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3 years ago

Express the solution of, x^3 + 2x^2 < x + 2, using interval notation.

Mathematics

1 answer:

Rudiy273 years ago

6 0

x³ + 2x² - x - 2 < 0

x³ - x + 2x² - 2 < 0

x(x² - 1) - 2(x² - 1) < 0

(x - 2)(x² - 1) < 0

(x - 2)(x - 1)(x + 1) < 0

by chacking we get the solution

x ∈ (-∞,-1) ∪ (-1,1)

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A number x is rounded to 3sf the result is 0.458 write down the error interval for x

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Answer:

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3 years ago

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3 years ago

A set of numbers is shown: {0, 1.4, 3.2, 4, 8, 12} Which of the following shows all the numbers from the set that make the inequ

stiv31 [10]

5x + 3 $\geq$ 23
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4 years ago

Describe the solutions for the quadratic equation shown below:

PtichkaEL [24]

The solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots

To determine the the type of roots the quadratic equation 9x² - 6x + 5 = 0, we use the quadratic formula to find the roots.

So, for a quadratic equation ax + bx + c = 0, the roots are

$x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}$

With a = 9, b = -6 and c = 5, the roots of our equation are

$x = \frac{-(-6) +/- \sqrt{(-6)^{2} - 4 X 9 X 5} }{2 X 9} \\x = \frac{6 +/- \sqrt{36 - 180} }{18} \\x = \frac{6 +/- \sqrt{-144} }{18} \\x = \frac{6 +/- \sqrt{-12} }{18}\\x = \frac{6}{18} +/- i\frac{12}{18} \\x = \frac{1}{3} +/- i\frac{2}{3} \\x = \frac{1 + 2i}{3} or \frac{1 - 2i}{3}$

Since the roots of the equation are (1 + 2i)/3 and (1 - 2i)/3, there are 2 complex roots.

So, the solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots

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3 years ago

What is .00000023 in scientific notation

Lisa [10]

Answer:

2.3 × 10^-7

Step-by-step explanation:

First, create an equation with the initial decimal being the coefficient multiplied by 10 to the power of 0.

(For example, let’s create the starting scientific notation equation for the decimal 475,000).

475,000 = 475,000 × 10^0

-------------------------------------------------------------------------------------------------------------

Now that we have an equation, the second step is to move the decimal point in the coefficient until there is 1 significant digit to the left of the decimal point. For each space the decimal point is moved to the left, increase the exponent by 1.

(Continuing the example above, move the decimal point to the left and increment the exponent.).

475,000 = 475,000.0 × 10^0

475,000 = 47,500.0 × 10^1

475,000 = 4,750.0 × 10^2

475,000 = 475.0 × 10^3

475,000 = 47.5 × 10^4

475,000 = 4.75 × 10^5

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4 years ago