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AlgebraQuestion and Answers: Page 83

Question Number 183556 Answers: 1 Comments: 0

Question Number 183424 Answers: 0 Comments: 0

Among the natural numbers not greater than 22 , the probability that the modulus of the difference of any two of the 3 randomly selected numbers is greater than 5 is equal to which of the following? a)15/22 b)1/7 c)1/22 d)1

$Among the natural numbers not$ $greater than 22, the probability that$ $the modulus of the difference of any$ $two of the 3 randomly selected numbers$ $is greater than 5 is equal to which of$ $the following ?$ $a) 1 5 / 22 b) 1 / 7 c) 1 / 22 d) 1$

Question Number 183381 Answers: 1 Comments: 2

((3n^5 + 4n^4 − 7n^3 + 5n^2 − 5)/(n + 1)) There can be no residue: a)0 b)2 c)4 d)5 e)9

$\frac{{3 n}^{5} + {4 n}^{4} - {7 n}^{3} + {5 n}^{2} - 5}{n + 1}$ $There can be no residue :$ $a) 0 b) 2 c) 4 d) 5 e) 9$

Question Number 183380 Answers: 0 Comments: 1

a>0 , b>0 { (((x−1)^2 + (y−7)^2 = a^2 )),(((x−2)^2 + (y−3)^2 = b^2 )) :} Find: (a+b)_(min) = ?

$a > 0, b > 0$ ${\begin{cases} {(x - 1)}^{2} + {(y - 7)}^{2} = a^{2} \\ {(x - 2)}^{2} + {(y - 3)}^{2} = b^{2} \end{cases}$ $Find : {(a + b)}_{\min} = ?$

Question Number 183592 Answers: 1 Comments: 0

{ (((√(x/y)) +(√(y/z)) +(√(z/x)) = 3)),(((√(y/x)) +(√(z/y)) +(√(x/z)) = 3)),(((√(xyz)) = 1)) :}

${\begin{cases} \sqrt{\frac{x}{y}} + \sqrt{\frac{y}{z}} + \sqrt{\frac{z}{x}} = 3 \\ \sqrt{\frac{y}{x}} + \sqrt{\frac{z}{y}} + \sqrt{\frac{x}{z}} = 3 \\ \sqrt{x y z} = 1 \end{cases}$

Question Number 183366 Answers: 0 Comments: 2

6 of the 23 given points in the plane lie on a circle. Let n be the number of circles passing through at least 3 of these points. What is the maximum number of n?

$6 of the 23 given points in the plane$ $lie on a circle . Let n be the number of$ $circles passing through at least 3 of$ $these points . What is the maximum$ $number of n ?$

Question Number 183363 Answers: 1 Comments: 0

Find: 2003∙2005^3 −2004∙2002^3

$Find :$ $2003 \cdot 2005^{3} - 2004 \cdot 2002^{3}$

Question Number 183354 Answers: 0 Comments: 2

Given three point.Find the for the plane through the point P(0,1,0) Q(3,1,4) R(−1,0,1)

$G i v e n t h r e e p o i n t . F i n d t h e$ $f o r t h e p l a n e t h r o u g h t h e p o i n t$ $P (0, 1, 0) Q (3, 1, 4) R (- 1, 0, 1)$

Question Number 183353 Answers: 1 Comments: 0

For the function f(x)= { ((x^2 −3 if x<4)),(((x^2 /(x+4)) if x≥4)) :} Find (i) lim_(x→−4) f(x) ii)lim_(x→+4) f(x)

$F o r t h e f u n c t i o n$ $f (x) = {\begin{cases} x^{2} - 3 i f x < 4 \\ \frac{x^{2}}{x + 4} i f x ⩾ 4 \end{cases}$ $F i n d (i) \lim_{x \to - 4} f (x) i i) \lim_{x \to + 4} f (x)$

Question Number 183352 Answers: 0 Comments: 0

For the function f(x)= { ((1−x^2 if x< 2)),((2x+1 if x≥2)) :} Find (i)lim_(x→^− 2) f(x) (ii) lim_(x→2^+ ) f(x)

$F o r t h e f u n c t i o n$ $f (x) = {\begin{cases} 1 - x^{2} i f x < 2 \\ 2 x + 1 i f x ⩾ 2 \end{cases}$ $F i n d$ $(i) \lim_{x \to^{-} 2} f (x) (i i) \lim_{x \to 2^{+}} f (x)$

Question Number 183350 Answers: 3 Comments: 2

Find (a)lim_(x→∞) ((3x+2)/(x^2 −x+1)) (b)lim_(x→∞) ((√(x^2 −1))/(2x+1)) (c)lim_(x→5) (((√(3x+1)) −4)/(x−5))

$F i n d$ $(a) \lim_{x \to \infty} \frac{3 x + 2}{x^{2} - x + 1}$ $(b) \lim_{x \to \infty} \frac{\sqrt{x^{2} - 1}}{2 x + 1}$ $(c) \lim_{x \to 5} \frac{\sqrt{3 x + 1} - 4}{x - 5}$

Question Number 183342 Answers: 3 Comments: 0

Find: 3 − (2/(3 − (2/(3 − (2/(...)))))) = ?

$Find : 3 - \frac{2}{3 - \frac{2}{3 - \frac{2}{. . .}}} = ?$

Question Number 183241 Answers: 1 Comments: 0

Find the equation of the line which is tangent to the parabola y^2 =12x and forms an angle of 45° with the line y=3x−4.

$F i n d t h e e q u a t i o n o f t h e l i n e w h i c h$ $i s t a n g e n t t o t h e p a r a b o l a y^{2} = 12 x$ $a n d f o r m s a n a n g l e o f 45 ° w i t h$ $t h e l i n e y = 3 x - 4 .$

Question Number 183205 Answers: 2 Comments: 0

Find the coefficient of x^(11) in (2x^2 +x−3)^6 .

$F i n d t h e c o e f f i c i e n t o f x^{11} i n$ ${(2 x^{2} + x - 3)}^{6} .$

Question Number 183167 Answers: 0 Comments: 2

In △ABC the following relationship holds: (m_b /b) + (m_c /c) ≤ (a/(2r)) ≤ (n_b /h_b ) + (n_c /h_c )

$In △ ABC the following relationship$ $holds :$ $\frac{m_{b}}{b} + \frac{m_{c}}{c} ⩽ \frac{a}{2 r} ⩽ \frac{n_{b}}{h_{b}} + \frac{n_{c}}{h_{c}}$

Question Number 183120 Answers: 2 Comments: 0

I−Incenter in △ABC A(2,2) , B(6,4) , C(4,8) , M(8,6) Find: MI = ?

$I - Incenter in △ ABC$ $A (2, 2), B (6, 4), C (4, 8), M (8, 6)$ $Find : MI = ?$

Question Number 183118 Answers: 0 Comments: 0

Question Number 183262 Answers: 0 Comments: 1

Simplify ^3 (√(56^3 (√(4 )) − 157^3 (√9) + 130^3 (√6) )) into a compound surd.

$S i m p l i f y^{3} \sqrt{56^{3} \sqrt{4} - 157^{3} \sqrt{9} + 130^{3} \sqrt{6}}$ $i n t o a c o m p o u n d s u r d .$

Question Number 183084 Answers: 1 Comments: 3

Question Number 183078 Answers: 0 Comments: 0

Question Number 183077 Answers: 0 Comments: 0

Question Number 183076 Answers: 1 Comments: 0

Question Number 183044 Answers: 4 Comments: 0

Find the equation of the line which passes through the point (3, 5) and is tangent to the circle (x−1)^2 +(y−1)^2 =4

$F i n d t h e e q u a t i o n o f t h e l i n e w h i c h$ $p a s s e s t h r o u g h t h e p o i n t (3, 5)$ $a n d i s t a n g e n t t o t h e c i r c l e$ ${(x - 1)}^{2} + {(y - 1)}^{2} = 4$

Question Number 183041 Answers: 1 Comments: 0

Find: (√(12−2(√(35)))) − (√(10−2(√(21)))) = ?

$Find :$ $\sqrt{12 - 2 \sqrt{35}} - \sqrt{10 - 2 \sqrt{21}} = ?$

Question Number 183019 Answers: 3 Comments: 2

Q f(x)=a^x +b^x g(x)=((f(x))/(f(x−2))) g(3)=?

$Q f (x) = a^{x} + b^{x} g (x) = \frac{f (x)}{f (x - 2)}$ $g (3) = ?$

Question Number 182999 Answers: 1 Comments: 0

(√(m^2 −4m+4)) + ((m−2n+8))^(1/4) = 0 n = ?

$\sqrt{m^{2} - 4 m + 4} + \sqrt[4]{m - 2 n + 8} = 0$ $n = ?$

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