To solve these mathematical problems, let’s analyze each part of the given function and the values we need to find.
Given the function:
[tex]\[ h(x) = |1 - 7x| \][/tex]
Let's tackle each point step-by-step.
10. Calculate [tex]\( h(l) \)[/tex]
For this step, we assume that [tex]\( l = 1 \)[/tex].
[tex]\[ h(l) = h(1) = |1 - 7 \cdot 1| \][/tex]
[tex]\[ h(1) = |1 - 7| \][/tex]
[tex]\[ h(1) = |-6| \][/tex]
Since the absolute value of [tex]\(-6\)[/tex] is [tex]\(6\)[/tex]:
[tex]\[ h(1) = 6 \][/tex]
Thus, [tex]\( h(l) = 6 \)[/tex].
11. Calculate [tex]\( h(-7) \)[/tex]
Next, we need to find [tex]\( h(-7) \)[/tex].
[tex]\[ h(-7) = |1 - 7 \cdot (-7)| \][/tex]
[tex]\[ h(-7) = |1 + 49| \][/tex]
[tex]\[ h(-7) = |50| \][/tex]
Since the absolute value of [tex]\(50\)[/tex] is [tex]\(50\)[/tex]:
[tex]\[ h(-7) = 50 \][/tex]
Thus, [tex]\( h(-7) = 50 \)[/tex].
12. Calculate [tex]\( 23 - h(9) \)[/tex]
Finally, solve for [tex]\( 23 - h(9) \)[/tex].
[tex]\[ h(9) = |1 - 7 \cdot 9| \][/tex]
[tex]\[ h(9) = |1 - 63| \][/tex]
[tex]\[ h(9) = |-62| \][/tex]
Since the absolute value of [tex]\(-62\)[/tex] is [tex]\(62\)[/tex]:
[tex]\[ h(9) = 62 \][/tex]
Now, calculate [tex]\( 23 - h(9) \)[/tex]:
[tex]\[ 23 - h(9) = 23 - 62 \][/tex]
[tex]\[ 23 - 62 = -39 \][/tex]
Thus, the expression [tex]\( 23 - h(9) \)[/tex] evaluates to [tex]\(-39\)[/tex].
Therefore, the values are:
- [tex]\( h(l) = 6 \)[/tex]
- [tex]\( h(-7) = 50 \)[/tex]
- [tex]\( 23 - h(9) = -39 \)[/tex]
