For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.
If we draw the diagonals of the square then the angles are divided by two, that is:
Thus, angle 3 measures 45 degrees.
By definition, the sum of the internal angles of a triangle is 180 degrees.
So:
Thus, angle 2 measures 45 degrees.
Answer:
45 degrees
For problems of this type, you need to look at the steps that only require elements that are already known. If a step requires something that hasn't been done yet. THEN THAT STEP COMES LATER. So looking at the 7 available steps, only the step "Construct horizontal PQ" is possible since that's just a matter of drawing a straight line and labeling the end points P and Q. In any case, here are the 7 steps in order. The number in parenthesis after the 1st number is the original scrambled order of that step.
1(2). Construct horizontal PQ
2(5). Construct a circle with point P as the center and a circle with point Q as a center, each circle having radius PQ
3(4). Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S
4(6). Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T
5(1). Construct a circle with point T as the center with radius TQ
6(7). Label the point of intersection of circle T and RS closest to point R, point
U, and the point of intersection of circle T and RS closest to point S, point V.
7(3). Construct PU, UQ, QV, and VP to complete square PUQV.
Sanjay needs 11 hours of sleep
Answer:
(4 x + 9) (16 x^2 - 36 x + 81)
Step-by-step explanation:
Factor the following:
64 x^3 + 729
64 x^3 + 729 = (4 x)^3 + 9^3:
(4 x)^3 + 9^3
Factor the sum of two cubes. (4 x)^3 + 9^3 = (4 x + 9) ((4 x)^2 - (4 x) 9 + 9^2):
(4 x + 9) ((4 x)^2 - 4 9 x + 9^2)
4×9 = 36:
(4 x + 9) ((4 x)^2 - 36 x + 9^2)
Multiply each exponent in 4 x by 2:
(4 x + 9) (4^2 x^2 - 36 x + 9^2)
4^2 = 16:
(4 x + 9) (16 x^2 - 36 x + 9^2)
9^2 = 81:
Answer: (4 x + 9) (16 x^2 - 36 x + 81)
Answer:
The tree that Laura had to cut had 306 apples.
Step-by-step explanation:
Given that Laura has 78 apple trees in her cider farm, with a mean of 460 apples per tree, but then she has had to get a tree cut down, and after that, the mean of apples per tree became 462, to determine how many apples were there on the tree that Laura had to cut down, the following calculation must be performed:
(78 x 460) - (77 x 462) = X
35.880 - 35.574 = X
306 = X
Thus, the tree that Laura had to cut had 306 apples.
