Question

1. solve for c.

$c^2 - 5 = 95$

1. find the lcm.

9 5

1. write a mixed number equal to 2.25 in the space below.
2. find the measure of angle x. (with an image of a straight line and an angle of 45° and angle x)
3. noreen drew a scale drawing of the local park. the playground, which is 120 meters long in real life, was 60 cm long in the drawing. what is the scale of the drawing?

Explanation:

Step1: Isolate $c^2$ term

Add 5 to both sides.
$c^2 - 5 + 5 = 95 + 5$
$c^2 = 100$

Step2: Solve for $c$

Take square root of both sides.
$c = \pm\sqrt{100} = \pm10$

Step1: List multiples of 9

$9, 18, 27, 36, 45, ...$

Step2: List multiples of 5

$5, 10, 15, 20, 25, 30, 35, 40, 45, ...$

Step3: Identify smallest common multiple

The first shared multiple is 45.

Step1: Separate whole and decimal parts

$2.25 = 2 + 0.25$

Step2: Convert decimal to fraction

$0.25 = \frac{25}{100} = \frac{1}{4}$

Step3: Combine into mixed number

$2 + \frac{1}{4} = 2\frac{1}{4}$

Step1: Recognize supplementary angles

$x$ and $45^\circ$ form a straight line (sum to $180^\circ$).

Step2: Calculate $x$

$x = 180^\circ - 45^\circ = 135^\circ$

Answer:

1. $c = 10$ or $c = -10$
2. 45
3. $2\frac{1}{4}$
4. $135^\circ$
5. $1:200$ (1 cm on drawing = 200 cm/2 meters in real life)