(a) Solve 2(x+2)−5=9. (b) Write as single fraction 32x+1+63x−2. (c) Rearrange T=2π8L to find L. (d) (I) Show f(x)=x3−13x+12 can be written as (x−1)(x2+x−12). (II) Completely factorise f(x).
Find the width of a rectangle with length 10 cm longer than width, if total perimeter is 220 cm. x cm width, x+10 cm length, total perimeter 2(x+x+10)=220. Solve for x.
1. Find the equation with solution k=−3.
A. 2k−5=−1 B. k−3=6 C. 3k−3=−6 D. 4k+1=−11 2. Anthony is 4 years older than his brother Felix. Their ages sum to 42. What equation can be used to find their ages?
A. 4f=42 B. 4f+f=42 C. f+f+4=42 D. 4f+f+4=42
A hiker hikes at a steady rate on a mountain. Which student wrote the correct equation y=−125x+5,775 to represent the linear relationship between hours hiked (x) and altitude (y)?
1. Given p=5−2i and q=−3+7i, write each expression in the form a+bi:
a. p+q−p×q
b. p−q−p÷q 2. a. Solve the equation 2x+1−4=−1.
b. Explain why 2x+1+4=−1 has no real solution.