Answer:
y = 60
Step-by-step explanation:
<h3>Step 1: Make sense of the given</h3>
"The ratio of y to x is 3"
This means that,
"The sum of y and x is 80"
This means,
<h3>Step 2: Make use of the facts</h3>
If , then .
We can plug this into the other equation by substitution:
This simplifies to:
Which we can solve out and get:
.
<h3>Step 3: Plug and Chug</h3>
We solved for x, but we need the value of y.
So, we go back to the equation we first derived: "".
And now we substitute the value of x, into this.
By solving this out, we get:
So, the value of y is 60.
Step-by-step explanation:
-5x + 4y = 2
+ (9x - 4y = 6)
=> 4x = 8, x = 2.
Therefore -5(2) + 4y = 2, 4y = 12, y = 3.
The solution pair is (2,3).
Answer:
The gear ratio of the bike = 3:1
Step-by-step explanation:
Question:
A gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket, what is the gear ratio for the bike?
Given:
Number of teeth on the front sprocket = 36
Number of teeth on the rear sprocket = 12
To find the gear ratio for the bike.
Solution:
The gear ratio of a bike is the ratio of the number of teeth on the front sprocket and the number of teeth on the rear sprocket.
Thus, the gear ratio can be given as:
⇒
Reducing to simple fraction by dividing the numerator and denominator by their GCF.
⇒
⇒
Thus the gear ratio can be given = 3:1
8668/25 + 4141/9 - 5533/25.....common denominator is 225
78012/225 + 103525/225 - 49797/225 =
181537/225 - 49797/225 =
131740/225 =
585 115/225 =
585 23/45
so the fraction part of the mixed number is 23/45
Answer:
Step-by-step explanation:
Given :
re - writing the equation , we have
we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.
The formula for finding the quadratic equation when the roots are known is :
- sum of roots(x) + product of root = 0
sum of roots = -2 + 4 = 2
product of roots = -2 x 4 = -8
substituting into the formula , we have:
, which could be written in inequality form as
comparing with , it means that :