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Pavlova-9 [17]
4 years ago
15

HELP 30 POINTS!!!!!!!!!!!!!!!!!!!!! Please explain this!!!

Mathematics
2 answers:
finlep [7]4 years ago
7 0

First, multiply the first equation by 3 to get:

3x+3y=-6

Then, add the two equations together to get

8x=16

We can follow that x=2. Plugging in x=2, we get that y=-4.

Therefore, the solution of (2,-4)

Lynna [10]4 years ago
5 0

Answer:

[2, -4]

Step-by-step explanation:

{y + x = -2

{5x - 3y = 22

-⅕[5x - 3y = 22]

{y + x = -2

{-x + ⅗y = -4⅖

_______________

1⅗y = -6⅖

____ ____

1⅗ 1⅗

y = -4 [Plug this back into both equations above to get the x-coordinate of 2]; 2 = x

I am joyous to assist you anytime.

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4 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5
DanielleElmas [232]

Answer:

1

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that csc(x)=1/sin(x) and sec(x)=1/cos(x).

Thus:

\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}

=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }

Let's do the first part first: (Recall how to divide fractions)

\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}

For the second term:

\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}

So, all together: (same denominator; combine terms)

\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}

Note the numerator; it can be derived from the Pythagorean Identity:

sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)

Thus, we can substitute the numerator:

\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1

Everything simplifies to 1.

7 0
3 years ago
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