Number Theory/Arithmetic
What is the sum of the two solutions of x2 * x - L2 - 0?
-1
If x, x + 2, and x + 3 are the first three terms of a geometric series, what is the sum of the first five terms of the series?
What is 31/4?
Determine the sum of the smallest and largest solution for the inequality |2x - 5| is greater than or equal to 11.
What is 5?
When rolling two fair dice, what is the probability of one die landing on a number less than three and the other die on an odd number?
11/36
Suppose two bicycle riders are headed toward each other, the first at 10 mph and the second at 15 mph. At the instant the bicyclists are 30 miles apart, a bird flying at 20 mph and headed in the same direction as the first rider, passes the first rider. When the bird reaches the second rider, it instantaneously changes direction and heads back toward the first rider. When the bird reaches the first rider it again instantaneously changes direction and heads toward the second rider. If the bird continues to go back and forth at20 mph, how far will it travel from the time the bikers are 30 miles apart until they reach each other?
What is 24 miles?
If f (x) = 1/2x + 7 and g(x) = -2x + 7, what is the following is the point of intersection of the graphs of f and g?
(2, 3)
Suppose an equilateral triangle is inscribed in a circle. Which of the following is closest the area of the triangle divided by the area of the circle?
a) .30 b) .35 c) .40 d) .45 e) .50
C
Let (x + 3y)2 = 10, what is the numerical value of 6x2 + 36xy + 54y2?
What is 60?
A bag contains red and blue marbles. When two marbles are drawn, the probability they are both red is equal to the probability they are both blue. The probability that one of each color is drawn is 4/7.The total number of marbles in the bag is?
What is 8?
Solve for x:
3 * 16x + 36x - 2 * 81x = 0.
What is 1/2?
Suppose a store owner wants to make a 100 pound mixture of peanuts and cashews to sell for $4.30 per pound. If peanuts sell for $2.50 per pound and cashews sell for $7.00 per pound, how many pounds of each should be used?
What is 60lbs of peanuts and 40 lbs of cashews
ABCD is a trapezoid. Leg AD = 9, base CD = 6 and m<D= 2m<B. Determine the length of the base AB.
What is 15?
How many real number solutions does this equation have? lx2 - 4l + lxl * 2x = 2
What is 2?
Two of the solutions of x in the equation x3 - 9x = 5x - 45 are selected at random. These two values are the solutions for y in the equation ay2 + by + c = 0, where a, b, and c are integers with no common factors and a>0. Determine the probability that b < 0. Express your answer as a simplified fraction.
What is 2/3?
There are two quadratic polynomials with real number coefficients, x2 + ax + b and x2 + cx + d, each of which will divide into x4 + 9 with no remainder. For these two quadratics a+b+c+d is?
What is 6?
The to solution of (x + 3)3 + (x + 5)3 = 8
What is -3?
The measures of two angles pf a triangle are in the ratio 2:3. The third angle measures 4 degrees more than the larger of the other acute angles. This is the degree measure of the exterior angle adjacent to the third angle of the triangle.
What is 110 degrees?
The product of the solutions for the equation x3 - 7x2 - 14x + 67 = 0.
What is -67?
A number is selected at random from set A, which consists of integers between -8 and 8 inclusive. Determine the probability that number selected is BOTH a solution for x to x2 - 3x - 28 < or equal to 0 and a possible length of the third side of a triangle with sides 5 and 7. Express your answer as a common fraction.
What is 5/17?
Let s, = 1! * 2l + 3! + "' + n! For how many integers n is ./3, is an integer?
2
If s1 = l!,s2= 1!+2!,s3 = 1! +2!+ 3!,s4 = 1! +2! + 3! + 4!,and so on, then what is the one's digit of s100?
What is 3?
In triangle ABC, the altitude from A to BC intersects BC between B and C and the foot of the altitude has coordinates (-2, 3). An equation of the perpendicular bisector is 2x + y = 4 and an equation of the median form A is 3x + 4y = 16. The coordinate of A written as an ordered pair is?
What is ( -4, 7)
Let k be the numerical value of the area of the region enclosed by |2x - 1| + |y + 3| = 8, this is the value of k.
What is 64?
Carly has 369 markers. Out of these 130 are black, 100 are blue and the others are neither black or blue. She chooses to markers at random. Find the probability that one of the two markers is black and the other marker is neither black or blue? Answer in decimal form rounded to the nearest thousandth.
.266
What is the sum of 1 x 2 + 2 x 3 + 3 x 4 +"'+100 x 101
what is 343,400?