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2 years ago

The The point (2,6) is on the line given by which equation below?

Mathematics

1 answer:

maria [59]2 years ago

3 0

Answer:

A y = 3x

Step-by-step explanation:

We can check each line to see if the point is on it

A y = 3x 6 = 2*3 6=6 this is true so the point is one the line

B y = 4-x 6 = 2-4 6 = -2 false

C y = -3x 6 = -3(2) 6=-6 false

D y =-x+4 6 = -2+4 6 = 2 false

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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

5 months ago

4.89 gallons of milk is sold for $12.79. If you have $21.44 in your wallet. How many

Mariulka [41]

Answer:

You can buy 8.18 gallons of milk.

Step-by-step explanation:

12.79/4.89 = 2.62

21.44/2.62 = 8.18

5 0

2 years ago

Solve this linear equation for p.

Fynjy0 [20]

Answer:

11.2

Step-by-step explanation:

divide 160 by 14.3

6 0

2 years ago

Read 2 more answers

Which value of x is in the solution set of -3X+8≥14? ) A. -3 B. -1 C. 0 D. 3

romanna [79]

Answer:

Step-by-step explanation:

Solving for x:

-3x + 8 ≥ 14

-3x ≥ 6

x ≤ -2

Notice the sign gets reversed when you divide or multiply by a negative number.

The only option less than -2 is -3, A.

Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation. This can save time on tests like the SAT or ACT.

Let's try it:

-3(-3) + 8 = 9 + 8 = 17

-3(-1) + 8 = 3 + 8 = 11

-3(0) + 8 = 0 + 8 = 8

-3(3) + 8 = -9 + 8 = -1

So you can see the answer is A.

7 0

2 years ago

? the coordinates of a, b, c, and d are a (-6, 1), b (-9, 4), c (-1, 1), and d (-7, 6). how are ab←→ and cd←→ related? they are

balandron [24]

AB :
(-6,1)(-9,4)
slope = (4 - 1) / (-9 - (-6) = 3 / -3 = - 1

CD:
(-1,1)(-7,6)
slope = (6 - 1) / (-7 - (-1) = -5/6

different slopes....slopes are not negative reciprocals...means they are not perpendicular, parallel, or coincident. These lines will intersect at one point.

4 0

2 years ago