Find the coordinates of the vertices of the triangle after a reflection across the line x= -1 and then across the line y = 1.F(-2,-3), G(-3,2), H(1,-1)
Answers
Answer:
a. F'(0, 5), G'(1, 0), H'(-3, 3)
Step-by-step explanation:
Reflection across x = -1 gives you the transformation ...
(x, y) ⇒ (-2 -x, y)
Reflection across y = 1 gives you the transformation ...
(x, y) ⇒ (x, 2 -y)
Together, these give you the transformation ...
(x, y) ⇒ (-2 -x, 2 -y)
Applying this to point F, we have ...
F(-2, -3) ⇒ F'(-2 -(-2), 2 -(-3)) = F'(0, 5) . . . . . . matches choice A
_____
How we found the transformation
In general, if M is the midpoint between A and B, then you have ...
M = (A+B)/2
2M = A+B
B = 2M - A
So, if we want x=-1 to be the midpoint between x' and x, then we have ...
x' = 2(-1) -x = -2 -x
Likewise, if we want y=1 to be the midpoint between y' and y, then we have ...
y' = 2(1) -y = 2 -y
So, the transformation is ...
(x, y) ⇒ (x', y') = (-2 -x, 2 -y)
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Six students are working to simplify the expression shown. Drag each student's answer to a box to show whether it is fully simplified, equivalent to the given expression but not fully simplified, or not equivalent to the given expression. 15 + 12x -5x +4y -7
Answers
the only factor pair of 11 is:
11&1
But, while these two number have a product of 11, they do not have a sum of 8
11+1=12
11+1≠8
Answers
The area of the second one would be the area of the triangle plus the area of the semicircle, so [(4*5)/2]*[(pi*2*2)/2]. That would be 20pi, or around 62.8319 ft squared
I'm not sure about the third one. Is it a trapezoid?
Answers
Answer:
7
Step-by-step explanation:
-x+2+5x=10(x-4)
4x+2=10x-40
2+40=10x-4x
42=6x
42/6=6x/6
7=x
Answer:
x = 7
Step-by-step explanation:
-x + 2 + 5x = 10 (x - 4)
=> 4x + 2 = 10x - 40
=> 4x - 10x = -40 - 2
=> -6x = -42
=> 6x = 42
=> x = 42/6
=> x = 7
Answers
b) What is that amount?
Answers
After 7 weeks Joy and Cullen will have the same amount of money in their money boxes and the amount is $230.
What is a linear system of equations?
A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) The given system of equations are y=30x+20 -----(i) and y=20x+90 -----(ii)
Fromm equation (i) and (ii), we have
30x+20=20x+90
30x-20x=90-20
10x=70
x=7
b) Substitute x=7 in equation (i), we get
y=30×7+20
y=210+20
y=230
Therefore, the solution of the system of equations is (7, 230).
To learn more about the linear system of an equations visit:
brainly.com/question/27664510.
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Answer:
The answer is D trust me i helped my friend Week 7 And the amount is 230$
Step-by-step explanation:
y=-|x|+1