Question

martha is renting a bike. there is an $18 reservation fee and an additional fee of $11 per hour. she needs to spend no more than $140. which expression best represents the approximate number of hours monica could rent the bike? use h for the number of hours. \\(\circ\\ h\leq11.1\\) \\(\circ\\ h<14.4\\) \\(\circ\\ h\geq11.1\\) \\(\circ\\ h>14.4\\) question 8 2.5 pts use a graphing calculator to solve the system of equations below. round your solution to the nearest thousandth. \\(3x - 5y = 6\\) \\(-x - 6y = 12\\) \\(\circ\\ (1.043, 1.826)\\) \\(\circ\\ (-1.043, -1.826)\\) \\(\circ\\ (1.043, -1.826)\\) \\(\circ\\ (-1.043, 1.826)\\) question 9 2.5 pts the equation of a line is given below. what is the x-intercept and the y-intercept? \\(y = -\frac{1}{3}x + 2\\) type your numerical answers below. x-intercept: \\(\square\\) y-intercept: \\(\square\\)

Explanation:

First Question (Bike Rental)

Step1: Set up cost inequality

$18 + 11h \leq 140$

Step2: Subtract 18 from both sides

$11h \leq 140 - 18$
$11h \leq 122$

Step3: Solve for h

$h \leq \frac{122}{11} \approx 11.1$

Step1: Isolate x from second equation

From $-x - 6y = 12$, we get $x = -6y - 12$

Step2: Substitute x into first equation

$3(-6y - 12) - 5y = 6$
$-18y - 36 - 5y = 6$
$-23y = 42$

Step3: Solve for y

$y = -\frac{42}{23} \approx -1.826$

Step4: Substitute y back for x

$x = -6(-1.826) - 12 \approx 10.956 - 12 = -1.044 \approx -1.043$

Step1: Find x-intercept (set y=0)

$0 = -\frac{1}{3}x + 2$
$\frac{1}{3}x = 2$
$x = 6$

Step2: Find y-intercept (set x=0)

$y = -\frac{1}{3}(0) + 2$
$y = 2$

Answer:

$h \leq 11.1$

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Question 8 (System of Equations)