a. Write two different expressions giving the perimeter of the donkey’s pen.
b. Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
c. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
a. Two different expressions for the perimeter of the donkey's pen could be:
Expression 1: P = 2a + 2b
Expression 2: P = 4a
Here, a and b represent the lengths of the sides of the pen.
b. Let's choose a value of a = 10. If a is equal to 10, then using Expression 1, the perimeter would be:
P = 2(10) + 2b
P = 20 + 2b
To find the value of b, we would need more information or given measurements of the pen.
c. I used Expression 1 to evaluate the perimeter of the donkey's pen because it accounts for both sides (a and b) of the pen. If we used Expression 2, it would only consider one side (a) of the pen and not give an accurate representation of the perimeter.
sorry forgot to add this
A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that a=1/3b
No problem! In that case, we know that a = (1/3)b.
Substituting this value for a in Expression 1, we can rewrite the expression for the perimeter as:
P = 2a + 2b
P = 2(1/3b) + 2b
P = (2/3)b + 2b
P = (8/3)b
b. Let's choose a value of b = 9. If b is equal to 9, then using the expression (8/3)b, the perimeter would be:
P = (8/3)(9)
P = 24
c. I used expression (8/3)b to evaluate the perimeter of the donkey's pen because it incorporates the relationship between a and b, as given in the problem a = (1/3)b. This ensures that the perimeter calculation accurately represents the dimensions of the pen.
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
b. Add a fourth row to the table showing the population information for the town
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
c. Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
a. Let's choose the town of Pleasantville.
Using the second column, the current estimated population of Pleasantville can be expressed as:
Expression 1: x - (2/100)x
Using the third column, the current estimated population of Pleasantville can also be expressed as:
Expression 2: x + (2/100)x
b. Adding a fourth row for the town of Concord:
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -3%
Using the second column, the current estimated population of Concord can be expressed as:
Expression 1: p - (3/100)p
Using the third column, the current estimated population of Concord can also be expressed as:
Expression 2: p + (-3/100)p or p - (3/100)p
c. Let's choose a value for p as 7,000.
Using Expression 1: p - (3/100)p
Estimated Current Population of Concord = 7,000 - (3/100)*7,000
Estimated Current Population of Concord ≈ 6,790
I used Expression 1 to make the calculation because the percentage change for Concord was stated as a negative value (-3%), indicating a decrease in population. Therefore, using subtraction in Expression 1 appropriately reflects the decrease in population for Concord.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry d – 5 10%
a. Write two expressions in terms of d to show how much Winona and Takoda
would pay in total if they buy their mother the set of power tools.
b. What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
c. Choose a value for d that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
a. If Winona and Takoda buy their mother the set of power tools, the total paid can be expressed as:
Expression 1: (1 - 0.15)d
Expression 2: 0.85d
b. The expression 0.90(d - 5) refers to the total paid for the jewelry present after a 5% discount is applied. We know this because the expression subtracts 5% of d from d and then multiplies the result by 0.90. This expression could also be written as:
Expression 3: 0.90d - 0.90(5)
Expression 4: 0.90d - 4.50
c. Let's choose a value for d as $70.
For the power tools:
Total Paid = 0.85d
Total Paid = 0.85(70)
Total Paid = $59.5
For the water skis:
Total Paid = (1 - 0.25)(d + 15)
Total Paid = 0.75(70 + 15)
Total Paid = 0.75(85)
Total Paid = $63.75
For the jewelry:
Total Paid = 0.90(d - 5)
Total Paid = 0.90(70 - 5)
Total Paid = 0.90(65)
Total Paid = $58.50
Based on the calculations, Winona and Takoda should buy their mother the set of power tools because it has the lowest total cost at $59.5. The total cost for water skis is $63.75, and for jewelry is $58.50.
Conor is going to the movie theater. A ticket to a movie costs t dollars, and there is a
15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost.
b. Choose a value for t greater than $12 and less than $13. Use one of the
expressions you wrote in part a to find Conor’s total cost, rounded to the
nearest penny. Show your work.
c. Suppose that Conor’s total cost to see the movie is greater than $17.50 and
less than $20. What could be a value of t to make that possible?
a. Conor's total cost for buying a ticket to see a movie can be expressed as:
Expression 1: t + (0.15t)
Expression 2: 1.15t
b. Let's choose a value for t as $12.50.
Using Expression 1: t + (0.15t)
Total Cost = 12.50 + (0.15 * 12.50)
Total Cost = 12.50 + 1.87
Total Cost ≈ $14.37
Conor's total cost to see the movie would be approximately $14.37.
c. To find a value of t that would make Conor's total cost fall within the range of $17.50 and $20, we can set up an inequality:
17.50 < t + (0.15t) < 20
Let's solve this inequality:
17.50 < 1.15t < 20
Dividing all sides of the inequality by 1.15:
15.22 < t < 17.39
Therefore, a possible value for t that would make Conor's total cost fall within the given range is between approximately $15.22 and $17.39.
danke bot
danke means thank you in german