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3 years ago

How do I solve this do we use the multiple choice

Mathematics

1 answer:

belka [17]3 years ago

5 0

Answer:

Step-by-step explanation:

You can solve each of the inequalities to see if their solutions match the given numbers, or you can start with the given numbers and see what sort of inequality you end up with.

If you plot the given "solution" on a number line, you find that the numbers -6 and 11 are the same distance from x=2.5. That distance is 8.5 units. (One way to deterimine this is to average -6 and 11, then subtract that average from 11 to find the distance.

So, we can write an inequality describing values of x that are more than 8.5 units from 2.5:

|x -2.5| > 8.5

and it will have the solution x < -6 or x > 11.

Multiplying this by 2, it can become ...

|2x -5| > 17

Of course, since the absolute value function doesn't care whether its argument is positive or negative, we can also write this as ...

|5 -2x| > 17

This tells you right away which answer choice is appropriate. Further confirmation can be had by multiplying this by 4:

4|5 -2x| > 68 . . . . . . matches selection C

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3 years ago

What is the median of these scores,<br> 98,82,100,84?

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Step-by-step explanation:

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3 years ago

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Which equation represents a linear function that has a slope of 4/5 and a y-intercept of –6?

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Use the form y=mx+b where m is the slope and b is the y-intercept: y=4/5x-6

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4 years ago

A student claims that 2i is the only imaginary root of a polynomial equation that has real coefficients. Explain the student's m

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Answer:

The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i

Step-by-step explanation:

1) This claim is mistaken.

2) The Fundamental Theorem of Algebra assures that any polynomial f(x)=0 whose degree is n ≥1 has at least one Real or Imaginary root. So by the Theorem we have infinitely solutions, including imaginary roots ≠ 2i with real coefficients.

$a_{0}x^{n}+a_{1}x^{2}+....a_{1}x+a_{0}$

For example:

3) Every time a polynomial equation, like a quadratic equation which is an univariate polynomial one, has its discriminant following this rule:

$\Delta < 0\\b^{2}-4*a*c$

We'll have <em>n </em>different complex roots, not necessarily 2i.

For example:

Taking 3 polynomial equations with real coefficients, with

$\Delta < 0$

$-4x^2-x-2=0 \Rightarrow S=\left \{ x'=-\frac{1}{8}-i\frac{\sqrt{31}}{8},\:x''=-\frac{1}{8}+i\frac{\sqrt{31}}{8} \right \}\\-x^2-x-8=0 \Rightarrow S=\left\{\quad x'=-\frac{1}{2}-i\frac{\sqrt{31}}{2},\:x''=-\frac{1}{2}+i\frac{\sqrt{31}}{2} \right \}\\x^2-x+30=0\Rightarrow S=\left \{ x'=\frac{1}{2}+i\frac{\sqrt{119}}{2},\:x''=\frac{1}{2}-i\frac{\sqrt{119}}{2} \right \}\\(...)$

2.2) For other Polynomial equations with real coefficients we can see other complex roots ≠ 2i. In this one we have also -2i

$x^5\:-\:x^4\:+\:x^3\:-\:x^2\:-\:12x\:+\:12=0 \Rightarrow S=\left \{ x_{1}=1,\:x_{2}=-\sqrt{3},\:x_{3}=\sqrt{3},\:x_{4}=2i,\:x_{5}=-2i \right \}\\$

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3 years ago

What is the value of x in the equation 4x+8y=40 when y=0.8

GREYUIT [131]

Substitute in 0.8 for y.

$4x+8y=40 \\ \\ 4x + 8(0.8) = 40 \\ \\ 4x + 6.5 = 40 \\ \\ 4x = 40 - 6.4 \\ \\ 4x = 33.6 \\ \\ x = 8.4 \\ \\$

The final result is: x = 8.4.

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4 years ago

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