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Nitella [24]
3 years ago
6

Which points represent a solution to the system graphed below? Select all that apply.

Mathematics
1 answer:
ira [324]3 years ago
7 0
I think the answer would be 0,7 and 4, 2 but I am not 100 percent sure
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Cos^2 x+4sin^2 x/2=1
lana [24]

Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2

=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2

\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}

6 0
3 years ago
Is this correct? Why or why not? 06 = 60%​
WARRIOR [948]

0.6

you forgot the decimal point

60% move the decimal one time to the left

5 0
3 years ago
Read 2 more answers
If p(x)=2x^2-4x and q(x)=x-3 what is (p*q)(x)
Tanya [424]

Answer: 2x³-10x²+12x or 2x(x²-5x+6)

Step-by-step explanation:

(p*q)(x) means p(x) and q(x) multiplied together.

(2x²-4x)(x-3)

2x³-6x²-4x²+12x

2x³-10x²+12x

You can also factor this by taking out a 2x.

2x(x²-5x+6)

4 0
3 years ago
Solve for t: d=rt. I need some help.
Elena L [17]
D = rt
/r    /r

D/r = T

*sample text*

7 0
3 years ago
Read 2 more answers
The median salary for the Dallas Cowboys was $441,300 in 2000 and $1,326,720 in 2008. Write a linear equation giving the median
maksim [4K]

 

The linear equation that is asked from the problem takes the form of:

y = m x + b

where,

y = the median salary

x = the number of years

m = the slope of equation

b = y-intercept

 

The slope of the equation (m) can be calculated using the formula:

m = (y2 – y1) / (x2 – x1)

m = (1326720 – 441300) / (2008 – 2000)

m = 110,677.5

 

The y-intercept is then obtained by using any of the data pair:

441300 = 110677.5 (2000) + b

b = -220913700

 

Therefore the complete equation is:

y = 110677.5 x – 220913700

 

The median salary in 2016 is therefore:

y = 110677.5 (2016) – 220913700

y = $2,212,140



Answer: 

$2,212,140

4 0
4 years ago
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