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rodikova [14]
3 years ago
7

A triangle has vertices atA(-7,6) B(4,9) C(-2,-3)What are the coordinates of each vertex if the triangle is

Mathematics
1 answer:
nexus9112 [7]3 years ago
5 0

Answer:

D

Step-by-step explanation:

A translation 4 units right means add 4 to the original x- coordinate.

A translation 6 units down means subtract 6 from the original y- coordinate.

The translation rule is (x, y ) → (x + 4, y - 6), thus

A(- 7, 6 ) → A'(- 7 + 4, 6 - 6 ) → A'(- 3, 0 )

B(4, 9 ) → B'(4 + 4, 9 - 6 ) → B'(8, 3 )

C(- 2, - 3 ) → C'(- 2 + 4, - 3 - 6 ) → C'(2, - 9 )

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Yesterday morning, at 6:00 AM, water started leaking from a tank at a constant rate. The tank contained8,496liters of water at 6
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A linear equation can be written as:

y = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

The answers are:

a) y = (-12 L/min)*t + 9,000 L

b) 6,840 L

a) Here we know that we can model this situation with a linear equation, we know that the leak starts at 6:00 am, then we define t = 0 as 6:00 am

We know that at 6:42 am  (at t = 42 mins) the tank has 8,496 liters.

And at 7:15 am (at t = 75 mins) the tank has 8,100 liters.

Then we have two points of the line:

(42 mins, 8,496 liters)

(75 mins, 8,100 liters)

Then the slope is:

a = \frac{8,100 liters - 8,496 liters }{75 mins -42 mins } = -12 L/min

So the line will be something like:

y = (-12 L/min)*t + b

To find the value of b, which is the initial volume of water in the tank, we use the point (75 mins, 8,100 liters)

This means that if t = 75 mins, then we have y = 8,100 L

So we can replace these two on the above equation:

8,100 L = (-12 L/min)*75 mins + b

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Then the linear equation is:

y = (-12 L/min)*t + 9,000 L

b) Now we want to know how much water is in the tank at 9:00 am.

Notice that 9:00 am is 3 hours after 6:00 am, our t = 0.

Then  9:00am is equivalent to t = 180 mins.

So to know the volume of water that there is in the tank at 9:00 am, we just need to evaluate the linear function at t = 180 mins.

y = (-12 L/min)*180 mins + 9,000 L = 6,840 L

If you want to learn more, you can read:

brainly.com/question/24594539

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