Question

1. simplify: $\frac{7 - (\frac{2}{3})(\frac{3}{5})}{3^{2}+\frac{1}{5}}$ a) $\frac{33}{46}$ b) 1 c) 7.15 d) 0
2. kinetic energy is the energy an object possesses due to its motion. the formula for kinetic energy is $ke=\frac{1}{2}cdot masscdot velocity^{2}$. an object has a mass of 34.2 kg and it is traveling at a velocity (speed) of 8 meters/sec. what is the objects kinetic energy (ke). round your answer to the nearest joule (1 joule is 1 $\frac{kgcdot meter^{2}}{sec^{2}}$)? must show the formula with numbers substituted. a) 18,714 joules b) 37,428 joules c) 1094 joules d) 17 joules
3. the formula for the area of a triangle is $a = \frac{1}{2}cdot basecdot height$. use the diagram to determine the area of the green triangle. a) 11 units² b) 13 units² c) 18 units² d) 9 units²

Explanation:

5.

Step1: Simplify numerator

First, calculate \((\frac{2}{3})(\frac{3}{5})=\frac{2\times3}{3\times5}=\frac{2}{5}\), then \(7 - \frac{2}{5}=\frac{35 - 2}{5}=\frac{33}{5}\).

Step2: Simplify denominator

Calculate \(3^{2}+\frac{1}{5}=9+\frac{1}{5}=\frac{45 + 1}{5}=\frac{46}{5}\).

Step3: Divide numerator by denominator

\(\frac{\frac{33}{5}}{\frac{46}{5}}=\frac{33}{5}\times\frac{5}{46}=\frac{33}{46}\)

Step1: Substitute values into formula

Given \(m = 34.2\) kg and \(v=8\) m/s, substitute into \(KE=\frac{1}{2}mv^{2}\), so \(KE=\frac{1}{2}\times34.2\times8^{2}\).

Step2: Calculate the result

First, \(8^{2}=64\), then \(\frac{1}{2}\times34.2\times64 = 17.1\times64=1094.4\approx1094\) Joules.

Step1: Determine base and height

Counting the grid - squares, the base of the triangle is 6 units and the height is 3 units.

Step2: Use area formula

Substitute into \(A=\frac{1}{2}bh\), so \(A=\frac{1}{2}\times6\times3 = 9\) square units.

Answer:

a) \(\frac{33}{46}\)

6.