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AlgebraQuestion and Answers: Page 236

Question Number 104782    Answers: 1   Comments: 0

Question Number 104758    Answers: 0   Comments: 0

Question Number 104811    Answers: 2   Comments: 0

Given { ((a+b(√3)−2c = 1)),((3b^2 +c^2 = 2a^2 )),((a^2 +4ac = 5c^2 )) :} find b

$${Given}\:\begin{cases}{{a}+{b}\sqrt{\mathrm{3}}−\mathrm{2}{c}\:=\:\mathrm{1}}\\{\mathrm{3}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \:=\:\mathrm{2}{a}^{\mathrm{2}} }\\{{a}^{\mathrm{2}} +\mathrm{4}{ac}\:=\:\mathrm{5}{c}^{\mathrm{2}} }\end{cases} \\ $$$${find}\:{b} \\ $$

Question Number 104717    Answers: 0   Comments: 0

In the a sport camp, 65% children know playing the football,70%−in voleyball,75%−in basketball.What is least number of children who know playing all above three sport games? (Answer 10%)

$$\mathrm{In}\:\mathrm{the}\:\mathrm{a}\:\:\mathrm{sport}\:\mathrm{camp},\:\mathrm{65\%}\:\mathrm{children}\:\mathrm{know} \\ $$$$\mathrm{playing}\:\mathrm{the}\:\mathrm{football},\mathrm{70\%}−\mathrm{in}\:\mathrm{voleyball},\mathrm{75\%}−\mathrm{in} \\ $$$$\mathrm{basketball}.\mathrm{What}\:\mathrm{is}\:\mathrm{least}\:\mathrm{number}\:\mathrm{of}\:\mathrm{children}\:\mathrm{who} \\ $$$$\mathrm{know}\:\mathrm{playing}\:\mathrm{all}\:\mathrm{above}\:\mathrm{three}\:\mathrm{sport}\:\mathrm{games}? \\ $$$$\left(\mathrm{Answer}\:\mathrm{10\%}\right) \\ $$

Question Number 104706    Answers: 1   Comments: 2

find the value of p (pls help) 1^3 +3^3 +5^3 +...+p^3 =8128

$${find}\:{the}\:{value}\:{of}\:\:{p}\:\left({pls}\:{help}\right) \\ $$$$\mathrm{1}^{\mathrm{3}} +\mathrm{3}^{\mathrm{3}} +\mathrm{5}^{\mathrm{3}} +...+{p}^{\mathrm{3}} =\mathrm{8128} \\ $$$$ \\ $$

Question Number 104696    Answers: 1   Comments: 0

Question Number 105301    Answers: 3   Comments: 0

Without using tables or calculator, compare 6^7 and 7^6

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{tables}\:\mathrm{or}\:\mathrm{calculator}, \\ $$$$\:{compare}\:\:\:\mathrm{6}^{\mathrm{7}} \:\mathrm{and}\:\:\:\mathrm{7}^{\mathrm{6}} \\ $$

Question Number 104676    Answers: 3   Comments: 4

Question Number 104657    Answers: 1   Comments: 0

(x+yi)^3 = ((10(2y+8i)^2 )/(3−i)) find x & y

$$\left({x}+{yi}\right)^{\mathrm{3}} \:=\:\frac{\mathrm{10}\left(\mathrm{2}{y}+\mathrm{8}{i}\right)^{\mathrm{2}} }{\mathrm{3}−{i}} \\ $$$${find}\:{x}\:\&\:{y} \\ $$

Question Number 104621    Answers: 1   Comments: 0

(1/((1−x)^2 ))−(4/((1+x)^2 ))=1

$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }−\frac{\mathrm{4}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }=\mathrm{1} \\ $$

Question Number 104588    Answers: 1   Comments: 1

solve in R ((96x−24)/(12x+5))=(√(−144x^2 +72x+7))

$${solve}\:{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{96}{x}−\mathrm{24}}{\mathrm{12}{x}+\mathrm{5}}=\sqrt{−\mathrm{144}{x}^{\mathrm{2}} +\mathrm{72}{x}+\mathrm{7}} \\ $$

Question Number 104517    Answers: 2   Comments: 0

Question Number 104516    Answers: 1   Comments: 1

Question Number 104450    Answers: 1   Comments: 0

(4/(99)) + (7/(999)) + ((11)/(999999)) = ? Can you solve this?

$$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104419    Answers: 2   Comments: 0

Now the sum of your father and your is 90 years. 5 years ago your father′s age was 3 times than your age. Write the your age and your father′s age 3 years after.

$$\boldsymbol{\mathrm{Now}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{is}} \\ $$$$\mathrm{90}\:\boldsymbol{\mathrm{years}}.\:\mathrm{5}\:\boldsymbol{\mathrm{years}}\:\boldsymbol{\mathrm{ago}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{age}} \\ $$$$\boldsymbol{\mathrm{was}}\:\mathrm{3}\:\boldsymbol{\mathrm{times}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{age}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{father}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{age}}\:\mathrm{3}\:\boldsymbol{\mathrm{years}} \\ $$$$\boldsymbol{\mathrm{after}}. \\ $$

Question Number 104413    Answers: 2   Comments: 0

The sum of two integers is 304 and their GCD is 19. What are the numbers?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{integers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{304} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{is}}\:\mathrm{19}.\:\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{numbers}}? \\ $$

Question Number 104410    Answers: 1   Comments: 0

If 11×11=121, 111×111=12321,1111×1111=1234321 then what is the answer of 111111×111111 ? (It is a short question)

$$\boldsymbol{\mathrm{If}}\:\mathrm{11}×\mathrm{11}=\mathrm{121}, \\ $$$$\mathrm{111}×\mathrm{111}=\mathrm{12321},\mathrm{1111}×\mathrm{1111}=\mathrm{1234321} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{answer}}\:\boldsymbol{\mathrm{of}} \\ $$$$\mathrm{111111}×\mathrm{111111}\:? \\ $$$$\left(\boldsymbol{\mathrm{It}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{short}}\:\boldsymbol{\mathrm{question}}\right) \\ $$

Question Number 104404    Answers: 1   Comments: 0

(4/5)=(?/(45))=((20)/?)=((144)/?)=((200)/?)

$$\frac{\mathrm{4}}{\mathrm{5}}=\frac{?}{\mathrm{45}}=\frac{\mathrm{20}}{?}=\frac{\mathrm{144}}{?}=\frac{\mathrm{200}}{?} \\ $$

Question Number 104391    Answers: 0   Comments: 1

(x−a)(x−b)(x−c)....(x−z) = ?

$$\left(\boldsymbol{{x}}−\boldsymbol{{a}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{b}}\right)\left(\boldsymbol{{x}}−\boldsymbol{{c}}\right)....\left(\boldsymbol{{x}}−\boldsymbol{{z}}\right)\:=\:? \\ $$

Question Number 104394    Answers: 1   Comments: 0

Question Number 104377    Answers: 1   Comments: 6

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 .... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{196}\:\:\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:....\:\left(\mathrm{iii}\right) \\ $$

Question Number 104369    Answers: 1   Comments: 0

Question Number 104326    Answers: 1   Comments: 2

Suppose you had x rupees. Your father gave you more 6 rupees. You gave y rupees to your brother. Now how many rupees you have? You will buy three shirts with the rupees that you have now. Write the cost of each shirt.

$$\boldsymbol{\mathrm{Suppose}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{had}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{Your}} \\ $$$$\boldsymbol{\mathrm{father}}\:\boldsymbol{\mathrm{gave}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{more}}\:\mathrm{6}\:\boldsymbol{\mathrm{rupees}}.\:\boldsymbol{\mathrm{You}} \\ $$$$\boldsymbol{\mathrm{gave}}\:\boldsymbol{{y}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{brother}}.\:\boldsymbol{\mathrm{Now}} \\ $$$$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}?\:\boldsymbol{\mathrm{You}}\:\boldsymbol{\mathrm{will}} \\ $$$$\boldsymbol{\mathrm{buy}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{shirts}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rupees}}\:\boldsymbol{\mathrm{that}} \\ $$$$\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{now}}.\:\boldsymbol{\mathrm{Write}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{cost}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{each}} \\ $$$$\boldsymbol{\mathrm{shirt}}. \\ $$

Question Number 104297    Answers: 1   Comments: 0

((3a^2 b^3 c)/(5b^4 c))+((6xy^3 z^(16) )/(10x^2 y^2 z^(10) )) = ? Can you solve this?

$$\frac{\mathrm{3}{a}^{\mathrm{2}} {b}^{\mathrm{3}} {c}}{\mathrm{5}{b}^{\mathrm{4}} {c}}+\frac{\mathrm{6}{xy}^{\mathrm{3}} {z}^{\mathrm{16}} }{\mathrm{10}{x}^{\mathrm{2}} {y}^{\mathrm{2}} {z}^{\mathrm{10}} }\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104294    Answers: 1   Comments: 0

1. ((1(1/2)+2(6/7))/(2(2/3)−3(4/5)))=? 2. 4×Π×Π=? 3. Transfer into fractions: 5.8^. 9^. , 9.6^. , 78.57^. 8^.

$$\mathrm{1}.\:\:\frac{\mathrm{1}\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{2}\frac{\mathrm{6}}{\mathrm{7}}}{\mathrm{2}\frac{\mathrm{2}}{\mathrm{3}}−\mathrm{3}\frac{\mathrm{4}}{\mathrm{5}}}=? \\ $$$$\mathrm{2}.\:\:\mathrm{4}×\Pi×\Pi=? \\ $$$$\mathrm{3}.\:\:\boldsymbol{\mathrm{Transfer}}\:\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fractions}}: \\ $$$$\:\:\:\:\:\:\mathrm{5}.\overset{.} {\mathrm{8}}\overset{.} {\mathrm{9}},\:\mathrm{9}.\overset{.} {\mathrm{6}},\:\mathrm{78}.\mathrm{5}\overset{.} {\mathrm{7}}\overset{.} {\mathrm{8}} \\ $$

Question Number 104278    Answers: 1   Comments: 0

x−(−(−x+(−x+x)))= ?

$${x}−\left(−\left(−{x}+\left(−{x}+{x}\right)\right)\right)=\:? \\ $$

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