Which of them does not show the commutative property of addition ?

The points A, B, C cannot be both collinear and form an equilateral triangle simultaneously. This is proven by applying the Pythagorean theorem and trigonometry laws for triangles, which show that the distances and angles do not match the requirements for an equilateral triangle if the points are collinear (on a straight line).

Given that points A,B,C are collinear and you've stated a variety of scenarios about the positioning of these points. Combining all these restrictions, however, leads to a contradiction. An equilateral triangle's points cannot all be collinear as you've mentioned in your last point. A collinear set of points exists on the same straight line. The points of an equilateral triangle do not fall on the same line. Therefore, it's impossible for points A,B,C to be collinear and also form an equilateral triangle ABC.

Applying the Pythagorean theorem to the positions of these points, we see that the distances on the sides of the triangle will not be equivalent if they are positioned in a straight line. Similarly, with the use of trigonometry laws for triangles, such as the ones for vector equations, the same result is found. The vector equations for collinear points lack the trigonometric components found in equilateral triangles.

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The number of pages is 35

To solve the inequality 7x + 55 ≥ 300 for x, we first subtract 55 from both sides to isolate the term with x:

7x + 55 - 55 ≥ 300 - 55

7x ≥ 245

Divide by 7 to solve for x:

x ≥ 35

This means the student needs to read at least 35 pages per day to have 300 pages of the novel read in a week.

Answer:

[tex]1\frac{17}{25} \\[/tex] bags

Step-by-step explanation:

Number of bags used by Jared for his garden

[tex]= 1\frac{2}{5} \\= \frac{7}{5}\\[/tex]-------------------------- Eq (A)

Number of bags of soil required for new garden

[tex]= \frac{1}{5} * \frac{7}{5} \\= \frac{7}{25} \\[/tex]-------------------------- Eq (B)

Total number of bags that will be used

[tex]= Eq (A) + Eq (B)\\= \frac{7}{5} + \frac{7}{25} \\= \frac{42}{25} \\= 1 \frac{17}{25}[/tex]

Hello!

When you flip the coordinates and move them 6 units to the left your coordinates would be: (-4, 8) (0, 8) (5, 1) (1, 3)

The answer to the question 5258 divided by 47 is approximately 111.87. This is solved using the mathematical operation of division.

To solve the question 5258 divided by 47, we need to use the division operation. Division is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication. In this case, we are dividing 5258 (the dividend) by 47 (the divisor).

Step 1: Start by placing 5258 under the division bar and 47 outside to the left.

Step 2: Divide 5258 by 47. This may be done manually, or by using a calculator. The answer you get is approximately 111.87 when rounded off to the nearest hundredth.

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Answer:

Package 10−pack of 2.3 ounce bars has the better price per bar

Step-by-step explanation:

Case 1) Package 10−pack of 2.3 ounce bars Cost ($) 17.35

Cost of Package 10−pack of 2.3 ounce bars = 17.35

Cost of Package 1−pack of 1 ounce bars = [tex]\frac{17.35}{10 \times 2.3}[/tex]

                                                                   = [tex]0.7543[/tex]

2)  12−pack of 1.6 ounce bars Cost ($)16.97

Cost of Package 12−pack of 1.6 ounce bars = 16.97

Cost of Package 1−pack of 1 ounce bars = [tex]\frac{16.97}{12 \times 1.6}[/tex]

                                                                   = [tex]0.8838[/tex]

Hence  Package 10−pack of 2.3 ounce bars has the better price per bar

If 3 liters of cappuccino are made, 21 teachers can drink it. To have enough cappuccino for 74 teachers, approximately 10.57 liters would be needed.

To answer the first part of the question, we can use a proportion to find out how many teachers can drink cappuccino if 3 liters are made. Since 7 teachers share 1 liter, we can set up the proportion: 7 teachers / 1 liter = x teachers / 3 liters. Solving for x, we get x = 21 teachers. Therefore, 21 teachers can drink cappuccino.

For the second part of the question, we can use a similar proportion to find how many liters of cappuccino would be needed for 74 teachers. From the previous proportion, we know that 7 teachers share 1 liter. So, we can set up the proportion: 7 teachers / 1 liter = 74 teachers / x liters. Solving for x, we get x = 10.57 liters. Therefore, you would need to make approximately 10.57 liters to have enough cappuccino for 74 teachers.

Step-by-step explanation:

Gross pay:

  Gross pay can be define as the wage before paying any taxes and all other deductions.

Net pay:

 Net pay can be define as the wages after paying all taxes and all other deductions.

So we can say that

Gross pay = Net pay +   taxes and all other deductions

So from above equation we can say that ,even two employees have same gross pay but can have different net pays .Because maybe they are paying different taxes and other deductions.

The final sales price of the dress is a fraction 12/25 of the original price after successive discounts of 20% and 40%.

To determine the final sales price of the dress after multiple discounts, we can apply each discount successively. Let's assume the original price of the dress is $10, as mentioned in the premise, although this might be a typo or an example figure since a dress would typically cost more.

First discount: 20% off the original price, which is 0.20 x 10 = $2. So the new price after the first discount is $10 - $2 = $8.

Second discount: An additional 40% off on the already reduced price of $8. The additional discount is 0.40 x 8 = $3.20. Therefore, the final sales price after the second discount is $8 - $3.20 = $4.80.

To find the fraction of the original price that the final sales price represents, we divide the final price by the original price: $4.80 / $10 = 0.48. Thus, the fraction of the original price is [tex]\frac{48}{100}[/tex] or 24/50 after simplification, which further simplifies to  12/25

Final answer:

The expanded form of the number 0.249 is the sum of each digit multiplied by its place value, which is 0.2 + 0.04 + 0.009.

Explanation:

The question asks to write the number 0.249 in expanded form. The expanded form of a number is the sum of each digit multiplied by its place value. For the number 0.249, the expanded form is:

2/10 + 4/100 + 9/1000

This can also be written as:

0.2 + 0.04 + 0.009

Breaking down the number 0.249 into its decimal place values helps one understand how each digit contributes to the overall value of the number.

Answer:

The gas mileage formula in miles per gallon (mpg) is:

[tex]gas mileage=\frac{miles driven}{gallons used}[/tex]   (1)

We know that Sally’s dad filled the tank when it was empty and the miles recorded in the SUV were 24033 miles.

We also know that at the destination, there was a quarter tank of gas left in the vehicle and the miles were recorded as 24297 miles.  

This means that the miles driven during the whole trip were 894 miles:

[tex]24927 miles-24033 miles=894 miles[/tex]

If at the beginning the tank was full and at the end is left with a quarter tank ([tex]\frac{1}{4}[/tex]), this means that the car wasted [tex]\frac{3}{4}[/tex] of the tank:

[tex]\frac{4}{4}-\frac{1}{4}=\frac{3}{4}[/tex]

Now, SUVs come in so many different sizes and models, hence it is difficult to assume an average size for a SUV gas tank. It may vary from the smaller ones that hold 16.5 gallons to larger SUVs that hold from 28 to 33.5 gallons.

In this case let’s assume that the tank holds 28 gallons

Then, if 1 tank holds 28 gallons, [tex]\frac{3}{4}[/tex] of a tank holds 21 gallons.

Knowing this, let’s apply the mileage formula ( equation 1):

[tex]\frac{894 miles}{21 gallons}=42.571mpg[/tex]    

If we round the result we have, the gas mileage in miles per gallon for the Jensen’s SUV is 43mpg