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Iteru [2.4K]
3 years ago
10

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

Minimum value of data = 32 & Maximum value of data = 99

So, Values of 5 no. that are to ne include in Boxplot are 32, 55.5, 69.5, 80.5, 99.

BoxPlot is attached with this ans.

7 0
3 years ago
[Please help] At the mall, Leona bought a T-shirt and a book for a total of $28. The book cost $12. How much did the T-shirt cos
podryga [215]

Answer:

the T-shirt cost is $16

Step-by-step explanation:

first, we know the total cost of the shirt and book was $28 so we substract 12 from 28 wich gives us 16 so the cost of the shirt is $16.

8 0
3 years ago
Fill in the blank to make equivalent rational expressions?
laiz [17]
The answer is -49 because you multiply by 7.
7 0
4 years ago
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