Which ordered pair is a solution of the equation 2x - 3y = 18?

Answer: Louisville was cooler in January (-9/2 F) than in December

(-3.5  F).

Step-by-step explanation: PLATO

Morgan rode her bike a total of 4600 meters after combining the distances from her house to her friend's, to and from the library, and back to her house.

To determine how many meters Morgan cycled in total, we first need to convert all distances into the same unit. Morgan rode 2 kilometers from her house to her friend's house, which is equal to 2000 meters. Then, she rode 600 meters in total going to and from the library. Since she needs to return home, she would ride the initial 2000 meters back. Therefore, the total distance Morgan cycled is the sum of these three distances.

Calculation

Distance from home to friend's house: 2000 meters

Traveling to and from the library: 600 meters

Distance from friend's house back to home: 2000 meters

Adding these distances gives us the total distance Morgan rode:

Total Distance = 2000m + 600m + 2000m = 4600 meters.

The shaded region represents the solution to the inequality y + 2 ≤ (1/4)x - 1. Graph A represent the inequality.

To graph the inequality y + 2 ≤ (1/4)x - 1, we need to first plot the corresponding boundary line, which is the equation y + 2 = (1/4)x - 1. Then, we'll determine the region of the graph that satisfies the inequality.

Step 1: Plot the boundary line:

To graph the line y + 2 = (1/4)x - 1, we'll first rewrite it in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

y + 2 = (1/4)x - 1

Subtract 2 from both sides:

y = (1/4)x - 3

Now, we can see that the slope (m) is 1/4, and the y-intercept (b) is -3.

Step 2: Plot the y-intercept and use the slope to find additional points:

Plot the y-intercept, which is -3, on the graph. Then, use the slope (1/4) to find other points. The slope of 1/4 means that for every increase of 1 unit in the x-direction, y increases by 1/4 units.

Let's find a few more points:

- If x = 0, y = (1/4) * 0 - 3 = -3 (giving us another point on the line).

- If x = 4, y = (1/4) * 4 - 3 = -2 (giving us another point on the line).

- If x = -4, y = (1/4) * (-4) - 3 = -4 (giving us another point on the line).

Step 3: Connect the points to draw the line:

Now, draw a straight line passing through all the points you've plotted. The line represents the boundary of the inequality.

Step 4: Determine the region that satisfies the inequality:

Since the inequality is y + 2 ≤ (1/4)x - 1, we need to determine which side of the line satisfies this inequality. One way to do this is to pick a test point that is not on the line (like the origin (0,0)), and check if it satisfies the inequality.

For (0, 0):

0 + 2 ≤ (1/4) * 0 - 1

2 ≤ -1

Since 2 is not less than or equal to -1, the region containing the origin (0,0) does not satisfy the inequality. Thus, we shade the other side of the line.

Step 5: Shade the region that satisfies the inequality:

Shade the region on the graph that is below the line y + 2 = (1/4)x - 1. This shaded region represents the solution to the inequality y + 2 ≤ (1/4)x - 1.

Graph A represent the inequality.

Learn more about graph here

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That is your answer if it is wrong i will try to fix it

Trisha's observation that three copies of a certain triangle can be arranged to form a straight line suggests that each interior angle of the triangle measures 60 degrees. This is because a straight line measures 180 degrees, which implies that the sum of the three angles is 180 degrees. Therefore, each angle must measure 60 degrees.

In this case, Trisha was able to arrange three copies of the triangle in such a way that their angles form a straight line. That straight line, or 180 degrees, is, in fact, the sum of all interior angles in a triangle. Hence, it can be inferred that the sum of the angles of each triangle she had must be 60 degrees, implying that each triangle is an equilateral triangle. Therefore the correct answer is: a. each interior angle of the triangle must measure 60*.

Step-by-step explanation: If you consider a straight line, it measures 180 degrees. If Trisha's three triangles are forming such a line, it implies that the three angles are combining to give 180 degrees. Assuming each angle is the same (because they are copies of the same triangle), then each angle in the triangle is 60 degrees (since 180/3 = 60).

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Jared is correct because the volume of a cone that has the same base and height as a cylinder is one-third the volume of the cylinder. This is due to the 1/3 factor in the formula for the volume of a cone. Therefore, the cone would indeed hold about 1,178 cm³ of sand.

Jared is indeed correct in his statement. The volume of a cone is found by using the formula 1/3 * base area * height, while the volume of a cylinder is found by using the formula base area * height. In this case, both the cone and the cylinder have the same base and height. However, the key difference lies in the 1/3 factor of the formula for a cone. This means that a cone with the same base and height as a cylinder would hold only one-third the volume of the cylinder.

In this case, the cylinder can hold about 4,712 cm³ of sand. As the cone is one third the size of the cylinder, it can hold about 1,178 cm³, which is precisely one third of the cylinder's volume, thus Jared's statement is correct.

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It's D, because the mean doesn't matter as much if it's only taken in a small variability. The mean was selected from 25 random pages in the book, that is why it is right.

Answer:

Step-by-step explanation:

According to Kim's calculations

Remember that a mean is defined as the quotient between the sum of all elements and the total number.

According to this calculations, the Math Book has more words per page, based on its greater mean.

Therefore, the right answer is the first choice.

Final answer:

Given 400 meters of fencing, constructing a square pen would result in an area of 10,000 square meters, while a circular pen would yield approximately 12,732 square meters, making the circular pen the larger option.

Explanation:

Ernesto wants to construct the largest possible pen for his iguana using 400 meters of fencing. To determine the maximum area of a rectangular pen, we can use the principle that a square will always provide the largest area for a given perimeter. In the case of a rectangular enclosure, we form a square with each side being one-fourth of the total available fencing, here being L/4 where L is 400 meters. Thus, each side of the square would be 400/4 = 100 meters. The area of such a square would be side × side = 100 m × 100 m = 10,000 square meters.

For the circular pen, the entire length of fencing would be the circumference of the circle. Given the formula for circumference is C = 2πr, where r is the radius, we set 400 = 2πr to solve for r, which is approximately 63.66 meters. The area of a circle is given by A = πr², which would then be approximately π(63.66)^2 ≈ 12,732 square meters. Therefore, a circular pen would provide a larger enclosed area compared to a square one given the same amount of fencing.

To solve for the expression mn with m=6 and n=4, the values are multiplied to get 6 × 4 = 24. Therefore, the answer is 24, which corresponds to Option A.

To evaluate the expression mn when m=6 and n=4, you simply multiply the values of m and n together.

The calculation is as follows:

Therefore, the value of mn is 24.

So, the correct answer is Option A: 24.

The correct answer is A. 24. The expression, mn is 24.

To evaluate the expression [tex]\( mn \)[/tex] when  [tex]\( m = 6 \)[/tex] and [tex]\( n = 4 \)[/tex], we simply multiply the two numbers together:

[tex]\( mn = (6)(4) \).[/tex]

Now, let's perform the multiplication:

[tex]\( 6 \times 4 = 24 \)[/tex].

Therefore, the value of [tex]\( mn \)[/tex] when [tex]\( m = 6 \)[/tex] and [tex]\( n = 4 \)[/tex] is 24.

The other options provided in the question are incorrect because they do not result from the multiplication of  [tex]\( m \)[/tex] and  [tex]\( n \)[/tex] as given:

B. [tex]\( 64 \) is \( 4^3 \) or \( 2^6 \)[/tex], which is not the product of  [tex]\( m \)[/tex] and  [tex]\( n \)[/tex].

C. [tex]\( 1,296 \) is \( 6^4 \) or \( 2^{10} \)[/tex], which is also not the product of  [tex]\( m \)[/tex] and  [tex]\( n \)[/tex].

D.[tex]\( 4,096 \) is \( 4^6 \) or \( 2^{12} \)[/tex], which again is not the product of [tex]\( m \)[/tex] and  [tex]\( n \)[/tex].

The only correct answer is A. [tex]\( 24 \)[/tex], which is the result of multiplying [tex]\( m \)[/tex] by [tex]\( n \)[/tex].

The given expression (9×10^−3)+(2.4×10^−5)÷0.0012 equals 2.9x10^-2 in scientific notation. The division operation was performed first and added to 9x10^-3, demonstrating the usefulness of scientific notation in simplifying arithmetic.

In order to evaluate the given expression (9×10^−3)+(2.4×10^−5)÷0.0012, you first need to perform the operations in parentheses which is the standard form of the expression to simplify it. Next, we must remember the order of mathematical operations, also known as BIDMAS or PEMDAS in mathematics: Brackets (or Parentheses), Indices (or Exponents), Division, Multiplication, Addition, and Subtraction.

However, in this expression we only have addition and a division to perform. The division operation takes precedence over addition, thus we first divide 2.4×10^−5 by 0.0012. The result of this can then be added to 9×10^−3. Let's perform these calculations:

So, the evaluated expression equals 2.9x10^-2 in scientific notation. This is a simplification of arithmetic using scientific notation, which helps to easily handle very large or very small numbers.

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All of the statistical measures are used to analyze a dot plot.

In mathematics and statistics, the term "mean" refers to the average of a set of variables. There are various ways to determine the mean, including geometric means, harmonic means, and simple arithmetic means (putting the numbers together and dividing the result by the quantity of observations).

All of the following measures can be determined by analyzing a dot plot:

Range: The difference between the highest and lowest values.

Median: The middle value when the data is arranged in order.

Mode: The value that appears most frequently in the data set.

Mean The average of all the values in the data set.

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Answer: 2 BATCHES

Step-by-step explanation: to produce one batch it takes 1/4 of oatmeal

Now the factory uses 1/2 batch of oatmeal

1=1/4 OATMEAL

X=1/2 OATMEAL

X=(1/2*1)/1/4

=1/2*4/1

=4/2

=2

It says that she withdrew 525 dollars from a saving account over a total period of 14 days.

As this amount is debited from her account, so it would be a negative number in her passbook i.e. -525 dollars.

To find the average change in the account balance, we can divide the total amount withdrawn from the account by the total number of days.

Average change in account balance = [tex]\frac{debited \;amount}{total \;time \;period}[/tex] .

Average change = [tex]\frac{-525}{14}[/tex]

Hence, option A is correct i.e. [tex]\frac{-525}{14}[/tex].