At the end of the year, Juan has 52.71 more than 4 times his balance at the beginning. Okay, let's set this up.

4x + 52.71
(4 times) (52.71 more)
His ending was 172.90, so
4x + 52.71=172.90
4x= 120.19
x= 30.05
He had $30.05 at the beginning of the year.

8 0

4 years ago

Solve the system of equations. 2y+7x=−5 5y−7x=12

3241004551 [841]

We can solve this by substitution method.

Look at the second equation. If we rearrange to find 7x, we can substitute in the value into the first equation.

$5y-7x=12$

$5y-7x-12=0$

$5y-12=7x$

Therefore, $7x=5y-12$

Now replace the 7x in the first equation with 5y - 12:

$2y+7x=-5$ (substitute in 7x = 5y - 12)

$2y+(5y-12)=-5$

$7y-12=-5$

$7y=7$

$y=1$

Now that we know y, we can find x by substituting in y = 1 into any equation we want. I will use the equation: 7x = 5y - 12

$7x=5y-12$ (substitute in y = 1)

$7x=5(1) -12$

$5x=5-12$

$7x=-7$

$x=-1$

__________________________________________________________

Answer:

$y=1\\x=-1$

4 0

3 years ago

Anybody know the right answer?

Dmitry_Shevchenko [17]

If we just have

$y = \cos x$

that's an amplitude of 1 and a period of $2\pi$

Let's modify this step by step.

Amplitude of 4. Four times the amplitude means a factor of 4 on the outside.

$y = 4 \cos x$

Period of π. Double the period means a factor of 2 on the inside.

$y = 4 \cos(2x)$

Horizontal shift of π/2 to the left. To the left means adding a positive number to x. The question appear ambiguous. It's not clear to me if we add to x or 2x; let's make it

$y = 4 \cos(2(x + \frac \pi 2))$