The options you provided are unclear to me, so I will respond in general terms: to determine if a point (ordered pair) lies on a line, you need to substitute the x-value from that pair into the line's equation and check if the resulting y-value matches the y-value of the ordered pair. For example, if your line is y = 4/3x + 1/3, we can check if (0, 0) and (2, 3) fit this line. We find that y = 4/3·0 + 1/3 gives us 1/3, which does not equal 0, indicating (0, 0) is not on the line. For (2, 3), substituting yields y = 4/3·2 + 1/3 = 3, meaning (2, 3) is on the line.
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
The slope equals $0.10 (since $1.00 per 10 tokens translates to $0.10 per token)
The y-intercept is $60 (the fixed yearly membership fee)
The linear equation is y = 0.10x + 60 (following y = mx + b)
The domain consists of all x values where x ≥ 0 (negative token quantities are impossible)
The range includes all y values with y ≥ 60 (plugging the domain values into the function)
The y-intercept of this function stands at $60
Response:
Dimensions of the rectangular fence:
x = 14 ft
w = 7 ft
A = 98 ft²
Detailed explanation:
Dimensions of the rectangular fence:
x = length, and w = width
Then x = 2*w ⇒ w = x/2
Perimeter is
p = 2*x + 2*w
p = 2*x + 2* x/2
p = 2*x + x
3*x = 42
x = 14 ft and w = 14/2 ⇒ w = 7 ft
The number of layers is calculated as 2^7 = 128. The overall thickness is then 128 multiplied by 0.1, resulting in 12.8 mm. I hope this information is useful.
