Answer:#1
if corresponding angles are congruent
#2
if alternate interior angles are congruent
#3
if consecutive, or same side, interior angles are supplementary
#4
if two lines are parallel to the same line
#5
if two lines are perpendicular to the same line
#6
if alternate exterior angles are congruent
2 = 2(-3) + 8
2 = -6 + 8
2 = 2
true.
2 = 3 + 1
2 = 4
false.
this is not a solution because both equations have to be true.
Answer:
15
Step-by-step explanation:
Answer:
<u>Proportion:</u>
<u>4/15 = 20/75</u>
<u>Sam will bike 37.5 km after 10 days.</u>
Step-by-step explanation:
1. Let's review the information given to answer the question correctly.
Number of days Sam has gone to work biking = 4
Amount of kilometers Sam has logged on his bike = 15
2. a. Set up a proportion to solve the amount of km he will log after 10 days on the bike.
Number of days Sam has gone to work biking = 4
Amount of kilometers Sam has logged on his bike = 15
2. a. Set up a proportion to solve the amount of km he will log after 10 days on the bike.
4/15 = 20/75
b. Solve for the amount of km in part (a).
Let's use the proportion, this way:
20/75 = 10/x
20x = 75 * 10
20x = 750
x = 750/20
x = 37.5
<u>Sam will bike 37.5 km after 10 days.</u>
2ty'=4y
Replacing y'=dy/dt in the equation:
2t(dy/dt)=4y
Grouping terms:
dy/y=4dt/(2t)
dy/y=2dt/t
Integrating both sides:
ln(y)=2ln(t)+ln(c), where c is a constant
Using property logarithm: b ln(a) = ln(a^b), with b=2 and a=t
ln(y)=ln(t^2)+ln(c)
Using property of logarithm: ln(a)+ln(b) = ln(ab), with a=t^2 and b=c
ln(y)=ln(ct^2)
Then:
y=ct^2
Using the initial condition: y(2)=-8
t=2→y=-8→c(2)^2=-8→c(4)=-8
Solving for c:
c=-8/4
c=-2
Then the solution is y=-2t^2
Comparing with the solution: y=ct^r
c=-2, r=2
Answer: T<span>he value of the constant c is -2 (c=-2) and the exponent r is 2 (r=2)</span>
