Answer:
the common difference is 6.
Step-by-step explanation:
Given;
first term of an AP, a = -7
let the common difference = d
The third term is written as;
T₃ = a + 2d
The eight term is written as;
T₈ = a + 7d
The ratio of the eight term to third term = 7:1
![\frac{T_8}{T_3} = \frac{7}{1} = \frac{a+ 7d}{a + 2d} \\\\7 = \frac{a+ 7d}{a + 2d}\\\\Recall, a = -7\\\\7 = \frac{-7+ 7d}{-7 + 2d}\\\\7(-7 + 2d) = -7+ 7d\\\\-49 + 14d = -7 + 7d\\\\14d -7d = -7 + 49\\\\7d = 42\\\\d = \frac{42}{7} \\\\d = 6](https://tex.z-dn.net/?f=%5Cfrac%7BT_8%7D%7BT_3%7D%20%3D%20%5Cfrac%7B7%7D%7B1%7D%20%3D%20%5Cfrac%7Ba%2B%207d%7D%7Ba%20%2B%202d%7D%20%5C%5C%5C%5C7%20%3D%20%20%5Cfrac%7Ba%2B%207d%7D%7Ba%20%2B%202d%7D%5C%5C%5C%5CRecall%2C%20a%20%3D%20-7%5C%5C%5C%5C7%20%3D%20%20%20%5Cfrac%7B-7%2B%207d%7D%7B-7%20%2B%202d%7D%5C%5C%5C%5C7%28-7%20%2B%202d%29%20%3D%20-7%2B%207d%5C%5C%5C%5C-49%20%2B%2014d%20%3D%20-7%20%2B%207d%5C%5C%5C%5C14d%20-7d%20%3D%20-7%20%2B%2049%5C%5C%5C%5C7d%20%3D%2042%5C%5C%5C%5Cd%20%3D%20%5Cfrac%7B42%7D%7B7%7D%20%5C%5C%5C%5Cd%20%3D%206)
Therefore, the common difference is 6.
The x variable, that is being multiplied.
Answer:
∆STR ~ ∆RTQ
Step-by-step explanation:
For two fugures to be considered similar, it means the corresponding sides are proportional, and as such, the ratio of their corresponding sides are equal.
However, the corresponding angles of two similar figures are the same and equal.
Taking a look at the figure of the triangle given, ∆STR is a right angle triangle, and it is similar to ∆RTQ as the angle formed at <T in ∆RTQ = 90°.
<T in ∆STR = <T in ∆RTQ.
Therefore, the correct similarity statement is ∆STR ~ ∆RTQ.
The last option is correct.
Answer:
8
Step-by-step explanation:
that;'s what i put the first time
Yea they are cuz they have the same side and angle measurements