A mercury thermometer records a temperature of 8 degrees Fahrenheit at 10:00am.If the Temperature drops by 3 degrees Fahrenheit
1 answer:
Given:
Temperature at 10:00 am = 8 degrees Fahrenheit
Temperature drops by 3 degrees Fahrenheit every hour.
To find:
The temperature by 2:00pm of the same day.
Solution:
Let y be the temperature after x hour after 10:00 am.
The temperature at 10:00 am is the initial temperature.
So, y-intercept of the linear function is 8.
Temperature drops by 3 degrees Fahrenheit every hour.
So, slope of linear function is -3. Here, negative sign represents the decrease in the temperature.
Slope intercept form of a linear function is
where, m is slope and b is y-intercept.
Substitute m=-3 and y=8 in the above equation.
Difference between 2:00pm and 10:00 am is 4 hours. So, substitute x=4 in the above equation.
Therefore, the temperature by 2:00pm of the same day is -4 degrees Fahrenheit.
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A function 
from a set A to a set B is defined as a relation that assings to each element 
in the set A exactly one element 
in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is feet, then we have a square patch as shown in the Figure below.
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let be the width of the tomato patch, then the function that matches this statement is:
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
1.a) Write the function Wa(x) representing the width of the bell pepper patch.
We know that she wants its width to be half the width of the tomato patch. Let
1.b) Write the function La(x) representing the length of the bell pepper patch.
In this case Melissa wants <span>its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:
</span>
<span>
2. Ar</span>ea of the bell pepper patch in terms of x.
Given that the bell pepper patch is a rectangle, then t<span>he area of a rectangle is the product of the length and width. So:
</span>
<span>
3. C</span><span>ombined area of the tomato patch and the bell pepper patch.
This function is the sum of both the area of the tomato patch and the bell pepper patch. So:
</span>
<span>
4. W</span>rite the function Aa(x) for the remaining planting area in the garden.
The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:<span>
</span>
5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.
Given that <span>Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:
</span>
<span>
Therefore the area of the remaining space is:
</span>
The limits for a C grade are 68 to 78.
Answer:
A. 180
Step-by-step explanation: