Given the directrix of y = −1 and focus of (0, 3), which is the equation of the parabola? y = one eighthx2 − 1 y = −one eighthx2 1 y = one eighthx2 1 y = −one eighthx2 − 1.
Answers
Check the picture below.
so as we can see, the focus point is above the directrix, meaning the parabola opens upwards, and since the vertex is halfway between the directrix and focus point, that means the vertex is at (0 , 1), and distance from the vertex to either the focus or directrix is 2, namely p = 2, and is positive since is opening upwards, thus
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]4(\stackrel{p}{2})(y-\stackrel{k}{1})=(x-\stackrel{h}{0})^2\implies 8(y-1)=x^2 \\\\\\ y-1=\cfrac{x^2}{8}\implies \boxed{y=\cfrac{1}{8}x^2+1}[/tex]
Related Questions
When a customer buys a family-sized meal at a certain restaurant, they get to choose 3 side dishes from 9 options. Suppose a customer is going to choose 3 different side dishes.
How many groups of 3 different side dishes are possible?
ANSWER: 84
Answers
Step-by-step explanation:
9! / (3! × (9-3)!) = 9! / (3! × 6!) = 9×8×7 / (3×2) =
= 3×4×7 = 84
this is a combination of picking 3 items out of possible 9, where the sequence does not matter, and there are no repetitions (3 DIFFERENT side dishes).
Please help me find x
Answers
Answer:
use the SOHCAHTOH method in the trigonometry
Step-by-step explanation:
How do you write 2,131/1,000 as a percentage?
Answers
2,131 / 1000 = 2.131
Answer:
Its 213.1%
Step-by-step explanation:
you want to convert the fraction to a decimal and then multiply by 100
A Ferris wheel has a radius of 50 feet and its center is 60 feet off the ground how many points on the Ferris wheel are
a. 30 feet off the ground?
b. 110 feet off the ground?
c. 5 feet off the ground
Answers
Answer: 5 feet off the ground
Step-by-step explanation:
Ms. Raguz's purchase totaled $135. In addition to that, she paid a tax of 6.5%.
Write and solve an equation to find out how much Ms. Raguz paid for her
purchase, including tax. Round to the nearest hundredth.
Answers
well, let's simply see how much is 6.5% of 135, or namely the tax
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 135}}{\left( \cfrac{6.5}{100} \right)135}\implies 8.775 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{cost}{y}=\stackrel{selling~price}{x}+\stackrel{tax}{\left( \frac{6.5}{100} \right)x}~\hfill y = 135+8.775\implies y \approx 143.88[/tex]
Combine like terms for
15-(-9x-5)
Answers
Answer:
9x+20
Step-by-step explanation:
15-1(-9x-5)
15+9x+5
9x+20
Hey there!
15 - (-9x - 5)
= 15 - 1(-9x - 5)
DISTRIBUTE -1 WITHIN the
PARENTHESES
= 15 - 1(-9x) - 1(-5)
= 15 + 9x + 5
COMBINE the LIKE TERMS
= (15 + 5) + (9x)
= 20 + 9x
= 9x + 20
Therefore, your answer is: 9x + 20
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Graph y=-2x. Give the domain and range. Is the function dicrete or continou?.
Answers
Answer:
all real numbers
continuous function
Step-by-step explanation:
y = -2x is a straight line which extends infinitely in both directions
linear equations are continuous functions
Find the area for each parallelogram! Hurry!
Answers
Answer:
1.) 8
2.) 630
3.) 91.52
Step-by-step explanation:
your welcome
SOMEONE HELP PLEASEEE IM CRYINGGGFG
Answers
Kardal did a study to determine the correlation between men’s heights, x, and their shoe sizes, y, and found the following data:
(60, 8.5), (65, 10), (66, 12), (68, 11.5), (63, 9.5), (72, 12.5), (62, 8.5), (69, 12.5), (70, 11.5)
Kardal used the line of best fit to predict that a man 80 inches tall would wear about a size 16 shoe. What can be concluded about this prediction? Check all that apply.
The prediction is reasonable.
The prediction is an interpolation.
No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.
A prediction cannot be made for a man who is 80 inches tall.
A man who is 80 inches tall will likely wear a size 12.5 shoe.
Answers
Answer:
first and third option:)
Step-by-step explanation:
Kardinal did a study to determine the correlation between men’s heights, x, and their shoe sizes y, the conclusion about this prediction is mathematically given as The prediction is reasonable, and No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted. Option A ,C.
What can be concluded about this prediction?Generally, the equation for the equation of the line is mathematically given as
y=0.377x-14.214
Where the value of R^2 =0.7784 and x=80
y=0.377x-14.214
Hence
y=0.377(80)-14.214
y=16
In conclusion, Although no data is provided in the scatterplot for a height of 80 inches, a shoe size may still be estimated.
Read more about scatterplot
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HELPP
Complete the ratio table.
5 1
30 6
60 _
75 _
80 _
Answers
Answer:
12 27 32 it could be wrong though
2(x+3)-17= 3x -7 +x how many solutions does it have?
Answers
Answer:
x=-2
Step-by-step explanation:
2x+6-17=4x-7
-2x=4
x=4/-2
Hi!
This has one solution.
2(x+3)-17= 3x -7 +x
Distibute on left side and add like terms on right.
2x + 6 - 17 = 4x - 7
Simplify left side.
2x - 11 = 4x - 7
Subtract both sides by 2x and add 7 to both sides.
-4 = 2x
Divide both sides by 2.
-2 = x
y= 1/2x -3 graph the linear equation. I DON'T KNOW!
Answers
Answer:
In the picture.
Step-by-step explanation:
hopes this helps.
Answer: You graph -3 on the y axis, for the y-intercept. Then up one over two (rise over run), and plot a dot down. To graph the dots on the left side of the graph, it’s down one left two, and plot a dot there.
Step-by-step explanation: As a way to check, you can always go to desmos to make sure your graphs are correct.
4x + 10 = -26Use your solutions to navigate through the question. Show all steps
Answers
Answer:
[tex]x=-9[/tex]
Step-by-step explanation:
[tex]4x+10=-26\\4x=-36\\x=-9[/tex]
Subtract 10 on both sides, divide both sides by 4 to isolate "x".
Answer:
4 hope it helps
Step-by-step explanation:
1. 26-10=16
2. 16÷4= 4
Please answer with clear instructions so that i can apply this to other questions.
Answers
Answer:
x= 1 and -4
Step-by-step explanation:
Factor out the common term 2
2(x²+3x-4)=0
Factor x²+3x-4
2(x-1)(x+4)=0
Solve for x
x= 1 and -4
Hope it helps
A population of wolves in a county is represented by the
equation P(t) = 80(0.98)', where t is the number of years
since 1998. What is the percent decrease of wolves per
year?
Answers
Answer: 98%
P(t)=80(0.98)t P ( t ) = 80 ( 0.98 ) t , where t is the number of years since 1998 Step-by-step explanation:
P(t)=80(0.98)t P ( t ) = 80 ( 0.98 ) t , where t is the number of years since 1998
Step-by-step explanation:
..... by the equation p(t)=80(0.98)^t
How can these models be used to find the sum 2.42 + 1.9?
Enter your answers in the boxes.
The models show a total of 3 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
. pls hurry 100 points
Answers
Answer:
4 wholes, 3 tenths and 2 hundredthsor
4.32Step-by-step explanation:
According to the model we have:
2.42 = 2 wholes, 4 tenths and 2 hundredths1.9 = 1 whole and 9 tenthsSum up:
2 + 1 = 3 wholes4 + 9 = 13 tenths = 1 whole and 3 tenths2 hundredthsRegroup the wholes to get:
3 + 1 = 4 wholes, 3 tenths and 2 hundredthsIn decimal form it is:
4.32Please help ASAP I JUST NEED THIS ONE
Answers
Answer:
the answer to this is D
Step-by-step explanation:
1 is 55
2 is 110
4 is 220
Which pair of measurements are possible if they are congruent figures?
Measure of angle W = 47 degrees and Measure of angle X = 94 degrees
Measure of angle X = 94 degrees and Measure of angle Z = 79 degrees
Measure of angle W = 47 degrees and Measure of angle Y = 140 degrees
Measure of angle X = 140 degrees and Measure of angle = 94 degrees
Answers
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
can anyone help me with this? i dont understand it, thank you.
Answers
Answer:
[tex]3(x + 2) = 2(x + 2) \\ 3x + 6 = 2x + 4 \\ 3x - 2x = 4 - 6 \\ x = - 2[/tex]
A pair of shoes usually sells for $66. If the shoes are 20% off, and sales tax is 7%, what is the total price of the shoes, including
tax?
OA. $52.97
ОВ.
$56.50
oc.
$60.03
Answers
Answer:
OB. 56.50
Step-by-step explanation:
$66 x 0.2 = $13.2
$66 - $13.2 = $52.8
$52.8 × 0.07 = $3.696
$52.8 + $3.696= $56.496 (round up)
what is 5 1/3 divided by 1 1/6
Answers
Answer:
32/7 or 4 4/7
Step-by-step explanation:
I used mathaway. JOKING!
Convert the fractions into mixed numbers.
So instead of 5 1/3 and 1 1/6
you will have 16/3 and 7/6
Apply the fraction rule
a/b ÷ c/d = a/b × c/d
= 16/1 x 2/7
then:
16 x 2
1 x 7
= 32/7
proper fraction: 4 4/7
Please Help me! Due in 10 Minutes. Thank You!
Answers
Answer:
pretty sure is 1,2, and 6
Step-by-step explanation: the three of them are a right angle and are trapezoids
A radio tower 200 ft. high casts a shadow 75 ft. long. What is the angle of elevation of the sun?
Answers
Angle of elevation of the sun: 69 degrees
Step-by-step explanation:
tan(x) = 200/75
x = tan^-1 (200/75)
x = 69 degrees
The angle of elevation of the sun is .
What is tangent of an angle?
The tangent of an angle is the ratio of height to base of the angle.
If we take the angle as Ф, then tan Ф = height/base.
Given, length of the tower is 200 ft. and the length of the shadow is 75 ft.
Let, the angle of elevation of the sun = Ф
Therefore, tan Ф = height/base = 75/200 = 0.375
Hence, Ф = [tex]tan{-1}[/tex](0.375) =
The angle of elevation of the sun is .
Learn more about the tangent of the angle here: https://brainly.com/question/15925556
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A college has a student hangout called
"The Lawn” where students play
ultimate frisbee, soccer, or just hang
out. The lawn is 84 ft long and 50 ft
wide. One student is in a hurry to get to
class and must walk to the opposite
corner of the field, as shown by the red
line below. How far does he walk?
Round to the nearest tenth.
Answers
Answer:
134
Step-by-step explanation:
first you have to add
Joyce paid $94.50 for an item at the store that was 55 percent off the original price. What was the original price?
Answers
Answer:
$210
Step-by-step explanation:
The original price of the item = 100%
If the item was reduced by 55%, then the discounted price of the item = 100% - 55% = 45%
Therefore, $94.50 = 45% of the original price.
45% = 45/100 as a ratio
Using ratios, and letting [tex]x[/tex] be the original price:
94.50/[tex]x[/tex] = 45/100
Cross multiply: 94.50 x 100 = 45 x [tex]x[/tex]
9450 = 45[tex]x[/tex]
Divide both sides by 45: 210 = [tex]x[/tex]
Therefore, the original price of the item was $210
Alternatively, divide 94.50 by 45 to get the cost per 1%. Then multiply this by 100 to get the original price (100%):
(94.50 ÷ 45) x 100 = 210
What is the distance between -7 and 6 on the number line?
Answers
Answer:
13 units
Step-by-step explanation:
from -7 to 6 there are a total of 13 units
-7-6
=-13
hope it helps
Given: 2×-7=4x+15 Prove: ×=-11
Answers
Answer:
2x - 4x = +7+15
-2x = +22
2x = -22
x = -11
Step-by-step explanation:
(put the numbers on one side and the letters on the other, just be careful about the symbols)
PLEASEEEEE I NEED IT NOWW!!! ILL MARK BRAINLIEST!!!!
01.01 LC)Which number line best shows how to solve −6 − (−8)?
Answers
Answer:
First number line
Step-by-step explanation:
-6 means 6 to the left, and subtracting -8 to it means 8 to the right.
Answer:
The first one
Step-by-step explanation:
It shows going from 0 to -6,
then since subtracting a negative is the same as adding a positive, it goes 8 spaces to the right.
edgar purchased three cheeseburgers for 5.75 fiona purchased five cheeseburgers for 7.50 who paid less
Answers
Answer:
edgar
Step-by-step explanation:
edgar - 5.75 times 3 = 17.25
fiona - 7.50 times 5 = 37.50
edgar payed least since he has the smallest value
