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madreJ [45]
3 years ago
8

A triangle is shown on the graph:

Mathematics
1 answer:
Nana76 [90]3 years ago
6 0

9514 1404 393

Answer:

  the image is congruent with the original, angles and lengths are unchanged

Step-by-step explanation:

Translation, rotation, and reflection are known as "rigid transformations". Effectively, you can cut the figure from some rigid material, and move it according to any of these transformations without causing it to deform in any way.

All lengths and angles retain their measures when the figure is rotated about any point, through any angle. The rotated figure is congruent with the original.

__

Here, the triangle is defined in the second quadrant. Rotating it 90° clockwise will move it to the first quadrant. The transformation of coordinates is ...

  (x, y) ⇒ (y, -x)

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Simplify the algebraic expression -2(x - 3) + 4(-2x + 8)
dangina [55]
The answer to this equation is :-10x+38 because
-2x(x-3)+4(-2x+8)
(-2x+6)+(-8x+32)
(-2x+6)(-8x+32)
-2x+6-8x+32
-10x+38
7 0
3 years ago
Spotlight Dance increased the number of dancers on its competition team. Last
Nana76 [90]

Answer:

80%

Step-by-step explanation:

To find percentage increase, we use the following formula:

Percentage Increase = \frac{New-Old}{Old}*100

Here

New means the latest value (which is 18 dancers)

Old means the previous value (which is 10 dancers)

The Multiplication by 100 is to convert the decimal answer to percentage.

So, we have:

New = 18

Old = 10

Now we substitute and find:

\frac{New-Old}{Old}*100\\\frac{18-10}{10}*100\\\frac{8}{10}*100\\80

So, there was an increase of 80%

3 0
3 years ago
Suppose you have 18 objects (10 of type A, 5 of type B, and 3 of type C). Objects of type A are indistinguishable from each othe
Paladinen [302]

Answer:

\binom{18}{5}= 8568

Step-by-step explanation:

Note that we have in total 18 items. Even though we are given information regarding the amounts of items per type, the general question asks the total number of ways in which you can pick 5 out of the 18 objects, without any restriction on the type of chosen items. Therefore, the information regarding the type is unnecessary to solve the problem.

Recall that given n elements, the different ways of choosing k elements out of n is given by the binomial coefficient \binom{n}{k}).

Therefore, in this case the total number of ways is just \binom{18}{5}=8568

5 0
3 years ago
Read 2 more answers
A boat travels 30 miles up the river in the same amount of time it takes to travel 38 miles down the same river. If the current
Ksenya-84 [330]
X miles per hour  -  <span> speed of the boat in still water
(x - 2)  -  speed up the river
(x + 2)  -  speed down the river
</span>
\frac{30}{x - 2} = \frac{38}{x + 2}
30 * (x + 2) = 38 * (x - 2)
30x + 60 = 38x - 76
- 8x = - 136
x = 17 miles per hour  -  <span>the speed of the boat in still water.</span>
5 0
3 years ago
There are 6 swimmers in a race. In how many ways can they finish in first and second place?
hodyreva [135]

Answer:

step 1. 6x2=12 first place way

step 2. 12×2=24

step 3. 24+6=30 second place way

6 0
2 years ago
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