Are 3x + 5 and 2x + 15 + x - 5 equivalent? Explain how you know.

A parabola can be drawn given a focus of (−6,−1) and a directrix of y=1. Write the equation of the parabola in any form.

kkurt [141]

Answer:

y = -(x + 6)²/4

Step-by-step explanation:

Since the equation of a parabola is given as the distance of a point to a given point(focus) being equal to the distance of the point fro a given line (directrix),

and our focus is at (-6,-1) and our directrix is y = 1, then by the distance equation, the distance from each point to the point (x, y) is

√[(x - x)² + (y - 1)²] = √[(x - (-6))² + (y - (-1))²]

√[0² + (y - 1)²] = √[(x + 6)² + (y + 1)²]

√(y² -2y + 1) = √[(x² + 12x + 36) + (y² + 2y + 1)]

squaring both sides, we have

y² - 2y + 1 = x² + 12x + 36 + y² + 2y + 1

collecting like terms, we have

y² - 2y - y² - 2y = x² + 12x + 36 + 1 - 1

simplifying, we have

- 4y = x² + 12x + 36

factorizing the expression in x, we have

-4y = (x + 6)²

y = -(x + 6)²/4

3 0

3 years ago

If parallelogram ABCD was reflected over the y-axis ,reflected over the x-axis, and rotated 180 where would point A’ lie?

Nesterboy [21]

The answer to this would be parentheses zero, -2 parentheses

5 0

3 years ago

Under typical conditions, 1 <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D" id="TexFormula1" title="\frac{1}{2}" alt="\

damaskus [11]

Answer:

2 $\frac{1}{3}$ inches

Step-by-step explanation:

First, I would try to get the mixed numbers into improper fractions. Then, I try to make them have the same denominator so it is easier.

1 $\frac{1}{2}$ feet --- 2 inches

$\frac{3}{2}$ feet --- 2 inches

$\frac{6}{4}$ feet --- 2 inches

1 $\frac{3}{4}$ feet --- ? inches

$\frac{7}{4}$ feet --- ? inches

$\frac{7}{4}$ feet --- $\frac{7}{6}$ × 2 inches

= 2 $\frac{1}{3}$ inches

3 0

3 years ago

0.98x0.23 what is 0.98 times 0.23?

fomenos

Answer:

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Step-by-step explanation:

3 0

3 years ago

Enter the value of x that makes the equation −11(x + 4) + 10x = 27 true

lara31 [8.8K]

Answer:

x = - 71

Step-by-step explanation:

-11x -44 + 10 x =27

-x = 71

x = - 71

4 0

3 years ago

Read 2 more answers