Answer:
Combination; number of ways = 15.
Step-by-step explanation:
Given that there are 6 people in the contest. So it means n = 6.
Two winners each win gift cards. So it means r = 2.
Each gift card is same, so both persons are equally important. It means the order does not matter here, so it is the case of Combinations. We will use nCr formula.
Total number of ways = 6C2 = (6*5)/2 = 15.
Hence, Combination; number of ways = 15.
(x - d) + x + (x + d) = 12 --> Create an equation using the first piece of information - "Three consecutive terms... have a sum of 12"
x - d + x + x + d = 12 --> Simplify the left side of this equation (d cancels out)
3x = 12 --> Divide both sides by 3
<u>x = 4
</u>
Use the value of x (x = 4) to find the value of d. To do this, set up another equation using the second piece of information.
(x - d) * (x + d) * x = - 80 --> "Three consecutive terms... have... a product of -80". Then, substitute the value of x (4) into this equation.
(4 - d) * (4 + d) * 4 = - 80 --> Multiply out the sets of brackets, the * 4 is dealt with afterwards
4(16 - 4d + 4d - d²) = - 80 --> Simplify the expression inside the brackets
4(16 - d²) = - 80 --> Multiply out these brackets by the 4
64 - 4d² = - 80 --> Subtract 64 from both sides
- 4d² = - 144 --> Divide both sides by - 4
d² = 36 --> Square root both sides
<u>d = 6
</u>Now, find the values of the terms of the sequence by using substituting the values of x and d into the expressions given.
<u>
</u><u />1. x - d = 4 - 6 = <u>- 2
</u><u></u>2.<u> x = 4</u>
3. x + d = 4 + 6 = <u>10
</u>
The three terms are - 2, 4, 10.
<u>
</u>
Answer:
18 & -2
Step-by-step explanation:
18 + -2 = 16
18 - -2 = 20
PQ peependicular to PS
Thus angle QPS = 90⁰
7x - 9 + 4x + 22 = 90⁰
11x = 77
x = 7
Thus angle QPR = 7(7) - 9 = 40⁰
Answer:
we can call a 21 sided polygon as henicosagon.
