$2\cos\left(2x+\dfrac{\pi}{4}\right)=\sqrt2\qquad\text{divide both sides by 2}\\\\\cos\left(2x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\to2x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+2k\pi\\\\2x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+2k\pi\ \vee\ 2x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+2k\pi\qquad\text{subtract}\ \dfrac{\pi}{4}\ \text{from all sides}\\\\2x=-\dfrac{2\pi}{4}+2k\pi\ \vee\ 2x=2k\pi\qquad\text{divide all sides by 2}\\\\x=-\dfrac{\pi}{4}+k\pi\ \vee\ x=k\pi\ \text{for}\ k\in\mathbb{Z}$

5 0

4 years ago

Your teacher is giving a test worth 100 points containing 40 questions. There are two point and four point questions on the tes.

BaLLatris [955]

Let x = questions with 2 points and y = questions with 4 points;
We solve the equation: x + y = 40 and 2x + 4y = 100;
Then, x = 40 - y;
2( 40 - y ) + 4y = 100;
80 - 2y + 4y = 100;
80 + 2y = 100;
2y = 20;
y = 10;
x = 40 - 10;
x = 30;

4 0

4 years ago

Read 2 more answers

Write an equation for the line that passes through (-4,-6) and has a slope of 7/8

Elina [12.6K]

I think answer is y=7/8x-5/2

5 0

3 years ago

On Monday, 400 students went on a trip to the zoo. All 9

Marat540 [252]

Answer:

44 students per bus

Step-by-step explanation:

400-4= 396.

396/9=44

3 0

3 years ago