A parabola can be drawn given a focus of (0, 2) and a directrix of y = 0. Write the
equation of the parabola in any form.
Given:
Focus of a parabola = (0,2)
Directrix: y=0.
To find:
The equation of parabola.
Solution:
The equation of parabola is
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex] ...(i)
where, (h,k) is vertex, (h,k+p) is focus, y=k-p is directrix.
Focus : [tex](h,k+p)=(0,2)[/tex]
On comparing both sides, we get
[tex]h=0[/tex]
[tex]k+p=2[/tex] ...(ii)
On comparing y=k-p and y=0, we get
[tex]k-p=0[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=2[/tex]
[tex]k=1[/tex]
Putting k=1 in (ii).
[tex]1+p=2[/tex]
[tex]p=2-1[/tex]
[tex]p=1[/tex]
Putting h=0, k=1 and p=1 in (i).
[tex]y=\dfrac{1}{4(1)}(x-(0))^2+(1)[/tex]
[tex]y=\dfrac{1}{4}x^2+1[/tex]
Therefore, the equation of required parabola is [tex]y=\dfrac{1}{4}x^2+(1)[/tex].
The original cost of Sam’s investment is $10,000. After liquidating the investment, Sam calculated his real return to be $10,700. What is the return on investment (ROI)?
Answer:
7%
Step-by-step explanation:
Step one:
given data
The original cost of Sam’s investment is $10,000
Sam calculated his real return to be $10,700
Required:
the interest made from the investment is
10700-10000= $700
Step two:
The ROI is a percentage that tells us the interest made
interest/investment*100
=700/10000*100
=0.07*100
= 7%
The ROI is 7%
Which rectangle is similar to a rectangle 12 inches wide and 18 inches long?
Answer:
Step-by-step explanation:
the answer is b add 8 to each side
A pair of pants was on sale for 40% off. The sale price of the pants was $18.00. What was the original price of the pants?
Answer:
The original price of the pants was $30.
Step-by-step explanation:
Let x be equal to the original price of the pants.
Because the pants are 40% off, their final price was 60% of the original price. 60% as a decimal is 0.6. Using this information, we can set up the following equation and solve:
0.6x=18
Divide both sides by 0.6
0.6x/0.6=18/0.6
x=30
I hope this helps!
What is the volume of this sphere?
Use a 3.14 and round your answer to the nearest hundredth.
9 cm
cubic centimeters
Answer:
3052.08
Step-by-step explanation:
We use the volume formula for spheres
[tex]\frac{4}{3}[/tex]πr³
Plug in 9cm for radius and evaluate
[tex]\frac{4}{3}[/tex]π(9)³
[tex]\frac{4}{3}[/tex]π*729
3052.08
Answer the following question and will mark Brainliest
a) f(4) = 3*4 - 4
= 8
b) h(-3) = 5 - ( - 3)
= 5 + 3 = 8
c) h(4) - f(-5) = 1 + ( -19)
= -18
have a nice day <3
PLEASE HELP ME I NEED AN ANSWER ASAP WILL MARK BRAINLY
Solve by factoring.
X2-9x-52=0
Answer:
Step-by-step explanation:
x^2-9x-52=0 What 2 numbers when multiplied equal -52 and added equals -9? -13 and 4
(x-13)(+4)
Help me please! Will mark brainiest :) ASAP
Answer:
Option C: Jayce's fee for his 10th drive is equal to K dollars is the correct answer.
Step-by-step explanation:
Given that:
M(n) models Jayce's fee (in dollars) for his nth drive on a certain day.
Here,
n means the number of drive.
The statement is given
M(10) = K
10 represents the nth drive of Jayce's.
Therefore,
The given statement represents Jayce's fee for his 10th drive is equal to K dollars.
Hence,
Option C: Jayce's fee for his 10th drive is equal to K dollars is the correct answer.
6 cm
5 cm
Determine the value of x.
A. 11 cm
O B. 461 cm
OC V11 cm
D. 3 cm
OE. 1 cm
Answer:
A.
Step-by-step explanation:
Today the temperature in New York City is -3 degrees and is expected to rise one half of a degree each day. It's 6 degrees in Juneau, Alaska and expected to fall 1 degree every 4 days. How long will it take for the temperature to be the same in the two cities? What will the temperature be?
Answer:
12 days
3 degrees
Step-by-step explanation:
Let y be the temperature of the cities after x days have passed.
Temperature of New York City
[tex]y=-3+\dfrac{1}{2}x[/tex]
In Juneau the temperature falls by 1 degree per 4 days. So, in 1 day the temperature falls be [tex]\dfrac{1}{4}[/tex] degree.
The minus sign is due to the fact that the temperature is falling
Temperature in Juneau Alaska
[tex]y=6-\dfrac{1}{4}x[/tex]
We need to find the value of x for which y will be equal
[tex]-3+\dfrac{1}{2}x=6-\dfrac{1}{4}x\\\Rightarrow \dfrac{1}{2}x+\dfrac{1}{4}x=6+3\\\Rightarrow \dfrac{3}{4}x=9\\\Rightarrow x=\\\Rightarrow x=9\times \dfrac{4}{3}\\\Rightarrow x=12\ \text{days}[/tex]
[tex]y=-3+\dfrac{1}{2}x=-3+\dfrac{1}{2}\times 12\\\Rightarrow y=3\ \text{degrees}[/tex]
Hence, in 12 days the temperature will be same in both the cities will be 3 degrees.
perfume discounted 25% on sale for $27
Soo, since it's 25% off, I multiplied 27x0.75, and I got 20.25
Soo, the answer is $20.25
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
Draw a Picture Cynthia has a piece of wood
that is 6 feet long. She cuts it into 3-foot pieces.
How many pieces does she have? Use the
number line to help you solve the problem.
0
2
3
You may divide the entire length of the wood by the length of each piece to get how many pieces she has: 6 feet / 3 feet / piece equals two parts. Cynthia therefore has 2, 3 foot long pieces of wood.
What does math divide mean?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
How do you multiply by four?There is a method for dividing by 4 that you can use: the the rule is to divide by 2 twice. For example, if you want to divide 12 by 4, you simply divide 12 by 2, which gives you 6, and then divide that number by 2, which, in this case, gives you 3.
To know more about Divide visit:
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Triangle C has vertices (2, −1), (2, 2), and (1, −1). Which triangle is similar to triangle C? Triangle X with vertices (−2, 2), (2, 4), and (1, −2) Triangle W with vertices (4, −3), (4, 0), and (2, −3) Triangle Z with vertices (4, −2), (4, 4), and (2, −2) Triangle Y with vertices (4, 1), (2, 3), and (2, 2)
Answer:
not triangel Z ill come back with an update
Step-by-step explanation:
They have nothing in common
Answer: Triangle Y
Step-by-step explanation: it’s the same triangle just double the size
julian needs to spend at least seven hours each week practicing the drums. he has already practiced five and one third hours this week. he wants to sp
The minimum number of hours is 5/6 and the inequality is x ≥ 5/6 hours.
What exactly is an inequality?An inequality is a relationship that compares two numbers and perhaps other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.
According to the given data:Let x = the number of hours practicing the drums
we know that Julian needs to spend at least seven hours each week practicing
the drums x ≥ 7 hours
He has already practiced 5*(1/3) hours this week.
Convert mixed number to an improper fraction 5*(1/3) = 16/3hours.
Subtract 16/3 from 7,
7 - (16/3)
= 5/3
Divide 5/3 by 2,
(5/3)/2
=5/6
Hence,
The inequality that represent the minimum number of hours he needs to practice on each of the two days is x ≥ 5/6 hours.
To learn more about inequality visit:
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The given question is not complete.
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced 5 1/3 hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
A cup of cereal has 12 grams of fiber, which is 40% of the amount of fiber Jared's
doctor recommends he consume each day.
How much fiber does Jared's doctor recommend he consume each day?
Answer:
Jared's doctor recommends he consume 30 grams of fiber each day.
Step-by-step explanation:
Jared's doctor recommends he consume 30 grams of fiber each day. We know this is the answer because, if we divide 12 grams by 40%, we get 30 grams which means, 12 grams is 40% of 30 grams.
Answer:
30 grams
Step-by-step explanation:
Let the doctors recommendation be
12g = 40/100 × x
x = 12g ÷ 40/100
x = 12g × 100/40
x = 12g × 5/
x = 60g/
x = 3g
What is the value of N?
Answer:
85
Step-by-step explanation:
Since the exterior angles of a triangle always add up to 360:
360 - 133 - 142 = 85
Step-by-step explanation:
all 3 indicated angles are outside angles of a triangle.
the sum of all outside angles of any polygon is 360°.
so,
N = 360 - 133 - 142 = 85°
A theater sold a total of 245,771 tickets last year.
They sold 52,669 child tickets.
The remaining tickets were adult tickets.
How many adult tickets were sold?
Answer:
193102
Step-by-step explanation:
245771-52669=193102
find all values of c in the open interval (a, b) such that f'(c)=(f(b)-f(a))/(b-a)
f(x)=√(4-x), [-5,4]
================================================
Work Shown:
Compute the function value at the endpoints
[tex]f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\[/tex]
With a = -5 and b = 4, we have
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\[/tex]
So,
[tex]f(x) = \sqrt{4-x}\\\\f'(x) = -\frac{1}{2\sqrt{4-x}}\\\\f'(c) = -\frac{1}{3}\\\\-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\[/tex]
Use algebra to solve for c
[tex]-\frac{1}{2\sqrt{4-c}} = -\frac{1}{3}\\\\\frac{1}{2\sqrt{4-c}} = \frac{1}{3}\\\\3 = 2\sqrt{4-c}\\\\2\sqrt{4-c} = 3\\\\\sqrt{4-c} = \frac{3}{2}\\\\4-c = \frac{9}{4}\\\\c = 4-\frac{9}{4}\\\\c = \frac{16-9}{4}\\\\c = \frac{7}{4}\\\\[/tex]
PLEASE HELP MEEEEE!!!!!
Answer:
The mass of 10mL of this liquid would be 25g.
Step-by-step explanation:
The formula for mass in relation to density and volume is:
mass=Density*volume
Knowing this, we could plug in the given volumes and solve:
m=Dv
m=(2.5g/mL)*(10mL)
m=25g
I hope this helps!
Mason had $24 to spend on 5 snacks. After buying them he had $4 left. How much did each snack cost?
Answer:
$4 each snack
Step-by-step explanation:
Answer:
x= 4.8
Step-by-step explanation:
5x = 24 and 24/5 = x
Which number on the number line shows the solution of 6x-12>-6?
Answer:
B
Step-by-step explanation:
We start by finding a solution to the linear inequality
6x-12 > -6
6x > -6 + 12
6x > 6
x > 6/6
x > 1
The correct number line is one with value at 1, facing the right and unshaded
3x + 4 = -11 what is the value of x in this equation?
Answer:
Step-by-step explanation:
3x + 4 = - 11
3x = - 11 - 4
3x = - 15
x = - 15/3
x = - 5
Answer:
x = -5
Step-by-step explanation:
3x + 4 = -11
Isolate 3x.
3x = -11 - 4
Evaluate.
3x = -15
Find x.
x = -15 ÷ 3
x = -5
simplify to create an equivalent expression 4(3x +2) - 7x
Answer:
5x + 8
Step-by-step explanation:
To create an equivalent expression, we are going to simplify the expression as far as we can. To do this, we are going to first distribute what we can.
1. 4(3x+2) -7x
2. Distribute the 4.
3. 12x + 8 - 7x
4. Combine like terms.
5. 12x - 7x = 5x
6. 5x + 8
Helpppppppppppppppppppppppppppppp Asapppppppppppppp
Answer:
x = 185
Step-by-step explanation:
Given:
Plan A
Fixed cost = $14.80
variable cost = 10 cents per min = $0.1 per minute
Plan B
Fixed cost = $18.50
variable cost = 8 cents per min = $0.08 per minute
Computation:
Assume
Plan A cost = Plan B cost
14.80 + 0.1x = 18.50 + 0.08x
x = 185
The points (9,4) and (7,w) fall on a line with a slope of 5. What is the value of w?
Answer:
-6Step-by-step explanation:
Equation .......[tex] \ slope\: = \frac{different \: \: in \: y}{different \: in \: x}[/tex]
So ,. [tex] \: \: \: \: \: \: \ \: \ \: \: \: \:5 = \frac{(y1 - y2)}{(x1 - x2)} [/tex][tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 = \frac{(4 - w)}{(9 - 7)} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 = \frac{4 - w}{2} [/tex]
5 × 2 = 4 - w 10 = 4 - w W = 4 - 10 W = -6 ..........Find the area with 12 and 4
Answer:
48
Step-by-step explanation:
The area is multiplying.
12 x 4 = 48
Hope It Helps
Sorry If I'm Wrong
6.
Write an equation of the line that passes through (3,8) and is perpendicular to the line y=5x−4.
Answer:
use desmos graphing and put (3,8) and y=5x-4 it help me
Which equation represents the linear function that is shown on the graph below ?
A. Y=1/2 x+4
B. Y=1/2 x-2
C. Y=4 x-2
D. Y= -2 x +4
Answer:
First one
Step-by-step explanation:
Y=1/2x+4
1. Name two angles that are supplementary to ∠DOE.
2. Name a pair of complementary angles.
3. Name two pairs of vertical angles.
Answer:
explain please and thank you