Simplify. 3a-2b+5a+6b-2 Write as an expression: The sum of a number and 8 Express as a fraction (in lowest terms): 8 out of 24 What is the coordinate point Q' for the translation of Q (from Day 3 above) 3 units to the right?

1. To simplify the expression $3a-2b+5a+6b-2$, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, $3a$ and $5a$ are like terms, and $-2b$ and $6b$ are like terms.<br /><br />Combining like terms, we get:<br />$3a + 5a = 8a$<br />$-2b + 6b = 4b$<br /><br />So, the simplified expression is:<br />$8a + 4b - 2$<br /><br />2. The sum of a number and 8 can be written as:<br />$x + 8$<br />where $x$ represents the unknown number.<br /><br />3. To express the fraction $8$ out of $24$ in lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of $8$ and $24$ is $8$.<br /><br />Dividing both the numerator and denominator by the GCD, we get:<br />$\frac{8}{24} = \frac{8 \div 8}{24 \div 8} = \frac{1}{3}$<br /><br />So, the fraction $8$ out of $24$ in lowest terms is $\frac{1}{3}$.<br /><br />4. To find the coordinate point $Q'$ for the translation of $Q$ 3 units to the right, we need to add 3 to the x-coordinate of $Q$.<br /><br />Let's assume the coordinates of $Q$ are $(x, y)$.<br /><br />The new coordinates of $Q'$ after translating 3 units to the right will be:<br />$Q' = (x + 3, y)$<br /><br />So, the coordinate point $Q'$ for the translation of $Q$ 3 units to the right is $(x + 3, y)$.