Answer: (6, 7) x = 6
y = 7
Isolate x in the first equation.
2x = 12 Divide by 2 to both sides
x = 6 Isolated x!
Substitute in (6) for x in the second equation.
(6) - 5y = -29 Remove parenthesises
6 - 5y = -29 Subtract 6 from both sides
-5y = -35 Divide by -5 to both sides
y = 7 Isolated y!
With x = 6 and y = 7:
(6, 7)
The formula is
I=prt
I interest earned 90
P amount invested?
R interest rate 0.04
T time 6/12
Solve the formula for p
P=I÷rt
P=90÷(0.04×(6÷12))
P=4,500 ....answer
6.
Josef receives 3$ per hour spent doing chores. So, after x hours of chores, he receives 3x dollars. This money must be added to the 10$ he would receive no matter what, so the total expression is

7.
We can test the options against the given patterns: in pattern 1, we have one black hexagon and 6 white hexagons. Let's see which equations fit: if we substitute b=1 and w=6 we have:
A)
- ok
B)
- wrong
C)
- ok
D)
- wrong
E)
- wrong
So, the only feasible answers are A or C, because all the other functions don't fit even the first pattern. Let's test the two survivors for pattern 2: we have two black hexagons and 8 white hexagons. Plugging b=2 and w=8 into A and C we have
A)
- wrong
C)
- ok
So, the answer is C, because it models correctly pattern 2 as well. For the sake of completeness, let's test this function against pattern 3 as well: we have 3 black and 10 white hexagons. Plugging b=3 and w=10 into C we have
C)
- ok
So, C models correctly all patterns, and thus describe the general rule.
Answer:
f(x) = -x^2 - 6x - 10
Step-by-step explanation:
Please write the original equation as f(x) = -(x + 3)2 - 1, as "(x + 3)2 is meaningless. We want:
f(x) = -(x + 3)^2 - 1, where " ^ " denotes exponentiation.
Expanding this, we get:
f(x) = -(x^2 + 6x + 9) - 1, or
f(x) = -x^2 - 6x - 9 - 1, or:
f(x) = -x^2 - 6x - 10 This matches the first answer choice.