Which is the standard form of the equation of a parabola with a focus of (0, -3) and its vertex at the origin?
x² =-12y
x² = 12y
O y = -12%
y? - 12
Answers
Answer: it’s A
Step-by-step explanation:
The standard form of the equation of a parabola with a focus of (0, -3) and its vertex at the origin is,
⇒ x² = - 12y
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We have to given that;
Focus = (0, - 3)
Vertex = (0, 0)
Now, We know that;
Standard form of parabola is,
⇒ (x - h)² = 4p(y - k),
where p ≠ 0. The vertex of this parabola is at (h, k).
The focus is at (h, k + p).
Here, Vertex = (0, 0)
Hence,
h = 0
k = 0
And, (h, k + p) = (0, 0 + p) = (0, p) = (0, - 3)
⇒ p = - 3
So, We get;
⇒ (x - h)² = 4p(y - k),
⇒ (x - 0)² = 4 x - 3 (y - 0)
⇒ x² = - 12y
Thus, The standard form of the equation of a parabola with a focus of (0, -3) and its vertex at the origin is,
⇒ x² = - 12y
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Related Questions
Brett bought three pairs of jeans and five polo shirts. The jeans that regularly sell for $79 were
35% off and the polo shirts that regularly sell for $39 were 15% off. If sales tax is 5.75% and he
gave the cashier $350, how much did he receive back in change?
Answers
A box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent. Then, the store marks down the item by 20 percent. A customer wants to buy three boxes of spaghetti. How much will the customer pay, including paying 8 percent sales tax? Round your answer to the nearest cent.
Look at the table below.
Steps
Moses’s work
Step 1
1 dollar and 60 cents (1.6) = 2 dollars and 56 cents
Step 2
2 dollars and 56 cents (0.80) = 2 dollars and 5 cents
Step 3
2 dollars and 5 cents (3) = 8 dollars and 20 cents
Step 4
8 dollars and 20 cents (1.08) = 8 dollars and 86 cents
Answers
Answer:
the answer is $8.29
Step-by-step explanation:
1.60 marked up by 60% in decimal form is .60
multiply that .60 by 1.60 and you get .64
you add .64 to 1.60 and you get 2.56
you multiply 2.56 by 3 and you get 7.68
you have a 8% sales tax so you multiply 0.08 by 7.68
you will get .61 you add that to 7.68 to get $8.29
Answer:
step 3
Step-by-step explanation:
Tim incorrectly rewrote the expression 1/2p - (1/4p + 4) as 1/2p + 1/2p - 4. Rewrite the expression without parentheses. What was Tim's error?
Answers
Answer:
1/2p - 1/4p - 4.
Step-by-step explanation:
1/2p - (1/4p + 4)
= 12p - 1/4p - 4
≠ 1/2p + 1/2p - 4
Instead of writing -1/4p, Tim wrote 1/2p
As a young girl, Tiana enjoyed watching her father make things in his woodworking shop. Now that she's grown up, Tiana builds wooden furniture for a living. Her most popular product is a cedar porch swing. There is a proportional relationship between the time (in days) Tiana spends making porch swings, x, and the number of swings she builds, y.
The equation that models this relationship is y=0.6x.
At this rate, how many swings can Tiana build in 20 days?
Answers
Answer: Tiana can build 12 swings in 20 days
Step-by-step explanation:
We know the equation:
y=0.6x
We can replace the variables.
y=0.6 x 20 (here, im using the x as a multiplication sign)
Now we calculate...
y=12
Answer: Tiana can build 12 swings in 20 days
The circle graph represents a family’s monthly budget. If the total monthly budget is $6,500.00, how much more does the family spend on housing than food?
Answers
Answer:
Use the percentages to help you.
Ask yourself, what is 25% of $6,500.00?
Turn your percent into a decimal which is 0.25
then multiply $6,500 by 0.25
you should get 1625.
Find the amount of money spent on the food and find the difference of the two.
Explanation:
Housing: 6,500/.25= $1,625
Food: 6,500/.19= $1,235
Subtraction:
$1,625 - $1,235= $390
The family spends $390.00 more dollars in housing than food.
Help me with this math question
Answers
Answer:
2x10-4
Step-by-step explanation:
help me its due today :')
Answers
Answer:
9 feet easy to solve this is answer
For each equation, what could you do first to each side of the equation so that there would be no fractions?
Select all the correct responses next to each equation.
\frac{3x-4}{8}=\frac{x+2}{3}3 x − 4 8 = x + 2 3
o Multiply each side by 8
o Multiply each side by 30
o Multiply each side by 48
o Multiply each side by 24
o Multiply each side by 60
o Multiply each side by 12
Answers
4t + 1/4=3 first answer will get brainliest
Answers
Answer:
t=11/16
Step-by-step explanation:
4t+1/4=3
-1/4 -1/4
4t=2 3/4
t=11/16
Answer:
Step-by-step explanation:
4t+1/4=3
We move all terms to the left:
4t+1/4-(3)=0
determiningTheFunctionDomain
4t-3+1/4=0
We multiply all the terms by the denominator
4t*4+1-3*4=0
We add all the numbers together, and all the variables
4t*4-11=0
Wy multiply elements
16t-11=0
We move all terms containing t to the left, all other terms to the right
16t=11
t=11/16
t=11/16
if you rolled two dice what is the probability that you would roll a sum of 10
Answers
The probability of rolling a sum of 10 with two dice is 1/12.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that two dice are rolled and find the probability of a sum of 10.
The sample space of the event of rolling two dice is
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
The total possible outcomes is 36.
The favorable outcomes that is the outcomes where the sum is 10 is
(1, 4), (2, 3), (3, 2).
The number of favorable outcomes are 3.
To find the probability of rolling a sum of 10 with two dice, write the sample space and then determine the number of favorable outcomes that is the outcomes where the sum is 10 and the total number of possible outcomes.
The formula to find out the probability of any event is:
\(\text{P(event)} = \dfrac{(\text{number of favorable outcomes})}{\text{total number of possible outcomes}}\)
By using the data and formula, the probability of rolling a sum of 10 is,
\(\text{P(event)} = \dfrac{(\text{number of favorable outcomes})}{\text{total number of possible outcomes}}\)
\(\text{P(rolling a sum of 10)} = \dfrac{3}{36}\)
On dividing both numerator and denominator by 3 gives,
\(\text{P(rolling a sum of 10)} = \dfrac{1}{12}\)
Hence, the required probability of rolling a sum of 10 with two dice is 1/12.
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The probability that you would roll a sum of 10 if you rolled two dice is 1/12.
We need to consider all the possible outcomes and count the favorable outcomes to determine the probability of rolling a sum of 10 when rolling two dice.
When rolling two dice, each die has six possible outcomes, ranging from 1 to 6. To find the total number of outcomes, we multiply the number of outcomes for each die: 6 * 6 = 36.
Next, we need to count the number of favorable outcomes, which are the combinations of two dice that result in a sum of 10. These combinations include:
1. Rolling a 4 on the first die and a 6 on the second die: (4, 6)
2. Rolling a 5 on the first die and a 5 on the second die: (5, 5)
3. Rolling a 6 on the first die and a 4 on the second die: (6, 4)
There are three favorable outcomes.
Therefore, the probability of rolling a sum of 10 when rolling two dice is:
Probability = (Number of favorable outcomes) / (Number of total outcomes) = 3/36 = 1/12.
Hence, the probability is 1/12.
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Chau runs each lap in 7 minutes. He will run at most 8 laps today. What are the possible numbers of minutes he will run today?
Use T for the number of minutes he will run today.
Write your answer as an inequality solved for T.
Answers
What is the measurement of the longest line segment in a right rectangular prism that is 11.2 centimeters long, 6.6 centimeters wide, and 6 centimeters tall?
Answers
Answer:
Step-by-step explanation:
3.1313109
Answer: the answer should equal 3.131
Step-by-step explanation: as this is the measurement of the longest line in right rectangular prism.
Please got brainliest
Laurie left home and ran to the lake at 10 mi/h. She ran back home at 8 mi/h. If the entire trip took 27 min, how far did she run in all?
Answers
Use a number line to order the numbers from least to greatest.
Answers
Assign the numbers to the number line in the following order:
2.15=2.15
220%=2.2
9/4=2.25
*2.15* is easy enough to place as it is already in decimal form. However, the other 2 options need to be converted to decimals in order to be placed. We have the fraction 9/4 and percentage 220%. 9/4 can either be simply divided on a calculator or turned into the mixed fraction 2 and 1/4, which is *2.25*. Finally, we know that converting a decimal to a percentage we multiply the decimal by 100. Therefore, to convert a percentage to a decimal we divide 100 or move the decimal to the left 2 places. With this conversion rule, 220% transforms to *2.2* and we have the third and final number for our number line. Arranging these three numbers from least to greatest:
2.15, 2.2, 2.25
if 4/4 is 1 then 9/4 is 2 whole with 1/4 left
220%=2.2 and 2.15 is still 2.15
Is this equation proportional or not?
y = 4 + x
Answers
Pls help on 1-3 ASAP
Answers
Answer:
1: Lowest-77 Higest: 99 Center: 88 Spread: 22
Step-by-step explanation:
Answer:
1)
Lowest: 77
Spread: 77 through 99
Highest: 99
Center: 88
2)
Lowest: 24
Spread: 24 through 84
Highest: 84
Center: 52
Step-by-step explanation:
The spread is just the numbers you are counting to so like in number 1 it is 77 through 99, does that make sense? Hope this helps!
Pls solve and show all work needed
Answers
2.5 x (4+5) x 2
2.5 x 9 = 22.5
22.5 x 2 = 45
Which gives you 45 in (option c)
Answer:
45 inches
Step-by-step explanation:
The perimeter of the picture before scaling is:
P = L+W+L+W
P = 4+5+4+5
P = 18
Multiply the perimeter by the scale factor.
P = 18 * 2.5
P =45
Order from least to greatest.
4.08, 4.3, 4.803, 4.038
Answers
Answer: 4.038,4.803,4.08,4.3
It's 4.038, 4.08, 4.3, 4.803.
Daisy wants to find out where the greatest number of people buy fast food for lunch. He surveys every fourth person on a random street and asks them where they get food for lunch regularly?
A. ask people their favorite lunch food.
B. survey all people in the Area.
C. ask people where they get breakfast.
Answers
Answer:
B
Step-by-step explanation:
that way when surveying everyone she’ll know the exact number
This is the correct answer because it’s a ways to get the whole crowds perspective. Hope this helped!!
help 3x6778=y +56789
Answers
Answer:
Step-by-step explanation:
y
=
3
x
6778
−
56789
Express -3(-2-1) on a number line
Answers
Answer:
9 on a number line
Step-by-step explanation:
-3(-2-1)
-3(-3)
9
Answer:
Step-by-step explanation:
-
-3(-3) = 9
let's draw a number line from 1 to 9 by taking a scale of 1
1_2_3_4_5_6_ 7 _8_ 9__
HELP MEE PLS
The product of 0.5 and a number is 10.
Represent the statement as an equation. Use n for the variable.
Determine the solution set using the replacement set 0.05,0.5,2,20.
Answers
Answer:
20 is a solution to the equation by using the replacement set.Let the unknown variable be n.
Given the following data: Output = 10
a. To represent the statement as an algebraic equation: In this exercise, you're required to write a mathematical expression (algebraic equation) that represents the word sentence given. Translating the word sentence into an algebraic expression, we have; The product of 0.5 and a number is 10:
b. To determine the solution set using the replacement set:
Let's use the following set of numbers (0, 1, 10, 20)
When n = 0.05:
When n = 0.5:
When n = 2:
When n = 20:
Therefore, 20 is a solution to the equation by using the replacement set.
Answer:20 is a solution to the equation by using the replacement set.
Let the unknown variable be n.
Given the following data:
Output = 8
a. To represent the statement as an algebraic equation:
In this exercise, you're required to write a mathematical expression (algebraic equation) that represents the word sentence given.
Translating the word sentence into an algebraic expression, we have;
The product of 0.4 and a number is 8:
b. To determine the solution set using the replacement set:
Let's use the following set of numbers (0, 1, 10, 20)
When n = 0:
When n = 1:
When n = 10:
When n = 20:
Therefore, 20 is a solution to the equation by using the replacement set.
Find more information on algebraic expression here: brainly.com/question/4728821
Step-by-step explanation:
Some students recorded how many minutes they spent on the phone in one day. They put the results in a Stem-and-Leaf Plot.
What is the mean number of minutes spent on the phone?
Answers
Explanation:
The data from the stem-and-leaf plot is:
10,
24,25,26,
30,30,32,33,
40,45,46
Add up those values
10+24+25+26+30+30+32+33+40+45+46 = 341
Then divide over n = 11 which is the sample size.
341/11 = 31 is the arithmetic mean.
Answer:
341/11 = 31 is the arithmetic mean.
Step-by-step explanation:
Of the pizzas sold last week at Luna's Pizzeria, 1/2 were large pizzas and 1/4 were extra-large pizzas. What fraction of the pizzas sold were either large or extra-large?
Answers
Answer:
4/8, and 2/8
Step-by-step explanation:
Explanation:
1/2=4/8, 1/4=2/8
Elena walked 12 miles. Then she walked 1/4 that distance. How far did she walk all together? Select all that apply.
Answers
Answer:
12(1/4)
Step-by-step explanation:
In other words, you are trying to find 1/4 OF 12. Of means multiply. 12 times 1/4
Edited: now you'll multiply 12 times 1/4 and after you get 3, you'll add it to 12
Elena walked 12 ( 1 + 1 / 4 ) miles all together
What is Linear Equation in 1 variable?
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution
Given data ,
Distance walked by Elena = 12 miles
Additional distance walked by Elena = 1/4 x Distance walked by Elena
= ( 1 / 4 ) x 12
= 3 miles
Total distance walked by Elena = 12 + 3
= 15 miles
15 miles = 12 ( 1 + 1/4 ) miles
Hence , the total miles walked by Elena is 12 ( 1 + 1 / 4 )
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Which product is negative? will mark brainliest
Answers
Neg*neg=pos
1. Has two neg and two negs make a pos
2. Has 4 neg which will also make pos
3. Has 3 neg. The first 2 will cancel out and make a pos but the last one will make the answer neg
4. Would just be 0 because its multiplying 0 but without it it would be neg.
So the answer is the third one
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $6100 and his stock in Company B was worth $6480. The stock in Company A has decreased 2% since last year and the stock in Company B has decreased 10%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
Answers
Investment in Company A by investor = $6100
Investment in Company B by investor = $6480
The decrease in value of the stock of company A is 2%
The decrease in value of the stock of company B is 10%
Value of wealth that investor lost in company A = 6100× 2/100
= 61×2
= $122
The decline in the value of the stock of company B = 6480×10/100
= 648×1/1
= $648
The total decline in the wealth of the investor= 122+648
= $770
The combined wealth of investor in both companies= 6100+6480
= $12580
Percentage of decline in the stock account of investor= 770×100/12580
= 77000/12580
= 6.1%
The total percentage decline in investor's stock account is 6.1%
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Work out the size of angle m.
Answers
Answer:
78+25+61+55+64=283
360-283=77
180+77=257
If you add up all the provided angles you get 283 degrees
The remaining angle to get to 360 is 77 since 360-283=77
Answer: m=77
Hope this helped!
Solve the system using elimination and find the y and x coordinates
Answers
Answer:(-1,1)
Step-by-step explanation:
Answer:
Your answer is: (2,-1). I provided a picture in case you need to show your work.
Last one! Please help
Answers
Answer: 19
Step-by-step explanation:
IF m = 39 and n=5,
we could write the equation like this :
39 - 4(5)
Then, :
39 - 20
=
19!
Hope this helps!