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3 years ago

Find the standard form of the equation of the parabola with the given characteristics. Vertex: (-6, 1); focus: (-6, 0)

Mathematics

1 answer:

GREYUIT [131]3 years ago

8 0

Answer: $(x+6)^2=-4(y-1)$

Step-by-step explanation:

Given

Vertex of the parabola $(-6,1)$

Focus of the parabola $(-6,0)$

As the x coordinate of vertex and focus is same and focus lie below the vertex, therefore the parabola is the type of

$(x+6)^2=-4a(y-1)$

distance between Vertex and focus is 1 unit

$\therefore a=1$

Parabola becomes

$\Rightarrow (x+6)^2=-4(y-1)$

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There are 6 red marbles 4 blue marbles to yellow marbles. Sabrina picks 2 marbles without putting the first one back what is the

Yanka [14]

Answer:

P = 3/11

Step-by-step explanation:

There are:

6 red marbles

4 blue marbles

2 yellow marbles.

So there are a total of 12 marbles in the bag, such that each one has the same probability of being randomly picked.

We want to find the probability that the first pick is not yellow (so it can be either blue or red), and the second pick is a blue marble.

Now there are two cases.

The first marble is red and the second blue

the first marble is blue and the second blue

We need to find the probability in each case.

The probability that the first marble is red is equal to the quotient between the number of red marbles (6) and the total number of marbles (12)

p = 6/12

Now, for the second draw, we need a blue marble, the probability in this case is the quotient between the number of blue marbles (4) and the total number of marbles in the bag (now there are 11, because one is already taken)

q = 4/11

The joint probability is equal to the product of the individual probabilities, then:

P₁ = p*q = (6/12)*(4/11) = 2/11

And for the other case, we draw two blue marbles:

For the first draw, the probability is:

p = 4/12

And for the second draw, now there are 3 blue marbles and 11 total marbles, then the probability is:

q = 3/11

The joint probability is:

P₂ = (4/12)*(3/11) = 1/11

The total probability is then:

P = P₁ + P₂ = 2/11 + 1/11 = 3/11

4 0

3 years ago

On a piece of paper, use a protractor to construct a triangle with angle measures of 50° and 70º.

Firlakuza [10]

Hello my Kings and Queens the answer would be 60 degrees because all angles of a triangle always add up to 180 degrees

7 0

3 years ago

Read 2 more answers

E B 30 24 25 20 А 15 с D 18 F The scale factor is

Finger [1]

Answer:

5:6

Step-by-step explanation:

20/4=5

24/4=6

20:24 ratio simplified is 5:6

sorry if wrong

3 0

2 years ago

Distance between parallel lines y=3x+10 and y=3x-20

Alecsey [184]

1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).

2. Use formula $d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$ to find the distance from point $(x_0,y_0)$ to the line Ax+By+C=0.

The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:

$d=\dfrac{|3\cdot 0-10-20|}{\sqrt{3^2+(-1)^2}}=\dfrac{30}{\sqrt{10}}=3\sqrt{10}$ .

3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.

Answer: $d=3\sqrt{10}$ .

4 0

3 years ago

a line with a slope of 3 passes through the point (2,5) write an equation for this line in point-slope form.

Bingel [31]

Answer:

Point Slope: y - 5 = 3 (x-2)

Slope Intercept : y=3x-1

Step-by-step explanation:

1.) y - 5= 3(x-2)

2.) y - 5 = 3x-6

3.) y=3x-1

4 0

3 years ago