Answer:
Step-by-step explanation:
Let the number = x
Read carefully the sentence part beginning with 4 times larger
4* something
4 times larger than the square of 1/2 the number
4 * (x/2)^2
4*(x/2)^2 = x
4*x^2/4 = x
x^2 = x be very careful how you handle this. It looks like 0 might be an answer, but it isn't. If you divide x on both sides and you allow 0, you will get 0 / 0 and that is undefined. You must exclude that possibility with some sort of statement.
x cannot be 0.
x^2/x= x/x
x = 1
(1) Answer: (D) Cubic (the highest power of x is 3)
(2) Answer: (C) Quadratic (power of x is 2)
(3) Answer: (B) Linear (highest degree 1)
(4) Answer: (A) Constant (the quadratic terms cancel out, constant left)
For this case we must simplify the following expression:
![\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B64%20%2A%20a%20%5E%206%20%2A%20b%20%5E%207%20%2A%20c%20%5E%209%7D)
We rewrite:

So:
![\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B4%20%5E%203%20%2A%20%28a%20%5E%202%29%20%5E%203%20%2A%20%28b%20%5E%202%29%20%5E%203%20%2A%20b%20%2A%20%28c%20%5E%203%29%20%5E%203%7D%20%3D%5C%5C%5Csqrt%20%5B3%5D%20%7B4%20%2A%20a%20%5E%202%20%2A%20b%20%5E%202%20%2A%20c%20%5E%203%29%20%5E%203%20%2A%20b%7D%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}](https://tex.z-dn.net/?f=4a%20%5E%202b%20%5E%202%20c%20%5E%203%20%5Csqrt%20%5B3%5D%20%7Bb%7D)
Answer:
Option B
A copy of the diagram is shown below
Point D is the intersection of three angle bisector.
BE is the angle bisector of ∠B
CF is the angle bisector of ∠C
AG is the angle bisector of ∠A
Point D is also the intersection between three perpendicular bisector
BE is the perpendicular bisector of AC
AG is the perpendicular bisector of BC
CF is the perpendicular bisector of AB
Hence the correct statements is statement 1 and statement 4
By Angle-Angle simlilarity postulate :
If two angles of one triangle congruent to two angles of another, then triangles must be similar.
So, I think the answer is
<span>All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
Because two base angles in </span>isosceles triangle are congruent, but it could be a lot of isosceles triangles that have different congruent base angles.
For example,
45-45-90 is an isosceles triangle, and 30-30-120 is an isosceles triangles, but they do not have 2 congruent angles.