Carcass wrote:
Which of the following statements are true?
(a) \(-5<3.1\)
(b) \(\sqrt{16} =4\)
(c) \(\frac{7}{0} =0\)
(d) \(0 < | - \frac{1}{7} |\)
(e) \(0.3 < \frac{1}{3}\)
(f) \((-1)^{87} = -1\)
(g) \(\sqrt{(-3)^2} <0\)
(h) \(\frac{21}{28} = \frac{3}{4}\)
(i) \(- | - 23 | = 23\)
(j) \(\frac{1}{2} > \frac{1}{17}\)
(k) \((59)^3(59)^2 = 59^6\)
(l) \(-\sqrt{25} < -4\)
(a) True (b) True (c) False; division by 0 is undeﬁned (d) True (e) True (f) True (g) False \(\sqrt{(-3)^2} = \sqrt{9} = 3 > 0\) (h) True (i) False; \(-|-23| = -23\) (j) True (k) False; \((59)^3(59)^2 = 59^{3+2} = 59^5\) (l) True
Math Review
Question: 8
Page: 220
Difficulty: medium
(a) \(-5<3.1\)
A POSITIVE value is always greater than a NEGATIVE value
TRUE(b) \(\sqrt{16} =4\)
TRUE(c) \(\frac{7}{0} =0\)
7/0 is not defined (i.e., not considered a real number), so it CANNOT equal 0
FALSE(d) \(0 < | - \frac{1}{7} |\)
Simplify: \(0 < \frac{1}{7}\)
TRUE(e) \(0.3 < \frac{1}{3}\)
Rewrite as: \(0.3 < 0.333333...\)
TRUE(f) \((-1)^{87} = -1\)
ODD exponents preserve the sign of the base.
That is: NEGATIVE^(ODD integer) = NEGATIVE, and POSITIVE^(ODD integer) = POSITIVE
So, \((-1)^{87} = -1\)
TRUE(g) \(\sqrt{(-3)^2} <0\)
Take: \(\sqrt{(-3)^2} <0\)
Evaluate part inside the root: \(\sqrt{9} <0\)
Evaluate the root: \(3<0\)
FALSE(h) \(\frac{21}{28} = \frac{3}{4}\)
Take: \(\frac{21}{28}\)
Divide numerator and denominator by 7 to get: \(\frac{3}{4}\)
TRUE(i) \(-|- 23| = 23\)
Simplify: \(-(23) = 23\)
Simplify: \(-23 = 23\)
FALSE(j) \(\frac{1}{2} > \frac{1}{17}\)
1/2 a pizza is MORE THAN 1/17 of a pizza
TRUE(k) \((59)^3(59)^2 = 59^6\)
\((59)^3(59)^2=59^5\)
FALSE(l) \(-\sqrt{25} < -4\)
Evaluate root: \(-(5) < -4\)
Simplify: \(-5 < -4\)
TRUECheers,
Brent
The square root of 16 can equal -4 as well as 4, so we don't know if B is true. Am I missing something?