Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her
2 answers:
Answer:
Her weekly expenses amount to $25.
Detailed reasoning:
Given: Jessica earns commissions for every sale but must cover her own spending costs.
She expresses her income function as , where x represents the number of doors she approaches in a week and E(x) denotes her weekly earnings in dollars.
To determine: What are plausible meanings for the y-intercept in Jessica's earnings function?
Working it out:
x symbolizes the doors knocked per week
E(x) reflects her weekly total earnings in dollars.
Calculating the y-intercept:
Set x = 0
Given that E(x) is the net earning after expenses,
the value 25 corresponds to her weekly expenses.
Since she is responsible for covering costs,
if she makes zero sales, these expenses still apply.
Therefore, the y-intercept realistically represents her $25 weekly expenses.
Answer:
The correct choice is D.
Step-by-step breakdown:
The provided equation is
.... (1)
where x stands for the weekly number of doors knocked, and E(x) is the weekly earnings in dollars.
The slope-intercept form of a linear equation is
.... (2)
Comparing (1) and (2), we identify
m=7 and b=-25
The slope of 7 means she earns $7 per door knocked.
The y-intercept -25 (with the negative sign indicating costs) means she has $25 in weekly expenses.
Thus, the accurate interpretation is D.
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<span>Which formula can be applied to find the side length of the rhombus?
The correct answer is the first choice: 10/Cos(30°)
Explanation:
1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:
Cos(</span>α)=Adjacent side/Hypotenuse
<span>
</span>α=30°
<span> Adjacent side=(20 in)/2=10 in
Hypotenuse=x
2. Inputting these numbers into the equation yields:
</span>
Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x
3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:
x=10/Cos(30°)
</span>
The correct answer is the first choice: 10/Cos(30°)
Explanation:
1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:
Cos(</span>α)=Adjacent side/Hypotenuse
<span>
</span>α=30°
<span> Adjacent side=(20 in)/2=10 in
Hypotenuse=x
2. Inputting these numbers into the equation yields:
</span>
Cos(α)=Adjacent side/Hypotenuse
<span> Cos(30°)=10/x
3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:
x=10/Cos(30°)
</span>
In this scenario, the first step is to assign variables.
We define:
x: time measured in minutes
y: distance covered.
The equations formulated are as follows:
For Kathleen:
For Arnob:
At the moment Arnob meets Kathleen, we have:
Next, we isolate x.
We now have:
Answer:
Arnob takes a total of 75 minutes to catch up to Kathleen:
d. 75