<h3>
Answer: y = 5x + 7</h3>
Work Shown:
y - y1 = m(x - x1)
y - (-3) = 5(x - (-2))
y + 3 = 5(x + 2)
y + 3 = 5x + 10
y = 5x + 10 - 3
y = 5x + 7
The equation is now in slope intercept form y = mx+b with m = 5 as the slope and b = 7 as the y intercept. Plugging x = -2 into this equation will lead to y = -3.
Side note: parallel lines have equal slopes but different y intercepts.
The question is what numbers satisfy A ∩ C.
The symbol ∩ means intersection, .i.e. you need to find the numbers that belong to both sets A and C. Those numbers might belong to the set C or not, because that is not a restriction.
Then lets find the numbers that belong to both sets, A and C.
Set A: perfect squares from A to 100:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
=> A = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
Set C: perfect fourths
1^4 = 1
2^4 = 16
3^4 = 81
C = {1, 16, 81?
As you see, all the perfect fourths are perfect squares, so the intersection of A and C is completed included in A. this is:
A ∩ C = C or A ∩ C = 1, 16, 81
On the other hand, the perfect cubes are:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 81
B = {1, 8, 27, 81}
That means that the numbers 1 and 81 belong to the three sets, A, B, and C.
In the drawing you must place the number 16 inside the region that represents the intersection of A and C only, and the numbers 1 and 81 inside the intersection of the three sets A, B and C.
Okay. To find the miles per gallon of B, we have to divide 100 by 2.6. 100/2.6 is 38.4615385 or about 38.5 miles per gallon when rounded to the nearest tenth. Car B goes approx. 38.5 miles per gallon.
Answer:
-4a²+4a³
Step-by-step explanation:
