give an example of two principal amounts and two periods of time for which the simple interest turned at 2.42 percent would be equal

To find the width and length of a rectangle given an area of 36 square meters and a perimeter of 30 meters, a system of equations can be set up and solved, showing the rectangle could have dimensions 9m x 4m or 4m x 9m.

To find the width and length of a rectangle with a known area and perimeter, we can use the following formulas: Area = length x width and Perimeter = 2(length + width). We know the area is 36 square meters and the perimeter is 30 meters. Let's denote the length as L and the width as W. Therefore, our system of equations will be:

L x W = 36

2(L + W) = 30

Dividing the perimeter equation by 2 gives us L + W = 15. We can express the width in terms of the length using this equation: W = 15 - L. Now we can substitute this expression for W into the area equation: L x (15 - L) = 36. Expanding this gives us a quadratic equation: [tex]L^2[/tex] - 15L + 36 = 0. We can solve this equation for L to find possible values for the length.

To find the length L, we look for factors of 36 that add up to 15. It turns out that 9 and 4 are such factors, so our lengths are 9 meters and 4 meters. We then use the expressions for W to find that W is 4 meters if L is 9 meters, and W is 9 meters if L is 4 meters. Hence, the rectangle could have dimensions 9m x 4m or 4m x 9m.

its d! hope i helped :)

Answer:

The answer is D

Step-by-step explanation:

Ivan needs to take out the trash at least 5 times to earn enough money to buy a double-scoop ice cream cone.

To buy a double-scoop ice cream cone, Ivan needs to earn enough money to cover the cost of the double-scoop cone, which is 75 cents for the first scoop and an additional 50 cents for the second scoop. Since Ivan earns 25 cents each time he takes out the trash, we can calculate how many times he needs to take out the trash to earn enough money.

Let's assume Ivan needs to take out the trash 'x' number of times. Each time he takes out the trash, he earns 25 cents, so the total amount he earns will be 25 cents multiplied by 'x'.

Setting up an equation, 25x >= 75 + 50. Simplifying, we have 25x >= 125. Dividing both sides of the inequality by 25, we get x >= 5. Therefore, Ivan needs to take out the trash at least 5 times to earn enough money to buy a double-scoop ice cream cone.

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Final answer:

To calculate the total amount of ribbon Diane needs, we multiply the number of gifts (7) by the amount of ribbon per gift (2 feet). Diane will need a total of 14 feet of ribbon to decorate 7 gifts.

Explanation:

The question asks how much ribbon Diane needs to decorate 7 gifts if she uses 2 feet of ribbon per gift. To find the total amount of ribbon, we multiply the number of gifts by the amount of ribbon used for each gift. The equation for this calculation is:

Total ribbon needed = Number of gifts times Ribbon per gift

Let's plug in the values:

Total ribbon needed = 7 gifts times 2 feet/gift

Total ribbon needed = 14 feet

Therefore, Diane needs 14 feet of ribbon to decorate her 7 gifts.

Final answer:

To find the costs, we set up two equations based on the given data. Using elimination, we first determine the cost of 1 kg of carrots and then the cost of 1 kg of potatoes. The final costs are $2 per kg for potatoes and $2.40 per kg for carrots.

Explanation:

The student's question involves solving a system of linear equations to determine the cost of potatoes and carrots per kilogram. We can set up two equations from the given information:

8 kg of potatoes (8P) + 5 kg of carrots (5C) = $28

2 kg of potatoes (2P) + 3 kg of carrots (3C) = $11.20

These equations can be solved using either substitution or elimination methods to find the price per kilogram (P and C) for potatoes and carrots, respectively.

Let's use the elimination method:

Multiply the second equation by 4 to align the potato coefficient with the first equation:

8 kg of potatoes (8P) + 5 kg of carrots (5C) = $28

8 kg of potatoes (8P) + 12 kg of carrots (12C) = $44.80

Now subtract the first equation from the modified second equation:

(8P + 12C) - (8P + 5C) = $44.80 - $28

7C = $16.80

Divide by 7 to find the price per kilogram of carrots:

C = $2.40

Substitute the value of C into the first equation and solve for P:

8P + 5($2.40) = $28

8P + $12 = $28

8P = $16

P = $2

The cost of 1 kg of potatoes is $2 and the cost of 1 kg of carrots is $2.40.

We are given the following data:

total discharge = 9.6 trillion gallons

number of household = 200 million

number of months = 6 months

So the average use of each household per month is:

average use = (9.6 trillion gallons) / (200 million households * 6 months)

average use = 8,000 gallons / household / month

So each household uses 8,000 gallons per month

Final answer:

To convert the inequality 5x - 5y ≥ 70 to slope-intercept form, we solve for y to get y ≤ −x − 14, which is most appropriately represented as option (b.) y ≤ x − 14 after rearranging terms.

Explanation:

To write the inequality 5x − 5y ≥ 70 in slope-intercept form, we need to solve for y. We start by isolating the y-term on one side of the inequality.

First, we subtract 5x from both sides: −5y ≥ 70 − 5x

Next, we divide each term by -5 (remembering to reverse the inequality symbol because we are dividing by a negative number): y ≤ (70/−5) + (5x/−5)

y ≤ −14 − x

Finally, we write x before the constant to follow conventional form:

y ≤ −x − 14

Comparing this result to the multiple-choice options, we can see that none of them exactly match the form we derived. However, we can rewrite our inequality as y ≤ x − 14 by multiplying through by -1 (which will not change the inequality because we are not dividing or multiplying the inequality itself, just rearranging the terms).

Therefore, the correct answer is (b.) y ≤ x − 14.

The area of an 11x13 rectangle is 143 square inches.

The area of an 11x13 rectangle can be calculated by multiplying the length and the width.

Area = Length x Width

Area = 11 inches x 13 inches

Area = 143 square inches

Therefore, an 11x13 area encompasses 143 square inches.

The zero of the function c=80-3.22n is approximately 25, which means that Jessica's CD would be completely filled after recording approximately 25 songs.

To find the zero of the function c=80-3.22n, we need to set the function to zero and solve for n. 0 = 80 - 3.22n. Solving this gives n = 24.84 (roughly).

In the context of this problem, this zero of the function means that after approximately 25 songs (as we can't have a fraction of a song), Jessica's CD would be completely filled with no remaining recording time.

It's important to note that the actual number of songs Jessica can record depends on the precise length of each song, since this equation assumes each song is the same length, which is unlikely to be strictly true in reality.

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add the point, x=-30, y=3:

y=kx

3=k*-30

3=-30k

-1/10=k

so the final answer:

k= -1/10

Graphs of the same function can look different based on the time frames, horizontal and vertical scalling, data grouping, and the chosen type of graph. However, it's crucial to remember that despite visual differences, the underlying mathematical function remains unchanged.

In the subject of mathematics, graphs depict the relationship between variables. The graphs of the same function can technically appear different based on numerous factors such as the range of data used, horizontal and vertical scaling, and the division of data groups. When the value of y is changing as a function of x, meaning different values of x correspond to different values of y, we can plot a graph using specific (x,y) data pairs.

This graph can appear different based on the frame of reference chosen; for example, certain timeframes might yield a linear graph, while another range could portray a curve. Similarly, the relative size of the vertical and horizontal axes can greatly impact the perception of the graph, and therefore, different scales of measurement can provide different visual perspectives of the same function.

Moreover, the type of graph used (e.g. line, bar, pie graph) also impacts visual understanding. Line graph shows the relationship between two variables, whereas a pie graph could make it easy to understand division of a whole into parts, and a bar graph can depict comparisons among different groups.

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