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07 Mar 2024, 02:38
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If \(x = (-0.00121)(456^2)\), then \(x\) satisfies which of the following inequalities?
A. \(x < -10,000\)
B. \(-10,000 < x < -1,000\)
C. \(-1,000 < x < -100\)
D. \(-100 < x < -10\)
E. \(-10 < x < 0\)
A. \(x < -10,000\)
B. \(-10,000 < x < -1,000\)
C. \(-1,000 < x < -100\)
D. \(-100 < x < -10\)
E. \(-10 < x < 0\)
07 Mar 2024, 02:38
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Official Solution:
If \(x = (-0.00121)(456^2)\), then \(x\) satisfies which of the following inequalities?
A. \(x < -10,000\)
B. \(-10,000 < x < -1,000\)
C. \(-1,000 < x < -100\)
D. \(-100 < x < -10\)
E. \(-10 < x < 0\)
Let's approximate:
\(4.5^2\) is between \(4^2 = 16\) and \(5^2 = 25\). Thus, \((-12)(4.5)^2\) will be approximately \((-12)(20) = -240\)
Answer: C
If \(x = (-0.00121)(456^2)\), then \(x\) satisfies which of the following inequalities?
A. \(x < -10,000\)
B. \(-10,000 < x < -1,000\)
C. \(-1,000 < x < -100\)
D. \(-100 < x < -10\)
E. \(-10 < x < 0\)
Let's approximate:
\((-0.00121)(456^2) = \)
\(= (-\frac{121}{100,000})(456^2) \approx \)
\(\approx (-\frac{120}{100,000})(456^2) = \)
\(= (-\frac{12}{10,000})(456^2) = \)
\(= (-\frac{12}{100^2})(456^2) = \)
\(= (-12)(\frac{456}{100})^2 \approx \)
\(\approx (-12)(4.5)^2\)
\(= (-\frac{121}{100,000})(456^2) \approx \)
\(\approx (-\frac{120}{100,000})(456^2) = \)
\(= (-\frac{12}{10,000})(456^2) = \)
\(= (-\frac{12}{100^2})(456^2) = \)
\(= (-12)(\frac{456}{100})^2 \approx \)
\(\approx (-12)(4.5)^2\)
\(4.5^2\) is between \(4^2 = 16\) and \(5^2 = 25\). Thus, \((-12)(4.5)^2\) will be approximately \((-12)(20) = -240\)
Answer: C
04 Jul 2025, 04:11
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Ans: C
converted everything into power 10 and approximation values
\(x = (-)* 121 * 10^-5 * 450^2)\)
\(x = (-)* 121 * 10^-5 * 50* 40 * 10^2\)
\(x = (-)* 121 * 10^-5 * 2000 * 10^2)\)
x = - 121*2 = -242
C. \(-1,000 < x < -100\)
converted everything into power 10 and approximation values
\(x = (-)* 121 * 10^-5 * 450^2)\)
\(x = (-)* 121 * 10^-5 * 50* 40 * 10^2\)
\(x = (-)* 121 * 10^-5 * 2000 * 10^2)\)
x = - 121*2 = -242
C. \(-1,000 < x < -100\)
