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: The answers are
(ii) The cost to attend Universal Studios increases by 1% each year,
(iii) An endangered species population is decreasing by 12% each year,
(iv) The population of a town that is growing by 5% each year.
Step-by-step explanation: We are given five functions and we are to select those which can be modelled with an exponential function.
(i) Here, height is varying with respect to time, so it will be a linear function.
(ii) Here, the cost to attend Universal Studios is increasing by 1% every year, so this will be an exponential function.
(iii) Here, an endangered species population is decreasing by 12% each year.
So, this will also be an exponential function.
(iv) Since we are considering the distance travelled by the bicycle at a constant speed of 25 mph, so this will be a linear function.
(v) Here also the population is growing by 5% each year. So, the function will be exponential.
Thus, the correct answer is second, third and fifth.
Delete as this is the wrong answer. Made a typo in the answer.
Answer:
x = 
y = 24
Step-by-step explanation:
-3x - 8y = 20 .... (1)
-5x + y = 19 .... (2)
What we can do is take the (2) equation
-5x + y = 19
and solve for y by adding 5x to both sides
y = 24
now that we have y we substitute it in for y in equation (1)
-3x - 8(24) = 20
-3x - 192 = 20
we want to solve for x so we need to get its self.
add 192 to both sides
-3x = 212
now we divide both sides by -3. It's going to be a fraction.
x =
Answer:
-18root7
Step-by-step explanation:
-3root 84*3
-3root4*7*3*3
-3(2*3)root7
-18root7
