Answer:
See below for answers and explanations
Step-by-step explanation:
4) 35° and x° are vertical angles, so they are congruent to each other. Therefore, x°=35°. Since y°+y°+35°=180° since they are all supplementary to each other, then y°=72.5° when solved.
5) A is true. Think of two adjacent angles measured 60° and 30° that are next to each other. They add up to 90° as well.
B isn't true. Vertical angles are congruent to each other, not supplementary.
C isn't true. The statement contradicts itself. Complementary angles add up to 90° while supplementary angles add up to 180°
Answer:
a) (x/2 +3)^2
b) (5a -3b)^2
c) (x/3 +y/5)^2
d) (10b -3c)^2
e) (a/4 -2b)^2
Step-by-step explanation:
Assuming you can do that, write the terms of the quadratic in lexicographical order. (The square terms will be first and last.) Then the binomial is the "sum" of the square roots of the first and last terms with the sign of the middle term.
Using (e) as an example, the term are already in order. (In (d), they need to be rearranged.) The first term is 1/16a^2, and its square root is 1/4a = a/4. The last term is 4b^2 and its square root is 2b. The sign of the middle term is negative, so these two roots will be separated by a minus sign:
(a/4 - 2b)^2
The expression you want is the square of the binomial.
_____
As a check, you can make sure that double the product of these terms is the middle term of the trinomial you started with.
In this example, that double product is 2·a/4·(-2b) = -ab, which exactly matches the middle term you started with.
Answer:
show the number line
Step-by-step explanation:
A great circle is a section of a sphere that passes through its center. If the earth were a sphere, a great circle would be the equator and its axis would be the line connecting the geographic north and south pole. The length of the axis is then equal to the diameter of the sphere. For this problem, the radius of the sphere is 12 inches. A section is formed by slicing through the sphere and all sections of a sphere are circles. Considering the plane to be cut above and parallel with the equator (which is a great circle), the distance of the plane from the center of the sphere would then be the distance between the centers of the sphere and section. It is also given that the radius of the section is 9 inches. A right triangle is formed by connecting the center of the sphere, an edge of the section, and back to the center of the sphere whose hypotenuse is 12 inches (radius of the sphere), one leg is the 9 inches (radius of the section), and another leg is the distance of the plane from the sphere's center. Thus, the distance can be calculated using the Pythagorean theorem, d = sqrt(12^2 - 9^2) = sqrt(144 - 81) = sqrt(63) = 3*sqrt(7).
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