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3 years ago

Solve (x + 2 < 5) (x - 7 > -6).

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

3 0

Answer:

(x + 2 < 5) (x - 7 > -6)=

1<x<3

Step-by-step explanation:

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Solve showing steps. Use Insert equation to get the symbol and Ctrl with . For exponents x2 + 3x - 4 = 0 9x2 + 12x + 4 =0 (leave

ipn [44]

Here all the given equations are in the form of

$ax^2+bx+c=0$

The value of $x$ can be determined by the perfect square method as follows:

$ax^2+bx+c=0$

$\Rightarrow x^2+\frac{b}{a}+\frac{c}{a}=0$

$\Rightarrow x^2+2\times\frac{b}{2a}+\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2+\frac{c}{a}=0$

$\Rightarrow \left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}$

$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\;\cdots(i)$

Now, for $x^2+3x-4=0$

$a=1, b=3, c=-4$

So, from equation (i)

$x=\frac{-3\pm\sqrt{3^2-4\times1\times(-4)}}{2\times1}$

$\Rightarrow x=\frac{3\pm\sqrt{9+16}}{2}$

$\Rightarrow x=\frac{3\pm5}{2}$

$\Rightarrow x=\frac{3+5}{2},\frac{3-5}{2}$

$\Rightarrow x= 4, -1$

Similarly, for $9x^2+12x+4=0$

$a=9, b=12, c=4$

So, from equation (i)

$x=\frac{-12\pm\sqrt{12^2-4\times9\times4}}{2\times9}$

$\Rightarrow x=\frac{-12\pm0}{18}$

$\Rightarrow x=\frac{-2}{3}$

For $x^2-2x-3=0$

$a=1, b=-2, c=-3$

$x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-3)}}{2\times1}$

$\Rightarrow x=\frac{2\pm\sqrt{16}}{2}$

$\Rightarrow x=\frac{2\pm4}{2}$

$\Rightarrow x=\frac{6}{2},\frac{-2}{2}$

$\Rightarrow x=3.00, -1.00$

For $x^2-6x+9=0$

$a=1, b=-6, c=9$

$x=\frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times9}}{2\times1}$

$\Rightarrow x=\frac{6\pm0}{2}$

$\Rightarrow x=3.00$

For $2x^2-4x-3=0$

$a=2, b=-4, c=-3$

$x=\frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-3)}}{2\times2}$

$\Rightarrow x=\frac{4\pm\sqrt{40}}{4}$

$\Rightarrow x=\frac{4\pm2\sqrt{10}}{4}$

$\Rightarrow x=\frac{4+2\sqrt{10}}{4},\frac{4-2\sqrt{10}}{4}$

$\Rightarrow x=2.58, -0.58$

5 0

4 years ago

170 is 1/10 of 17 true or false 170 is 1/10 of 17 true or false

Zarrin [17]

Let's see if that's really true! :)

170=x(17)
170=17x
17x=170
17x / 17=170 / 17
x=10

So the answer to your question is false.

170 is actually 10/1 OR 10 of 17.

6 0

4 years ago

The test scores of 32 students are listed below. Construct a boxplot for the data set and include the values of the 5-number sum

zhenek [66]

Answer:

Boxplot is constructed using quartiles and 5 No. summary means including minimum value of data, 1st quartile, 2nd quartile, 3rd quartile and maximum value of data.

As data already in increasing order, we find quartiles using the following formula,

$value\:of\:K_{th}\:Quartile\:,\, Q_k=\:value\:of\:(\frac{k\times{(n+1)}}{4})\,\:th\,observation$

where n = No. of Observations.

∴, 1st Quartile,

$Q_1 = \frac{1\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=8.25\,th\:observation\\\: \:\:= 8th\,+0.25(9th-8th)\\\:\:\:= 55 + 0.25(57-55)\\\:\:\:= 55.5$

2nd Quartile,

$Q_2 = \frac{2\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=16.5\,th\:observation\\\: \:\:= 16th\,+0.5(17th-16th)\\\:\:\:= 69 + 0.5(70-69)\\\:\:\:= 69.5$

3rd Quartile,

$Q_3 = \frac{3\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=24.75\,th\:observation\\\: \:\:= 24th\,+0.75(25th-24th)\\\:\:\:= 79 + 0.75(81-79)\\\:\:\:= 80.5$