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3 years ago

Which sequence of transformations maps pre-image ABC to

Mathematics

1 answer:

matrenka [14]3 years ago

3 0

Triangle ABC was reflected over the y-axis and then translated 2 units up and 2 units to the right

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point up, down, left or right. If a point A(x, y) is translated b units up and a units to the right, the new point is A'(x + a, y + b).

Reflection is the flipping of a figure. If a point A(x, y) is reflected along the y axis the new point is A'(-x, y).

Triangle ABC is at A(1, 2), B(4, 6) and C(7, 3). If it is reflected over the y-axis, the new point is A*(-1, 2), B*(-4, 6) and C*(-7, 3). If it is then translated 2 units up and 2 units to the right, the new image is:

A'(1, 4), B'(-2, 8) and C'(-5, 5)

Hence, Triangle ABC was reflected over the y-axis and then translated 2 units up and 2 units to the right

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Paul was thinking of a number. Paul adds 1.2 to the number the doubles the result to get an answer of 68.3. Form an equation wit

Nikitich [7]

Answer:

(x+1.2)2=68.3

Step-by-step explanation:

(x+1.2)2=68.3

6 0

3 years ago

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co

lisov135 [29]

Answer:

The complete solution and step by step explanation is written below.

Note:

Here is the complete question you were probability asking as you may have unintentionally missed to mention the parts (a) and (b). So, after a little research, I figured out that this was probably the complete question you had meant to ask. So, I am answering based on the reference of this complete question that may indeed clear your concepts.

Complete Question:

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs $2.40 per gallon, and milk from dairy II costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9% butterfat, and dairy II can supply at most 80 gallons averaging 2.9% butterfat. Answer parts a and b.

A. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? (Also, what IS the maximum amount of butterfat?)

B. The solution from part A leaves both dairy 1 and dairy 2 with excess capacity. Calculate the amount of additional milk each dairy could produce.

Step-by-step explanation:

Let A be number of gallons of the amount of milk the company bought from Dairy 1.

(100 - X) be the number of gallons of the amount of milk the company bought from Dairy 2.

Milk from dairy I costs $2.40 per gallon and milk from dairy II costs $0.80 per gallon.

So, the equation of total cost available for purchasing the milk be:

Cost = 2.40A + ( 100 - A)0.80

As $144 is the total cost available for purchasing the milk.

Hence, Cost equation would be as follows:

Cost = 2.40A + ( 100 - A)0.80

144 = 2.40A + ( 100 - A)0.80

144 = 2.40A + 80 - 0.80A

1.6A = 64

So, A = 64 ÷ 1.6

= 40 gallons

Calculation of gallons of Dairy 1 and Dairy 2:

gallons of Dairy 1 ⇒ A = 40 gallons

gallons of Dairy 1 ⇒ 100 - A = 100 - 40 = 60 gallons

The equation for Fat will be:

Fat for dairy 1 = 40 × 3.9% = 1.56

Fat for dairy 2 = 60 × 2.9% = 1.74

ADD = 1.56 + 1.74 = 3.3 %

Calculation Part B:

Dairy 1 will have = 50 - 40 = 10 gallons ( excess)

Dairy 2 will have = 80 - 60 = 20 gallons (excess)

Keywords: word problem, equation solving

Learn more about word problems and equation solving from brainly.com/question/8917703

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5 0

3 years ago

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together the

klasskru [66]

The rate charged per hour by each mechanic was: x = 75 $ / hr and y = 115 $ / hr.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.

Together they charged a total of $3225.

For this case we have the following variables:

x be the amount of $ / hr that the mechanic obtains 1.

y be the amount of $ / hr obtained by mechanic 2.

An equation to express this would be:

x + y = 190

20x + 15y = 3225

Solving the system of equations we have:

20x + 15(190 -x) = 3225

20x + 2850 - 15x = 3225

5x = 375

x = 75

simililary

y = 190 - x

y = 115

Hence, the rate charged per hour by each mechanic was:

x = 75 $ / hr

y = 115 $ / hr

Learn more about equations here;

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6 0

2 years ago

Plz stop doing this not cool

Andrew [12]

Answer: So True

Step-by-step explanation:

4 0

3 years ago

Write an absolute value inequality that describes the acceptable weights, w, of a 20-ounce bottle of sports drink.

Shtirlitz [24]

Answer: $0\leq w\leq 20$

Step-by-step explanation:

Since, Here w represents the weight of the bottle.

And, According to the question, he acceptable weights, w, of a 20-ounce bottle of sports drink.

That is, weight of the bottle can not be higher than 20 or the it can be atleast 20.

Therefore, $w\leq 20$

And, the weight can not be negative.

Therefore, $0\leq w$

Thus, the required inequality is,

$0\leq w\leq 20$

5 0

3 years ago