The graph would be the normal parent function of f(x) but all points would be 6 units up.
There's an upward vertical shift of 6. To graph this, you need to graph the function f(x) and then add 6 units to all the y values.
Number of 1/2-inch cubes length-wise = 8 1/2 ÷ 1/2 = 17
Number of 1/2-inch cubes width-wise = 5 1/2 ÷ 1/2 = 11
Number of 1/2-inch cubes height-wise = 2 1/2 ÷ 1/2 = 5
Number of 1/2-inch cubes = 17 x 11 x 5 = 935
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Answer: 935 1/2-inch cubes are needed.
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Let us evaluate each pair of expressions one at a time.
8. (n²+4) - n² and 4n.
(n²+4) - n² = n²+ 4 - n² = 4 which is not equal to 4n.
NOT EQUIVALENT
9. 3x + 5 and 2(x + 3)
2(x + 3) = 2x + 6 which is not equal to 3x + 5.
NOT EQUIVALENT
10. 15 - 6x and 15(1 - 6x)
15(1 - 6x) = 15 - 90x which is not equal to 15 - 6x
NOT EQUVALENT
11. (y + y + 2 + y) + 3y and 6y + 2
(y +y +2 + y) + 3y = y+y+y +2 + 3y = 3y + 2 + 3y = 6y + 2.
It matches the other expression.
EQUIVALENT
12. 8y - 3 + 10y and 3(6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3
3(6 - 1) = 3(5) = 15
The two expressions do not match.
NOT EQUIVALENT.
Answer: Only the expressions in number 11 are equivalent.
1. 376.0 / 92 = ?
2. 376 / 93.01 = ?
So the question asks us which quotient will be greater. In plain English it is asking which of the two, ?, will be greater. Seeing how the question is asking for a logical answer we are not going to actually solve the problem. Instead we will use logic.
First let's do some examples, and explain more in-depth how division works.
A. 6/3 = 2
B. 6/2 = 3
In this case, B is greater than A.
Greater than being any number that is larger than another on a scale reading from left to right, so if you were to count out all the way to the number the one that comes first is lower in value than the one that comes second.
Division works like this: Say we have a full delicious pie. We want to divide it up into 12 pieces so all our friends can have some. What we're doing is simply finding a value that if multiplied by 12 would equal our 1 pie. If you instead divided it by 24 you would have even SMALLER pieces of pie.
A. 5/2
B. 5/3
You might not be able to answer this one, but say our pie is equal to 5. For A. imagine we take a pie and cut it in half. Now for B. imagine a pie and cut it into 3 equal sized pieces. Which one will have the bigger individual pieces? A. will!
Keep in mind that the individual size of the piece would be the quotient (the quotient just means the answer to a division problem).
Now to quickly dismiss the 376.0, When you add 0's to the DECIMAL you do not change the value.
If you did then, 0.0 wouldn't still be 0. Or 1.0 wouldn't still be 1. The .0 is just a place holder and signifies nothing. Don't get this confused with adding a zero to the end of a number, because that does change the value (except in the case of 0). 1 with an extra zero becomes 10, and so on.
So let's tackle this problem!
A. 376.0 / 92
B. 376 / 93.01
In the end the .0 is meaningless so it's the same as this:
A. 376 / 92
B. 376 / 93.01
All we are looking for is the dividend that is smaller. (A dividend being what is dividing a number. In the case of 4/2 the dividend is 2. 5/2, the dividend is 2. 6/3, the dividend is 3. So in other words the dividend is the number after the division symbol, or in this case the slash (they are the same)).
So let's see, which is smaller? 92, or 93.01.
Whichever is smaller is going to have a bigger slice of pie than the other one. So, 92. Is our answer.
Note that this reasoning worked, because the numerator (376) is the same on both division problems. If they differed we wouldn't be able to use the same logic (at least as easily as we did in this problem!).
