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To find the value of the expression [tex]\(\sqrt{a^3 - 7} + |b|\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[ a^3 = 2^3 = 8 \][/tex]
2. Substitute [tex]\(a^3\)[/tex] into the expression [tex]\(a^3 - 7\)[/tex]:
[tex]\[ a^3 - 7 = 8 - 7 = 1 \][/tex]
3. Find the square root of [tex]\(1\)[/tex]:
[tex]\[ \sqrt{1} = 1.0 \][/tex]
4. Calculate the absolute value of [tex]\(b\)[/tex]:
[tex]\[ |b| = |-4| = 4 \][/tex]
5. Add the results from step 3 and step 4:
[tex]\[ 1.0 + 4 = 5.0 \][/tex]
Therefore, the value of the expression when [tex]\(a=2\)[/tex] and [tex]\(b=-4\)[/tex] is [tex]\(5.0\)[/tex].
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[ a^3 = 2^3 = 8 \][/tex]
2. Substitute [tex]\(a^3\)[/tex] into the expression [tex]\(a^3 - 7\)[/tex]:
[tex]\[ a^3 - 7 = 8 - 7 = 1 \][/tex]
3. Find the square root of [tex]\(1\)[/tex]:
[tex]\[ \sqrt{1} = 1.0 \][/tex]
4. Calculate the absolute value of [tex]\(b\)[/tex]:
[tex]\[ |b| = |-4| = 4 \][/tex]
5. Add the results from step 3 and step 4:
[tex]\[ 1.0 + 4 = 5.0 \][/tex]
Therefore, the value of the expression when [tex]\(a=2\)[/tex] and [tex]\(b=-4\)[/tex] is [tex]\(5.0\)[/tex].
Answer: 5
Step-by-step explanation:
First, plug in the numerical values of the variables and rewrite the equation:
[tex]\sqrt{a^{3} - 7 } +|b|[/tex] = [tex]\sqrt{2^{3} - 7 } +|-4|[/tex]
Next, solve for the equation under the radical [tex](\sqrt{ } )[/tex] symbol:
[tex]\sqrt{2^{3} - 7 } = \sqrt{8 - 7 } = \sqrt{1}[/tex] = 1
The equation is now [tex]1+ |-4|[/tex]
Absolute value is distance between a number and zero. It is represented by | n |, where n is a positive or negative integer. To learn more about absolute value, visit https://brainly.com/question/12928519
Now, with this is mind, you can find the absolute value of -4. -4 is 4 units away from zero, meaning [tex]|-4| = 4[/tex].
The final equation is 1 + 4. The value of the expression is 5
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