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Reika [66]
2 years ago
14

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(4, −8), Q(0, 12), and R(−4, 0). Triangle P′Q′R′ has

vertices P′(1, −2), Q′(0, 3), and R′(−1, 0).
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)

Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)

Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Mathematics
1 answer:
Tom [10]2 years ago
6 0

Part A:

The scale factor is 1/4, because you obtain the coordinates of points P', Q', R' by dividing the coordinates of P, Q and R respectively by 4.

Part B:

Reflecting about the y axis causes a sign swap in the x coordinate. So, the new point will be

P''(-1, -2),\quad Q''(0, 3),\quad R''(1, 0)

Part C:

The triangles are similar, but not congruent. When you transform PQR into P'Q'R', you get a scaled version of the original triangle. This means that the angles and the proportion between sizes will be the same, but the length are scaled by 1/4, and the area is consequentially scaled by 1/16.

Triangles P'Q'R' and P''Q''R'' are congruent, so they are both similar but not congruent to the original triangle.

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Would you need to use the chain rule to find the derivative of this function?
Nutka1998 [239]

Answer:

TRUE. We need to use the chain rule to find the derivative of the given function.

Step-by-step explanation:

Chain rule to find the derivative,

We have to find the derivative of F(x)

If F(x) = f[g(x)]

Then F'(x) = f'[g(x)].g'(x)

Given function is,

y = \sqrt{2x+3}

Here g(x) = (2x + 3)

and f[g(x)] = \sqrt{2x+3}

\frac{dy}{dx}=\frac{d}{dx}(\sqrt{2x+3}).\frac{d}{dx} (2x+3)

y' = \frac{1}{2}(2x+3)^{(1-\frac{1}{2})}.(2)

   = (2x+3)^{-\frac{1}{2}}

y' = \frac{1}{\sqrt{2x+3}}

Therefore, it's true that we need to use the chain rule to find the derivative of the given function.

8 0
3 years ago
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail
sergey [27]

Answer:

Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

Step-by-step explanation:

Let's rule out the options given one by one.

Option 1: Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.

This is not true, because 1.2 is a rate, it just means that the carrier can finish 1 house in a minute, and also have time to get started delivering to the second house. The total number of houses has to be a whole number, but the rate doesn't.

Option 2: Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.

This option is also incorrect. Delivering mail for 7.5 minutes just means 7 minutes and 30 seconds, which is definitely possible.

Option 3: Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.

This option is correct. 1.2 is the rate of which the carrier delivers mail.

Option 4: Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.

This option is also incorrect. Although it is possible to deliver mail for 7.5 minutes, it is not the unit rate, it is the total amount of time it would take.

4 0
3 years ago
Read 2 more answers
The Marrieds are planning to serve 380 guests at a breakfast event. They plan to serve tomato juice, which comes in 46 oz. cans.
Anna35 [415]
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7 0
2 years ago
a group of students decided to collect as many paise (1/100 RS.) from each member of the group as is the number of members. If t
Softa [21]

Answer:

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Hope this helps!

8 0
2 years ago
Elena walked 12 miles. Then she walked `\frac{1}{4}` that distance.  How far did she walk all together?  
zzz [600]

Answer:

15 miles

Step-by-step explanation:

12 + ( 1/4 x 12) = ?

12 + 3 = 15

7 0
3 years ago
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