(3r)/(r-5) = (r+2)/(r+3)
(3r)(r+3)=(r-5)(r+2)
3r^2 +9r= r^2-3r-10
2r^2+12r+10=0
2(r^2+6r+5)=0
2(r+5)(r+1)=0
r=-1 or r=-5
Answer:
100+10n
Step-by-step explanation: a(10)
100+10(10)
100+100 = 200
28 - s - 6(Sophias age) = Sophia is twenty two and eric is 16.
Answer:
B. The graph flips over the x-axis
Step-by-step explanation:
<u>Properties of : c · f(x)</u>
- Graph opens wider/more narrow
- If the absolute value of c is greater than one, the shape narrows
- If the absolute value of c is less than one, it widens
- It can also affect any applied horizontal/vertical shifts
- If c is negative, the shape is reflected over the x-axis (upside-down)
<em><u>In this case, the question is only asking if the function flips a certain way. As seen, "c," (as shown above) is -1, which is less than one. This means that the function will be flipped over the x-axis.</u></em>
<em><u></u></em>
Answer:
- f(x) = x^3
- g(x) = (2x+4)^2
Step-by-step explanation:
There are many ways to decompose h(x) into f(x) and g(x). The main purpose of the exercise seems to be to get you to think about the operations that are performed on x, then divide that list of operations into two parts.
In the function ...
h(x) = (2x +4)^6
the variable x is ...
- multiplied by 2
- 4 is added to the sum
- the sum is raised to the 6th power
Of course, the 6th power can be considered as the cube of a square or the square of a cube, if you like.
In the decomposition shown in the answer above, we have chosen to put most of this list in g(x), including the square of the sum. Then we have made f(x) be the cube of that square.
h(x) = f(g(x)) = (2x+4)^6
When f(x) = x^3, this is ...
h(x) = f(g(x)) = g(x)^3 = ((2x+4)^2)^3
so ...
g(x) = (2x+4)^2 . . . and . . . f(x) = x^3
_____
Other possible decompositions are ...
or
- g(x) = (x+2)
- f(x) = (2x)^6
or
or ... (many others)
