Algebra Answers

Let f(x) = 3tan^4x+2k and g(x) = -tan^4x+8ktan^2 x + k for 0 ≤ x ≤ 1, where 0 < k < 1. The graphs of f and g intersect at exactly one point. Find k. My book gets an answer of 1/4 where as I get k=4. Please explain.

A Ferris wheel can accommodate 55 people in 25 minutes. How many people could ride the Ferris wheel in 6 hours? What was the rate per hour?

find the values of k for which the following equations have no real roots.

(a) kx^2-4x+8=0

(b) 3x^2+5x+k+1=0

(c) 2x^2+8x-5=kx^2

(d) 2x^2+k=3(x-2)

(e) kx^2+2kx=4x-6

(f) kx^2+kx=3x-2

find the values of k for which the following equations have two distinct roots.

(a) x^2+8x+3=k

(b) 2x^2-5x =4-k

(c) kx^2-4x+2=0

(d) kx^2+2(k-1)x+k=0

(e) 2x^2=2(x-1)+k

(f) kx^2+(2k-5)x=1-k

find the values of k for which the following equations have two equal roots.

(a)4x^2+4(k-2)x+k=0

(b)(k+2)x^2+4k=(4k+2x)

(c)x^2-2x+1=2k(k-2)

(d)(k+1)x^2+kx-2k=0

(e)4x^2-(k-2)x+9=0

Of the members of three athletic teams in a school 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, and 12 play football and cricket. Eight play all the three games. The total number of members in the three athletic teams is

How would i solve| (x-2)(x²+8x-1).                    (X+4)(x²-5x+9), I have to find the answer to these, then add them together.

A one litre box of juice is three quarters full.you pour out one fifth of the litre of juice.how much of the litre of juice is now left in the box

Solve for the values of x for each of the following exponential equations and

inequalities.

1. 6𝑥+2 = 362𝑥−3

2. 5𝑥−1 = 625

3. 54𝑥 ≥ 253𝑥+2

On a certain map, the straight-line distance between The Pas and Winnipeg is 4.1cm. If the scale

of the map is 1cm = 120 km, how far apart are The Pas and Winnipeg, to the nearest kilometer?