The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
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The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
U have a solid line...meaning there is an equal sign in the problem
u have a y int of -1 (the y int is where ur line crosses the y axis)
u have a slope of : 1
it is shaded below the line...so it is less then
so ur inequality is : y < = x - 1 <==
Answer:
12 and 93.
Step-by-step explanation:
Let the grandsons age be x then Mr. Roger's age = 8x - 3.
Five years ago the grandson's age was x-5 and Mr Rogers was 8x - 8 years old , so:
8x - 8 - (x - 5) = 81
8x - 8 - x + 5 = 81
7x = 81 + 8 - 5 = 84
x = 12.
So the grandson is 12 and Mt Rogers is 8*12 - 3 = 93.
Answer: 75%
Step-by-step explanation:
The test had 32 questions and from these 32 you were able to get 24 questions right.
The percentage of questions you got right is the percentage of 32 that 24 is.
= Number of correct questions / Total number of questions * 100%
= 24 / 32 * 100%
= 75%
