Functions
Express 2x2 - 18x + 49 in the form a(x - b)2 + c
2(x - 9/2)2 +17/2
Solve the equation Log3 243+Log3 9=
7
Given that sin(x)=3/5 where "x" is an acute angle, find cos(x)
4/5
Find the number of ways in which 7 toys can be arranged on a shelf
7! = 5040
x + 5y = 7
−2x − 7y = −5
x = -8
y=3
When the function q (x) = x3 + kx2 − 7x + 3 is divided by (x +1) the remainder is seven times the remainder that is found when the function is divided by (x + 2) .
Find the value of k.
k=-2
find log10(4) - log10(40)
In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.
How many students like only tea?
60
Out of forty students, 14 are taking English Composition and 29 are taking Chemistry.
If five students are in both classes, how many students are in neither class?
2
Is there a solution to this system?
x − 2y − 6z = 12
2x + 4y + 12z = −17
x − 4y − 12z = 22
No
In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.
How many students like only one of tea or coffee?
100
Consider a = log23 × log34 × log45 × … × log 3132. Given that a∈Z, find the value of a.
a=5
In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basket ball both. 5% liked watching none of these games.
How many students like watching all the three games?
49%
Four numbers have mean of 13, median is 14, and mode is 15
Find the four numbers
9, 13, 15, 15
2x + z = −8
x − 2y − 3z = 0
−x + y + 2z = 3
x=-4
y=-5
z=2
Expand (2-3x)5
32-240x+720x2-1080x3+810x4-243x5
Find integer values of m and n for which
m - nlog32 = 10 log96
m=5
n=-5
Solve the equation 0.5(x+2) = |x-2|
x=2/3
x=6
log3x - log35 = 1 + log34
60
The sum of the squares of five consecutive positive integers is 9255. What is the value of the square of the next integer?
2116
Find the sum of all integers between 10 and 100 that are divisible by 7
728
Solve the equation 4x + 2x+2 = 3
x= log2 (-2+root7)
Find the solution to
|x+1| = |x-3|
1
3ln3 - ln9 = -lnx
find x
x = 1/3
xx...=1/3
1/27