A shopper uses a department-store gift card to pay for 3 sweaters priced at $27 each. What is the change in the value of the gift card?

Answer:

2/5

Step-by-step explanation:

The highest score on the test is 47, found by setting up and solving a system of equations based on the information given in the question.

The problem described in the question can be solved using algebra. Let's denote the highest score as H and the lowest score as L. According to the question, we have two equations:

We can solve this system of equations step by step. Since both equations have H, they can be set equal to each other: 3L - 4 = 30 + L. If you simplify this equation by subtracting L from both sides, you get 2L - 4 = 30. Then add 4 to both sides to isolate 2L on one side: 2L = 34. Divide both sides by 2, to solve for L: L = 17. Then substitute L into one of your original equations (H = 3L - 4), so H = 3*17 - 4 = 51 - 4 = 47. So, the highest test score is 47.

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To solve for x and y in a right triangle, use the Pythagorean Theorem (x² + y² = h²) and trigonometric relationships (x = hcosΘ and y = hsinΘ). The Isosceles Triangle Theorem, which states the base angles of an isosceles triangle are equal, isn't directly used to solve for x and y.

In solving for x and y using isosceles triangle theorems, we often utilize the Pythagorean Theorem and trigonometric relationships. Since this involves a right triangle, where x is the adjacent side, y is the opposite side, and h is the hypotenuse, we can use the formula for the Pythagorean Theorem, x² + y² = h².

To find x, we rearrange the trigonometric definition of cosine (cosΘ= x/h) to get x = hcosΘ. Similarly, we can find y using the definition of sine (sinΘ = y/h) and get y = hsinΘ. These solutions use trigonometry.

Keep in mind, the Isosceles Triangle Theorem states that the base angles of an isosceles triangle (a triangle with at least two equal sides) are equal. However, this theorem isn't directly involved in solving for x and y. Instead, the trigonometric relationships and Pythagorean Theorem solves for these values within a right triangle.

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Answer:

The king left his castle with 44 silver coins.

Step-by-step explanation:

A king left his castle with a bag of silver coins and he gave his coins to 3 peasants in an order. Finally he went home with two coins left.

To solve this question we calculate it in reverse order.

Finally the king has in his bag = 2 coins

Before it he met third peasant king had =

= (2+2) × 2

= 4×2 = 8

Before the king met third peasant, he had 8 coins.

Before he met Second peasant king had :

= (8+2) × 2

= 10 × 2 = 20

Before he met second peasant king had 20 coins.

Before he met first peasant he had :

= (20+ 2) × 2

= 22 × 2 = 44

Before King met first peasant he had 44 silver coins.

It should be congruent angles, for "congruent angles" are angles that have the same measures

vertical angles measurements are also equal, however, you want to be as broad as possible

hope this helps

Answer: a -3

Step-by-step explanation:

The bacteria in your culture appear to be experiencing exponential growth, doubling in population size every 20 minutes. This is common in organisms that reproduce by binary fission like bacteria, but the growth rate can be influenced by various environmental factors.

Based on your data, the number of bacteria in your culture seems to double every 20 minutes. This type of growth pattern is known as exponential growth, which is common in prokaryotes and other organisms that reproduce by binary fission.

For example, if you were to start with 1000 bacteria in a nutrient-rich environment, after one hour (or three 20-minute intervals), each bacterial cell would've divided several times, increasing the total population size from 1000 to 8000. This is based on the principle that in exponential growth, the number of new organisms added to the population in each round of division (or generation) increases as the population size increases. This results in a 'J-shaped' growth curve when plotted over time, illustrating the increasing rate of population growth.

However, please note that in reality, bacterial growth is influenced by several factors including nutrient availability and environmental conditions and the growth rate may not remain constant over time. For a more accurate analysis, you could take readings at more frequent intervals and plot a graph of population size versus time to observe the growth pattern.

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Answer:

1/40 pound

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Make a diagram. Two geometric figures intersect if they have one or more points in common. Draw two circles which intersect in  points. Draw a line which intersects the two circles in  points. Draw another line which intersects the two circles in  points and also intersects the first line. There are 11 points of intersection. 

A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money. To solve the problem, isolate the variable x by subtracting 2x from both sides and dividing both sides by 4.

A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. Let's say you have $8 and you are earning $2 per hour. On the other side, you have $6 and you are earning $6 per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money.

To solve the problem, you need to isolate the variable x. Start by subtracting 2x from both sides to get 8 = 4x. Then, divide both sides by 4 to get x = 2. Therefore, it will take 2 hours for your earned money to equal $6.