Answer: GCF of 40 and 42 is 2
I think the correct answer from the choices listed above is option C. Creating the rule 3x+12 to describe a sequence of numbers is an example of the usage of deductive reasoning. <span>Deduction is logical reasoning based on the understanding of all pieces in a given scenario.</span>
Answer:
2π/7
Step-by-step explanation:
A cosine wave is:
y = A cos(2π/T x + B) + C
where A is the amplitude,
T is the period,
B is the horizontal shift,
and C is the vertical shift.
In this case:
7 = 2π/T
T = 2π/7
9514 1404 393
Answer:
(f/g)(x) = 1/(2x)
x ≠ 1/2
Step-by-step explanation:

The domain restriction x ≠ 1/2 comes from the requirement to prevent the denominator factor 6x-3 from being zero.
Answer:
<em>The fraction of the beads that are red is</em>
Step-by-step explanation:
<u>Algebraic Expressions</u>
A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:
r:y = 2:3
y:b = 5:4
We are required to find r:s, where s is the total of beads in the bag, or
s = r + y + b
Thus, we need to calculate:
![\displaystyle \frac{r}{r+y+b} \qquad\qquad [1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B1%5D)
Knowing that:
![\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7By%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B2%5D)

Multiplying the equations above:

Simplifying:
![\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B6%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B3%5D)
Dividing [1] by r:

Substituting from [2] and [3]:

Operating:



The fraction of the beads that are red is 