What is the equation of the parabola with focus (0, 1/2) and directrix y= -1/2
Answers
keeping in mind that the vertex is half-way between the focus point and the directrix, and since the focus point is above the directrix, meaning the parabola is a vertical parabola opening upwards, the parabola will more or less look like the one in the picture below, with a distance from the vertex of "p" being positive since it's opening upwards.
[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] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} h=0\\ k=0\\ p=\frac{1}{2} \end{cases}\implies 4(\frac{1}{2})(y-0)~~ = ~~(x-0)^2\implies 2y=x^2\implies y=\cfrac{1}{2}x^2[/tex]
Related Questions
Help help math math help
Answers
Answer:
The answer to this equation is 2
Step-by-step explanation:
x-2 = 3(2-x) \4
x-2= 6 -3x/4
cross multiply
4(x-2)= 6-3x
4x-8 = 6-3
collect like terms
4x+3x = 6+8
7x = 14
divide both sides by 7
7x/7= 14/7
x = 2
The mean on a statewide biology test was 76 with a standard deviation of 11. Harris county sampled the scores of some of its students and reported a mean of 80 with a margin of error of ± 2.3.
What is the range of reasonable means for Harris County's sample?
Range: ____ to ____
Answers
The margin of error would tell how many percentage differs from Harris County's sample
The range of reasonable means for Harris County's sample is 77.7 to 82.3
How to determine the range?The given parameters are:
Population mean, [tex]\mu = 76[/tex]Population standard deviation, [tex]\sigma = 11[/tex]Sample mean, [tex]\bar x = 80[/tex]Margin of error , [tex]E = 2.3[/tex]The range (R) is calculated as:
[tex]R = \bar x \pm E[/tex]
Substitute known values
[tex]R = 80 \pm 2.3[/tex]
Expand
[tex]R = (80 - 2.3,80 + 2.3)[/tex]
Evaluate the difference and sum
[tex]R = (77.7,82.3)[/tex]
Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3
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I need help with this question please
Answers
[tex]v(y) = 0[/tex]
[tex] - 32t + 105 = 0[/tex]
[tex]t = \frac{ - 105}{ - 32} = 3.28[/tex]
[tex]h = - 16(3.28) {}^{2} + 105(3.28) + 17[/tex]
[tex]h = 189.26[/tex]
Question 17 of 30 Will the answer to the subtraction problem below be odd or even? 743 - 353 = ? O A. Odd B.Even
Answers
Answer:
answer is 390 which is even number
any number you see has 0,2,4,6,8 at the end of a number is considered as an even number.
any number you see has 1,3,5,7,9 at the end of a number is considered as an odd number.
Georgia is a coffee enthusiast and drinks three coffee drinks a day from a local coffee shop costing $1.25 each. Being concerned with the expense of her coffee habit Georgia looks into making her own manual brewed coffee. A bag of premium coffee beans costs $70.00, a coffee grinder costs $120.00, and the manual coffee brewer costs $40.00. If a bag of coffee makes enough for 100 cups, how many full bags of coffee does she need to consume before saving money.
Answers
She needs to consume 3 full bags of coffee before saving money.
Amount calculationSince Georgia is a coffee enthusiast and drinks three coffee drinks a day from a local coffee shop costing $1.25 each, and being concerned with the expense of her coffee habit Georgia looks into making her own manual brewed coffee, and a bag of premium coffee beans costs $70.00, a coffee grinder costs $120.00, and the manual coffee brewer costs $40.00, to determine, if a bag of coffee makes enough for 100 cups, how many full bags of coffee does she need to consume before saving money, the following calculation must be performed:
70 x 1 + 120 + 40 = 230 / 100 = 2.370 x 2 + 120 + 40 = 300 / 200 = 1.570 x 3 + 120 + 40 = 370 / 300 = 1.23Therefore, she needs to consume 3 full bags of coffee before saving money.
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Please help! These data show the number of miles each of the 9 members of a track team ran for the week.
11 11.5 10.5 17 14.5 14.5 18 17 19
What is the IQR (interquartile range) for these data?
6.25
7.00
14.50
17.50
Answers
Answer:
14.50
Step-by-step explanation:
i took the quiz on k12 truse me i wish luck
The IQR for these data is 6.25.
Answer choice A is correct.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
To find the IQR, we first need to find the first and third quartiles.
First, we need to order the data from smallest to largest:
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19
Next, we find the median (middle value) of the data set.
Since we have an odd number of data points, the median is the middle number, which is 14.5.
To find the first quartile (Q1), we need to find the median of the lower half of the data set.
That is, we need to find the median of 10.5, 11, 11.5, and 14.5.
The median of this subset is (11 + 11.5) / 2 = 11.25.
To find the third quartile (Q3), we need to find the median of the upper half of the data set.
That is, we need to find the median of 17, 17, 18, and 19.
The median of this subset is (17 + 18) / 2 = 17.5.
Now we have the first quartile (Q1) = 11.25 and the third quartile (Q3) = 17.5. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
= 17.5 - 11.25
= 6.25
Therefore,
The IQR for these data is 6.25.
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What is the domain of this graph?
Answers
Answer:
x > 2
Step-by-step explanation:
The graph starts at x = 2
The graph goes up and to the right so x can't be less than 2.
There are 40%bananas and 50% apples in a bowl. How many more percentage points apples should be there so that apples become 50% more than bananas
Answers
Answer:
This means 50% of the total should be apples regardless of how many fruits there are in the bowl. If the reader only has 40% apples, they know they need to increase the number of...
Step-by-step explanation:
If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
Answers
The value of x in the direct and indirect varoation is calculated as: x = 2.
What is Direct and Indirect Variation?If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.
With the information stated, we would have the following:
z = kx/y³
Find k, by plugging in the values of x, y, and z:
12 = k(8/2³)
12 = k(8/8)
12 = k
k = 12
Find x when y = 1 and z = 24:
24 = 12(x)/1³
24 = 12x
24/12 = x
x = 2.
Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.
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A High School’s football Stadium holds a total of 7,000 fans. A survey shows that of the total number of fans, 68% root for the home team. How many fans attending a football game are rooting for the home team?
A. 4,760
B.2,240
C. 47,600
D. 5,512
Answers
Answer:
the answer is; 68% of 7000 which gives 4760 football fans rooting for the home team
Given the expression which operation would you perform first?
Answers
Hey there!
Let's use PEMDAS:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
So, let's use this formula in order to solve this problem.
We have:
3(4²)+4+16-9
According to PEMDAS, the first operation is
Parentheses (in this case, exponents)
Hence, the answer is
[tex]\boxed{\boxed{\bold{Option\;B}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions; if so, please comment.
#LearningDoesn'tEnd
#LearningIsFun
[tex]\rule{200}{2}[/tex]
Please help (also please write the formula on how to get the answer)
Answers
x= -1 , x= 0, x= 1, x= 2, x= 3, x= 4
Width:____feet
Height_____feet
Answers
Step-by-step explanation:
Let w = width and h = height. Then we have
w = 3*h - 17
and
4*w + h = 30 (4 shelves and 1 sides).
Plug in the first equation into the second and solve for h:
4*(3*h - 12) + h = 30
12*h - 48 + h = 30
13*h = 78
h = 78/13
h = 6
Plug that in the first equation to find w = 3*6 - 17 = 1
So width = 1 feet.
height = 6 feet
Find the mean of the data.
55,64,58,43,49,67 Please!!
Answers
a triangle has one side that is 4cm long and one that is 9cm long the third side is a whole number of cm. what is the shortest possible third side?
Answers
Answer:
Step-by-step explanation:
Since it must be an integer, 5 would make it up to the full length of the longest line. What you get is not quite a triangle. The way to get a triangle is to add one more to the 5 to make 6
Answer: 6 cm
Help me please!!!!!!!!!!
Answers
Answer:
p(3,2)=====P'(-2,3)....
The directions are with the pic below. It’s 2 parts of this equation. I’ll send the other part. Couldn’t all fit on the page.
Answers
Answer:
Step-by-step explanation:
In how many ways can first, second, and third prizes be awarded in a contest with 210 contestants?
Answers
Answer:
Not entirely sure about this because it was grabbed from someone else
There are 210 ways to win 1st place
There are 209 ways to win 2nd place
There are 208 ways to win 3rd place
Every time an award is won, a spot if taken, therefore one person is eliminated from possibly taking that spot.
Hope that makes sense :)
The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
The number of contestants is 210.
The number of ways of contestants who won the first prize will be given as,
⇒ ²¹⁰C₁
⇒ 210
The number of ways of contestants who won the second prize will be given as,
⇒ ²⁰⁹C₁
⇒ 209
The number of ways of contestants who won the third prize will be given as,
⇒ ²⁰⁸C₁
⇒ 208
Then the total number of ways of contestants can win first, second, and third prizes will be
⇒ 210 x 209 x 208
⇒ 9,129,120
The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.
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To visit the top of the Empire State Building, a ticket cost $ 4.00 in 1999. In 2009, the price rose to $ 20.00. What was the percent charge
Answers
Answer:
500%
Step-by-step explanation:
500% is 500/100 which is just 5*4=20
Your company offers three cell phone plans. The details are below:
Plan A allows 450 minutes for $39.99 with .25/minute for each minute over 450.
Plan B allows 900 minutes for $59.99 with .30/minute for each minute over 900.
Plan C allows 1500 minutes for $99.99 with .35/minute for each minute over 1500.
Write a report detailing the following:
An equation or inequality to represent each plan above.
Determine for how many minutes each plan is the best option for two customers. Customer Smith uses roughly 750 minutes per month. Customer Jones uses roughly 1350 minutes per month. Which plan should they choose and why?
Include a detailed explanation of your work, which scenario is better, and why.
Write a summary paragraph for your employees that will be answering and making phone calls.
Answers
Answer:
Smith should use 900 minute plan and Jones should use 1500 minute plan
Step-by-step explanation:
There are best answers
1. Equations/Inequalities for Each Plan:
Plan A: Cost = $39.99 + 0.25 * (m - 450), m ≤ 450
Plan B: Cost = $59.99 + 0.30 * (m - 900), m ≤ 900
Plan C: Cost = $99.99 + 0.35 * (m - 1500), m ≤ 1500
2. Best Plan for Customers:
Customer Smith (750 min): Plan B ($59.99)
Customer Jones (1350 min): Plan C ($84.99)
3. For both customers, Plan B offers the best value for 750 minutes, while Plan C is optimal for 1350 minutes due to its lower cost per minute overages.
4. Plan A is the least cost-effective for both. The chosen plans reflect the importance of base minutes and overage charges.
1. Equations/Inequalities for Each Plan:
Let's denote the number of minutes used as "m."
Plan A:
Cost: $39.99 for 450 minutes, then $0.25/minute for each additional minute.
Equation: Cost = $39.99 + 0.25 * (m - 450), if m > 450
Inequality: m ≤ 450
Plan B:
Cost: $59.99 for 900 minutes, then $0.30/minute for each additional minute.
Equation: Cost = $59.99 + 0.30 * (m - 900), if m > 900
Inequality: m ≤ 900
Plan C:
Cost: $99.99 for 1500 minutes, then $0.35/minute for each additional minute.
Equation: Cost = $99.99 + 0.35 * (m - 1500), if m > 1500
Inequality: m ≤ 1500
2. Determine the Best Plan for Customers:
Let's evaluate the cost for both customers using the given plans:
Customer Smith:
Usage: 750 minutes
Plan A: Cost = $39.99 + 0.25 * (750 - 450) = $112.49
Plan B: Cost = $59.99
Plan C: Cost = $99.99
Best Plan: Plan B ($59.99)
Customer Jones:
Usage: 1350 minutes
Plan A: Cost = $39.99 + 0.25 * (1350 - 450) = $297.49
Plan B: Cost = $59.99 + 0.30 * (1350 - 900) = $374.99
Plan C: Cost = $99.99 + 0.35 * (1350 - 1500) = $84.99
Best Plan: Plan C ($84.99)
3. Explanation and Recommendation:
Customer Smith's usage of roughly 750 minutes falls within the range of Plan B's base minutes (900) and is more cost-effective with Plan B. However, for Customer Jones, who uses around 1350 minutes, Plan C offers a lower overall cost due to its higher base minutes (1500). Plan A is the least cost-effective option for both customers due to its lower base minutes and higher per-minute charges.
4. Summary for Employees:
Dear Team,
When assisting customers with choosing a cell phone plan, please consider the following options:
Plan A: $39.99 for 450 minutes, then $0.25/minute.
Plan B: $59.99 for 900 minutes, then $0.30/minute.
Plan C: $99.99 for 1500 minutes, then $0.35/minute.
For customers using around 750 minutes per month, recommend Plan B for its competitive pricing. For customers using around 1350 minutes, advise them to opt for Plan C to optimize cost efficiency. Always ensure to guide customers toward the most suitable plan based on their usage patterns.
Thank you for your dedication to excellent customer service.
Sincerely,
[Your Name]
[Your Position]
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How many sweatshirts sold is BEST predicted with an outside temperature of 5 °F? A) 170 B) 200 C) 230 D) 250
Answers
A student could run 2 miles. After extensive training, the student could run five times as far as she could before the training. How far can the student run now?
Answers
Answer:
10 miles
Step-by-step explanation:
He could run 2 miles.
Now he can run 5 times as far.
Now he can run 5 times 2 miles.
5 × 2 miles = 10 miles
Original price 770$ is on sale at a 9% off what is the discount amount and sale price ?
Answers
Answer:
770 x 9/100 = 69.3
the discound amount = 69.3$
the sale price = 770 - 69.3 = 700.7$
700.7 is the sale price
Evaluate 4a when a = 7.
The value is
Answers
Answer:
28
Step-by-step explanation:
a is equal to 7,
so where there is 'a' you replace
with 7
4(7)=7×4=
28
What is the slope-intercept equation
for the following line?
Answers
Answer:
y=-1/3 x+1
Step-by-step explanation:
3 (2a + 6) what is the valur of this exspression when a = 4
please help!!
Answers
2a means = 2 x a
if a = 4
3 x (2 x 4 + 6) = 3 x (8 + 6) = 3 x 14 = 42
Juan and Matthew each have gardens. Juan's garden is 16 feet long and 12 feet wide. Matthew's garden is 18 feet long and 21 feet wide. Area is found by multiplying length and width. What is the total area of the two gardens?
Answers
Answer:
570 ft²
Step-by-step explanation:
Basically, you find the area of Juan and Matthew's gardens then add them up.
First let's find the area of Juan's garden.
Area is equal to length times width ([tex]a = lw[/tex])
So you do 16 * 12 which equals 192.
Now let's find the area of Matthew's garden.
So you do 18 * 21 which equals 378.
Then you add up both areas.
192 + 378 = 570
the rectangle below initially has dimensions of 10 inches and 14 inches as shown. after both dimensions have been increased by a length of x, the total area of the resulting rectangle is 320 square inches. algebraically determine the value of x.
Answers
The value of x determined algebraically given the total area of the rectangle is 1.5 inches
How to find area of a rectangleInitial dimensions:
Length = 14 inches
Width = 10 inches
New dimensions:
Length = 14 + x
Width = 10 + x
Area = 320 square inches
Area of a rectangle = Length × Width
320 = (14 + x) × (10 + x)
320 = 14x × 10x
320 = 140x²
x² = 320/140
x² = 2.28571428571428
x = √2.28571428571428
x = 1.511857892036908908858066144936720243
Approximately,
x = 1.5
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I am struggling on this and I need help
Answers
Answer:
I think so Last 3 figured are the correct answer
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
Volume
Step-by-step explanation:
Length times width times height, is volume and the formula of finding what is inside something.
Volume :- it's the amount of the mass a body can hold