Answer:
35 because they relevantly parrel which explains it alll
The value of gf(5) for the given two expressions is 135.
According to the question,
We have the following information:
f(x)= x +4
g(x) = 3x
Now, in order to find the value of gf(5), we will first find the value of gf.
Now, we will multiply these two expressions:
3x(x+4)
Now, the terms outside the brackets need to multiplied inside the bracket:

Now, we will put the value of x in this expression as 5 and solve the expression further by multiplication and addition:
3*5*5+12*5
75+60
135
Hence, the value of gf(5) for the given two expressions of f(x) and g(x) is 135.
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The number of visits Liam can make to earn his first free movie ticket is: 8.4.
<h3>
Number of visits Liam can make</h3>
Let x represent the number of visits
Formula
55+12.5×x=160
Re-arrange
12.5x=160-55
12.5x=105
Divide both side by 12.5x
x=105/12.5
x=8.4 visits
Therefore the number of visits Liam can make to earn his first free movie ticket is: 8.4.
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To factor both numerator and denominator in this rational expression we are going to substitute

with

; so

and

. This way we can rewrite the expression as follows:

Now we have two much easier to factor expressions of the form

. For the numerator we need to find two numbers whose product is

(30) and its sum

(-11); those numbers are -5 and -6.

and

.
Similarly, for the denominator those numbers are -2 and -5.

and

. Now we can factor both numerator and denominator:

Notice that we have

in both numerator and denominator, so we can cancel those out:

But remember than

, so lets replace that to get back to our original variable:

Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is


The solution of the equations is (-2, -1)
<h3>System of equation:</h3>
2x - 3y = -1
11x - 9y = -13
Using elimination method let multiply the first equation by -3.
Therefore,
-6x + 9y = 3
11x - 9y = -13
5x = -10
x = -10 / 5
x = -2
let's find y as follows;
2(-2) - 3y = -1
-4 - 3y = -1
-3y = -1 + 4
-3y = 3
y = 3 / -3
y = -1
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