Let's say the original price was "x", thus "x" is the 100%, and we know that 15 is 80% of that, thus
Represent 'a number' by x
7 times x equals 9 more than 4 times x
7 times x=9+4 times x
7x=9+4x
subtract 4x from both sides
3x=9
divide 3
x=3
the number is 3
Answer:
f(g(x)) = 4x² + 16x + 13
Step-by-step explanation:
Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.
<h3><u>Definitions:</u></h3>
- The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
- In the <u>composition of function</u><em> f </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).
In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).
<h3><u>Solution:</u></h3>
Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:
f(x) = 4x + 5
g(x) = x² + 4x + 2
f(g(x)) = 4(x² + 4x + 2) + 5
Next, distribute 4 into the parenthesis:
f(g(x)) = 4x² + 16x + 8 + 5
Combine constants:
f(g(x)) = 4x² + 16x + 13
Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.
Answer:
FG = 39
Step-by-step explanation:
From the question given:
FH = 9x + 15
GH = 5x + 4
FG = ?
From the question given above, we can say that G is the midpoint of FH. This implies that:
FH = FG + GH
With the above idea in mind, we can obtain FG as follow:
FH = 9x + 15
GH = 5x + 4
FG = ?
FH = FG + GH
9x + 15 = FG + 5x + 4
Rearrange
FG = 9x + 15 - 5x - 4
FG = 9x - 5x + 15 - 4
FG = 4x + 11
Next, we shall determine the value of x. This can be obtained as follow:
Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e
FG = GH
With the above idea in mind, we can obtain the value of x as follow:
FG = 4x + 11
GH = 5x + 4
FG = GH
4x + 11 = 5x + 4
Collect like terms
11 - 4 = 5x - 4
7 = x
x = 7
Thus, we can obtain the value of FG as follow:
FG = 4x + 11
x = 7
FG = 4x + 11
FG = 4(7) + 11
FG = 28 + 11
FG = 39
***Check ***
FH = 9x + 15
x = 7
FH = 9(7) + 15 = 63 + 15 = 78
GH = 5x + 4
x = 7
GH = 5(7) + 4 = 35 + 4 = 39
FG = 4x + 11
x = 7
FG = 4(7) + 11 = 28 + 11 = 39
FH = FG + GH
FH = 78
FG = 39
GH = 39
FH = FG + GH
78 = 39 + 39
78 = 78
