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3 years ago

What is the answer to both and how am i suposed to do it

Mathematics

1 answer:

Feliz [49]3 years ago

6 0

First you could switch the order of the numbers were the two fractions are that would now be 1/4 + 4/3(-12)
when you add 1/4 + 4/3 you would get 1 7/12. then you would do 1 7/12 x -12. Multiplying is easy just go straight across. but since its whole and mixed number you would put a one under the -12.

1 7/12 x -12 is -19

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The answer is 8/9

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Two members of the Math Competition Team solve 13 problems in 1 hour. Assume all team members solve problems at the same rate. H

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3 years ago

Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

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Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

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This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

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