Question

1. given two supplementary angles

\ and \2n + 3\, find the value of the two angles.
a) 59° and 121°
b) 60° and 120°
c) 54° and 126°
d) 59° and 31°

1. calculate the area of a square with a diagonal of $5\sqrt{6}$ inches.

a) 150 sq. in.
b) 75 sq. in.
c) 50 sq. in.
d) 25 sq. in.

1. the oldest person in the learning lab is 75 years old. the youngest person is 18 years old. to calculate the difference in the ages is which measure of central tendency?

a) mean
b) median
c) mode
d) range

1. joann can mow her grandparents yard in 1 hour and 10 minutes. her brother ricky can mow the same lawn in 50 minutes. if they work together to mow the lawn, about how many minutes will it take them if they work together?

a) between 29 and 30 minutes
b) between 32 and 33 minutes
c) between 24 and 25 minutes
d) between 30 and 31 minutes

Explanation:

Question 17

Step1: Recall supplementary angles sum to 180°

Supplementary angles add up to \(180^\circ\), so \(n + (2n + 3) = 180\).

Step2: Solve for n

Simplify the equation: \(3n + 3 = 180\). Subtract 3: \(3n = 177\). Divide by 3: \(n = 59\).

Step3: Find the other angle

Substitute \(n = 59\) into \(2n + 3\): \(2(59) + 3 = 118 + 3 = 121\). So the angles are \(59^\circ\) and \(121^\circ\).

Step1: Recall square diagonal formula

For a square with side \(s\), diagonal \(d = s\sqrt{2}\). Given \(d = 5\sqrt{6}\), but wait, correction: Wait, the diagonal of a square is \(s\sqrt{2}\), so if diagonal is \(d\), then \(s=\frac{d}{\sqrt{2}}\). Area \(A = s^2=\frac{d^2}{2}\).

Step2: Calculate \(d^2\)

\(d = 5\sqrt{6}\), so \(d^2=(5\sqrt{6})^2 = 25\times6 = 150\).

Step3: Find area

\(A=\frac{150}{2}=75\) square inches.

Mean is average, median is middle, mode is most frequent, range is max - min. Age difference is \(75 - 18\), which is range (max - min).

Answer:

a) \(59^\circ\) and \(121^\circ\)

Question 18