Answer:
One rational solution
Step-by-step explanation:
proof
5x2 - 2x - 3=0, the sum of coefficients is 5-2-3=0, so the equation has exactly two solutions, x=1, and x = -3/5 this last is the one rational solution
Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x) First plug in the numbers
(9x + 4)(x) Add h(x) and t(x)
(9x² + 4x) Then multiply it by x
x(9x + 4) Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x Simplified Answer: x(9x + 4)
Part B
(h x t)(x)
(5x - 2)(4x + 6)(x) First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x) Next we multiply h(x) and t(x)
(20x² + 22x -12)(x) Simplify it a little
(20x³ + 22x² - 12x) After that, multiply the whole thing by x
(2x)(10x² + 11x - 6) Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3) Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x) Simplified Answer: (2x)(5x - 2)(2x + 3)
Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)] Plug in the numbers
(5x - 2)(4x² + 6x) Multiply t(x) and x
(20x³ + 30x² - 8x² -12x) Multiply that by h(x)
(20x³ + 22x² -12x) Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3) This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x) Simplified Answer: (2x)(5x-2)(2x+3)
Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!
321 / 100 = 3.21 as you are dividing by 10, and then 10 again
Step-by-step explanation:
Pathagory and Theorem
a^2+b^2=c^2
(x-3)^2+(x-4)^2=6^2
expand:
2x^2-14x+25=36
2x^2-14x-11=0
x=(\sqrt{71}+7)/2
perimeter=(x-3)+(x-4)+6=2x-1
insert the value for x into 2x-1
+6=perimeter
Hope that helps :)
