Answer:
The value of a = 14
Step-by-step explanation:
Given
(x₁, y₁) = (2, 4)
(x₂, y₂) = (6, a)
(x₃, y₃) = (-1, 1)
A = 9 sq.units
Area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:
substituting the values (x₁, y₁) = (2, 4), (x₂, y₂) = (6, a), (x₃, y₃) = (-1, 1), A = 9 in th formula
Multiply both sides by 2
simplify
As the area is always positive.
so
Add 18 to both sides
simplify
Divide both sides by 3
Thus, the value of a = 14
m = the number of miles
30 + 0.18m ≤ 75
[They charge $30 plus $0.18 per mile(m), she can spend no more than $75. So $75 is the maximum/most she can spend, she can't spend over $75.]
Your answer is C
Now you need to find the solution of the inequality in order to graph it.
30 + 0.18m ≤ 75 Isolate "m". Subtract 30 on both sides
0.18m ≤ 45 Divide 0.18 on both sides
m ≤ 250 [this means that she can drive 250 miles on $75]
Next you need to graph it on a number line.
When the sign is ≤ or ≥, the dot is filled in
When the sign is < or >, the dot is an open circle/not filled in
m ≤ 250 [m is less than or equal to 250, so m can be 250 or any number less than 250]
The graph shows that she can only drive 250 miles or less on $75
