Answer:
First option is the correct answer.
Step-by-step explanation:
This is true. It would only be incorrect if dilations were there, because dilations don’t keep the shapes congruent.
Answer:
(2, -8)
Step-by-step explanation:
The coordinates of M are the average of the coordinates of X and Y.
-3 = (x + -8) / 2
-1 = (y + 6) / 2
Solving:
x = 2
y = -8
Answer:
(22, 9)
Step-by-step explanation:
The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller). I'll call the two integers a and b.
a - b = 13 a + b² = 103
<u> +b +b</u>
a = 13 + b plug this into the second equation
a + b² = 103
(13+b) + b² = 103 subtract 103 from both sides to get one side equal to zero
<u>-103 -103</u>
b² + b - 90 = 0 what factors (two numbers multiply) to -90 that also add up
to 1? The only two that work are -9 and 10.
(b-9)(b+10) = 0 so b-9 = 0 or b+10 = 0
<u>+9 +9</u> or <u>-10 -10</u>
b = 9 or b = -10 but both numbers must be positive
b = 9 and a = 13 + b so a = 13 + 9 = 22
(22, 9)
Answer:
92.6 inches
Step-by-step explanation:
All you have to do is look at the 3D pyramid in a 2D plane. You have base and slant height and you're trying to find height. This is just a right triangle. The slant height is the hypotenuse of the triangle. And half of the base is one of the legs. You are trying to find height, AKA the other leg. Since a^2+b^2=c^2 and you have a and c. Just square HALF of the base height. Then square the slant height. Then subtract a^2 from c^2 and you'll get b^2. Then you take the square root of b^2 to get b.
23.6/2=11.8
11.8^2+b^2=93.3^2
139.2+b^2=8704.9
b^2=8565.7
=b
=92.6
b=92.6
