2+ day, 4+ hour ago (342+ words) What is the value of x in the equation above? For the quadratic function y = f(x), (x " 3) is a factor and'x = k is a positive zero. If (5, c) is the maximum point on the graph of y = f(x), what is the value of k? Which of the following expresses a in terms of b and c? The function f is defined by f(2x " 1) = 4x + 3 and the function g is defined by g(x) = f(x) " 1. What is the value of g(10)? The line shown in the xy-plane passes through the point (0, 0) and the point' (a, b), where a > b. Which of the following could be the slope of this line? A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the…...

1+ week, 2+ day ago (896+ words) Two numbers are in the ratio 6 : 5. If their HCF is 3, then'what is the LCM of the two numbers? A merchant has 120 liters and 180 liters'of two kinds of oil. He wants to sell the oil by filling the two kinds in tins of equal volumes. Find the greatest volume of such a tin. But, the target of the question is, the volume of oil filled in tins must be greatest. So, we have to find the largest number which exactly divides 120 and 180. That is the highest common factor (HCF) of (120, 180). HCF (120, 180) = 60 liters The 1st'kind 120'liters is sold in 2 tins of of volume 60 liters in each tin. The 2nd'kind 180 liters'is sold in 3 tins of volume 60 liters'in each tin. Hence, the greatest volume of the tin is 60'liters. Find the least number of square tiles by which the floor of a room of…...

1+ week, 2+ day ago (375+ words) The curve y= ax " b passes through points (c, 8)and (2c, 350). Find the value of b. The function p is defined by p(x) = a((x + 7)2 " b)((x + 7)2 " c), where a, b and c are constants. In the xy-plane, the graph of y = p(x) passes through the points ("12, 45) and (0, 256). What is the value of p("2) + p("14)? In the xy-plane above, O is the center of the circle and the measure of'POQ is k. What is the value of k? Which expression is equivalent to 16x4 " 81? A) (4x2 + 9)2 B) (2x + 3)2(2x " 3)2 C) (4x2 + 27)(4x2 " 3) D) (4x2 + 9)(2x + 3)(2x " 3) Two numbers, p and q, are each greater than zero, and the square of p is equal to the cube root of q. For what value of x is p1 " x equal to the square root of q? The given equation relates the positive real numbers x, y and z.Which equation correctly expresses x in terms y and z? C) x = y2 + z2 + 2yz " 3 D) x = z2 + y2 " 2zy " 3 In circle P,…...

1+ week, 2+ day ago (628+ words) If a number when divided by 296 gives a remainder 75, find the remainder when 37 divides the same number. x = 378k + 372 + 1 x = 37(8k + 2) + 1 So, the remainder is "1" when the number "x" is divided by 37. Find the number of prime factors of From 6107175527, we have to write each base in terms of multiplication of its prime factors. The no. of prime factors = sum of the exponents = 10 + 10 + 17 + 27 + 27 So, the number of prime factors is 91. Find the unit digit of Take the last two digits in the power and unit digit in the base. They are 43 and 2.Step 2 : Divide the last two digits of the power by 4 (in all the problems) and get the remainder. That is, when 43 is divided by4, the remainder is 3.Step 3 : Now this remainder 3 has to be taken as exponent of the unit digit 2.That is, 23= 8. So, the unit digit of the given number…...

1+ week, 2+ day ago (780+ words) Find the highest common factor (HCF) of the numbers 48 and 64 using division method. The product of common factors of 48 and 64 is = 222 2 2 So, HCF (48, 64) = 16. Find the highest common factor of the numbers 18, 24 and 30 by factor tree method. Using factor Tree Method, find the factors of 18, 24 and 30. The factors of 18 are1,2,3,6, 9 and 18. The factors of 24 are1,2,3, 4,6, 8, 12 and 24. The factors of 30 are1,2,3, 5,6, 10, 15 and 30. The factors that are common to all numbers 18, 24 and 30 are 1, 2, 3, 6 In the above common factors, 6 is the largest value. So, HCF (18, 24, 30) = 6. Find the highest common factor of the numbers 84 and 182 by prime factorization method. Write the prime factors of 84 and 182 as shown below. The prime factors that are common to 84 and 182 are So, HCF (84, 182) = 14. When 62, 78 and 109 are divided by the greatest number, leaving remainders 2, 3 and 4 respectively. 62 - 2 = 60 78 - 3 = 75 109 - 4 = 105 Get all the common factors of 60, 75 and 105 and see that the common factors will divide them all....

2+ week, 1+ day ago (436+ words) In the figure below, O is the center of the circle and RT is tangent to the circle at X. If triangle RST is equilateral, what is the value of RT/YZ? In triangle XYZ, the measure of angle X is x, the measure of angle Y is y, and the measure of angle Z is 31. If x > y > 31, which of the following additional pieces of information is NOT sufficient to determine the values of x and y? A)" The value of 31 " x " 3y B)" The value of 31 + 3x + y D)" The value of 31 " 3x " 3y Let the function p defined as" h(x) = x3 + ax2 + bx + c The function h is defined above, where a, b and c are integer constants. If the zeros of the function are "5, 6 and 7, what is the value of c? For the exponential function f, the value of f(1) is k, where k is a…...

2+ week, 5+ day ago (1698+ words) When 23 is decreased from 5 times a number. the result is 57. Find the number. If four times of Liam's age 9 years ago be subtracted from thrice of his age 4 years hence, the result would be equal to his present age. Find the present age of Liam. The denominator of a fraction is 1 less than twice the numerartor. If 1 be added to both numerator and denominator, the fraction becomes. Find the fraction. Sum of the digits in a two digit number is 11. Switching the digits results a number which is less than the original number by 45. Find the number. The demand equation for a certain item is'd = 15(p - 10)', where d is demand in lbs and p is price in dollars.The supply equation giving the supply sin lbs. for a price p in dollars per lb. is 's = 20(17 - p)'. What is the equilibrium…...

2+ week, 6+ day ago (378+ words) The length x, and width y, of a rectangle can be related by the following system of equations. If both the length and width are integers, what is the area of the rectangle? If (a " 3)2 + (b " 4)2 + (c + 5)2 = 0, what is the value of a + b + c? In the given equation, p > 1 and t > 1. If t = p2n " 1, where n is a constant, what is the value of n? If (px + 5)(qx + 3) = 8x2 + rx + 15 for all values of x,and p + q = 6, what are two possible values for r? A) 2 and 4 B) 7 and 12 C) 22 and 26 D) 29 and 39 The graph of a circle intersects the x-axis andy-axis at four distinct points, one of which lies on the negative x-axis at (k, 0). If k is a constant, what is its value? If x" 0 and y" 0, which of the following is equivalent to the above expression? (ax + 3)(5x2 " bx + 4) = 20x3 " 9x2 " 2x + 12 The equation above is…...

3+ week, 2+ day ago (395+ words) In the equation above, k is a constant. If the equation has one solution, what is the value of k? The perimeter of a right isosceles triangle is 256 + 2562.What is the length of the hypotenuse? Two lines intersect at exactly one point, forming two acute angles and two obtuse angles. The measure of one of these angles is (7x " 80). Which of the following could NOT be the sum of the measures of any two of these angles? A) (14x " 160) B) ("14x + 520) C) (14x " 520) A data set contains consecutive positive integers. The range of the data set is 30 and the largest integer in the data set is seven times the smallest one. If one of the integers is selected at random from the data set, what is the probability that the selected integer is a multiple of both 4 and 5? Length of a rectangle is half of the square…...

3+ week, 5+ day ago (383+ words) f(t) = 55t " 2t2 The function f is defined by the given equation.The function g is defined by g(t) = f(t) + 3. Which expression represents the maixmum value of g(t)? A) 3 + (55/4)2 B) 3 + 2(55/4)2 C) 3 - 2(55/4)2 D) 3 - (55/4)2 The function g is defined by g(x) =|x|/a " 14, where a < 0. What is the product of g(15a) and g(7a)? Consider the line q which be written as y = mx + b.It is given that the points (2a, 4 " 3a) and (4a, 4 " 6a)lie on the line q. Determine the value of b. One of the factors of 2b3 " 24b2 + 70b is b " c,where c is a constant. What is the largest possiblevalue of c? The functions g and h are defined by the givenequations, where x " 0. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where x " 0 ? I. g(x) = 18(1.16)(1.14)x + 2 II. h(x) = 18(1.4)x + 4 C) I and II D) Neither I nor II Function f is defined by f…...