r²
divide both-side of the equation by 3.14
17.83 = r²
take the square root of both-side
√17.83 = √r²
4.2 =r
r= 4.2 units
but diameter = 2 r
diameter = 2×4.2
diameter = 8.4 units
Diameter of the circle is 8.4 units
WIll MARK BRAINLIEST IF ANSWER IN 2 MINUTES!!!! Which represents the equation 6 x + 3 y = 12 when solved for y? y = negative 2 x + 4 y = 2 x + 4 y = negative 2 x minus 4 y = 2 x minus 4
Answers
Answer:
y=-2x+4
Step-by-step explanation:
6x+3y=12
3y=-6x+12
y=-2x+4
Answer:
The correct answer is y A.) = -2x + 4
Step-by-step explanation:
i just did the test on edge 2020 and got it right
Simply Savings Bank offers a simple interest rate of 10% per year. Compound Capital Bank offers an interest rate of 8% per year compounded continuously. If Shakira plans to invest $200 for 5 years, which bank should she choose?
Answers
Answer:
She should choose the Simply Savings Bank, since she'll earn around 2 dollars more in comparison to the other bank.
Step-by-step explanation:
A simple interest rate account yields a return that follows the formula below:
[tex]return = C + C*r*t[/tex]
Where C is the invested money, r is the interest rate and t is the elapsed time in years.
While a compound interest rate account yields a return that follows the formula below:
[tex]return = C*e^{r*t}[/tex]
Therefore for the Simply Saving Bank she'll earn:
[tex]return_{1} = 200 + 200*0.1*5\\return_{1} = 200 + 100\\retrun_{1} = 300[/tex]
While the Capital Bank she'll earn:
[tex]return_2 = 200*e^{0.08*5}\\return_2 = 200*e^{0.4}\\return_2 = 200*1.49182\\return_2 = 298.364[/tex]
She should choose the Simply Savings Bank, since she'll earn around 2 dollars more in comparison to the other bank.
Can someone help me with this?
will mark as brainliest.
What angle corresponds to ∠M?
Answers
Answer: Angle B
Step-by-step explanation:
Since the two shapes are similar. The angles stay with the shape. This means that angle M should correspond to angle B.
Answer: angle b .
Step-by-step explanation:
pls help me any bit can help need it asap though. only need part lll the words cutt of are show work
Answers
Answer:
y = 4/3 x - 3.
Step-by-step explanation:
III
y - 5 = 4/3(x - 6)
y = 4/3(x - 6) + 5
y = 4/3 x - 8 + 5
y = 4/3 x - 3.
Please help ! I really don’t understand:((
Answers
Answer: B
Step-by-step explanation:
just took that
Answer:
the answer is B
Step-by-step explanation:
Na figura, OC é bissetriz do ângulo AOB. A medida de BÔC está representada,em graus, por uma expressão algérica.
A: Represente, por uma expressão algébrica, a medida de AÔB em graus.
B: Calcule a medida de BÔC e AÔB para x=9
Answers
Answer:
We know by given that OC bisects the angle, which means it divides the angle AOB in two equal parts. So,
[tex]m \angle AOB = 3x +5 + 3x +5 =6x+10[/tex]
If [tex]x=9[/tex], then we use this value to find each angle.
[tex]m \angle BOC = 3x+5 =3(9)+5=27+5=32[/tex]
Therefore, angles BOC and AOC measure 32°.
Among 120 people , 80 drink tea and 40 drink
coffee. 20 of them drink neither tea or coffee;
answer the following question with the help of
a venn-diagram
1.how many of them drink tea only
Answers
[tex]please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps....[/tex]
plslslslsl help ASAPPPP 10 points and you win brainlist
Answers
Answer:
71
Step-by-step explanation:
Take the cost of the item and multiply by the commission percent
800 * 8.875%
Change to decimal form
800*.08875
71
Answer:
71
Step-by-step explanation:
Simon earns 8.875 for a commission. yet for him to sold a rowboat that cost $800.
800*8.875
=$71
Jordan is putting a fence around a garden that is shaped like a half circle and rectangle
Answers
Answer:
92 ft
Step-by-step explanation:
Assume the garden has the shape shown below.
The length of fencing equals the distance around three sides of the rectangle plus that around the semicircle.
1. Around the rectangle
Distance = 28 ft + 14 ft + 28 ft = 70 ft
2. Around the semicircle
For a circle.
C = 2πr
For the semicircle,
½C =½(2πr) = πr
D = 14 ft, so
r = 7 ft
[tex]\text{Distance} = \dfrac{22}{7} \times \text{7 ft} = \text{22 ft}[/tex]
3. Total distance
Distance = 70 ft + 22 ft = 92 ft
Jordan will need 92 ft of fencing.
what is to be added to -1 to get the number 7 by 5
Answers
Answer:
Step-by-step explanation:
let the number be x
-1 + x = 7/5
x = 7/5 +1
x = 12 /5
please mark me as the brainliest
Answer:
x=12/5
Step-by-step explanation:
20 POINTS !! PLEASE ANSWER THIS MATH QUESTION !!
Answers
Answer:
7.8
Step-by-step explanation:
Sine 50=6/x
x= 6/Sine 50
x=7.8
Answer:
h ≈ 7.8 cm
Step-by-step explanation:
Use sines to determine the length of the hypotenuse. You know that there is a 50 degree angle, and that the ratio for sine is opposite/hypotenuse. You know that the opposite side from that angle is 6 cm, so you can set up the following equation:
sin50 = 6/h
sin50h = 6
h ≈ 7.8 cm
Find the measure of angle DEH:
E
D
ti
+
F
56°
다.
G
Value: 10
The measure of angle DEH is ___ degrees.
Answers
Answer:
62
Step-by-step explanation:
I did 180-56=124
124/2 which was 62