A. True. We see this by taking the highest order term in each factor:
B. True. Again we look at the leading term's degree and coefficient. f(x) behaves like -3x⁶ when x gets large. The degree is even, so as x goes to either ± ∞, x⁶ will make it positive, but multiplying by -3 will make it negative. So on both sides f(x) approaches -∞.
C. False. f(x) = 0 only for x=0, x = 5, and x = -2.
D. False. Part of this we know from the end behavior discussed in part B. On any closed interval, every polynomial is bounded, so that for any x in [-2, 5], f(x) cannot attain every positive real number.
E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).
F. False. (0, 2) corresponds to x = 0 and f(x) = 2. But f(0) = 0 ≠ 2.
Answer:
8
Step-by-step explanation:
It depends what mathematics you know
Perhaps the most basic way would be by approximation. You could start with, say, 5. 5*5*5= 125. Then 5 is to small to be the cube root of 512.
Try 10: 10*10*10=1000: Too bi. But now we know that the number we want is between 5 and 10.
Try 8: 8*8*8=512.
Answer:
1. 4x + 6
2. -15x + 11
5. -x + 4
6. -4x + 7
9. 5x - 2
12. x + 16
Step-by-step explanation:
Remove the parenthesis for each one so everything's out in the open. Next, you group like terms. The numbers with variables on one side, and the other numbers on the other side. For example:
x + 3x - 2 + 8
Then, you combine like terms:
4x + 6
That's mostly how you do each one.
Answer:
Your answer is correct here's an example.
Step-by-step explanation:Viruses are like hijackers. They invade living, normal cells and use those cells to multiply and produce other viruses like themselves. This can kill, damage, or change the cells and make you sick. Different viruses attack certain cells in your body such as your liver, respiratory system, or blood
Answer:
Step-by-step explanation:
Assuming that the tree is perpendicular with the ground, we can use trigonometric ratios to find the height of the tree.
First, let's draw a diagram. From the point on the ground to the base, it is 120 feet and forms a 30 degree angle. We want to find the height of the tree, which is labeled h. (The diagram is attached and not to scale).
Next, recall the ratios.
- sin(θ)= opposite/hypotenuse
- cos(θ)= adjacent/hypotenuse
- tan(θ)= opposite/adjacent
We see that the height is opposite the 30 degree angle and 120 is adjacent.
Since we are given opposite and adjacent, we must use tangent.
Substitute the values in.
We are solving for h, so we must isolate it. It is being divided by 120 and the inverse of division is multiplication. Multiply both sides by 120.
Round to the hundredth place (2 decimal places). The 2 in the thousandth place tells us to leave the 8 in the hundredth place.
The height of the tree is about <u>69.28 feet.</u>
