Answer:
4v+3+5v+6=180(being linear pair)
9v+9=180
9v=180-9
v=171/9
v=19
Step-by-step explanation:
Answer: Approximately 390,244 people per square mile
Work Shown:
Density = population/area
Density = (8 million people)/(20.5 square miles)
Density = 390,243.9024 approximately
This rounds to 390,244 since we're talking about the number of people.
Answer:
8.75h = 50
Step-by-step explanation:
h is the number of hours Thomas needs to groom the dogs.
The rate is $8.75 per hour.
His goal is $50.
$8.75 × h = $50
$8.75h = $50
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
Answer: 142°
Step-by-step explanation:
∡BAC= 38°
∡BAN= 180°-38° = 142°
