Answer:
x = -3, x = 0 is a extraneous solution
Step-by-step explanation:
Step 1: Cross-multiply
3x² = 4x² + 3x
Step 2: Isolate <em>x</em>'s
0 = x² + 3x
Step 3: Factor
0 = x(x + 3)
Step 4: Find roots
x = 0, -3
Step 5: Double check work
Plug in both to see if they both work. Only x = 0 should be extraneous. We now have our answer!
so, this is a quadratic equation, meaning two solutions, and we have a factored form of it, meaning you can get the solutions by simply zeroing out the f(x).
![\bf \stackrel{f(x)}{0}=-(x-3)(x+11)\implies 0=(x-3)(x+11)\implies x= \begin{cases} 3\\ -11 \end{cases} \\\\\\ \boxed{-11}\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}-4\stackrel{\textit{\large 7 units}}{\rule[0.35em]{10em}{0.25pt}}\boxed{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7B0%7D%3D-%28x-3%29%28x%2B11%29%5Cimplies%200%3D%28x-3%29%28x%2B11%29%5Cimplies%20x%3D%20%5Cbegin%7Bcases%7D%203%5C%5C%20-11%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B-11%7D%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D-4%5Cstackrel%7B%5Ctextit%7B%5Clarge%207%20units%7D%7D%7B%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%7D%5Cboxed%7B3%7D)
so the zeros/solutions are at x = 3 and x = -11, now, bearing in mind the vertex will be half-way between those two, checking the number line, that midpoint will be at x = -4, so the vertex is right there, well, what's f(x) when x = -4?
![\bf f(-4)=-(-4-3)(-4+11)\implies f(-4)=7(7)\implies f(-4)=49 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{vertex}{(-4~~,~~49)}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20f%28-4%29%3D-%28-4-3%29%28-4%2B11%29%5Cimplies%20f%28-4%29%3D7%287%29%5Cimplies%20f%28-4%29%3D49%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7Bvertex%7D%7B%28-4~~%2C~~49%29%7D~%5Chfill)
Answer: 35
the age of Roberto is x (x > 3)(x ∈ N)
because Roberto is 3 years older than Carolyn => the age of Carolyn is x - 3
in 7 years, the age of Roberto is x + 7; the age of Carolyn is x - 3 + 7 = x + 4
because In 7 years the sum of their ages will be 81 =>
x + 7 + x + 4 = 81
⇔ 2x + 11 = 81
⇔ 2x = 70
⇔ x = 70/2 = 35
=> the age of Roberto is 35
Step-by-step explanation:
X, y - the numbers
The numbers add to 9 and multiply to -70.
The numbers are
-5 and 14.
Answer:
Segment EF is twice as long as segment AB.
The length of segment EH is 16 units.
Step-by-step explanation:
its
