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e-lub [12.9K]
3 years ago
9

Please help me with this question I also need to see the steps if possible!

Mathematics
1 answer:
umka21 [38]3 years ago
4 0

Hi there!

To solve, we must use the following trig identity:

sin(u - v) = sin(u)cos(v) - sin(v)cos(u)

We can rewrite the left hand side of the equation as:

\frac{sin(u)cos(v)-sin(v)cos(u)}{sin(u)cos(v)}

Split the fraction:

\frac{sin(u)cos(v)}{sin(u)cos(v)} - \frac{sin(v)cos(u)}{sin(u)cos(v)} =

First fraction reduces to 1:

1 - \frac{sin(v)cos(u)}{sin(u)cos(v)} =

Simpify each with common arguments:

1 - tan(v)cot(u)

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Answer:

Answers are in bold

Step-by-step explanation:

<u></u>

<u>Part 1A</u>

Use the Zero Product Property to find the x-intercepts:

0=-(x+4)(x-1)

0=(x+4)(x-1)

0=(x+4)

-4=x

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For the y-intercepts, plug in x=0:

f(x)=-(0+4)(0-1)

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f(x)=4

So the y-intercept is y=4 which is also (0,4)

<u>Part 1B</u>

In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k

For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:

f(x)=-(x+4)(x-1)

f(x)=-(x^2+3x-4)

f(x)=-x^2-3x+4

So now we know a=-1 and b=-3, therefore we can plug them in:

x=-b/2a

x=-(-3)/2(-1)

x=3/-2

x=-3/2

x=-1.5

So the equation of the axis of symmetry is x=-1.5

<u>Part 1C</u>

We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:

f(x)=-(-1.5+4)(-1.5+1)

f(x)=-(2.5)(-0.5)

f(x)=-(-1.25)

f(x)=1.25 <-- y-coordinate

So the coordinates of the vertex are (-1.5,1.25)

<u>Part 1D</u>

See the image below

I'll let someone else do the last 4 questions as I am unable to answer them.

<u></u>

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What information is found in the left column of a two column proof?
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The left column is for statements and the right column is for reasons which justify the corresponding statement. 

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