which is the directrix of parabola with equation x^2=4y
Answer:
[tex]y=-1[/tex]
Step-by-step explanation:
We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.
First of all, we will divide both sides of our given equation by 4.
[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]
[tex]\frac{x^2}{4}=y[/tex]
[tex]y=\frac{x^2}{4}[/tex]
Now, we will compare our equation with vertex form of parabola:
[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.
We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].
Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].
Substituting the value of a in above formula, we will get:
[tex]p=\frac{1}{4*\frac{1}{4}}[/tex]
[tex]p=\frac{1}{1}=1[/tex]
We know that directrix of parabola is [tex]y=k-p[/tex].
Substituting the value of k and p in above formula, we will get:
[tex]y=0-1[/tex]
[tex]y=-1[/tex]
Therefore, the directrix of our given parabola is [tex]y=-1[/tex].
A function that can be written in the form f(x)=ax2+bx+c, where a, b & c are real numbers and a is not equal to zero.
A quadratic function seems to be a second-order polynomial function. Another quadratic function has the following general form:
[tex]f (x) = ax^2 + bx + c[/tex]here,
a, b, and c = real numbersand,
a ≠ 0The quadratic formula is obtained by completing the square on some kind of quadratic equation instead in the standard format. Because the largest power equals two, it is indeed a 2nd-degree polynomial equation.
As a result, the aforementioned response is correct.
Learn more about quadratic equation here:
https://brainly.com/question/19942005
50 points! Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled, and the sum of their outcomes is found. Each player gets a chance to guess the correct sum, and the player that guesses the correct sum wins the game.
Dustin decides to guess a sum of six. Melanie decides to guess a sum of seven.
Which player made the better decision? ________
Answer:
Melanie is the right answer
Step-by-step explanation:
Melanie made the better decision if Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
If the sum is 6:
The possible outcomes are = {(3,3), (2,4), (4,2), (1,5), and (5,1)}
Total outcomes = 5
If the sum is 7:
The possible outcomes are = {(1,6), (6,1), (5,2),( 2,5), (3, 4), (4,3)}
Total outcomes = 7
Thus, Melanie made the better decision if Dustin and Melanie are playing a game, where two standards, six-sided number cubes are rolled.
Learn more about the probability here:
brainly.com/question/11234923
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two positive integers have a sum of 17 and a product of 66
If there are 15 girls and 9 boys in an art class, the ____________ of girls to boys in the class is 5:3.
Describe the vertical asymptotes and holes for the graph of y=x-4/x^2+3x+2,
at 4:00 am,there were 800,000 gallons of water remaining at a reservoir.after 4 hours of irrigation,there were 100,000 gallons of water remaining.write an equation that describes the number of gallons of water as a function of the time the field has been irrigated
Rewrite the radical exponent as a radical
a/an ______ angle measures less than 90degrees°, a/an ______ angle measures 90degrees°, a/an ______ angle measures more than 90degrees° and less than 180degrees°, and a/an ______ angle measures 180degrees°.
Using the law of cosines, in triangle RST, if r=14 yd, s=9 yd, t=16 yd find m angle s
Help? Thank you
What is the perimeter of the triangle expressed as a polynomial? 8x-2 5x-4 9x-3
The shorter leg of a right triangle is 1414 feet less than the other leg. find the length of the two legs if the hypotenuse is 3434 feet.
Solve this easy question and get points!!!
There are two trains. Both trains are going to the same place, taking the same stops, and are going the exact same speed. But one train arrives in
80 Mins and the other train arrives in 1 Hour and 20 Mins. How is this possible?
What is the solution of log6x+log6(x+5)=2?
Answer:4
Step-by-step explanation:just did it on edge
To solve log6(x) + log6(x + 5) = 2, combine the logarithms, rewrite in exponential form, and solve the resulting quadratic equation. The solutions are x = -9 and x = 4, but since logarithms of negative numbers are undefined, the final answer is x = 4.
To solve this logarithmic equation, follow these steps:
Combine the logarithms: Use the property of logarithms that states logb(a) + logb(c) = logb(a × c).Final Answer: x = 4.
Use the data to create a scatter plot.
Size (lb)
8
12
9.5
5
7
7.5
Time (h)
5
6.5
4
3.5
2
5
Which of the symbols correctly relates the two numbers below? Check all that apply.
55 ? 35
A.
B.
C. <
D.
E. =
F. >
The other symbols dont want to show so if its another on plz tell me or add me on fb if you guys wanna help me i need to finish this,
Describe the graph of the following inequality: 2x - 5y ≤ 6
To graph the inequality 2x - 5y ≤ 6, plot the line 2x - 5y = 6 with a solid boundary, test a point to determine the solution region, and shade the region that satisfies the inequality, which is below and to the right of the boundary line.
Explanation:To graph the inequality 2x - 5y ≤ 6, you must first draw the boundary line of the inequality. This line is created by graphing the equation 2x - 5y = 6.
Start by finding the intercepts. For the x-intercept, set y to 0 and solve for x, which gives x = 3. For the y-intercept, set x to 0 and solve for y, which gives y = -6/5. These two points can be used to draw the boundary line. Since the inequality is '≤', this line will be solid to show that points on the line satisfy the inequality.
Now you must determine which side of the line contains the solutions to the inequality. You can do this by choosing a test point that is not on the line, like (0,0). Substitute this point into the inequality: 2(0) - 5(0) ≤ 6 is true, so the area containing (0,0), which is below and to the right of the line, is the solution region. Shade this area to show all points that satisfy the inequality 2x - 5y ≤ 6.
what is the answer to f(2)=2-5(2)
when does a rhombus have 4 congruent angles?
How long would it take to travel 630 miles at the rate of 35 miles per hour? 18 h 35 h 220 h 350 h
Answer:
18h
Step-by-step explanation:
Factor completely. x^2−3x−40
To factor the quadratic expression x² -3x -40, we find that the expression factors into (x - 8)(x + 5).
The question involves factoring the quadratic expression x² -3x -40 completely. To factor this expression, we look for two numbers that multiply to -40 and add to -3. The numbers that meet these conditions are -8 and 5, since
(-8) * 5 = -40 and
(-8) + 5 = -3.
Therefore, the expression can be factored into (x - 8)(x + 5).
Jade is painting a rectangular wall. The wall is 414 yards long and 223 yards high.The formula for the area of a rectangle is A=bh. What is the area of the wall?
The formula for the area of the rectangle is actually A = LW. The length of the rectangular wall is 414 yards while its width is 223 yards. To compute for its area, you just have to follow the formula:
A = 414 (223)
A = 92,322 yards^2
Therefore, the area of the wall is 92,322 square yards.
Answer:
hey the answer is 11 1/3
Step-by-step explanation:
ive taken the quiz and this is the answer 100%
) the length of a rectangle is 5 cm less than twice the width. if the area of the rectangle is 88 , find the dimensions of the rectangle.
A line includes the points (2, 10) and (1, 4). what is its equation in slope-intercept form?
If the measurement of a central angle is 77 degrees find the length of its intercepted arc in a circle with a radius of 15 inches.
Answer:
20.2 inches ;)
Step-by-step explanation:
In a tessellation, what must the sum of the angles be where the vertices meet?
90° 180° 360° 60°
In a billiards game, Pete hits a ball that is 20in. from a wall. The ball travels 34 in. until it hits the wall and bounces to a position that is 16 in. from the wall. What proportion can be used to find the distance, x, the ball traveled after it bounces off the wall to get to the ending position? CHECK ALL THAT APPLY!
options
34/x =20/16
20/16 = 34/x
16/20 = x/34
20/16 = x/34
To find the distance the ball traveled after it bounces off the wall, we can use the proportion 34/x = 20/16, which simplifies to x = 27.2 inches.
To find the proportion that can be used to find the distance, x, the ball traveled after it bounces off the wall, we can use the equation:
34/x = 20/16
After cross multiplying, we get:
34 × 16 = 20x
Simplifying further:
544 = 20x
Dividing both sides by 20, we find:
x = 27.2
Therefore, the distance the ball traveled after it bounces off the wall is 27.2 inches.
How do you determine whether to draw the boundary line of the graph of a linear inequality dashed or solid?
What is the average of the first n positive even numbers?
Solution:
we have been asked to find the average of the first n positive even numbers.
Let the firm n positive even numbers be
[tex] 2,4,6,8,10,12,.........2(n-1), 2n [/tex]
As we know that average of numbers[tex] =\frac{\text{Sum of Numbers }}{Total number of Numbers}\\ [/tex]
Required Average[tex] =\frac{2+4+6+2(n-1)+2n}{n}\\ [/tex]
Required Average[tex] =\frac{2(1+2+3+....+(n-1)+n)}{n} [/tex]
As we know the sum of first n terms[tex] =\frac{n(n+1)}{2} [/tex]
Required Average[tex] =\frac{2n(n+1)}{2n}=n+1 \\ [/tex]
In a class, every student knows French or German (or both). 15 students know French, and 17 students know German. What is the largest possible number of students in that class?
Solution:
we are given that
In a class, every student knows French or German (or both).
15 students know French, and 17 students know German.
Suppose there are x student who knows both French and German.
Then Total number of student in the class will be [tex] (15+17-x)=32-x [/tex]
But to guess the largest possible number of student in the class we can assume x=0
Hence the largest Possible number of Student in the class=32