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Tanya [424]
3 years ago
8

If f(x)=7x-3 and g(x)=x^2-4x-8, Find (f+g)(x)

Mathematics
2 answers:
IrinaK [193]3 years ago
6 0

For this case we have the following functions:

f (x) = 7x-3\\g (x) = x ^ 2-4x-8

We must find (f + g) (x):

By definition we have to:

(f + g) (x) = f (x) + g (x)\\(f + g) (x) = 7x-3 + x ^ 2-4x-8

We add similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

(f + g) (x) = x ^ 2 + 3x-11

Answer:

(f + g) (x) = x ^ 2 + 3x-11

Xelga [282]3 years ago
3 0

Answer:

Step-by-step explanation:

The value of (f+g)(x) is x^2 + 3x - 11

You can combine this by simply adding the like terms. Start by adding together all of the x^2 terms. Since only g(x) has one of those, we use that in its entirety.

x^2

Next we add together the x terms. f(x) has 7x and g(x) has -4x.

7x + -4x = 3x

Finally, we add together the constants. f(x) has -3 and g(x) has -8.

-3 + -8 = -11

With all of the like terms combined, we simply take the answers and put them together.

x^2 + 3x - 11

Read more on Brainly.com - brainly.com/question/10711144#readmore

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y = amount of the 40% solution

we know the 18% solution has only 18% of alcohol, the rest is maybe water or something, now, how many liters is 18%?  well, 18% of anything is just (18/100) * anything, so, 18% of x is just (18/100) *x or 0.18x, and that's how many liters are there.

likewise, how many liters are there in the 40% solution?  well, (40/100) * y, or 0.4y, that many.

we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that?  well, (20/100) * 10, or 2 liters.

\bf \begin{array}{lccclll}&#10;&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\&#10;&------&------&------\\&#10;\textit{18\% solution}&x&0.18&0.18x\\&#10;\textit{40\% solution}&y&0.40&0.4y\\&#10;------&------&------&------\\&#10;mixture&10&0.20&2&#10;\end{array}

\bf \begin{cases}&#10;x+y=10\implies \boxed{y}=10-x\\&#10;0.18x+0.4y=2\\&#10;----------\\&#10;0.18x+0.4\left( \boxed{10-x} \right)=2&#10;\end{cases}&#10;\\\\\\&#10;0.18x-0.4x+4=2\implies -0.22x=-2&#10;\\\\\\&#10;x=\cfrac{-2}{-0.22}\implies x=\cfrac{100}{11}\implies x=9\frac{1}{11}

how much of the 40% solution?  well y = 10 - x
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