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AysviL [449]
3 years ago
8

What is the simplified form of the quantity of x plus 8, all over the quantity of 3x plus 7 + the quantity of x plus 7, all over

the quantity of x plus 4?
x+8/3x+7 + x+7/x+4
PLEASE help!
I don't understand it at all!
Mathematics
2 answers:
Temka [501]3 years ago
6 0
\frac{x+8}{3x+7} + \frac{x+7}{x+4}  \\ = \frac{(x+8)(x+4)+(x+7)(3x+7)}{(3x+7)(x+4)}  \\ = \frac{ x^{2} +12x+32+3 x^{2} +28x+49}{3 x^{2} +19x+28}  \\ = \frac{4 x^{2} +40x+81}{3 x^{2} +19x+28}
enot [183]3 years ago
4 0

Answer:

\frac{4x^2+40x+81}{3x^2+19x+28}

Step-by-step explanation:

We have been given an expression \frac{x+8}{3x+7}+\frac{x+7}{x+4}. We are asked to find the simplified form of our given expression.

Since the denominators of our given expression is not equal, so we need to make a common denominator to add our given expression as:  

\frac{(x+8)(x+4)}{(3x+7)(x+4)}+\frac{(x+7)(3x+7)}{(x+4)(3x+7)}

Using FOIL we will get,  

\frac{x*x+4x+8x+8*4}{(3x*x+3x*4+7x+7*4}+\frac{x*3x+7x+7*3x+7*7}{x*3x+7x+4*3x+7*4}

\frac{x^2+12x+32}{3x^2+12x+7x+28}+\frac{3x^2+7x+21x+49}{3x^2+7x+12x+28}  

\frac{x^2+12x+32}{3x^2+19x+28}+\frac{3x^2+28x+49}{3x^2+19x+28}  

Since he denominators are equal, so we can add numerators as:

\frac{x^2+12x+32+3x^2+28x+49}{3x^2+19x+28}  

\frac{4x^2+40x+81}{3x^2+19x+28}  

Therefore, the sum of our given expression would be \frac{4x^2+40x+81}{3x^2+19x+28}.

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The equation looks like this \frac{ x^{2} }{16} + \frac{ y^{2} }{25} =1.  In an ellipse, a is always the bigger value, so a^2 = 25.  This bigger value also tells us which axis is the major one.  Sine the bigger value a is under the y^2 of the equation, the major axis is the y-axis.  This is a vertical ellipse.  The center is always found within a set of parenthesis that exist with the x^2 and the y^2.  Since there are no parenthesis with either, there is no side to side movement, nor is there any up or down movement.  So the center doesn't move from the origin (0, 0).  The vertex is also along the major axis, and if a^2 is 25, then a = 5, so the vertices go up 5 from the center and down 5 from the center.  Vertices are (0, 5) and (0, -5).  The foci follow the formula c^{2}= a^{2}- b^{2}.  c is the distance that the foci are from the center.  c^{2}=25-16 and c = 3.  The foci also lie on the major axis, so the coordinates for the foci are (0, 3) and (0, -3).  There you go!
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Suppose that the value of a stock varies each day from $13 to $24 with a uniform distribution. (a) Find the probability that the
bogdanovich [222]

Answer:

a. P= 0.6364

b. P = 0.3636

c. Q = $21.25

d. P = 0.5

Step-by-step explanation:

given data

value of a stock varies = $13 to $24

solution

P (stock value is more than $17)

P = \frac{(24-17)}{(24-13)}

P =  \frac{7}{11}

P = 0.6364

and

P (value of the stock is between $17 and $21)

P = \frac{(21-17)}{(24-13)}

P = \frac{4}{11}

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and  

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