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AlgebraQuestion and Answers: Page 259

Question Number 101568    Answers: 1   Comments: 0

Question Number 101563    Answers: 2   Comments: 0

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

Question Number 101459    Answers: 0   Comments: 0

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 ]

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

Question Number 101225    Answers: 0   Comments: 4

Question Number 101156    Answers: 1   Comments: 0

Find the range of the function: h : x = 2 − x^2 sin(x), x ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}: \\ $$$$\:\:\:\:\:\mathrm{h}\::\:\mathrm{x}\:\:\:=\:\:\mathrm{2}\:\:−\:\:\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{x}\right),\:\:\:\:\:\:\mathrm{x}\:\:\geqslant\:\:\mathrm{0} \\ $$

Question Number 101104    Answers: 2   Comments: 0

(d/dx)(x!)=?

$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}!\right)=? \\ $$

Question Number 101096    Answers: 1   Comments: 2

find the oblique asymptote of f(x)=x∙e^(1/x) i need your help

$$\mathrm{find}\:\mathrm{the}\:\mathrm{oblique}\:\mathrm{asymptote}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\centerdot\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \:\:\:\:\: \\ $$$$\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help} \\ $$

Question Number 101085    Answers: 1   Comments: 1

Question Number 101062    Answers: 1   Comments: 0

Question Number 101056    Answers: 5   Comments: 1

If the equation 4x^2 −4(5x+1)+p^2 =0 has one root equals to two more then the other, then the value of p is equal to ___

$$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}\left(\mathrm{5}{x}+\mathrm{1}\right)+{p}^{\mathrm{2}} =\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{one}\:\mathrm{root}\:\mathrm{equals}\:\mathrm{to}\:\mathrm{two}\:\mathrm{more} \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{other},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${p}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\_\_\_ \\ $$

Question Number 101052    Answers: 2   Comments: 0

Given a=^3 (√(7+(√(50)))),b=^3 (√(7−(√(50)))).Prove that a^7 +b^7 is an even number.

$$\mathrm{Given}\:\mathrm{a}=\:^{\mathrm{3}} \sqrt{\mathrm{7}+\sqrt{\mathrm{50}}},\mathrm{b}=\:^{\mathrm{3}} \sqrt{\mathrm{7}−\sqrt{\mathrm{50}}}.\mathrm{Prove} \\ $$$$\mathrm{that}\:\mathrm{a}^{\mathrm{7}} +\mathrm{b}^{\mathrm{7}} \mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{number}. \\ $$

Question Number 100976    Answers: 0   Comments: 1

find all possible values of x,y,z in terms of a,b,c gor a triplet (x,y,z) that satisfy x+(1/y)=a y+(1/z)=b z+(1/x)=c

$${find}\:{all}\:{possible}\:{values}\:{of}\:{x},{y},{z}\:{in}\:{terms} \\ $$$${of}\:{a},{b},{c}\:{gor}\:{a}\:{triplet}\:\left({x},{y},{z}\right)\:{that}\:{satisfy} \\ $$$$ \\ $$$${x}+\frac{\mathrm{1}}{{y}}={a} \\ $$$$ \\ $$$${y}+\frac{\mathrm{1}}{{z}}={b} \\ $$$$ \\ $$$${z}+\frac{\mathrm{1}}{{x}}={c} \\ $$

Question Number 100960    Answers: 0   Comments: 1

{ (((√(x^2 −6x+9)) = 3−x)),(((√(x^2 +6x+9)) = x+3)) :}

$$\begin{cases}{\sqrt{{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}}\:=\:\mathrm{3}−{x}}\\{\sqrt{{x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{9}}\:=\:{x}+\mathrm{3}}\end{cases}\: \\ $$

Question Number 100954    Answers: 2   Comments: 1

{ (((1/(2x−y)) + (√y) = 1)),((((√y)/(2x−y)) = −6)) :}

$$\begin{cases}{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}\:+\:\sqrt{{y}}\:=\:\mathrm{1}}\\{\frac{\sqrt{{y}}}{\mathrm{2}{x}−{y}}\:=\:−\mathrm{6}}\end{cases} \\ $$

Question Number 100879    Answers: 2   Comments: 1

Solve the equation 2^x +8x=4

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{2}^{\mathrm{x}} +\mathrm{8x}=\mathrm{4} \\ $$

Question Number 100815    Answers: 1   Comments: 0

Question Number 100806    Answers: 1   Comments: 3

Question Number 100793    Answers: 1   Comments: 1

Question Number 100792    Answers: 1   Comments: 0

Question Number 100730    Answers: 0   Comments: 1

((2z^2 )/(z^2 +∣z+1∣)) < 1

$$\frac{\mathrm{2}{z}^{\mathrm{2}} }{{z}^{\mathrm{2}} +\mid{z}+\mathrm{1}\mid}\:<\:\mathrm{1}\: \\ $$

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