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.
For this case we must simplify the following expression
We know that, by definition:
So, rewriting the expression we have:
We add similar terms taking into account that:
- Equal signs are added and the same sign is placed.
- Different signs are subtracted and the major's sign is placed:
Answer:
Answer:
simple interest
Step-by-step explanation:
this is because r is interest rate, p is principal, and t is time
Answer:
-5/4
Step-by-step explanation:
y2 - y1
x2 - x1
________
-2 - 3 = -5
5 - 1 = 4
Slope = -5/4
to solve for the dimensions (x+7)(x+2)=66,
we can first use the foiling method to simplify the left side.
x^2 + 2x + 7x + 14 = 66
x^2 + 9x + 14 = 66
now, subtract 66 from both sides.
x^2 + 9x - 52 = 0
now, split this into two parentheses.
(x + 13)(x - 4)
since the root of -13 would give you negative values, x=4. This means that the dimensions of the rectangle are 11 and 6.
