Question

1. the hottest day recorded in oklahoma was 120° fahrenheit. what was the temperature of the hottest day in oklahoma in celsius to the nearest tenth of a degree?

$f = \frac{9}{5}c + 32$
a. 158.4° c b. 88.0° c c. 34.7° c d. 48.9° c
9.
$y = \frac{1}{2}x + 3$
$y = \frac{1}{2}x + 5$
which statement is true about these equations?
a. the equations represent perpendicular lines. b. the equations represent the same lines. c. the equations represent lines that intersect but are not perpendicular. d. the equations represent parallel lin

Explanation:

Question 8

Step1: Substitute F = 120 into the formula

We know the formula for converting Fahrenheit to Celsius is \( F=\frac{9}{5}C + 32 \). Substitute \( F = 120 \) into the formula: \( 120=\frac{9}{5}C+32 \).

Step2: Solve for C

First, subtract 32 from both sides: \( 120 - 32=\frac{9}{5}C \), which simplifies to \( 88=\frac{9}{5}C \). Then, multiply both sides by \( \frac{5}{9} \) to solve for C: \( C = 88\times\frac{5}{9}=\frac{440}{9}\approx48.9 \).

The slope - intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the line \( y=\frac{1}{2}x + 3 \), the slope \( m_1=\frac{1}{2} \) and the y - intercept \( b_1 = 3 \). For the line \( y=\frac{1}{2}x+5 \), the slope \( m_2=\frac{1}{2} \) and the y - intercept \( b_2 = 5 \).

• If two lines have the same slope (\( m_1=m_2 \)) and different y - intercepts (\( b_1

eq b_2 \)), the lines are parallel.

• If two lines are perpendicular, the product of their slopes is \( - 1\) (i.e., \( m_1\times m_2=-1 \)). Here, \( m_1 = m_2=\frac{1}{2} \), so \( m_1\times m_2=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}

eq - 1 \), so they are not perpendicular.

• Since \( m_1 = m_2 \) and \( b_1

eq b_2 \), the lines are parallel, not the same line, and they do not intersect (parallel lines never intersect).

Answer:

d. \( 48.9^{\circ}\text{C} \)

Question 9