F '(x<span>) = </span>2(3x2<span> + 5) + 6x(</span>2x<span> - </span>1<span>) ... + </span>3), s(x<span>) = </span>x<span> - 4. Use the </span>product<span> rule table. below to get: r'(</span>x) = 20x + 11. s'(x<span>) = </span>1<span> ... f'(</span>x) = (x<span> - 4</span>)(20x + 11) - (5x<span> - </span>2)(2x<span> + </span>3)/(x<span> - 4)</span>2<span>.</span>First, we will distribute 2x<span> to (</span>x<span> + 5), then we will distribute </span>3<span>. ... </span>5x<span>. That is,. multiplying binomials. 6x − </span>x<span>= </span>5x<span>. Example </span>2<span>. Multiply (3x − </span>1)(x<span> + </span>2). Answer. 3x2<span> + </span>5x<span>
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We have a rectangle with length L that is 3 inches more than the width W. Then we can write this as:
The area of the rectangle is 180 square inches.
We have to find the width W.
As the area is equal to the product of the length and the width, we can write this equation and solve for W as:
We have a quadratic equation. The roots of this equation will be the mathematical solutions.
We can find the roots using the quadratic formula:
![\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ W=\frac{-3\pm\sqrt[]{3^2-4\cdot1\cdot(-180)}}{2\cdot1} \\ W=\frac{-3\pm\sqrt[]{9+720}}{2} \\ W=\frac{-3\pm\sqrt[]{729}}{2} \\ W=\frac{-3\pm27}{2} \\ W_1=\frac{-3-27}{2}=-\frac{30}{2}=-15 \\ W_2=\frac{-3+27}{2}=\frac{24}{2}=12 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20W%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20W%3D%5Cfrac%7B-3%5Cpm%5Csqrt%5B%5D%7B3%5E2-4%5Ccdot1%5Ccdot%28-180%29%7D%7D%7B2%5Ccdot1%7D%20%5C%5C%20W%3D%5Cfrac%7B-3%5Cpm%5Csqrt%5B%5D%7B9%2B720%7D%7D%7B2%7D%20%5C%5C%20W%3D%5Cfrac%7B-3%5Cpm%5Csqrt%5B%5D%7B729%7D%7D%7B2%7D%20%5C%5C%20W%3D%5Cfrac%7B-3%5Cpm27%7D%7B2%7D%20%5C%5C%20W_1%3D%5Cfrac%7B-3-27%7D%7B2%7D%3D-%5Cfrac%7B30%7D%7B2%7D%3D-15%20%5C%5C%20W_2%3D%5Cfrac%7B-3%2B27%7D%7B2%7D%3D%5Cfrac%7B24%7D%7B2%7D%3D12%20%5Cend%7Bgathered%7D)
The solutions are W = -15 and W = 12.
The first one is not valid, as W has to be greater than 0.
Then, the solution to our problem is W = 12 in.
Answer: the width is W = 12 inches.
<span>I got 2^(3/5) as the answer</span>
Answer:
depends
Step-by-step explanation:
Quotient means the answer
Dividend is the first number that is being divided
Divisor is the number dividing the first number
