Question

3 multiple choice 2 points which numbers could represent the lengths of the sides of a triangle? 7, 7, 15 3, 6, 8 1, 2, 4 5, 9, 14 4 multiple choice 2 points the graph of the line passing through the points (6,7) and (4,2) has a slope of 3/2 -5/2 -1/2 5/2 5 multiple choice 2 points the expression (10w³)²/5w is equivalent to 20w⁵ 2w⁵ 20w⁸ 2w⁸

Explanation:

Question 3

Step1: Apply triangle - side rule

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the rule is \(a + b>c\).

• For \(7,7,15\): \(7 + 7=14<15\), so it cannot form a triangle.
• For \(3,6,8\): \(3+6 = 9>8\), \(3 + 8=11>6\), \(6 + 8=14>3\).
• For \(1,2,4\): \(1+2 = 3<4\), so it cannot form a triangle.
• For \(5,9,14\): \(5 + 9=14\), not greater than \(14\), so it cannot form a triangle.

Question 4

Step1: Use the slope formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 6,y_1=7,x_2 = 4,y_2 = 2\).

Step2: Calculate the slope

\(m=\frac{2 - 7}{4 - 6}=\frac{-5}{-2}=\frac{5}{2}\)

Question 5

Step1: Simplify the numerator

First, \((10w^{3})^{2}=10^{2}\times(w^{3})^{2}=100w^{6}\) (using \((ab)^n=a^{n}b^{n}\) and \((a^{m})^{n}=a^{mn}\)).

Step2: Divide by the denominator

\(\frac{100w^{6}}{5w}=\frac{100}{5}\times w^{6 - 1}\) (using \(\frac{a^{m}}{a^{n}}=a^{m - n}\)).
\(20w^{5}\)

Answer:

1. B. 3, 6, 8
2. D. $\frac{5}{2}$
3. A. $20w^{5}$