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AlgebraQuestion and Answers: Page 32

Question Number 208090 Answers: 0 Comments: 0

Question Number 208076 Answers: 2 Comments: 0

(5 − ∣x∣)^(− (1/3)) (x^2 − 4) < 0

$$\left(\mathrm{5}\:−\:\mid\mathrm{x}\mid\right)^{−\:\frac{\mathrm{1}}{\mathrm{3}}} \:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right)\:<\:\mathrm{0} \\ $$

Question Number 208075 Answers: 1 Comments: 0

Find: ∫ sin (2x − (π/4)) = ?

$$\mathrm{Find}:\:\:\:\int\:\mathrm{sin}\:\left(\mathrm{2x}\:−\:\frac{\pi}{\mathrm{4}}\right)\:=\:? \\ $$

Question Number 208071 Answers: 0 Comments: 6

((4 ∙ 10^n − 52)/3) The numbers are 38 in total Find: n = ?

$$\frac{\mathrm{4}\:\centerdot\:\mathrm{10}^{\boldsymbol{\mathrm{n}}} \:−\:\mathrm{52}}{\mathrm{3}} \\ $$$$\mathrm{The}\:\mathrm{numbers}\:\mathrm{are}\:\:\mathrm{38}\:\:\mathrm{in}\:\mathrm{total} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$

Question Number 208063 Answers: 1 Comments: 0

{ ((x + (3/5) y = 5)),(((3/5) x + y = 11)) :} ⇒ x + y = ?

$$\begin{cases}{\mathrm{x}\:+\:\frac{\mathrm{3}}{\mathrm{5}}\:\mathrm{y}\:=\:\mathrm{5}}\\{\frac{\mathrm{3}}{\mathrm{5}}\:\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{11}}\end{cases}\:\:\:\:\:\Rightarrow\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:? \\ $$

Question Number 208037 Answers: 1 Comments: 0

Find: 2 log_(√5) sin (π/7) ∙ log_(√(sin (𝛑/7))) 5 = ?

$$\mathrm{Find}:\:\:\:\mathrm{2}\:\mathrm{log}_{\sqrt{\mathrm{5}}} \:\:\mathrm{sin}\:\frac{\pi}{\mathrm{7}}\:\centerdot\:\mathrm{log}_{\sqrt{\boldsymbol{\mathrm{sin}}\:\frac{\boldsymbol{\pi}}{\mathrm{7}}}} \:\:\mathrm{5}\:\:=\:\:? \\ $$

Question Number 208020 Answers: 1 Comments: 0

{ (((1/x)+(1/y)=((14)/(625)))),(((√x)+(√y)=8)) :} Find all solutions.

$$\begin{cases}{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{14}}{\mathrm{625}}}\\{\sqrt{{x}}+\sqrt{{y}}=\mathrm{8}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{solutions}. \\ $$

Question Number 207986 Answers: 1 Comments: 0

(x−3)^(√(x−3 )) = 3

$$\left({x}−\mathrm{3}\right)^{\sqrt{{x}−\mathrm{3}\:}} \:\:=\:\mathrm{3} \\ $$

Question Number 207984 Answers: 1 Comments: 0

Question Number 207963 Answers: 0 Comments: 1

⋖

$$\:\:\:\underline{\underbrace{\lessdot}} \\ $$

Question Number 207943 Answers: 0 Comments: 11

Find: lim_(x→2^− ) (((x + 2)∙(x + 1))/(∣x + 2∣)) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$

Question Number 207930 Answers: 0 Comments: 1

a_n number series a_(k+3) ^2 + a_k = a_(k+2) + a_(k+7) find: k = ?

$$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:\:\:\mathrm{number}\:\mathrm{series} \\ $$$$\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{3}} ^{\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}} \:\:=\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{2}} \:\:+\:\:\mathrm{a}_{\boldsymbol{\mathrm{k}}+\mathrm{7}} \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{k}}\:=\:? \\ $$

Question Number 207919 Answers: 1 Comments: 1

⇃

$$\:\:\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 207897 Answers: 3 Comments: 0

Find: (√(12 ∙ 13 ∙ 14 ∙ 15 + 1)) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{12}\:\:\centerdot\:\:\mathrm{13}\:\:\centerdot\:\:\mathrm{14}\:\:\centerdot\:\:\mathrm{15}\:\:+\:\:\mathrm{1}}\:\:=\:\:? \\ $$

Question Number 207885 Answers: 0 Comments: 7

Find: i^4 + i^8 + i^(12) + i^(16) + i^(20) + i^(24) +...+ i^(100) = ?

$$\mathrm{Find}: \\ $$$$\boldsymbol{\mathrm{i}}^{\mathrm{4}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{8}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{12}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{16}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{20}} \:+\:\boldsymbol{\mathrm{i}}^{\mathrm{24}} \:+...+\:\boldsymbol{\mathrm{i}}^{\mathrm{100}} \:=\:? \\ $$

Question Number 207876 Answers: 1 Comments: 1

Find: ln (((2 tg 22,30°)/(1 − tg^2 22,30°))) = ?

$$\mathrm{Find}:\:\:\:\mathrm{ln}\:\left(\frac{\mathrm{2}\:\mathrm{tg}\:\mathrm{22},\mathrm{30}°}{\mathrm{1}\:−\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{22},\mathrm{30}°}\right)\:=\:? \\ $$

Question Number 207866 Answers: 2 Comments: 0

If the system { ((y=−mx^2 −2)),((4x^2 +y^2 = 4)) :} have only one solution them m = (A) (1/3) (B)(1/( (√2))) (C) 1 (D) (√2) (E) (√3)

$$\:\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{system}\:\begin{cases}{\mathrm{y}=−\mathrm{mx}^{\mathrm{2}} −\mathrm{2}}\\{\mathrm{4x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{4}}\end{cases} \\ $$$$\:\:\mathrm{have}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{them}\:\mathrm{m}\:=\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\left(\mathrm{B}\right)\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\:\left(\mathrm{C}\right)\:\mathrm{1}\:\:\:\:\left(\mathrm{D}\right)\:\sqrt{\mathrm{2}}\:\:\:\left(\mathrm{E}\right)\:\sqrt{\mathrm{3}} \\ $$$$\:\: \\ $$

Question Number 207852 Answers: 2 Comments: 0

Question Number 207846 Answers: 1 Comments: 0

Question Number 207845 Answers: 2 Comments: 0

Find: 1 + (1/(1+2)) + (1/(1+2+3)) +...+ (1/(1+2+3+...+40))

$$\mathrm{Find}: \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+...+\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{40}} \\ $$

Question Number 207779 Answers: 1 Comments: 0

Question Number 207771 Answers: 1 Comments: 0

Simplify: (((b)^(1/4) (√c) − (c)^(1/4) (√b))/( (b)^(1/4) (√c) − (c)^(1/4) )) = ?

$$\mathrm{Simplify}:\:\:\:\:\:\frac{\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}\:\:\sqrt{\boldsymbol{\mathrm{b}}}}{\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{b}}}\:\:\sqrt{\boldsymbol{\mathrm{c}}}\:\:−\:\:\sqrt[{\mathrm{4}}]{\boldsymbol{\mathrm{c}}}}\:\:=\:\:? \\ $$

Question Number 207747 Answers: 3 Comments: 0

find the value of y given that y^(y ) =3^(y+9)

$${find}\:{the}\:{value}\:{of}\:{y}\:{given}\:{that}\:{y}^{{y}\:} =\mathrm{3}^{{y}+\mathrm{9}} \\ $$

Question Number 207730 Answers: 0 Comments: 3

Question Number 207718 Answers: 1 Comments: 0

∣x−3∣ + ∣x +2∣ = 9 find: x = ?

$$\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{x}\:+\mathrm{2}\mid\:=\:\mathrm{9} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207717 Answers: 1 Comments: 0

lg^2 (10x) − lg 10x + 1 = 6 − lg x find: x = ?

$$\mathrm{lg}^{\mathrm{2}} \:\left(\mathrm{10x}\right)\:−\:\mathrm{lg}\:\mathrm{10x}\:+\:\mathrm{1}\:=\:\mathrm{6}\:−\:\mathrm{lg}\:\mathrm{x} \\ $$$$\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

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