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evablogger [386]
2 years ago
11

11. Write the equation of a line passing through the two points. First find the slope and the y-

Mathematics
1 answer:
tensa zangetsu [6.8K]2 years ago
8 0

Answer:

Y intercept is (0,3)

Step-by-step explanation:

Check out the image

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How do you solve x^4 - 3x^3 - 3x^2 - 75x - 700
madam [21]

Answer:

  = (x +4)(x -7)(x^2 +25)

  roots are -4, 7, ±5i

Step-by-step explanation:

You have not said what "solve" means in this context. An expression by itself doesn't have a solution. We have assumed you want to find the factoring and/or roots of it.

I like to use a graphing calculator to find the real roots. For this expression, there are two of them, one positive and one negative. (You know there will be one positive real root, and at least one negative real root, from Descartes's rule of signs.)

Then those roots can be factored out and the solution to the remaining quadratic determined. That factoring can occur by polynomial long division, synthetic division, or other means.

I like to see what happens when I plot the graph of the function divided by the known factors. (We expect a parabola that doesn't cross the x-axis.) The vertex of that parabola can be used to find the remaining roots.

The x-intercepts of the given expression are -4 and +7, so two of the factors are (x+4) and (x-7). Dividing these from the given expression (by synthetic division or other means) gives (x^2 +25). This only has imaginary roots (±5i).

____

If you're constrained to doing this "by hand" with only a scientific calculator, Descartes's rule of signs tells you there is one positive real root. (Only one sign change in the sequence of coefficient signs: +----.)

The rational root theorem tells you it will be a divisor of 700. Various estimates of the maximum magnitude of it will tell you it is probably less than 14 (easily checked). So, the numbers you can test as roots would be 1, 2, 4, 5, 7, 10, 14. You will find that 7 is a root, and then you can reduce the problem to the cubic x^3 +4x^2 +25x +100.

When odd-degree term signs are changed, there will be 3 sign changes (-+-+), hence at least one negative real root. The rational root theorem tells you it is a divisor of 100, so possible choices are -1, -2, -4, -5. By trial and error or other means, you can find the root to be -4. Then the problem reduces to the quadratic x^2 +25.

Roots of that are ±√(-25) = ±5i.

This process generally entails a fair amount of trial-and-error work, which is why I prefer one that makes some use of technology.

_____

We have presumed you have some familiarity with ...

  • Descartes's rule of signs
  • Rational Root Theorem
  • synthetic division

This will usually be the case when you're presented with problems like this. If you need additional information on any of these, it is readily available on the internet (and probably also in your reference material).

4 0
3 years ago
Bianca deposited $1500 into asavings account for whichsimple interest is calculatedquarterly. If her $1500 grew to$1509 after 3
Furkat [3]

Solution:

Given;

P=1500,A=1509,t=3months=0.25year\begin{gathered} A=P(1+\frac{r}{4})^{4t} \\  \\ 1509=1500(1+\frac{r}{4})^{4(0.25)} \\  \\ \frac{1509}{1500}=1+\frac{r}{4} \\  \\ 1.006-1=\frac{r}{4} \\  \\ r=4(0.006) \\  \\ r=0.024 \end{gathered}

Thus, the yearly interest rate on Bianca's account is 2.4%

6 0
1 year ago
Eric has saved $18,300 toward a down payment on a house. He makes a salary of $59,750 a year. What is the maximum Eric could spe
dimaraw [331]
The answer should be B) $119,500. The benchmark is his annual salary, and this amount is twice his annual salary, but not thrice larger. For mortgages, your debt should generally not be larger than three times your gross annual salary. 
5 0
3 years ago
Read 2 more answers
6,7,8,8 and 10 need to be answered
Zarrin [17]
Number 6. 12 1/2 pt
Number 7. 7 qt
Number 8. 4 pt
Number 9. 2 pt 1 c
Number 10. 6 pt
5 0
3 years ago
What is the value of p?
aksik [14]

Answer:

P = 18

Step-by-step explanation:

:) that the answer.

3 0
2 years ago
Read 2 more answers
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