Description : Evaluate each of the following using identities: (i) (399)2 (ii) (0.98)2 (iii) 991 x 1009 (iv) 117 x 83 -Maths 9th
Last Answer : answer:
Description : Simplify: (i) (a + b + c)2 + (a – b + c)2 (ii) (a + b + c)2 – (a – b + c)2 (iii) (a + b + c)2 + (a – b + c)2 + (a + b – c)2 (iv) (2x + p – c)2 – (2x – p + c)2 (v) (x2 + y2 – z2)2 – (x2 – y2 + z2)2 -Maths 9th
Description : Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x - 2x = (- 2) (3-x) (iii) (x - 2) (x + 1) = (x - 1) (x + 3) (iv) (x - 3) (2x + 1) = x (x + 5) (v) (2x - 1) (x - 3) = (x ... vi) x2 + 3x + 1 = (x - 2)2 (vii) (x + 2)3 = 2x(x2 - 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th
Last Answer : this is the correct answer!
Description : Evaluate each of the following: (i) (103)3 (ii) (98)3 (iii) (9.9)3 (iv) (10.4)3 (v) (598)3 (vi) (99)3 -Maths 9th
Description : Evaluate using identities -Maths 9th
Last Answer : (i) 1023 = (100 + 2)3 = (100)3 + 3(100)2 (2) + 3(100) (2)2 + 23 = 10,00,000 + 60,000 + 1200 + 8 = 10,61,208 (ii) 993 = (100 - 1)3 = 1003 - 3(100)2 (1) + 3(100) (1)2 - 13 = 10,00,000 - 30,000 + 300 - 1 = 9,70,299
Description : Evaluate using the identities -Maths 9th
Last Answer : (i) 505 × 503 = (500 + 5) (500 + 3) = 5002 + (5 + 3) (500) + 5 × 3 = 250000 + 4000 + 15 = 254015 (ii) 37 × 16 = (30 + 7) (30 - 4) = 302 + (7 - 4) (30) - 7 × 4 = 900 + 90 - 28 = 962
Description : Evaluate each of the following: (i) 1113 – 893 (ii) 463 + 343 (iii) 1043 + 963 (iv) 933 – 1073 -Maths 9th
Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th
Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x
Description : If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p (1/2). -Maths 9th
Last Answer : Solution of this question
Description : If x + y = 5 and xy = 4 , find x - y , using identities. -Maths 9th
Last Answer : (x+y)2 = x2 - 2xy + y2 = x2 + 2xy + y2 - 4xy = (x+y)2 - 4xy = 52 - 4 × 4 = 25 - 16 = 9 ∴ x - y = √9 = 3
Description : What is the solution when y equals 2x plus 1 is a tangent to the circle 5y2 plus 5x2 equals 1?
Last Answer : If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 thenthe point of contact is at (-2/5, 1/5) because it has equalroots
Description : If both (x+1) and (x -1) are factors of ax3 + x2 - 2x + b , find a and b. -Maths 9th
Last Answer : Let p(x) = ax3 + x2 - 2x + b Since (x+1) and (x-1) are the factors of p(x), ∴ p(-1) = 0 and p(1) = 0 ∴ p(-1) = a(-1)3 + (-1)2 - 2 (-1) + b = 0 ⇒ - a + 1 + 2 + b = 0 ⇒ a - b = 3 ---- (i) ... 0 ⇒ a + 1 - 2 + b = 0 ⇒ a + b = 1 ----- (ii) solving equations (i) and (ii) we get a = 2 and b = -1
Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th
Last Answer : The value of a
Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th
Last Answer : p(x) = (k2 – 14) x2 – 2x – 12 Here a = k2 – 14, b = -2, c = -12 Sum of the zeroes, (α + β) = 1 …[Given] ⇒ − = 1 ⇒ −(−2)2−14 = 1 ⇒ k2 – 14 = 2 ⇒ k2 = 16 ⇒ k = ±4
Description : In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (i) quadrilateral ABED is a parallelogram ( ... CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ΔABC ≅ ΔDEF. -Maths 9th
Last Answer : . Solution: (i) AB = DE and AB || DE (Given) Two opposite sides of a quadrilateral are equal and parallel to each other. Thus, quadrilateral ABED is a parallelogram (ii) Again BC = EF and BC || EF ... (Given) BC = EF (Given) AC = DF (Opposite sides of a parallelogram) , ΔABC ≅ ΔDEF [SSS congruency]
Description : Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5)?
Last Answer : 104
Description : Using identities , find the value of -Maths 9th
Last Answer : (i) 1012 = (100 + 1)2 = 1002 + 2 100 1 + 12 = 10000 + 200 + 1 = 10201 (ii) 982 = (100 - 2)2 = 1002 - 2 100 2 + 22 = 10000 - 400 + 4 = 9604 (iii) 0.982 = (1- 0.02)2 = 12 - 2 1 0 ... 102 - 12 = 99 (v) 190 190 - 10 10 = 1902 - 102 = (190 + 10 ) (190 - 10) = 200 180 = 36000
Description : Using identities solve 103^ -Maths 9th
Last Answer : NEED ANSWER
Last Answer : FRIEND YOUR QUESTION IS NOT CLEAR
Description : Solve the following in equalities `(i) |x+7| gt 5` `(ii) |x+3| lt 10` `(iii) (x+2) lt |x^(2)+3x+5|``(iv) |(2x-1)/(x-1)| gt 2` `(v) |x-6| le x^(2)-5x+9
Last Answer : Solve the following in equalities `(i) |x+7| gt 5` `(ii) |x+3| lt 10` `(iii) (x+2) lt |x^(2)+3x+5|``(iv) ... -5) lt 0` `(viii) |x-1|+|x-2|+|x-3| le 6`
Description : Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|`
Last Answer : Solve for `x` `(i) |x+1|=4x+3` `(ii) |x+1|=|x+3|` `(iii) 7|x-2|-|x-7|=5` `(iv) ||x-1|-2|=6x+8` `(v) |2x^(2)-3x+1|=|x^(2)+x-3|`
Description : Evaluate : `int_0^1x(1-x)^5dx`
Last Answer : Evaluate : `int_0^1x(1-x)^5dx`
Description : In quadratic equation ax^2 + bx + c = 0 , Identities the sum and product of Roots? -Maths 9th
Last Answer : If the two roots of the quadratic equation ax2 + bx + c = 0 obtained by the quadratic formula be denoted by a and b, then we have α = \(\frac{-b+\sqrt{b^2-4ac}}{2a},\) β = \(\frac{-b-\sqrt{b^2-4ac}}{2a}\) ∴ Sum of roots ... then α + β = - (- \(\frac{5}{6}\)) = \(\frac{5}{6}\), ab = \(\frac{7}{6}\).
Description : Let x be the mean of x1, x2,….,xn and y be the mean of y1, y2, ……,yn the mean of z is x1, x2,….,xn , y1, y2, ……,yn then z is equal to -Maths 9th
Last Answer : According to question find the value of z
Description : Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15 -Maths 9th
Last Answer : Consider the equation x + y + z = 15 From algebraic identities, we know that (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) So, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz) From the question, x2 + y2 + z2 ... y3 + z3 - 3xyz = 15(83 - 71) => x3 + y3 + z3 - 3xyz = 15 12 Or, x3 + y3 + z3 - 3xyz = 180
Description : If x sin3|+ y cos3|=sin|cos| and xsin|=ycos|, prove x2+y2=1. -Maths 9th
Last Answer : xsin3θ+ycos3θ=sinθcosθ (xsinθ)sin2θ+(ycosθ)cos2θ=sinθcosθ (xsinθ)sin2θ+(xsinθ)cos2θ=sinθcosθ xsinθ=sinθcosθ x=cosθ Again, ycosθ=xsinθ ycosθ=cosθsinθ y=sinθ Therefore, x2+y2=sin2θ+cos2θ=1.
Description : What is 2x plus 1x plus 9?
Last Answer : They are terms of an algebraic expression that can be simplifiedto: 3x+9 or factored to 3(x+3)
Description : Convert each of the following into a fraction: (i) 32% (ii) 614% (iii) 2623% (iv) 120% (v) 6.25% (vi) 0.8% (vii) 0.06% (viii) 22.75% -Maths
Description : What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?
Last Answer : If: y = 2xThen: y^2 = 4x^2If: x^2 +y^2 -8x -y +5 = 0Then: x^2 +4x^2 -8x -2x +5 = 0Transposing terms: 5x^2 -10x +5 = 0Dividing all terms by 5: x^2 -2x +1 = 0Factorizing the above: (x-1)(x-1) = 0 meaning x = 1By substitution into original equations point of contact is madeat: (1, 2)
Description : Using factor theorem, factorise the polynomial x3 + x2 - 4x - 4. -Maths 9th
Last Answer : Solution :-
Description : Write the coefficient of x2 in each of the following -Maths 9th
Last Answer : The coefficient of x2 in each of the following .
Description : ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (i) ∠A = ∠B (ii) ∠C = ∠D (iii) ΔABC ≅ ΔBAD (iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.] -Maths 9th
Last Answer : ] Solution: To Construct: Draw a line through C parallel to DA intersecting AB produced at E. (i) CE = AD (Opposite sides of a parallelogram) AD = BC (Given) , BC = CE ⇒∠CBE = ∠CEB also, ∠A+∠CBE = ... BC (Given) , ΔABC ≅ ΔBAD [SAS congruency] (iv) Diagonal AC = diagonal BD by CPCT as ΔABC ≅ ΔBA.
Description : Find the following products: (i) (3x + 2y + 2z) (9x2 + 4y2 + 4z2 – 6xy – 4yz – 6zx) (ii) (4x -3y + 2z) (16x2 + 9y2+ 4z2 + 12xy + 6yz – 8zx) (iii) (2a – 3b – 2c) (4a2 + 9b2 + 4c2 + 6ab – 6bc + 4ca) (iv) (3x -4y + 5z) (9x2 + 16y2 + 25z2 + 12xy- 15zx + 20yz) -Maths 9th
Description : Find the equation of the line which passes through the point of intersection of the lines 2x – y + 5 = 0 -Maths 9th
Last Answer : (a) 45º 3x + y - 7 = 0 ⇒ y = -3x + 7 ⇒ Slope (m1) = -3 x + 2y + 9 = 0 ⇒ y = \(rac{-x}{2}\) - \(rac{9}{2}\) ⇒ Slope (m2) = \(-rac{1}{2}\)If θ is the angle between the given lines, then tan θ = \(\ ... \bigg|rac{-rac{5}{2}}{1+rac{3}{2}}\bigg|\)= \(\bigg|rac{-rac{5}{2}}{rac{5}{2}}\bigg|\) = 1∴ θ = 45°.
Description : Convert each of the following fraction into a percentage: (i) 47 100 (ii) 9 20 (iii) 3 8 (iv) 8 125 (v) 19 500 (vi) 4 15 (vii) 2 3 (viii) 1 3 5 -Maths
Last Answer : We have the following: (i) 47100=47100×100% = 47% (ii) 920=920×100% =9×5%= 45% (iii) 38=38×100% =3×252%=752%=3712% (iv) 8125=8125×100%=8×45%=325%=6.4% (v) ... ;203%=803%=2623% (vii) 23=23×100%=2003%=6623% (viii) 135=85=85×100%=(8×20)%=160%
Description : If 2x^2 – 7xy + 3y^2 = 0, then the value of x : y is -Maths 9th
Description : If x + y + z = 0, then x^2/(2x^2+yz)+y^2/(2y^2+zx)+z^2/(2z^2+xy) = -Maths 9th
Description : If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e , show that a + c + e = b + d = 0. -Maths 9th
Last Answer : Since x2 - 1 = (x - 1) is a factor of p(x) = ax4 + bx3 + cx2 + dx + e ∴ p(x) is divisible by (x+1) and (x-1) separately ⇒ p(1) = 0 and p(-1) = 0 p(1) = a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0 ... (b+d) = 0 ⇒ b + d = 0 ---- (iii) comparing equations (ii) and (iii) , we get a + c + e = b + d = 0
Description : If one of the roots of the equation x^2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b = 0 is three -Maths 9th
Description : If `f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))|,` then f(100) is equal to - (i)`0` (ii)`1` (iii)`100` (iv)`-100`
Last Answer : If `f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1))|,` then f(100) is equal to - (i)`0` (ii)`1` (iii)`100` (iv)`-100`