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)
![\displaystyle \frac{y}{b}=\frac{5}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7By%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B4%7D)
Multiplying the equations above:
![\displaystyle \frac{r}{y}\frac{y}{b}=\frac{2}{3}\frac{5}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7By%7D%5Cfrac%7By%7D%7Bb%7D%3D%5Cfrac%7B2%7D%7B3%7D%5Cfrac%7B5%7D%7B4%7D)
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:
![\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+y/r+b/r}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%3D%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B1%2By%2Fr%2Bb%2Fr%7D)
Substituting from [2] and [3]:
![\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+3/2+6/5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%3D%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B1%2B3%2F2%2B6%2F5%7D)
Operating:
![\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{\frac{10+3*5+6*2}{10}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%3D%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B%5Cfrac%7B10%2B3%2A5%2B6%2A2%7D%7B10%7D%7D)
![\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{10+15+12}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%3D%5Cdisplaystyle%20%5Cfrac%7B10%7D%7B10%2B15%2B12%7D)
![\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{37}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%3D%5Cdisplaystyle%20%5Cfrac%7B10%7D%7B37%7D)
The fraction of the beads that are red is ![\mathbf{\frac{10}{37}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B10%7D%7B37%7D%7D)
I'm pretty sure it's Identity I hope it helps :)
Sub y = 0 in to find x intercept and x = 0 in to find y intercept
Answer:
a. 11x + d
b. 15m + 10n
Step-by-step explanation:
a. 2(4c+5d) + 3(x-3d)
Break the brackets:
2*4c + 2*5d + 3*x - 3*3d
= 8x + 10d + 3x - 9d
Collect like termsL
= 8x + 3x + 10d - 9d
= 11x + 1d
b. 6(3m+n) - 4(m-n)
Break the brackets:
= 6*3m + 6*n - 3*m - 4*(-n)
= 18m + 6n - 3m - (-4n)
= 18m -3m + 6n + 4n
= 15m + 10n
Hope this helped :3
Answer:
<h2>x = -3</h2>
Step-by-step explanation:
![4^x=\left(\dfrac{1}{8}\right)^{x+5}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\4^x=(8^{-1})^{x+5}\\\\(2^2)^x=\bigg((2^3)^{-1}\bigg)^{x+5}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2x}=2^{-3(x+5)}\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3](https://tex.z-dn.net/?f=4%5Ex%3D%5Cleft%28%5Cdfrac%7B1%7D%7B8%7D%5Cright%29%5E%7Bx%2B5%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7Ba%7D%5C%5C%5C%5C4%5Ex%3D%288%5E%7B-1%7D%29%5E%7Bx%2B5%7D%5C%5C%5C%5C%282%5E2%29%5Ex%3D%5Cbigg%28%282%5E3%29%5E%7B-1%7D%5Cbigg%29%5E%7Bx%2B5%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C2%5E%7B2x%7D%3D2%5E%7B-3%28x%2B5%29%7D%5Ciff2x%3D-3%28x%2B5%29%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%5C%5C2x%3D-3x-15%5Cqquad%5Ctext%7Badd%7D%5C%203x%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5C%5C%5C5x%3D-15%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%205%7D%5C%5C%5C%5Cx%3D-3)