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prohojiy [21]
3 years ago
14

Solve the equation 2x2 + 13x + 15 = 0 by factoring. Show all steps.

Mathematics
1 answer:
natita [175]3 years ago
4 0

Answer:

(2x + 3)(x + 5)

Step-by-step explanation:

2x² + 3x + 15 = 0

(2x + 3)(x + 5)

2x + 3 = 0

2x = -3

x = -3/2

x + 5 = 0

x = -5

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VashaNatasha [74]

Answer:

x=94

Step-by-step explanation:

I hope I'm correct. Here's my explanation: x+9 and 2x-111 would equal 180, hence the line (supplementary). So x+9+2x-111=180

x=94

hope this helps.

5 0
3 years ago
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Simplify f+g / f-g when f(x)= x-4 / x+9 and g(x)= x-9 / x+4
steposvetlana [31]

f(x)=\dfrac{x-4}{x+9};\ g(x)=\dfrac{x-9}{x+4}\\\\f(x)+g(x)=\dfrac{x-4}{x+9}+\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)+(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2+x^2-9^2}{(x+9)(x+4)}=\dfrac{2x^2-16-81}{(x+9)(x+4)}=\dfrac{2x^2-97}{(x+9)(x+4)}\\\\f(x)-g(x)=\dfrac{x-4}{x+9}-\dfrac{x-9}{x+4}=\dfrac{(x-4)(x+4)-(x-9)(x+9)}{(x+9)(x+4)}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x^2-4^2-(x^2-9^2)}{(x+9)(x+4)}=\dfrac{x^2-16-x^2+81}{(x+9)(x+4)}=\dfrac{65}{(x+9)(x+4)}


\dfrac{f+g}{f-g}=(f+g):(f-g)=\dfrac{2x^2-97}{(x+9)(x+4)}:\dfrac{65}{(x+9)(x+4)}\\\\=\dfrac{2x^2-97}{(x+9)(x+4)}\cdot\dfrac{(x+9)(x+4)}{65}\\\\Answer:\ \boxed{\dfrac{f+g}{f-g}=\dfrac{2x^2-97}{65}}

6 0
3 years ago
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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th
Burka [1]

Answer:

Confidence interval : 21.506 to 24.493

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = \bar{x}=\frac{\sum x}{n}

Sample mean = \bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}

Sample mean = \bar{x}=23

Sample standard deviation = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}

Sample standard deviation = \sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}

Sample standard deviation= s = 1.72

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table t_{\frac{\alpha}{2} = 3.883

Formula of confidence interval : \bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}

Substitute the values in the formula

Confidence interval : 23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}

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Confidence interval : 21.506 to 24.493

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34kurt

Answer:

Equation of line 1  is 3 X - 4 Y = 20

Equation of line 2 is 3 X  + 4 Y = 20

Step-by-step explanation:

Given co ordinates of points as,

( -4 , 8)  and (0 , 5)

From the given two points we can determine the slop of a line

I. e slop (m) = \frac{(y2 - y1)}{(x2 - x1)}

Or,           m  = \frac{(5 - 8)}{(0 + 4)}

So,           m = \frac{(-3)}{(4)}

Now equations of line can be written as ,

Y - y1 = m ( X - x1)

<u>At points ( -4 , 8)</u>

Y - 8   = \frac{(-3)}{(4)} (X + 4)

So , Equation of line 1  is 3 X - 4 Y = 20

<u>Again with points ( 0 , 5)</u>

Y - 5   = \frac{(-3)}{(4)} ( X - 0)

So, Equation of line 2 is 3 X  + 4 Y = 20

Hence Equation of line 1  is 3 X - 4 Y = 20  and Equation of line 2 is 3 X  + 4 Y = 20   Answer

4 0
3 years ago
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