What is the equation of the line passing through the points (2/5, 19/20) and (1/3, 11/12)in slope-intercept form?

Part 2: Use the information provided to write the vertex form equation of each parabola.

Serggg [28]

Answer: 1. x = -2(y - 4)² + 1

2. x = -y² + 5

3. y = -5(x + 1)² + 2

Step-by-step explanation:

Notes: The vertex formula of a parabola is x = a(y - k)² + h or y = a(x - h)² + k

(h, k) is the vertex
p is the distance from the vertex to the focus

$\bullet\quad a=\dfrac{1}{4p}$

1)

$\text{Vertex}=(1,4)\qquad \text{Focus}:\bigg(\dfrac{7}{8},4\bigg)\\\\\text{Given}: (h,k)=(1,4)\\\\\\p=focus-vertex=\dfrac{7}{8}-\dfrac{8}{8}=\dfrac{-1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{8})}=\dfrac{1}{-\frac{1}{2}}=-2$

Now input a = -2 and (h, k) = (1, 4) into the equation x = a(y - k)² + h

x = -2(y - 4)² + 1

***********************************************************************************

2)

$\text{Vertex}=(5,0)\qquad \text{Directrix}:x=\dfrac{21}{4}\\\\\text{Given}: (h,k)=(5,0)\\\\\\p=vertex-directrix=\dfrac{20}{4}-\dfrac{21}{4}=\dfrac{-1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{4})}=\dfrac{1}{-1}=-1$

Now input a = -1 and (h, k) = (5, 0) into the equation x = a(y - k)² + h

x = -1(y - 0)² + 5 → x = -y² + 5

***********************************************************************************

3)

$\text{Vertex}=(-1,2)\qquad \text{Directrix}:y=\dfrac{41}{20}\\\\\text{Given}: (h,k)=(-1,2)\\\\\\p=vertex-directrix=\dfrac{40}{20}-\dfrac{41}{20}=\dfrac{-1}{20}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{20})}=\dfrac{1}{-\frac{1}{5}}=-5$

Now input a = -5 and (h, k) = (-1, 2) into the equation y = a(x - h)² + k

y = -5(x + 1)² + 2

8 0

3 years ago

QUESTION 3 The probability that it will rain on a given day is 63%. A child has a 12% chance of falling in dry weather and is th

attashe74 [19]

Answer + Step-by-step explanation:

the probability that a child will not fall on any given day :

= (63 × 64 + 27 × 88) ÷ 100

= 64.08 %

the probability that a child will fall in dry weather :

= (27 × 12) ÷ 100

= 3.24 %

3 0

1 year ago

Choose the correct definition of a random variable from the list below. A random variable is O one whose values describe the out

kodGreya [7K]

Answer:

“A random variable is one whose values describe the outcome of some chance process”

Step-by-step explanation:

Roughly speaking, a random variable is a function whose values depend on outcomes of a random phenomenon.

The phenomenon could be an experiment created by human beings, a natural process or any other kind of event that produces results that cannot be foreseen with a deterministic model like a differential equation or formula of any kind.

The random variable must also be a measurable function.

Since its value cannot be predicted in a deterministic way, we usually approximate its possible values with probabilistic measures.

So, from the possible choices of answer, the one that fits the best is

“A random variable is one whose values describe the outcome of some chance process”

5 0

3 years ago

Shown in picture, PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Sidana [21]

Option 1 is the answer...

3 0

3 years ago

7 3/9 - 2 4/9 = 11 3/4 - 5 1/4 =

jeka57 [31]

1.)

$7 \frac{3}{9} - 2 \frac{4}{9} \\ = \frac{66}{9} - \frac{22}{9} \\ = \frac{44}{9} \\ = 4 \frac{8}{9}$

2.)

$11 \frac{3}{4} - 5 \frac{1}{4} \\ = \frac{47}{4} - \frac{21}{4} \\ = \frac{26}{4} \\ = \frac{13}{2} \\ = 6 \frac{1}{2}$

Hope it helps and is useful :)

6 0

3 years ago