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3 years ago

Multiply and Simplify. 4x+4/x^2 × (x+2)(x-1)/x+1

Mathematics

1 answer:

NARA [144]3 years ago

5 0

Answer:

Step-by-step explanation:

(x^2 - 4)(x^2 - 4)

Simplifying

(x2 + -4)(x2 + -4)

Reorder the terms:

(-4 + x2)(x2 + -4)

Reorder the terms:

(-4 + x2)(-4 + x2)

Multiply (-4 + x2) * (-4 + x2)

(-4(-4 + x2) + x2(-4 + x2))

((-4 * -4 + x2 * -4) + x2(-4 + x2))

((16 + -4x2) + x2(-4 + x2))

(16 + -4x2 + (-4 * x2 + x2 * x2))

(16 + -4x2 + (-4x2 + x4))

Combine like terms: -4x2 + -4x2 = -8x2

(16 + -8x2 + x4)

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Is 17.156489 rational

Sav [38]

Answer:No

Step-by-step explanation:No

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3 years ago

What is the decibel level of the radio with intensity 10−7 watts per square inch? Use a logarithmic model to solve.

BaLLatris [955]

Answer:

$D = 50$

Step-by-step explanation:

Given

$I = 10^{-7}W/m^2$ --- Intensity

Required

Determine the decibel level (D)

This is calculated as:

$D = 10 * log(\frac{I}{I_n})$

Where:

$I_n =$ The threshold intensity

$I_n =1 * 10^{-12}W/m^2$

So, we have:

$D = 10 * log(\frac{I}{I_n})$

This gives:

$D = 10 * log(\frac{10^{-7}W/m^2}{1 * 10^{-12}W/m^2})$

$D = 10 * log(\frac{10^{-7}}{10^{-12}})$

Apply law of indices

$D = 10 * log(10^{-7--12})$

$D = 10 * log(10^{5})$

Apply law of logarithm

$loga^b = b\ log(a)$

So, we have:

$D = 10 * 5 * log(10)$

$log(10) =1$

So:

$D = 10 * 5 *1$

$D = 50$

<em>Hence, the decibel level is 50</em>

7 0

3 years ago

Match each equation on the left with the number and type of its solutions on the right.

klemol [59]

Answer:

Step-by-step explanation:

1). Given equation is,

2x² - 3x = 6

2x² - 3x - 6 = 0

To find the solutions of the equation we will use quadratic formula,

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

Substitute the values of a, b and c in the formula,

a = 2, b = -3 and c = -6

x = $\frac{3\pm\sqrt{(-3)^2-4(2)(-6)}}{2(2)}$

x = $\frac{3\pm\sqrt{9+48}}{4}$

x = $\frac{3\pm\sqrt{57}}{4}$

x = $\frac{3+\sqrt{57}}{4},\frac{3-\sqrt{57}}{4}$

Therefore, there are two real solutions.

2). Given equation is,

x² + 1 = 2x

x² - 2x + 1 = 0

(x - 1)² = 0

x = 1

Therefore, there is one real solution of the equation.

3). 2x² + 3x + 2 = 0

By applying quadratic formula,

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

x = $\frac{-3\pm\sqrt{3^2-4(2)(2)}}{2(2)}$

x = $\frac{-3\pm\sqrt{9-16}}{4}$

x = $\frac{-3\pm i\sqrt{7}}{4}$

x = $\frac{-3+ i\sqrt{7}}{4},\frac{-3- i\sqrt{7}}{4}$

Therefore, there are two complex (non real) solutions.

3 0

2 years ago

Please helppp meee I don’t know the answer

Fynjy0 [20]

Answer:

First use the protractor then round the number to the nearest 10

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3 years ago

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Why can a fraction, a decimal, or a percent be written in equivalent forms?

Inessa [10]

Answer:

Because there are many ways you can simplify an equation, and it will still be the same.

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2 years ago