First picture)
I: 5x+2y=-4
II: -3x+2y=12
add I+(-1*II):
5x+2y-(-3x+2y)=-4-12
8x=-16
x=-2
insert x=-2 into I:
5*(-2)+2y=-4
-10+2y=-4
2y=6
y=3
(-2,3)
question 6)
I: totalcost=115=3*childs+5*adults
II: 33=adults+childs
33-adults=childs
insert childs into I:
115=3*(33-adults)+5*adults
115=99-3*adults+5*adults
16=2*adults
8=adults
insert adults into II:
33-8=childs
25=childs
so it's the last option
question 7)
a) y<6 and y>2 can also be written as 2<y<6, so solution 3 exist for example
b) y>6 and y>2 can also be written as 2<6<y, so solution 7 exist for example
c) y<6 and y<2 inverse of b: y<2<6, so for example 1
d) y>6 and y<2: y<2<6<y, this is impossible as y can be only either bigger or smaller than 2 or 6
so it's the last option
question 8)
I: x+y=12
II: x-y=6
subtract: I-II:
x+y-(x-y)=12-6
2y=6
y=3
insert y into I:
x+3=12
x=9
(9,3)
question 9)
I: x+y=6
II: x=y+5
if you take the x=y+5 definition of II and substitute it into I:
(y+5)+y=6
which is the second option :)
Answer:
3 1/2
Step-by-step explanation:
You have to do 7 divided by 2 or 1/2 x 7
<span>A) 2a + 3b = 12
B) ab = 6 solving for a
B) a = 6 / b then we substitute this into equation A)
</span><span>A) 12 / b + 3b = 12 </span><span>multiplying this by "b"
A) 12 + 3b^2 = 12b
A) 3b^2 -12b +12= 0 dividing by "3"
A) b^2 -4b + 4 = 0
Factoring
(b-2) * (b-2) = 0
b = 2
Since b = 2 then a = 3
</span>NOW, we put these numbers into:
<span>8a^3 +27b^3
</span>
8*3*3*3 + 27*2*2*2
216 + 216
The answer is 512
Answer: The answer would be f^-1 (x) = x/2 - 3/2
Answer:
f(2) = g(2)
General Formulas and Concepts:
<u>Alg I</u>
- Reading a Cartesian Plane
- Identifying Coordinates
- Solutions of systems of equations
Step-by-step explanation:
We see from the graph that f(x) and g(x) intersect at x = 2. Therefore, the point at x = 2 would be equivalent in both graphs/be a solution to both equations.
Therefore, f(2) must equal g(2), as they intersect each other at that point and have the same value of 0.
