Math Problems?

Question

(^2 means squared)
The graph of y=(x-3)^2 is shifted left 4 units and down 2 units. What is the axis of symmetry of the transformed graph?
A)x= -2 B)x=1 C)x= -1 D)x= 7



A company calculates its profit by finding the difference between revenue and cost. the cost function of producing x hammers is C(x)=4x+170. If each hammer is sold for $10, the revenue function for selling x hammers is R(x)=10x.
How many hammers must be sold to make a profit?
How many hammers must be sold to make a profit of $100.?

Solve system of equations algebraically: 9x^2+y^2=9
3x-y=3


whats the minimum point of the graph of the equation
y=2x^2+8x+9

These are the Qs I cant remember how to do
I forgot my notebook and my parents arent good @ math
help will be greatly appreciated!!

Answer 1

D) x = 7

10x > 4x + 170
6x > 170
x > 28.3, so 29 hammers

3x - y = 3 → y = 3x - 3, plug it in:
9x² + (3x - 3)² = 9
9x² + 9x² - 18x + 9 = 9
18x² - 18x = 0
x² - x = 0
x(x-1) = 0
x = 0, y = -3 ........ (0,-3)
or x = 1, y = 0 ...... (1,0)

y = 2x² + 8x + 9
line of symmetry at -8 / 2(2) = -2
y = 8 - 16 + 9 = 1
min point (-2,1)

Answer 2

1) Initially the axis is at x=3 so now the axis is shifted left 4 units and it will be at x= -1

2)suppose, the profit function is P(x)=R(x)-C(x)=6x-170
Now according to the problem, P(x)>0
so,6x-170>0
then x>170/6 or x>28.33=29

3) y=3(x-1) so 9x^2+9(x-1)^2=9
so, 2x^2-2x=0
so, x=1 or x=0

4) dy/dx= 4x+8
putting dy/dx=0 we get, x= -2
putting x= -2 in the given eqn we get, y(min)=1
so the min point is (-2,1)



AND Philo's FIRST ANSWER IS WRONG