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)
As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.
As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.
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a ) Two matrices cannot be multiplied.
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b )
The answer is | 20 - 4 - 12 |
| 8 2 19 - |
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Answer:
(5, 4 )
Step-by-step explanation:
Given the 2 equations
3x - y = 11 → (1)
- 2x - 4y = - 26 → (2)
Multiplying (1) by - 4 and adding to (2) will eliminate the y- term
- 12x + 4y = - 44 → (3)
Add (2) and (3) term by term to eliminate y
- 14x + 0 = - 70
- 14x = - 70 ( divide both sides by - 14 )
x = 5
Substitute x = 5 into either of the 2 equations and solve for y
Substituting into (1)
3(5) - y = 11
15 - y = 11 ( subtract 15 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
solution is (5, 4 )
Answer:
-60
Step-by-step explanation:
Distribute
6 x -3 = -18
6 x -7 = -42
-18 - 42 = -60
If my answer is right, please give it the brainliest.
