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galina1969 [7]
3 years ago
11

Solve 10 (2y +2) - y =2 (8y- 8)

Mathematics
1 answer:
Jet001 [13]3 years ago
8 0

The answer is y = −12

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Which symbol is used to name a line with two points A and B
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AB

Step-by-step explanation:

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Carlos bought 80 feet of rope for $17.60. He needs 20 more feet. If the unit price is the same how much will he pay for the extr
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Another 20 feet would be +4.40$

so the total would be $22

Step-by-step explanation:

17.60/4 because 80/20 is 4.

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Area of a trapezium​
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Answer:

The area of a trapezium is computed with the following formula: Area = 1 2 × Sum of parallel sides × Distance between them.

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The sqaure root of 130 falls between which consecutive numbers
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Find f(g(x)). State the domain of the composite function.<br> f(x) = 3x-2/x+1<br> g(x) = x+5/2x-3
AnnyKZ [126]

Answer:

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

g(x)=\dfrac{x+5}{2x-3}\Longrightarrow 2x-3\neq 0\iff \boxed{x\neq\dfrac{3}{2}}

- Domain of f(g(x)): We'll find its expression:

f(x) = \dfrac{3x-2}{x+1}\\\\f(g(x)) = \dfrac{3g(x)-2}{g(x)+1}\\\\f(g(x)) = \dfrac{3\cdot\dfrac{x+5}{2x-3}-2}{\dfrac{x+5}{2x-3}+1}=\dfrac{~~~\dfrac{3(x+5)-2(2x-3)}{2x-3}~~~}{\dfrac{(x+5)+(2x-3)}{2x-3}}\\\\f(g(x)) =\dfrac{3(x+5)-2(2x-3)}{(x+5)+(2x-3)}=\dfrac{3x+15-4x+6}{x+5+2x-3}\\\\\boxed{f(g(x)) =\dfrac{21-x}{3x+2}}

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

f(g(x)) =\dfrac{21-x}{3x+2}\Longrightarrow 3x+2\neq0\iff \boxed{x\neq-\dfrac{2}{3}}

Lastly, we may write the domanin of f(g(x)):

D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[

or, just writing in a shorter way:

\boxed{D(f(g(x)) = \mathbb{R}-\left\{-\dfrac{2}{3},\dfrac{3}{2}\right\}}

7 0
2 years ago
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