Answer:
C. Ari and Matthew collide at 4.8 seconds.
Explanation:
Ari and Matthew will collide when they have the same x and y position. Since Ari's path is given by
x(t) = 36 + (1/6)t
y(t) = 24 + (1/8)t
And Matthew's path is given by
x(t) = 32 + (1/4)t
y(t) = 18 + (1/4)t
We need to make x(t) equal for both, so we need to solve the following equation
Ari's x(t) = Matthew's x(t)
36 + (1/6)t = 32 + (1/4)t
Solving for t, we get
36 + (1/6)t - (1/6)t = 32 + (1/4)t - (1/6)t
36 = 32 + (1/12)t
36 - 32 = 32 + (1/12)t - 32
4 = (1/12)t
12(4) = 12(1/12)t
48 = t
It means that after 48 tenths of seconds, Ari and Mattew have the same x-position. To know if they have the same y-position, we need to replace t = 48 on both equations for y(t)
Ari's y position
y(t) = 24 + (1/8)t
y(t) = 24 + (1/8)(48)
y(t) = 24 + 6
y(t) = 30
Matthew's y position
y(t) = 18 + (1/4)t
y(t) = 18 + (1/4)(48)
y(t) = 18 + 12
y(t) = 30
Therefore, at 48 tenths of a second, Ari and Mattew have the same x and y position. So, the answer is
C. Ari and Matthew collide at 4.8 seconds.
Step-by-step explanation:
1. ∠2 and ∠5 are supplementary
This is the information that was given in the problem statement.
2. ∠3 ≅ ∠2
∠2 and ∠3 are vertical angles, and therefore congruent.
3. ∠3 and ∠5 are supplementary
By combining statements 1 and 2, we can show through substitution that ∠3 and ∠5 are supplementary.
4. l || m
∠3 and ∠5 are consecutive interior angles. By the converse of consecutive interior angles theorem, if consecutive interior angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
Answer:
1/84
Step-by-step explanation:
3+2+1+3 = 9
3/9 × 2/8 × 1/7 = 1/84
= 0.0119047619
= 0.0119 (3 sf)
Answer:
J all rational numbers are real numbers
Step-by-step explanation:
(46.6 -47)/4 = -1
(47.4-47)/4 = 1
So, +/- 1 std, that is 95% So, (D)!
