The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown. The coordinat

m = 6.57 and n = -2

Detailed explanation:

To solve this question, convert the thickness of a dollar bill into standard notation and compare the two thicknesses.

0.07 compared to 0.0043 results in 0.0657

0.0657 = 6.57 x 10^-2

Thus, a quarter is thicker than a dollar by 6.57 x 10^-2.

m = 6.57 and n = -2

It takes 5.22 hours to install carpet in a room. Step-by-step explanation: To start, let's explore the relationship among yards, feet, and inches. 1. 1 yard = 3 feet. 2. 1 foot = 12 inches. 3. Therefore, 1 yard = 36 inches. Now, let's convert all measurements to inches. ∵ 1 yard = 36 inches ∴ 1 yard² = (36)² inches². - Fine Floors can outfit 15 square yards of carpeting in 4 hours and 30 minutes. ∵ 15 yard² equals 15 × (36)² inches², so 15 yards² = 19440 inches². ∵ 1 hour equals 60 minutes, thus 30 minutes = 0.5 hours. Consequently, 4 hours and 30 minutes = 4.5 hours, implying Fine Floors covers 19440 inches² in 4.5 hours. The dimensions of the room are 11 feet 9 inches by 13 feet 4 inches. ∵ 1 foot = 12 inches, therefore, 11 feet 9 inches = 11 × 12 + 9 = 141 inches, and 13 feet 4 inches = 13 × 12 + 4 = 160 inches. Hence, the room’s area is 141 × 160 = 22560 inches². Using the ratio method, we have area of carpeting (in²): time of carpeting (hr) hence, 19440: 4.5 = 22560: h. By cross-multiplying, 19440h = 4.5 × 22560 yields 19440h = 101520. Dividing both sides by 19440 results in h = 5.22 hrs.

1) Equilateral Triangles: Triangles of this type have uniformly equal side lengths and angles. Therefore, if the side measurements are identical, the triangle is categorized as equilateral.

2) Isosceles Triangles: Such triangles feature two sides of the same length, with the third side differing. Given this, if the provided side lengths include two equal sides, it is classified as an isosceles triangle.

3) Scalene Triangles: These triangles have all sides of differing lengths. When all side lengths are distinct, it indicates a scalene triangle.

I hope this explanation is helpful!:) 

Answer:

Part a) Your budget is $40.

Part b) The price for one gallon of gasoline is $3.55, while a car wash costs $8.

Part c)

Part d) Refer to the explanation below.

Step-by-step explanation:

Please see the complete question in the attached image.

Part a) The budget is expressed by the equation

y = 40

therefore,

Your budget amounts to $40.

Part b) In terms of costs, how much is a gallon of gasoline and what is the car wash price?

Let

y ------> denote the total cost for a gallon of gasoline along with a car wash

x -----> define the volume of gasoline in gallons

We can express the relationship as

y = 3.55x + 8

For calculations, when x = 0, we have:

y = 3.55(0) + 8 = 8

The y-intercept signifies the cost of the car wash, being $8.

Now, to identify the price of one gallon of gasoline:

We know the slope of the linear function is

m = $3.55 per gallon

This confirms that a gallon of gasoline costs $3.55.

Part c) Formulate an inequality representing the potential quantity of gasoline you can purchase:

We have:

Now, solve for x:

Part d) Utilize the graph to determine the solution of the inequality from part c)

We can set up the system:

y = 40

y = 3.55x + 8

The solution lies at the intersection of both graphs. By observing the graph, the intersection appears to be around (9, 40).

This indicates that the maximum volume of gasoline purchasable within your budget is approximately 9 gallons.

Answer:

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Given: CD = EF and AB = CE

To Show: AB = DF

Following the steps outlined:

1. CD + DE = EF + DE by the (addition) Property of Equality.

This shows that the same value has been added to both sides of the equation.

2. CE = CD + DE and DF = EF + DE through (segment addition).

This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.

3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.

So, CE = EF + ED = FD (via substitution) Property of Equality.

4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.

This follows the rule that if x = y and y = z, then x = z.