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2 years ago

Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

Mathematics

1 answer:

romanna [79]2 years ago

8 0

Answer:

$x=2+\sqrt{11},\:x=2-\sqrt{11}$

Step-by-step explanation:

$x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}$

$x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}$

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Let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes. If the random var

jeka57 [31]

Answer:

The parameters of this exponential distribution is $\lambda$ = $\frac{1}{27}$ .

Step-by-step explanation:

We are given that the random variable X is known to be exponentially distributed and let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes.

<u><em>So, X = time it takes for a person to choose a birthday gift</em></u>

The probability distribution function of exponential distribution is given by;

$f(x) = \lambda e^{-\lambda x} , x >0$ where, $\lambda$ = parameter of distribution.

Now, the mean of exponential distribution is = $\frac{1}{\lambda}$ which is given to us as average value of 27 minutes that means $\lambda = \frac{1}{27}$ .

So, X ~ Exp( $\lambda = \frac{1}{27}$ ) .

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2 years ago

Construct a truth table for the logical operator NAND.

Nata [24]

Answer:

The output for NAND gate is false if all the inputs are true. it is true if either A or B is False.

Step-by-step explanation:

Step1

NAND operator:

NAND is a logic or Boolean expression and is a combination of NOT and AND Gate.

NAND gate is built using various junction diodes and transistors.

Step2

The output of NAND can be 0 or 1. Here, LOW (0) and HIGH (1). 0 or 1 is commonly named as FALSE or TRUE respectively.

It is basically the complement of AND gate. If all its inputs are True or 1, then the output is False or 0 else if either A or B is 0 or 1 then it will give the output as TRUE.

Step3

Here, A and B are 2 inputs used to make the truth table for NAND.

In 1st row, when A and B are both 0, the output for NAND is 1.

Likewise, in 2st row and 3rd row, when either A or B is 0 or 1, the output for NAND is 1 that is TRUE.

But in last row, when both inputs A and B are true, then the output for NAND gate is FALSE or 0.

The diagram and truth table for NAND is shown below.

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3 years ago