Answer:
3x^2 + 3 --> 6, 15, 30, 51
2x^2 - 1 --> 1, 7, 17, 31
x^2 + 2 --> 3, 6, 11, 18
Step-by-step explanation:
Let's start with the first equation; 3x^2 + 3
Substitute 1 (the first digit in a sequence) for x.
3(1^2) + 3
3(1) + 3
3 + 3 = <u>6</u>
3(2^2) + 3 Then the second digit.
3(4) + 3
12 + 3 = <u>15</u>
Since the two numbers we have so far are 6 and 15, there is only one sequence this could match. 6, 15, 30, 51.
2(1^2) - 1
2(1) - 1
2 - 1 = <u>1</u>
This equation represents 1, 7, 17, 31.
These same steps apply to the other equation as well.
1^2 + 2, then 2^2 + 2, then 2^2 + 2, and so on. (But we don't need to do extra work to figure that out.)
Answer: 5x^2 + 3x + 1
Step-by-step explanation:
1.) Put the two equations together into an addition problem.
<em>3x^2 + 4x + 2x^2 - x + 1</em>
2.) Combine like terms.
<em>3x^2 + 2x^2 = 5x^2</em>
<em>4x - x = 3x</em>
<em>1 = 1</em>
3.) Order the like terms together.
<em>5x^2 + 3x + 1</em>
Answer:
16.43 meters
Step-by-step explanation:
If the shape of the rise is a triangle, then the center of it is half the total length from the end. We can find the rise (y) using the Pythagorean theorem:
1500.09² = 1500² +y² . . . . .dimensions in meters
270.0081 = y²
y = √270.0081 ≈ 16.43 . . . . meters
About the most it would rise is 16.43 meters.
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If the shape is an arc of a circle, the height is about 14.2 meters.
Answer:
x=30º
∠CAB=60°
∠ACB=80°
Step-by-step explanation:
Because the angles of every triangle add up to 180º, we know that:
x=30º
Plug that in for x on both angles, and you will get
∠CAB=60°
∠ACB=80°
