Prove that the inequality |cos(x)| is greater than or equals to 1 - sin^2 (x)

x  

2

+y  

2

+2xy=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x  

2

+2yx+y  

2

=0

This equation is in standard form: ax  

2

+bx+c=0. Substitute 1 for a, 2y for b, and y  

2

 for c in the quadratic formula,  

2a

−b±  

b  

2

−4ac

​  

​  

.

x=  

2

−2y±  

(2y)  

2

−4y  

2

​  

​  

Square 2y.

x=  

2

−2y±  

4y  

2

−4y  

2

​  

​  

Add 4y  

2

 to −4y  

2

.

x=  

2

−2y±  

0

​  

​  

Take the square root of 0.

x=−  

2

2y

​  

Divide −2y by 2.

x=−y

x  

2

+y  

2

+2xy=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

y  

2

+2xy+x  

2

=0

This equation is in standard form: ax  

2

+bx+c=0. Substitute 1 for a, 2x for b, and x  

2

 for c in the quadratic formula,  

2a

−b±  

b  

2

−4ac

​  

​  

.

y=  

2

−2x±  

(2x)  

2

−4x  

2

​  

​  

Square 2x.

y=  

2

−2x±  

4x  

2

−4x  

2

​  

​  

Add 4x  

2

 to −4x  

2

.

y=  

2

−2x±  

0

​  

​  

Take the square root of 0.

y=−  

2

2x

​  

Divide −2x by 2.

y=−x

Step-by-step explanation:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!