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(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>
Let <em>n</em> represent the unknown number
<em>n</em>-10=9
+10 +10
—————
<em>n</em>=19
Brainliest??
50% is just half of the price. you could also times the original price by 1/2 and get the same answer.
Answer:
The correct answer is x = 12.
Step-by-step explanation:
To solve this problem, we must remember that an angle bisector divides the angle into two smaller, equal angles. This means that we can set the values for each of these smaller angles equal to one another, given that the angle is bisected. This is modeled below:
9x - 54 = 4x + 6
Now, we can solve this equation like any other. The first step is to subtract 4x from both sides.
9x - 4x - 54 = 4x - 4x + 6
5x - 54 = 6
Then, we should add 54 to both sides.
5x - 54 + 54 = 6 + 54
5x = 60
Finally, we can divide both sides by 5.
5x/5 = 60/5
x = 12
Therefore, the correct answer is x = 12.
Hope this helps!
