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3 years ago

What is the focal length of the parabola with equation shown below?

1 answer:

4 0

Patterns: vertical : y = a(x - h)² + k horizontal: x = a(y - k)² + h

Look at the patterns above and remember these key points.

1) if the x is squared, the parabola is vertical. It either opens up or down. 
if the y is squared, the parabola is horizontal. It either opens left or right.

2) if a is positive, the parabola opens up or to the right.
if a is negative, the parabola opens down or to the left

3) the vertex is at (h,k). Be very careful. locations of h and k varies if the parabola is vertical or horizontal. its sign is also different in those positions

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Determine the equation of each line

katovenus [111]

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

(a)

here m = - $\frac{3}{4}$ and c = 6, hence

y = - $\frac{3}{4}$ x + 6 ← equation of line

(b)

here m = 6, hence

y = 6x + c ← is the partial equation

to find c substitute (2, - 6 ) into the partial equation

- 6 = 12 + c ⇒ c = - 6 - 12 = - 18

y = 6x - 18 ← equation of line

(c)

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 3) and (x₂, y₂ ) = (4, 7)

m = $\frac{7-3}{4+1}$ = $\frac{4}{5}$ , hence

y = $\frac{4}{5}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 3 ), then

3 = - $\frac{4}{5}$ + c → c = 3 + $\frac{4}{5}$ = $\frac{19}{5}$

y = $\frac{4}{5}$ x + $\frac{19}{5}$ ← equation of line

3 0

3 years ago

- What is g(x)= -4(x - 5)2 + 8 in standard form

Ulleksa [173]

Answer:

g(x) = -8x + 48

4 0

2 years ago

Who can help to develop and solve an algebraic equation for this question?

mixer [17]

Answer:

25 mins

Step-by-step explanation:

Harpeet worked -- x mins

Aiysha worked -- 2x mins

If Aiysha worked 50 mins, Harpeet worked:

2x = 50

x = 25 mins

Thenks and mark me brainliest :))

3 0

3 years ago

What is the definition of constant

Pie

Answer: If you mean the math definiton then a quantity or parameter that does not change its value whatever the value of the variables, under a given set of conditions.

7 0

3 years ago

Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 53 ve

kari74 [83]

21 cars, 32 motorcycles.
create a system of equations using x for cars and y for motorcycles.
$\left \{ {{x+y=53} \atop {4x+2y=148}} \right.$
multiply the top equation by 2 to prepare for elimination method
$\left \{ {{2x+2y=106} \atop {4x+2y=148}} \right.$
subtract terms
$\left \{ {{2x+2y=106} \atop {-4x-2y=-148}} \right. = (-2x = -42)$
divide both sides by negative 2 to solve for x
x =21
plug in x into original equation to solve for y.
21 + y = 53
subtract both sides by 21
y=32

8 0

3 years ago