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AlgebraQuestion and Answers: Page 259

Question Number 102186 Answers: 0 Comments: 0

Question Number 102179 Answers: 1 Comments: 0

Question Number 102178 Answers: 1 Comments: 0

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Question Number 102078 Answers: 5 Comments: 0

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Question Number 101921 Answers: 1 Comments: 1

Please, help i cannot solve problems such as: x^4 =1, x^5 =1, or x^n =1 n∈N...

$$\boldsymbol{{Please}},\:\boldsymbol{{help}}\:\:\boldsymbol{{i}}\:\:\boldsymbol{{cannot}}\:\boldsymbol{{solve}}\:\boldsymbol{{problems}} \\ $$$$\boldsymbol{{such}}\:\boldsymbol{{as}}:\:\boldsymbol{{x}}^{\mathrm{4}} =\mathrm{1},\:\boldsymbol{{x}}^{\mathrm{5}} =\mathrm{1},\:\boldsymbol{{or}}\:\boldsymbol{{x}}^{\boldsymbol{{n}}} =\mathrm{1}\:\boldsymbol{{n}}\in\mathbb{N}... \\ $$

Question Number 101803 Answers: 1 Comments: 2

((√2)−1)^x +((√2)+1)^x =((√6))^x

$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{{x}} +\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{{x}} =\left(\sqrt{\mathrm{6}}\right)^{{x}} \\ $$

Question Number 101800 Answers: 1 Comments: 3

Question Number 101742 Answers: 3 Comments: 0

{ ((ab+a+b = 5)),((bc + b+c = 14)),((ac + a+c = 9)) :} find a+b+c = ___

$$\begin{cases}{{ab}+{a}+{b}\:=\:\mathrm{5}}\\{{bc}\:+\:{b}+{c}\:=\:\mathrm{14}}\\{{ac}\:+\:{a}+{c}\:=\:\mathrm{9}}\end{cases} \\ $$$$\mathrm{find}\:{a}+{b}+{c}\:=\:\_\_\_ \\ $$

Question Number 101693 Answers: 3 Comments: 2

There are 4 identical mathematics books, 2 identic physics books and 2 identical chemistry books . How many ways to compile the eight books on the condition of the same book are not mutually adjacent?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{4}\:\mathrm{identical}\:\mathrm{mathematics} \\ $$$$\mathrm{books},\:\mathrm{2}\:\mathrm{identic}\:\mathrm{physics}\:\mathrm{books} \\ $$$$\mathrm{and}\:\mathrm{2}\:\mathrm{identical}\:\mathrm{chemistry}\:\mathrm{books} \\ $$$$.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{compile}\: \\ $$$$\mathrm{the}\:\mathrm{eight}\:\mathrm{books}\:\mathrm{on}\:\mathrm{the}\:\mathrm{condition} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{book}\:\mathrm{are}\:\mathrm{not}\:\mathrm{mutually} \\ $$$$\mathrm{adjacent}? \\ $$

Question Number 105306 Answers: 1 Comments: 1

(1/(2+(√2))) +(1/(3(√2)+2(√3) ))+(1/(4(√3)+3(√4)))+...+(1/(100(√(99))+99(√(100))))

$$\frac{\mathrm{1}}{\mathrm{2}+\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}+\mathrm{2}\sqrt{\mathrm{3}}\:}+\frac{\mathrm{1}}{\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{3}\sqrt{\mathrm{4}}}+...+\frac{\mathrm{1}}{\mathrm{100}\sqrt{\mathrm{99}}+\mathrm{99}\sqrt{\mathrm{100}}} \\ $$

Question Number 101607 Answers: 0 Comments: 0

f(x)=(√(2x+7))+log_3 x f^(−1) (x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2x}+\mathrm{7}}+\mathrm{log}_{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=?\:\:\:\:\:\: \\ $$

Question Number 101871 Answers: 1 Comments: 0

if a_1 = −4 , a_2 =−1 and a_n = a_(n+1) +a_(n+3 ) . find a_4 −a_1 ?

$${if}\:{a}_{\mathrm{1}} =\:−\mathrm{4}\:,\:{a}_{\mathrm{2}} =−\mathrm{1}\:{and}\: \\ $$$${a}_{{n}} \:=\:{a}_{{n}+\mathrm{1}} +{a}_{{n}+\mathrm{3}\:} .\:{find}\: \\ $$$${a}_{\mathrm{4}} −{a}_{\mathrm{1}} ? \\ $$

Question Number 101568 Answers: 1 Comments: 0

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Question Number 105345 Answers: 1 Comments: 0

If the point ((√2) ,p) and (−(√2),q) lie on the graph y=x^3 +ax^2 +bx+c and q−p = 3 , then what the value of b ?

$${If}\:{the}\:{point}\:\left(\sqrt{\mathrm{2}}\:,{p}\right)\:{and}\:\left(−\sqrt{\mathrm{2}},{q}\right) \\ $$$${lie}\:{on}\:{the}\:{graph}\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:{q}−{p}\:=\:\mathrm{3}\:,\:{then}\:{what}\:{the} \\ $$$${value}\:{of}\:{b}\:?\: \\ $$

Question Number 101514 Answers: 2 Comments: 4

Question Number 101498 Answers: 1 Comments: 3

If 4^x = 5^y = 20^z . what is z in term of x and y. ★♠

$$\mathrm{If}\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{y}} \:=\:\mathrm{20}^{\mathrm{z}} \:. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{z}\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}. \\ $$$$\bigstar\spadesuit \\ $$

Question Number 101489 Answers: 1 Comments: 0

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Question Number 101425 Answers: 3 Comments: 2

A student wrote three papers in mathematics examinations. Her marks for the two of papers were 77 and 72 respectively. To obtain grade A, an average of not less than 75 marks is required for the three papers. How many marks must she get in the third paper to get grade A?

$$\mathrm{A}\:\mathrm{student}\:\mathrm{wrote}\:\mathrm{three}\:\mathrm{papers}\:\mathrm{in}\:\mathrm{mathematics} \\ $$$$\mathrm{examinations}.\:\mathrm{Her}\:\mathrm{marks}\:\mathrm{for}\:\mathrm{the}\:\mathrm{two}\:\mathrm{of} \\ $$$$\mathrm{papers}\:\mathrm{were}\:\mathrm{77}\:\mathrm{and}\:\mathrm{72}\:\mathrm{respectively}.\:\mathrm{To} \\ $$$$\mathrm{obtain}\:\mathrm{grade}\:\mathrm{A},\:\mathrm{an}\:\mathrm{average}\:\mathrm{of}\:\mathrm{not}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{75}\:\mathrm{marks}\:\mathrm{is}\:\mathrm{required}\:\mathrm{for}\:\mathrm{the}\:\mathrm{three} \\ $$$$\mathrm{papers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{marks}\:\mathrm{must}\:\mathrm{she}\:\mathrm{get} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{third}\:\mathrm{paper}\:\mathrm{to}\:\mathrm{get}\:\mathrm{grade}\:\mathrm{A}? \\ $$

Question Number 101363 Answers: 1 Comments: 0

The solution set of inequality (((√((3x−7)^2 ))−2)/(x−3)) ≤ ((3−(√x^2 ))/(x−3)) is __ (A) (−∞, (1/2)] (D) [(1/2), ∞) (B) [(1/2),1 ] (E) (−∞,(2/3)] (C) (−∞,1 ]

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{inequality} \\ $$$$\frac{\sqrt{\left(\mathrm{3x}−\mathrm{7}\right)^{\mathrm{2}} }−\mathrm{2}}{\mathrm{x}−\mathrm{3}}\:\leqslant\:\frac{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}−\mathrm{3}}\:\mathrm{is}\:\_\_ \\ $$$$\left(\mathrm{A}\right)\:\left(−\infty,\:\frac{\mathrm{1}}{\mathrm{2}}\right]\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\:\infty\right) \\ $$$$\left(\mathrm{B}\right)\:\left[\frac{\mathrm{1}}{\mathrm{2}},\mathrm{1}\:\right]\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:\left(−\infty,\frac{\mathrm{2}}{\mathrm{3}}\right] \\ $$$$\left(\mathrm{C}\right)\:\left(−\infty,\mathrm{1}\:\right]\: \\ $$

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