The translation that maps triangle ABC to A prime B prime C prime would be a reflection across the y axis. This is because when you reflect something, you are pretty much flipping it. When you reflect across the y axis, you are flipping the triangle across the y axis. Take one point for example. I will use C. Notice how the point C is 3 units away from the y axis. So the same way you would move the point 3 units right from the y axis, and that would be your new point. This sounds kind of complicated, so I will give you a list of rules to make it more simple.
Reflection across y axis: (x,y) would be equal to (-x, y)
Reflection across x axis: (x,y) would be equal to (x, -y)
Reflection across y = x: (x,y) would be equal to (y,x)
Reflection across y = x: (x,y) would be equal to (-y,-x).
A reflection across y = x would be when you have a line that for every 1 it rises, it goes right 1. It is a positive line, as opposed to the y = -x line. It also has a slope of 1. I will try attaching a graph if I can.
Anyway, as I was saying. So pretty much if you don't want to go through the logic, to see whether a figure is reflected, just try each of these rules and if one works then you have your answer. Otherwise it would not be a reflection.
Thanks for being a great mod and hope this helps! :D
Answer:
360 votes
Step-by-step explanation:
Move the decimal to the left 2 times and you'll get .144. Multiply that by 2500, and you have your answer.
Answer:
91
Step-by-step explanation:
Let x be the smallest one:
● x is the first number
● x+1 is the second number
● x+2 is the third number
The sum of these numbers is 276
● x+(x+1)+(x+2) =276
● x+x+1+x+2 = 276
● 3x + 3 = 276
Substract 3 from both sides:
● 3x+3-3 = 276-3
● 3x = 273
Divide both sides by 3
● (3x)/3 = 273/3
● x = 91
So the smallest one is 91
Answer:
(3,-3)
y= -3
x= 3
Step-by-step explanation:
5x+2y=9
2x-3y=15
solve the equation
x=9/5-2/5y
2x-3y=15
substitute the value of x into an equation
2(9/5-2/5y)-3y=15
distribute
18/5-4/5y-3y=15
subtract -4/5 to -3
18/5-19/5y=15
subtract 18/5 from both sides
-19/5=57/5
divide both sides by -19/5
y= -3
substitute the value of y into an equation
x=9/5-2/5(-3)
distribute
x=9/5+6/5
add 9/5 to 6/5
x=3
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(3,-3)
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<h2><u>
Answer with explanation</u>
:</h2>
Let 
be the population mean.
As per given , we have
Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.
Also, population standard deviation is given 
, so we perform one-tailed z-test.
Test statistic : 
, where = Population mean
= Population standard deviation
n= sample size
= Sample mean
For n= 18 , 
, , 
, we have
P-value (for right tailed test): P(z>2.12) = 1-P(z≤ 2.12) [∵ P(Z>z)=1-P(Z≤z)]\
=1- 0.0340=0.9660
Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.
[We reject null hypothesis if p-value is larger than the significance level . ]
Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .
