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 
Answer:
they are equivalent
Step-by-step explanation:
simplifying 12r + p -4r + 6p you get 8r + 7p
so yes they are equal
Answer:
3:6
Step-by-step explanation:
8:24 and 24:72 reduce down to 1:3. 3:6 is 1:2.
Answer:
4x + 5y = - 23
Step-by-step explanation:
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 4y - 5x = 20 into this form
add 5x to both sides
4y = 5x + 20 ( divide all terms by 4 )
y = 
x + 5 ← in slope-intercept form
with slope m =
given a line with slope m then the slope of a line perpendicular to it is
= - 
, hence
= - 1 / = - 
y = - x + c ← is the partial equation
to find c substitute (- 2, - 3) into the partial equation
- 3 = 
+ c ⇒ c = - 
y = - x - ← in slope-intercept form
multiply all terms by 5
5y = - 4x - 23 ( add 4x to both sides )
4x + 5y = - 23 ← in standard form
Answer:
3/4=21/28
Step-by-step explanation:
21/28÷7/7=3/4
