Answer:
x = 27
Step-by-step explanation:
To find the value of x, create a proportion. A proportion is two equal ratios for similar figures. The two triangles are similar because they are the same shape but not the same size. Create ratios between corresponding sides of figures.
To solve for x, cross multiply:
(x+8)(14) = (10)(2x-5)
14x + 112 = 20x -50
112 = 6x - 50
162 = 6x
27 = x
Part a .
A arithmetic sequence with a third term of 8 and a common difference of 5 .
To find the first five therms, since the common difference is 5, so we add 5 to get the fourth term and add 5 to fourth term to get the fifth term .
And for first two terms, we will subtract 5 from 8 to get the second term and subtract 5 from the second term to get the first term. And we will get
Part b:A geometric sequence with a fifth term of 1/3 and constant ratio of 1/3.
TO find the first five terms, since the constant ratio of 1/3, so we multiply 1/3 to third term to get fourth term, and multiply fourth term by 1/3 to get fifth term .
And to get the first two terms, we will divide third term by 1/3, to get the second term and divide the second term by 1/3 to get the first term, that is