Which is the focus of a parabola with equation y2=-12x
Answers
y²=-12x
the vertex is the point (0,0)------------- > see the attached figure
standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
vertex(0,0)
4p=-12---- > p=-12/4
p=-3
Focus:(-3,0)
the answer is (-3,0)
Related Questions
Evaluate the function for
f(x) = x + 3 and g(x) = x2 − 2.
(f − g)(0)
(f − g)(0) =
Answers
To evaluate (f - g)(0), find f(0) and g(0) for the functions f(x) = x + 3 and g(x) = x^2 - 2, and then subtract the latter from the former. For f(0) we have 3, and for g(0) we have -2. Subtracting, we get (f - g)(0) = 5.
Explanation:To evaluate the expression (f - g)(0), it means we need to find the value of the function f at x = 0, subtract the value of the function g at x = 0, and combine them. Given the functions f(x) = x + 3 and g(x) = x^2 − 2, let's calculate their values at x = 0:
For f(x), we have f(0) = 0 + 3 = 3For g(x), we have g(0) = (0)^2 − 2 = 0 − 2 = −2Now, let's subtract g(0) from f(0):
(f - g)(0) = f(0) - g(0) = 3 - (-2) = 3 + 2 = 5
Therefore, the value of (f - g)(0) is 5.
helppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
The first thing we are going to do is decompose the numbers 16 and 54 into prime factors:
[tex]16=2^{4} [/tex] and [tex]54=(2)(3^{3} )[/tex]
Now we are going to separate each term into cubes:
[tex]2 ^{4} =(2)(2^{3} )[/tex]
[tex]x ^{6} =( x^{3} )( x^{3} )[/tex]
[tex]y^{5} =(y^{2})(y^{3} ) [/tex]
After that we can rewrite the expression:
[tex]2( \sqrt[3]{(2)(2^{3})x^{3}y }) +4( \sqrt[3]{(2)( 3^{3})( x^{3})( x^{3})(y^{2})(y^3}) } )[/tex]
Finally we can take out the cubes and simplify:
[tex]2(2)(x) \sqrt[3]{2y} +4(3)(x)(x)(y) \sqrt[3]{2 y^{2} } [/tex]
[tex]4x \sqrt[3]{2y} +12 x^{2} y \sqrt[3]{2 y^{2} } [/tex]
The first choice, [tex]4x \sqrt[3]{2y} +12 x^{2} y \sqrt[3]{2 y^{2} } [/tex], is the correct answer.
2[(16x³y)^(1/3)]+4[(54x³x³y³y²)^(1/3)]
2[(2³2x³y)^(1/3)]+4[(3³2x³x³y³y²)^(1/3)]
2[2x(2y)^(1/3)]+4[3x²y(2y)^(1/3)]
4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
the answer is the option A) 4x[(2y)^(1/3)]+12x²y[(2y)^(1/3)]
Using graph paper graph the following equation then click on the graph until the correct one is display. 3x-y-1=0
Answers
3x-y-1=0-------------------> y=3x-1
using a graph tool
see the attached figure
the x-intercept is the point (0.333,0)
the y-intercept is the point (0,-1)
the slope is m=3
The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.
Further explanation:
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The equation is [tex]3x - y - 1 = 0.[/tex]
Explanation:
The given equation is [tex]3x - y - 1 = 0.[/tex]
Solve the equation to obtain the standard form.
[tex]\begin{aligned}3x - y - 1&= 0\\y&= 3x - 1\\\end{aligned}[/tex]
Compare [tex]y = 3x - 1[/tex] to the standard equation [tex]y= mx + c.[/tex]
The slope of the line is 3 and the y-intercept is -1.
Substitute 0 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y &= 3 \times 0 - 1\\y&= 0 - 1\\y&= - 1\\\end{aligned}[/tex]
Substitute 1 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y&= 3 \times 1 - 1\\y&= 3 - 1\\y&= 2\\\end{aligned}[/tex]
Substitute 2 for [tex]x[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y&= 3 \times 2 - 1\\y&= 6 - 1\\y&= 5\\\end{aligned}[/tex]
The graph of the equation [tex]3x - y - 1 = 0[/tex] is attached below.
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445.Learn more about equation of circle brainly.com/question/1506955.Learn more about range and domain of the function https://brainly.com/question/3412497Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
What is the sum of the geometric series
Answers
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256
The polygons are similar. Find the value of x
Answers
big side/ small side = big side / small side
16/12 = x-1 / 6
Simplify
4/3 = x-1 / 6
multiply both sides by 6
24/3 = x-1
simplify
8 = x - 1
add 1 to both sides
9 = x
Hope this helps
A publisher pays 6% royalty to a book writer for the first 1,000 copies sold, and 5% on any number of copies above 1,000. They will print 3,000 copies. Find the sale price of the book if the writer expects to be paid $5,000.
Answers
What is Y=x^2+6x+4 in vertex form?
Answers
Starting time 2:15 elapsed time 45 minutes
Answers
which number is a common factor of 32,48,and 80?
Answers
Answer:
Step-by-step explanation:
The GCF is found by listing the factors of all the numbers and picking the largest one that occurs in each. The factors of your numbers are as follows:
32: 1, 2, 4, 8, 16, 32
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Looking at those factors you can pick out anything you'd like: all the common factors, the greatest common factors, whatever you need.
Final answer:
The number 16 is a common factor of 32, 48, and 80, as it is the only number among the options given that divides evenly into all three numbers.
Explanation:
To find a common factor of 32, 48, and 80, we need to identify a number that divides evenly into all three numbers. A systematic way to do this is to list out the factors of each number and see which ones they have in common.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
From these lists, we see that the numbers 1, 2, 4, 8, and 16 are common factors of all three numbers. However, among the options provided (3, 9, 10, 16), 16 is the only number that appears in all lists and is therefore a common factor of 32, 48, and 80.
Need help on 8,9,10,11 and 12
Answers
[tex]0.3x=12 \\ \\ x = 40[/tex].
The answer is 40.
9) 45% of 20 is [tex]0.45(20)=9[/tex].
The answer is 9.
10) 18 is [tex](18/30 = 60)[/tex]% of 30.
The answer is 60%.
11) 56 is 80% of some number x. We write
[tex]0.8x=56 \\ \\ x = 70[/tex].
The answer is 70.
12) If the total cost on an item that costs $4.00 is $4.32, then the tax is 32¢. We want to find the percent of the total 4 that is .32. [tex] \frac{0.32}{4} = 0.08=8[/tex]%.
The answer is 8%.
Eli and Karl each throw a basketball straight up in the air at the same time. Eli is standing on a deck and the height of his ball, in meters, is given by the function f(x)=−4.9x2+12x+2.5 , where x is the number of seconds after the ball is released from his hands.
Karl is standing on the ground and the height of his ball, in meters, is given by the function g(x)=−4.9x2+14x , where x is the number of seconds after the ball is released from his hands.
There is a moment when the basketballs are at the same height.
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.
Answers
Answer:
Just took the K12 quiz, and like killdrone said in the comments, the correct answer is 9.8 m
Step-by-step explanation:
The height at which both basketballs are at the same height is approximately 16.3 meters.
Explanation:To find the moment when the basketballs are at the same height, we need to find the common height value for both functions.
Setting the functions equal to each other, we get: -4.9x^2 + 12x + 2.5 = -4.9x^2 + 14x
Simplifying the equation, we get 2x = 2.5, which means x = 1.25.
Substituting this value back into the original function for Eli, we get f(1.25) = -4.9(1.25)^2 + 12(1.25) + 2.5 = 16.325
Therefore, the height at which both basketballs are at the same height is approximately 16.3 meters.
please someone help me on this
Brainliest available :)
Answers
Find the exact volume of the cylinder.
Answers
Suppose Karel wants to be the least expensive babysitter in the neighborhood. How much should she charge?
Suppose Karel wants to charge the same hourly rate as most of the other baby-sitters. How much should she charge?
Suppose Karel wants her hourly rate to be higher than the rate of half of other baby-sitters, but lower than the hourly rate of the rest of the babysitters. How much should she charge?
In addition to the babysitting rates charged by others, what might Karel consider when she sets her rates?
Answers
B. She should charge $2.75 if she wants to charge what most other sitters are charged because this amount occurs more than any other(the mode).
C. She should also charge $2.75 if she wants to be in the middle (median).
D. When deciding on a rate, Karel should also consider if there are any rates that are a lot lower or a lot higher because there might be a reason (more kids, unusual hours, relatives, etc...).
To be the least expensive babysitter, Karel should charge less than $2.00. If she wants her hourly rate to be higher than half the babysitters but lower than the other half, she could charge slightly less than $2.75. Beyond these rates, Karel should consider factors like her own experience, the specific tasks she'll perform, and the hours she'll work.
Explanation:To determine how much Karel should charge for her babysitting services, we need to consider the other babysitting rates and find the midpoint. The other students charge the following amounts: Stephanie-$2.75, Jessica-$2.00, Michael-$3.00, Raoul -$2.50, Rolanda-$2.75, Harry -$2.25, Samuel-$2.25, Anita-$2.75.
To be the least expensive, Karel should charge less than the lowest rate, which is $2.00 charged by Jessica. So, Karel could charge $1.75, for example.
Now, suppose Karel wants to have an hourly rate higher than half the babysitters but lower than the other half. We need to organize the rates in ascending order, and then find the median value. If we do this, we find that the middle value (the median) is $2.75. Therefore, Karel could charge slightly less than this, for example, $2.70.
Lastly, Karel should also consider other factors when setting her rates. These might include her experience and skills as a babysitter, the average babysitting rates in her neighborhood or city, the specific tasks she'll be expected to perform, and the hours she'll be working.
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Which graphic organizer would help you visualize important events in the history of the U.S. space program? timeline point-by-point diagram cause-and-effect chart Venn diagram
Answers
Answer with explanation:
If we have to visualize important events in the history of the U.S. space program, we have to keep following things in mind
Year Program
19... Satellite A
19.. On Moon ....
.... ............
...... .........
So, while scaling , we will keep year , that is time on any of the axis and program on another axis.
→→The Appropriate option will be
(a) Time line
Help me please !!!!!!!
Sandy is observing the velocity of a runner at different times.
After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. Part B: How can you graph the equations obtained in Part A for the first 4 hours?
Answers
Use the given times and velocities to make two points: (1,4) and (2,2)
Part A:
Slope is the change in Y over the change in X from the two pints you made:
Slope = (2-4) / (2-1 )= -2
Now you have the slope, calculate the Y-intercept
y = -2x + b
Using (1,4)
4 = -2(1) + b = 4 =-2 +b. b = 6
Equation is: y = -2x+6
Part B:
using the above equation replace x with 1, 2, 3, and 4 and solve for the Y
then plot those onto a graph
Which transformations can be used to show that circle P is similar to circle Q?
Circle P: center (2, −3) and radius 4
Circle Q: center (2, 3) and radius 28
.
Select each correct answer.
Circle Q is a translation of circle P, 6 units up.
Circle P is a dilation of circle Q with a scale factor of 24.
Circle Q is a translation of circle P, 6 units left.
Circle Q is a dilation of circle P with a scale factor of 7.
Answers
Similar figures can result when a figure is translated (moved or slid) to a different position or when it remains the same shape but in a different size (dilation).
Answer: The answer is below i am in k12 just took the test
Circle Q is a dilation of circle P with a scale factor of 7. "
Circle Q is a translation of circle P, 6 units up.
Step-by-step explanation:
Which is the graph of the system x + 3y > –3 and y < 1/2x + 1?
Answers
The y-intercept of the second inequality is +1.
The fourth graph has these correct.
The answer to this question is D.
What is the sum of −3x+6 and 7x−8 ?
Answers
Answer:
-80
Step-by-step explanation:
If the radius of a circle is 14 ft, then the diameter of the circle is _____.
A.) 7 ft
B.) 28 ft
C.) 42 ft
D.) 87.92 ft
Answers
[tex]14 \times 2 = 28[/tex]
its B.) 28ft
Diameter to radius= 28÷2= 14 radius
When given the radius, multiply it by 2 to get the diameter.
ANSWER: B) 28 feet
Hope this helps! :)
How do you write 50% as a fraction or whole number in simplest form?
Answers
because 2/4 is equivalent to 1/2 50% is 1/2
which of the following is a radical equation? 1. x+sqrt(5)=12 2. x^2=16 3. 3+xsqrt(7)=13 4. 7sqrt(x)=14
Answers
Answer:
4. [tex]7\sqrt{x}=14[/tex]
Step-by-step explanation:
Radical equation is a equation that has a variable under the radical .
From the given options we have radical square root
We need to choose an option that has a variable under the square root.
1.[tex]x+\sqrt{5}=12[/tex]
This equation has 5 under the radical square root. Variable is outside, So this is not a radical equation.
2. x^2=16
Here there is not radical . So this is not a radical equation.
3. [tex]3+x\sqrt{7}=13[/tex]
This equation has 7 under the radical square root. Variable is outside, So this is not a radical equation.
4. [tex]7\sqrt{x}=14[/tex]
This equation has x under the radical square root. So this is a radical equation.
Donna Bakes biscuits on a rectangular cookie sheet that is 30 centimeters by 50 centimeters.Each biscuit had a diameterof 8 centimeters. What is the maximum number of biscuits donna can make on the sheet at once on the cookie sheet.
Answers
Donna can make a maximum of 94 biscuits on the rectangular cookie sheet at once.
Explanation:To find the maximum number of biscuits Donna can make on the rectangular cookie sheet, we need to calculate the area of the sheet and divide it by the area of each biscuit.
The area of the sheet is given by length x width, so it is 30 cm x 50 cm = 1500 cm².
The area of each biscuit is given by πr², where r is the radius (half the diameter) of the biscuit. In this case, the radius is 8 cm / 2 = 4 cm. So the area of each biscuit is π x 4 cm x 4 cm = 16π cm².
To find the maximum number of biscuits, we divide the area of the sheet by the area of each biscuit:
Maximum number of biscuits = Area of the sheet / Area of each biscuit = 1500 cm² / 16π cm² ≈ 94.25 biscuits.
Since we can't have a fraction of a biscuit, the maximum number of biscuits that Donna can make on the sheet at once is 94 biscuits.
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You want to measure the length of a ribbon in inches. You only have a centimeter ruler. The length of the ribbon is 16 cm. Is the ribbon longer or shorter than 16 inches? How many inches long is it?
Answers
Answer- it will be shorter than 16 inches. !6 centimeters to the inch is 6.29921 inches
Alvin financed $3,450 to buy a new car. If he made 36 payments of $138.50 each, how much interest did he pay on the loan? a. $153.60 b. $415.50 c. $1,536 d. $4,986
Answers
Multiply 138.50 by 36. (4,986)
Then, subtract 4,986 by 3,450.
A rectangular playground is 888 meters wide. It is 333 times as long as it is wide.What is the area of the playground?
Answers
The required area of the playground is given as, 192 square meters.
Given that,
A rectangular playground is 888 meters wide. It is 333 times as long as it is wide. The area of the playground is to be determined.
Surface area is defined as the measure of a region or surface is called as surface area.
Here,
The area of the playground = l × w
As mentioned in the question,
l = 3w = 3 × 8 = 24
Area = 24 × 8
Area = 192 square meters.
Thus, the required area of the playground is given as, 192 square meters.
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A certain animated movie earned $1.1 * 10^9 in revenues at the box office. The movie lasts 9.1*10^1 minutes. How much revenue was earned per minute of the movie?
Answers
To find the revenue per minute of the movie, divide the total revenue ( [tex]\$1.1 \times 10^9[/tex]) by the length of the movie ( [tex]9.1 * 10^1[/tex]). The trick is to divide the numerical portions and the power of ten portions separately. The answer is approximately [tex]\$1.20879 \times 10^7[/tex] per minute.
Explanation:The subject of this question is mathematics and it involves a concept called division in scientific notation. To find the revenue per minute for this movie, we'll divide the total earnings ($1.1 * 109) by the length of the movie in minutes (9.1 * 101).
Step 1: Place the two values with scientific notation over each other, akin to a typical division problem. This means $1.1 * 109 / 9.1 * 101.
Step 2: Divide the two numerical portions separately from the power of ten portions. This is dividing 1.1 by 9.1 and 109 by 101.
Step 3: The former (from step 2) gives you approximately 0.120879 and the latter simplifies to 108 (because when you divide with the same base, you subtract the exponents).
So the earnings per minute of this movie were approximately $0.120879 * 108, or $1.20879 * 107.
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16 POINTS. Find x and y intercepts and show work.
I’m looking for number six.
Answers
y = (x^4 - 3x^3 + 4x)^2
y = x^2(x^3 - 3x^2 + 4)^2
Go to Wolframalpha and put the above equation into the input line.
You see that there are 2 solutions at -1
There are 2 solutions at 0
There are 2 solutions at 2
You know that there are 2 solutions for each because the graph just touches the x axis. I wouldn't both to try and solve this thing using algebra.
that's what the graph would leave you to believe. There are 2 other solutions and they must be imaginary.
Note to moderator. Wolfram dot com just shows graphs. the work is mine and I'm just using a tool to explain my answer.
Find the lateral area and the total area of the prism.
27 sq. ft.
36 sq. ft.
54 sq. ft.
Answers
1) the lateral area----------------> L=P*h
P=(3+3+3) h=6
L=(3+3+3)*6=54 in²
the answer part 1) is the lateral area is 54 in²
2) the total area=------------- > S=P*h+2B
2B=2*[3*3/2] P*h=54
S=2*[3*3/2]+54=63 in²
the answer part 2) is the total area is 63 in²
Answer:
54 sq. ft.
Step-by-step explanation:
LA=ph or in other words Lateral Area= base perimeter * height
The perimeter of the base is 9 because 3+3+3=9.
The height is 6. So 6 * 9 = 54
Which graph shows a system of equations with a solution at (–1, 1)?
Answers
Answer:- The second graph shows a system of equations with a solution at (–1, 1) .
Explanation:-
In the given pictures we have different lines intersecting parabola .
Given point is (-1,1) ,here x coordinate is negative and y coordinate is positive , which happen only in second quadrant of a Cartesian plane.
In graph 1 , there are two intersection points and none of them lie in the second quadrant. In graph 2 , there are two intersection points and one of them lie in the second quadrant and that is (-1,1). Therefore it shows a system of equations with a solution at (–1, 1) .In graph 3 , there are two intersection points and none of them lie in the second quadrant. In graph 4 , there are two intersection points and none of them lie in the second quadrant.