Ortiz Mcdonald
12/15/2023 · High School
Find the value of : (a) \( 8 x^{2}+3 x-2 \) for \( x=5 \) (c) \( 9 x^{2}+8 x-6 \) for \( x=\frac{1}{3} \)
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Step-by-step Solution
Substitute \( x=5 \) into the expression \( 8x^2+3x-2 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(8x^{2}+3x-2\)
- step1: Substitute:
\(8\times 5^{2}+3\times 5-2\)
- step2: Multiply the terms:
\(200+3\times 5-2\)
- step3: Multiply the numbers:
\(200+15-2\)
- step4: Calculate:
\(213\)
Substitute \( x=\frac{1}{3} \) into the expression \( 9x^2+8x-6 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(9x^{2}+8x-6\)
- step1: Substitute:
\(9\left(\frac{1}{3}\right)^{2}+8\times \frac{1}{3}-6\)
- step2: Multiply the terms:
\(1+8\times \frac{1}{3}-6\)
- step3: Multiply:
\(1+\frac{8}{3}-6\)
- step4: Subtract the numbers:
\(-5+\frac{8}{3}\)
- step5: Reduce fractions to a common denominator:
\(-\frac{5\times 3}{3}+\frac{8}{3}\)
- step6: Calculate:
\(-\frac{15}{3}+\frac{8}{3}\)
- step7: Transform the expression:
\(\frac{-15+8}{3}\)
- step8: Add the numbers:
\(\frac{-7}{3}\)
- step9: Calculate:
\(-\frac{7}{3}\)
(a) When \( x=5 \), the value of \( 8x^{2}+3x-2 \) is 213.
(c) When \( x=\frac{1}{3} \), the value of \( 9x^{2}+8x-6 \) is -7/3 or -2 1/3 or -2.3.
Quick Answer
(a) \( 8x^{2}+3x-2 \) for \( x=5 \) equals 213.
(c) \( 9x^{2}+8x-6 \) for \( x=\frac{1}{3} \) equals -7/3.
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