Answer:
-2 < x < 4
Step-by-step explanation:
1) circumference of the first bead = 0.25 in
2) circumference of the second bead = (0.25 + 0.15) in
3) circumference of the third bead = 0.25 + 0.15*2 in
4) circumference of the nth bead = 0.25 + 0.15 * (n -1) in
5) circumference of the 24th bead = 0.25 + 0.15 * (24 - 1) = 3.7 in
6) circumference = 2π*radius => radius = circumference / (2π)
7) radius of the 24th bead = circumference of the 24th bead / (2π)
radius of the 24th bead = 3.7 inches / (2π) = 0.5889 in ≈ 0.59 in
Answer: 0.59 in
8.5 - 7 = a
Convert the fraction to a decimal and solve for a.
a = 1.5
I prefer adding polynomials horizontally because its quick to just group and add like terms. Plus you read things horizontally so it seems more natural. if you add them vertically you have to line up the like terms and place a zero where there are none.
Horizontal
5x³ + 2x² + 6 + x³ - 6x² + 3x - 4 = 6x³ - 4x² + 3x + 2
Vertical
5x³ + 2x² + 0 + 6
+ x³ - 6x² + 3x - 4
------------------------
6x³ - 4x² + 3x + 2
For question one, you would need to use the formula pi r ^2. So first you have 4.5, which is your radius(stands for r). Then you square it, which is 20.25. Then, you multiply 20.25 with pi. Then for circumference, you do 2 x pi x the radius which is 4.5. So for area, you get 63.62. Then for circumference you get 28.27.
For question 2, it is basically the same steps but instead you a diameter, not a radius. To get the radius, divide by 2, which the radius will be 6. Then from there, the radius is 6, and you solve the question.