- f (x) = 3x² + x
- Find f (-5).
Given,
Now, we have to find f (-5). To find this, we just need to substitute -5 in the place of x.
So,
If the graph has exactly the same shape, and just moved up 3 units,
the equation of this new graph is
f(x) = x² + 3
Answer:
The perpendicular equation is y = -3x -21
Step-by-step explanation:
Perpendicular lines have the exact opposite slope as the other equation and they never have the same y-intercept.
To find the perpendicular slope just look at the slope in the original equation and get the exact opposite.
First let's simplify the equation.
-5 + x = 3y (divide by 3 on both sides to get y by itself)
-5/3 + 1/3x = y or y = 1/3x + 5/3
The exact opposite of this slope would be -3.
Now plug in the point you were given so that we can find the y-intercept.
6 = -3(-9) + b (b = y-intercept)
6 = 27 + b (subtract 27 on both sides)
-21 = b
So the perpendicular equation looks like this.
y = -3x -21
There is 1 way to make 30 cents using only pennies. (i.e. 30 pennies = 30 cents)
There is 1 way to make 30 cents using only nickels. (i.e. 6 nickels = 30 cents)
There is 1 way to make 30 cents using only dimes. (i.e. 3 dimes = 30 cents)
There are 5 ways to make 30 cents using only pennies and nickels. (i.e. 25 pennies + 1 nickel = 30 cents, 20 pennies + 2 nickels = 30 cents . . . )
There are 2 ways of making 30 cents using only pennies and dimes. (i.e. 20 pennies + 1 dime = 30 cents, 10 pennies + 2 dimes = 30 cents)
There is 1 way of making 30 cents using only pennies and quarters. (i.e. 5 pennies + 1 quarter = 30 cents)
There are 2 ways of making 30 cents using only nickels and dimes. (i.e. 4 nickels + 1 dime = 30 cents, 2 nickels + 2 dimes = 30 cents)
There is 1 way of making 30 cents using only nickels and quarters. (i.e. 1 nickel + 1 quarter = 30 cents)
There are 4 ways to make 30 cents using only pennies, nickels and dimes. (i.e. 15 pennies + 1 nickel + 1 dime = 30 cents, 10 pennies + 2 nickels + 1 dime = 30 cents . . .
)
Adding all the possible combinations therefore, there are 18 <span>different ways are there to make 30 cents with pennies nickels dimes or quarters.</span>
The lowest common multiple of two numbers that have no common factors greater than 1 is 1. The answer is 1. That is the only common factor they have in common.
Example: 19, and 13
