Answer: Downhill:10mph Uphill:5mph
Step-by-step explanation:
We are looking for Dennis’s downhill speed.
Let
r=
Dennis’s downhill speed.
His uphill speed is
5
miles per hour slower.
Let
r−5=
Dennis’s uphill speed.
Enter the rates into the chart. The distance is the same in both directions,
20
miles.
Since
D=rt
, we solve for
t
and get
t=
D
r
.
We divide the distance by the rate in each row and place the expression in the time column.
Rate
×
Time
=
Distance
Downhill
r
20
r
20
Uphill
r−5
20
r−5
20
Write a word sentence about the time.
The total time traveled was
6
hours.
Translate the sentence to get the equation.
20
r
+
20
r−5
=6
Solve.
20(r−5)+20(r)
40r−100
0
0
0
=
=
=
=
=
6(r)(r−5)
6
r
2
−30r
6
r
2
−70r+100
2(3
r
2
−35r+50)
2(3r−5)(r−10)
Use the Zero Product Property.
(r−10)=0
r=10
(3r−5)=0
r=
5
3
The solution
5
3
is unreasonable because
5
3
−5=−
10
3
and his uphill speed cannot be negative. So, Dennis's downhill speed is
10
mph and his uphill speed is
10−5=5
mph.
Check. Is
10
mph a reasonable speed for biking downhill? Yes.
Downhill:
10 mph
5 mph⋅
20 miles
5 mph
=20 miles
Uphill:
10−5=5 mph
(10−5) mph⋅
20 miles
10−5 mph
=20 miles
The total time traveled was
6
hours.
Dennis’ downhill speed was
10
mph and his uphill speed was
5
mph.
Answer:
{x = -3
, y=2 (Isolved for both variables be elimination)
Step-by-step explanation:
Solve the following system:
{3 x + 5 y = 1 | (equation 1)
7 x + 4 y = -13 | (equation 2)
Swap equation 1 with equation 2:
{7 x + 4 y = -13 | (equation 1)
3 x + 5 y = 1 | (equation 2)
Subtract 3/7 × (equation 1) from equation 2:
{7 x + 4 y = -13 | (equation 1)
0 x+(23 y)/7 = 46/7 | (equation 2)
Multiply equation 2 by 7/23:
{7 x + 4 y = -13 | (equation 1)
0 x+y = 2 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{7 x+0 y = -21 | (equation 1)
0 x+y = 2 | (equation 2)
Divide equation 1 by 7:
{x+0 y = -3 | (equation 1)
0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = -3
, y=2
The question is asking to states the plot the could represent the data in the table, and base on my further research and understanding the table, the answer would be <span>A dot plot line labeled Ice Cream and titled Ice Cream Flavors. Four tick marks labeled Chocolate, Pistachio, Strawberry, and Vanilla. I hope this would help </span>
