In order to add or subtract fractions, they must have the
same denominator. You need to change both of these
fractions to have the same denominator ... without changing
their values, of course.
The smallest common denominator for these fractions is 20 .
3/4 is the same amount as 15/20 .
3/5 is the same amount as 12/20 .
Now that they have the same denominator, you can do
the subtraction.
Part A: The slope of f(x) is three times as great as the slope of g(x).
Part B: The y-intercept of g(x) is 12 larger than the y-intercept of f(x).
In order to find these two answers, you need to find a model for f(x). You can do that by first finding the slope. The formula is below.
slope (m) = (y2 - y1)/(x2 - x1)
In this equation (x1, y1) is the first point and (x2, y2) is a second point. For this purpose, we'll pick (1, 0) and (0, -6)
slope (m) = (-6 - 0)/(0 - 1)
m = -6/-1
m = 6
Now we know that the slope is 6, which is 3 times as great as the first slope. Now to find the y-intercept, we can use either point and the slope in slope intercept form.
y = mx + b
0 = 6(1) + b
0 = 6 + b
-6 = b
So we know the y-intercept is -6, which is 12 less than the y-intercept of g(x).
Answer:
15%
Step-by-step explanation:
Let
Selling price = SP
Cost price = CP
If CP = 100
Profit = selling price - cost price
x% = SP - x% of 100
x% + 100x% = SP
SP = 100 (1 + x/100) (1)
If CP = 92
SP = 92 (1+ {x+10}/100)
Equate both SP
100 (1 + x/100) = 92 (1+ {x+10}/100)
100 + x = 92 + [{23/25} * (x+10)]
{2/25}x = 30/25
x = 30/25 ÷ 2/25
= 30/25 × 25/2
= 30/2
x = 15%
|Ω| = 6 - number of all results
A = {1, 3} → |A| = 2 - number of (a) results
P(A) = 2/6 = 1/3
Combine like terms to get:
4w + 27 = 3
4w = -24
w = -6