Answer:
Step-by-step explanation:
The given absolute value function is
This is the base or the parent function.
The transformation 
will shift the parent function b units to the left and c units up.
From the question, b=4 units and c=2 units.
The new equation is
Answer:
Step-by-step explanation:
Let's call x the length of each piece in yards
If the ribbon is cut into 8 equal pieces then the sum of the pieces is:
Then:
Now we solve the equation for x
Divide both sides of equality by 8
So the length of each piece is 
of a yard.
This is: 1.125 yards
Let's begin by listing the first few multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44. So, between 1 and 37 there are 9 such multiples: {4, 8, 12, 16, 20, 24, 28, 32, 36}. Note that 4 divided into 36 is 9.
Let's experiment by modifying the given problem a bit, for the purpose of discovering any pattern that may exist:
<span>How many multiples of 4 are there in {n; 37< n <101}? We could list and then count them: {40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100}; there are 16 such multiples in that particular interval. Try subtracting 40 from 100; we get 60. Dividing 60 by 4, we get 15, which is 1 less than 16. So it seems that if we subtract 40 from 1000 and divide the result by 4, and then add 1, we get the number of multiples of 4 between 37 and 1001:
1000
-40
-------
960
Dividing this by 4, we get 240. Adding 1, we get 241.
Finally, subtract 9 from 241: We get 232.
There are 232 multiples of 4 between 37 and 1001.
Can you think of a more straightforward method of determining this number? </span>
Answer:
Step-by-step explanation:
Area of the shaded region = Area of the square with side 25 ft - Area of the semicircle with radius (25/2) = 12.5 ft.
