5. Select all the expressions that are equivalent to $$ \frac{1}{2} z $$. A. $$ z+z $$ B. $$ z \div 2 $$ C. $$ z \cdot z $$ D. $$ \frac{1}{4} z+\frac{1}{4} z $$ E. $$ 2 z $$ (From Unit 6, Lesson 8.) 6. a. What is the perimeter of a square with side length: 3 cm ? 7 cm ? $$ s \mathrm{~cm} $$ ? b. If the perimeter of a square is 360 cm , what is its side length? c. What is the area of a square with side length: 3 cm ? 7 cm ? $$ s \mathrm{~cm} $$ ? d. If the area of a square is $$ 121 \mathrm{~cm}^{2} $$, what is its side length? (From Unit 6, Lesson 6.) 7. Solve each equation. $$ 10=4 a $$ $$ 5 b=17.5 $$ $$ 1.036=10 c $$ $$ 0.6 d=1.8 $$ $$ 15=0.1 e $$

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UpStudy AI · Accepted Answer

To solve the given equations, we will substitute the values of the variables into the equations and then solve for the variables.

1. $$ 10 = 4a $$
   - Substitute the value of $$ a $$ into the equation: $$ 10 = 4a $$
   - Solve for $$ a $$: $$ a = \frac{10}{4} = 2.5 $$

2. $$ 5b = 17.5 $$
   - Substitute the value of $$ b $$ into the equation: $$ 5b = 17.5 $$
   - Solve for $$ b $$: $$ b = \frac{17.5}{5} = 3.5 $$

3. $$ 1.036 = 10c $$
   - Substitute the value of $$ c $$ into the equation: $$ 1.036 = 10c $$
   - Solve for $$ c $$: $$ c = \frac{1.036}{10} = 0.1036 $$

4. $$ 0.6d = 1.8 $$
   - Substitute the value of $$ d $$ into the equation: $$ 0.6d = 1.8 $$
   - Solve for $$ d $$: $$ d = \frac{1.8}{0.6} = 3 $$

5. $$ 15 = 0.1e $$
   - Substitute the value of $$ e $$ into the equation: $$ 15 = 0.1e $$
   - Solve for $$ e $$: $$ e = \frac{15}{0.1} = 150 $$

Therefore, the solutions to the given equations are:
- $$ a = 2.5 $$
- $$ b = 3.5 $$
- $$ c = 0.1036 $$
- $$ d = 3 $$
- $$ e = 150 $$
The solutions to the equations are: - $$ a = 2.5 $$ - $$ b = 3.5 $$ - $$ c = 0.1036 $$ - $$ d = 3 $$ - $$ e = 150 $$

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