Answer:
Step-by-step explanation:
The option C is correct
Answer:
x = 5
Step-by-step explanation:
To break this down, I'll start from the first thing the question gives you. Triangle ACB is congruent to triangle DCE. This means that the angles and the sides of each triangle is the same. Now this next part is important. The way in which the letters are ordered is corresponds to what angles are the same. Since the triangles are congruent, ∠A in ΔACB would correspond to ∠D in DCE. Another example: ∠C in ACB is congruent to ∠C in ΔDCE. So if ∠A is congruent, or the same as ∠D, this means ∠D is 50°. Now, we just solve for x:
∠D = 10x
50° = 10x
Divide each side by 10 to isolate x:
50/10 = 10x/10
x = 5
namely, how many times does 1/4 go into 3/8?
![\bf \cfrac{3}{8}\div \cfrac{1}{4}\implies \cfrac{3}{\underset{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\implies \cfrac{3}{2}\implies 1\frac{1}{2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B3%7D%7B8%7D%5Cdiv%20%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B%5Cunderset%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%208%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%5Ccdot%20%5Ccfrac%7B~~%5Cbegin%7Bmatrix%7D%204%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%5Cimplies%201%5Cfrac%7B1%7D%7B2%7D)
130 =
2 * 5 * 13
The prime factors are 2, 5, and 13.
No prime factors are used more than once.
The only exponents to write might be the understood 1.
130 = 2^1 * 5^1 * 13^1
