Answer:
Step-by-step explanation:
1.
(a) n ≤ 21
(b) n ≥ 5
(c) n > 3/5
2.
(d) n < 14
(e) n ≥ 14
Answer:
B
Step-by-step explanation:
parallel lines have the same gradient,
and for y = 3x-2; m= 3
Answer:
Step-by-step explanation:
Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.
The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.
The system is
6h + 1d = 40
4h + 3d = 36
The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,
1d = 40 - 6h.
Now that we know what d equals, we can sub it into the second equation where we see a d. In order,
4h + 3d = 36 becomes
4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!
4h + 120 - 18h = 36 and
-14h = -84 so
h = 6.
That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:
1d = 40 - 6(6) and
d = 40 - 36 so
d = 4.
That means that each duck costs $4.
2x-15=3(x-15)
2x-15=3x-45
2x+30=3x
30=x
Let's check this work!
2(30)-15=3(30-15)
60-15=3(15)
45=45
She worked 45 hours each week
*the reason it is 2x-15 and not 15+2x is because "more than" is considered a "turn around word" meaning it is the opposite
Answer:
a) 910
b) 828100
c) 144320
Step-by-step explanation:
a. ∑y
This is the sum of all values of y. So
b. (∑y)^2
This is the square of the sum, so the square of 910, that we found in the previous item.
910² = 828100
c. ∑y^2
This is the sum of the squares of each amount spent. So
