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3 years ago

What is the solution?

Mathematics

1 answer:

Anika [276]3 years ago

5 0

Answer:

(1,-1)

Step-by-step explanation:

The solution is the point where the two lines intersect.

It is (1, -1)

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If x -9 is a factor of x^2 -5x-36 , what is the other factor ?

faust18 [17]

Answer:

(x + 4) (x - 9)

Step-by-step explanation:

Factor the following:

x^2 - 5 x - 36

The factors of -36 that sum to -5 are 4 and -9. So, x^2 - 5 x - 36 = (x + 4) (x - 9):

Answer: (x + 4) (x - 9)

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Simplify the expression csc(-x)/1+tan^2x)

Charra [1.4K]

Assuming ya meant $\frac{csc(-x)}{1+tan^2(x)}$

to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos

for the pythaogreaon identity
$cos^2(x)+sin^2(x)=1$
divide both sides by $cos^2(x)$
$1+tan^2(x)=sec^2(x)$ since $\frac{sin(x)}{cos(x)}=tan(x)$
subsitute
$\frac{csc(x)}{sec^2(x)}$

recall that $csc(x)=\frac{1}{cos(x)}$
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore $csc(-x)=\frac{1}{cos(-x)}=\frac{1}{cos(x)}=csc(x)$
so we get

$\frac{csc(x)}{sec^2(x)}$
decompose them into $\frac{1}{cos(x)}$ and $\frac{1}{sin^2(x)}$ to get $\frac{\frac{1}{cos(x)}}{\frac{1}{sin^2(x)}}$
multiply by $\frac{sin^2(x)}{sin^2(x)}$ to get
$\frac{sin^2(x)}{cos(x)}$
we can furthur simlify to get
$(\frac{sin(x)}{cos(x)})(sin(x))=tan(x)sin(x)$
the expression simplifies to tan(x)sin(x)

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