Response:
Detailed explanation:
The final result is 3 /8/33.
step by step breakdown
Initially, we write:
x
=
3
.
¯¯¯¯
24
After that, we will multiply each side by
100
leading to:
100
x
=
324
.
¯¯¯¯
24
Subsequently, we will subtract the first equation from the second equation:
100
x
−
x
=
324
.
¯¯¯¯
24
−
3
.
¯¯¯¯
24
We can then solve for
x
in the following manner:
100
x
−
1
x
=
(
324
+
0
.
¯¯¯¯
24
)
−
(
3
+
0
.
¯¯¯¯
24
)
(
100
−
1
)
x
=
324
+
0
.
¯¯¯¯
24
−
3
−
0
.
¯¯¯¯
24
99
x
=
(
324
−
3
)
+
(
0
.
¯¯¯¯
24
−
0
.
¯¯¯¯
24
)
99
x
=
321
+
0
99
x
=
321
99
x
99
=
321
99
99
x
99
=
3
×
107
3
×
33
x
=
3
×
107
3
×
33
x
=
107
33
Next, we convert this improper fraction to a mixed numeral:
x
=
107
33
=
99
+
8
33
=
99
33
+
8
33
=
3
+
8
33
=
3
8
33
3
.
¯¯¯¯
=
3
8
33
Response:
9.55 minutes
Step-by-step breakdown:
x hours to reach the river
0.25-x hours for the return trip, as 15 minutes equals 0.25 hr.
to the river 40 mph * x hours =40x miles
from the river 70 mph (0.25-x) hours=17.5-70x
these two equations are equivalent
40x=17.5-70x
110x=17.5
x=17.5/110=0.159 hours
9.55 minutes
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
9 45
10 55
11 66
12 78
13 91
14 105
15 120
16 136
17 153
18 171
19 190
20 210
21 231
22 253
23 276
24 300
Here’s a chart to aid in understanding the staircase issue. Observe that for 1 step, there is 1 block; for 2 steps, 3 blocks; for 3 steps, 6 blocks, and so forth. Note that the blocks corresponding to each step are a combination of that step and all the blocks used in the steps beneath it. For instance, constructing 14 steps requires 105 blocks.
If you’re familiar with summation, you would sum the blocks for each step with all the steps below it. For example, 5 steps would require 5 + 4 + 3 + 2 + 1, resulting in a total of 15 blocks. I hope this helps you begin. As for the second part, I'm confused by the problems since they don't represent equations. NO equal signs
glad if it helps
