Answer: -258
<u>Step-by-step explanation:</u>
Given the sequence {-8, 16, -32, 64, ... , a₇} we know the following
- the first term (a₁) = -8
- the common ratio (r) = -2
- the number of terms (n) = 7
Input the information above into the Sum formula:
![S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\S_7=\dfrac{-8(1-(-2)^7)}{1-(-2)}\\\\.\quad =\dfrac{-8(1-(-128))}{1+3}\\\\.\quad =\dfrac{-8(129)}{4}\\\\.\quad =-2(129)\\\\.\quad =-258](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%5C%5C%5C%5CS_7%3D%5Cdfrac%7B-8%281-%28-2%29%5E7%29%7D%7B1-%28-2%29%7D%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B-8%281-%28-128%29%29%7D%7B1%2B3%7D%5C%5C%5C%5C.%5Cquad%20%3D%5Cdfrac%7B-8%28129%29%7D%7B4%7D%5C%5C%5C%5C.%5Cquad%20%3D-2%28129%29%5C%5C%5C%5C.%5Cquad%20%3D-258)
Answer:
x would equal 8. because you would add AB and BC together and set it equal to AC
Hoped I helped
Can I get a brainliest
Subtract 89 from -42. k=-131
Answer:
A) 150 m
B) 180.28 m
Step-by-step explanation:
A) In order to find the horizontal distance from the base of the cliff to the speed boat, use the Pythagorean theorem to calculate the length of the missing side.
We are told that one of the sides is 80 m and the hypotenuse is 170 m. Therefore,
- a² + b² = c²
- (80)² + b² = (170)²
- b² = 170² - 80²
- b² = 22500
- b = 150
The horizontal distance between the base of the cliff and the boat is 150 m.
B) Now, the side that was 80 m is now 100 m (includes the height that the helicopter is above Jumbo). The horizontal distance remains the same, 150 m, but the hypotenuse is different. Solving for the hypotenuse will give us the distance between the helicopter and the speed boat.
- (100)² + (150)² = c²
- 32500 = c²
- 180.28 = c
The distance between the helicopter and the speed boat is 180.28 m.