IX - 4I ≤ 4
Step-by-step explanation:
The number line indicates that the possible values of x fall within the range:
0 ≤ x ≤ 8
We aim to create an absolute value equation to encompass this set of potential solutions.
An example of such an equation is:
IX - 4I ≤ 4
To form this, we find the midpoint M of our set, which is 4 in this case.
Then, we write:
Ix - MI ≤ IMI
It's important to note my use of the inclusive sign, as the filled dots indicate that the endpoints x = 0 and x = 8 are part of the solution, differing from empty dots which denote an open set requiring < > signs.
The equation that demonstrates a proportional relationship, maintaining a constant of proportionality equal to 14, is: Here, and are proportional with a constant of proportionality of 14.
Response:
The width of the arch measures 105 meters
Detailed explanation:
The function that describes the width of the arch is
f(x) = -0.016(x - 52.5)² + 45
where x denotes the horizontal distance from the left end of the arch or the width at its base
f(x) indicates the vertical height of the arch
According to the given quadratic equation, the vertex coordinates of the parabola are (52.5, 45).
The vertex coordinates indicate that
the arch's height is 45 meters
and half the horizontal span from the left end is 52.5 meters
Therefore, the bridge's total width is calculated as 2 times the half span from the left side, which is 2 × 52.5
resulting in 105 meters
Consequently, the bridge's width is 105 meters.
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
