Answer:
X''(2, -5), Y''(3, -3)
Step-by-step explanation:
You know that reflection in the x-axis changes the sign of the y-coordinate. Points that used to be above the axis are now below by the same amount, and vice versa.
Rotation counterclockwise by 270° is the same as clockwise rotation by 90°. That maps the coordinates like this:
(x, y) ⇒ (y, -x)
The two transformations together give you ...
(x, y) ⇒ (x, -y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection across y=-x.
Using this mapping, we have ...
X(5, -2) ⇒ X''(2, -5)
Y(3, -3) ⇒ Y''(3, -3) . . . . . . on the equivalent line of reflection, so invariant
_____
The attachment shows the original segment in red, the reflected segment in purple, and the rotated segment in blue. The equivalent line of reflection is shown as a dashed green line.
Answer:
b and c
Step-by-step explanation:
The Triangle Inequality Theorem lets us know that the sum of the two shortest sides of the triangle must be greater than the third side of the triangle.
In both A and D, the sum of the shortest two sides are equal to, not greater than the third side, so they will not form a triangle.
In B, 12+20 is 32, which is greater than 25. And in C, 18+24 is 42, which is greater than 30, so they both will form a triangle.
Answer:
Step-by-step explanation:
Given
Represent Boys with B and Girls with G
Required
Find the probability or having 1 boy 2 girls
Since the order is not important, the probability is calculated as follows;
Substitute 
for P(B) and P(G)
<em>Hence, the fractional probability is </em>
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Answer:
C
Step-by-step explanation:
We are given that FGH is a triangle, which means that...
Angle F + Angle G + Angle H = 180
Start by substituting the given angle measurements into the equation:
4x+2+13x-7+3x+5=180
Combine like terms
20x=180
Divide both sides by 20 to isolate x
x=9
Plug 9 back in for x to solve for each angle
Angle F = 4(9)+2=36+2=38
Angle G = 13(9)-7=117-7=110
Angle H = 3(9)+5=27+5=32
A. 9 and 7+2x
B. 1 and 2 respectively.
C. 2 from 2x
