Answer:
1. Reflection
2. Dilation
3. Rotation
Step-by-step explanation:
Hey!
You can tell number one is a reflection because it didn’t change side or turn upside down or anything, it just flipped over to the other side.
You can tell number two is a dilation because it changes size.
You can tell number three is rotation because it rotated.
Hope this helps! :D
If you have any further questions, comment down below!
Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
Answer:
The number of ways are 16! or 20,922,789,888,000.
Step-by-step explanation:
Consider the provided information.
We need to determine the number of different ways 16 numbered pool balls be placed in a line on the pool table.
For the first place we have 16 balls.
For the second place we have 15 balls left.
Similarly for the third place we have 14 balls as two balls are already arranged and so on.
Or we can say that this is the permutation of 16 things taking 16 at a time.
Thus the number of ways are: 
or 
Hence, the number of ways are 16! or 20,922,789,888,000.
Answer:
He paid $1.11
Step-by-step explanation:
2.50 * 0.4 (he paid for 40% of the original price, since it was a 60% discount) = 1
1 * 0.11 (11% sales tax) = 0.11
1 + 0.11 = 1.11
You first need to find the LCD (lowest common denominator). You will need to find the smallest number that is a multiple of all numbers that is the denominator (2, 16, 8). Or, to say it another way, all the numbers in the denominator need to be a factor of this number.
You can find this by first checking if the largest number that is the denominator-- in this case 16-- is already the LCD, which means 16 is divisible by all the other numbers.
If this does not work, then multiply all the numbers together to get the LCD-- since you multiplied them together, you know that they will all be factors of the product.
However, you will be able to see that 16 is indeed the lowest common denominator:
2 × 8=16
8 × 2=16
16 × 1=16
So, after you find the LCD, multiply both the numerator and the denominator by the number that you would need to multiply the denominator to get the LCD (the whole point is that you want to get the denominator to be the LCD, but to do that you need to multiply both the top and bottom by the same number to keep the fraction the same).
(1/2) x (8/8)= 8/16
(3/16) x (1/1)= 3/16
(7/8) x (2/2)= 14/16
