The triangle drawn in the question shows a small single line drawn across two sides of the triangle.
This means that those two sides are equal in length.
Hence, the triangle is an isosceles triangle.
In isosceles triangles, the angles opposite to the equal sides are also equal.
Hence, we know that the two angles other than x is 56°.
The sum of the interior angles of a triangle is 180°
x + 56 + 56 = 180
x = 180 - 56 - 56
x = 180 - 112
x = 68°
Hence, the answer is A.
To solve this function, all we need to do is substitute -4.3 in for wherever "x" appears and then simplify.
f(x) = 7.45x + 33.7; x = -4.3
f(-4.3) = 7.45(-4.3) + 33.7
f(-4.3) = -32.035 + 33.7
f(-4.3) = 1.665
This means that, when x = -4.3, f(x) = 1.665.
Note: It may help to remember that, in a function such as this, f(x) can be thought of as the "y" value that corresponds to the given "x" value (in fact, when writing it out with words, f(x) is the same as "function of x"). And, if you are given a value for f(x), then the opposite is true. Just substitute in the value given for f(x) and solve for x.
Hope this helps!
The rows add up to
, respectively. (Notice they're all powers of 2)
The sum of the numbers in row
is
.
The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When
,
so the base case holds. Assume the claim holds for
, so that
Use this to show that it holds for
.
Notice that
So you can write the expansion for
as
and since
, you have
and so the claim holds for
, thus proving the claim overall that
Setting
gives
which agrees with the result obtained for part (c).
Answer:
No
Step-by-step explanation:
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