Well, I bet you want your answer right away! So here it is.
<span>Given <span>f (x) = 3x + 2</span> and <span>g(x) = 4 – 5x</span>, find <span>(f + g)(x), (f – g)(x), (f × g)(x)</span>, and <span>(f / g)(x)</span>.</span>
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
<span>\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}<span><span>(<span><span>g</span><span>f</span><span></span></span>)</span>(x)=<span><span><span>g(x)</span></span><span><span>f(x)</span></span><span></span></span></span></span><span>= \small{\dfrac{3x+2}{4-5x}}<span>=<span><span><span>4−5x</span></span><span><span>3x+2</span></span><span></span></span></span></span>
My answer is the neat listing of each of my results, clearly labelled as to which is which.
( f + g ) (x) = –2x + 6
( f – g ) (x) = 8x – 2
( f × g ) (x) = –15x2 + 2x + 8
<span>\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}<span><span>(<span><span>g</span><span>f</span><span></span></span>)</span>(x)=<span><span><span>4−5x</span></span><span><span>3x+2</span></span><span>
Hope I helped! :) If I did not help that's okay.
-Duolingo
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Answer:
C) (x-3)(x+3)
Note:
Just a tip there is an app called Desmos where you can put in equations like this and it will graph them for you.
Answer:
11.2 units
Step-by-step explanation:
From (-7, -7) to (-2, 3) is 5 units horizontally and 10 units vertically. Thus we have a right triangle with sides 5 and 10 respectively. The length of the hypotenuse of this triangle is the distance between (-2, 3) & (-7, -7):
d = √(5² + 10²) = √(25 + 100) = √125 = √25√5, or 5√5.
This is approximately 11.2 units
3x + 6y = 10 is the equation to determine of an apple x and the price of an orange y
<em><u>Solution:</u></em>
Let the price of each apple = $ x
Let the price of each orange = $ y
Martha bought 3 apples and 6 oranges
She had $10 in her wallet which was enough money for the purchase
Thus the equation is:
Total amount = 3 apples(price of each apple) + 6 oranges(price of each orange)
Thus we get,
Thus the equation is found
Width is x - 3
A
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2
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6
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27
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9
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