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4vir4ik [10]
3 years ago
13

What is the solution to the equation x+3/x+2=3+1/x

Mathematics
2 answers:
victus00 [196]3 years ago
8 0

Answer:

x=-1

Step-by-step explanation:

x+3

------- = 3 + 1/x

x+2

Get a common denominator on the right

3*x/x + 1/x

3x/x + 1/x = (3x+1)/x


x+3       3x+1

------- = ---------

x+2         x


We can use cross products to solve

(x+3) *x = (3x+1) * (x+2)

x^2+3x = 3x*x +x + 3x*2 +2

Simplifying

x^2 + 3x = 3x^2 +7x+2

Subtract x^2 from each side

x^2 -x^2 + 3x = 3x^2-x^2 +7x+2

3x = 2x^2 +7x+2

Subtract 3x from each side

3x-3x = 2x^2 +7x -3x+2

0 = 2x^2 +4x +2

Divide by 2

0 = x^2 +2x +1

Factor

0 = (x+1) (x+1)

Using the zero product property

x+1 =0

x=-1

marishachu [46]3 years ago
6 0

Answer:

The solution set is { -1 }.

Step-by-step explanation:

If we multiply each term by the LCM of x and x+ 2 ( = x(x + 2))  we get:-

x(x + 3) = 3x(x + 2)  + x + 2

x^2 + 3x = 3x^2 + 6x + x + 2

0 = 3x^2 - x^2 - 3x + 6x + x + 2

2x^2 +4x + 2 = 0

2(x^2 + 2x + 1) = 0

2( x + 1)(x + 1) = 0

x = -1    Multiplicity 2

The solution set  only contains 1 * -1 . Elements in a set are not repeated

So   its {-1}  (answer)


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What is the slope line perpendicular to the equation 4x+3y=9
aleksandrvk [35]

Answer:

m=3/4

Step-by-step explanation:

first, let's put the line 4x+3y=9 from standard form (ax+by=c) into slope-intercept form (y=mx+b)

we have the equation 4x+3y=9

subtract 4x from both sides

3y=-4x+9

divide by 3

y=-4/3x+3

perpendicular lines have slopes that are negative and reciprocal. If the slopes are multiplied together, the result is -1

so to find the slope of the line perpendicular to the line y=-4/3x+3, we can take the slope of y=-4/3x+3 (-4/3) multiply it by a variable (this is our unknown value), and have that set to -1

(m is the slope value)

-4/3m=-1

multiply by -3/4

m=3/4

therefore the slope of the perpendicular line is 3/4

hope this helps!! :)

7 0
3 years ago
What is the volume of the cylinder
evablogger [386]
The answer is the first option, you multiply 14^2 by 9
4 0
3 years ago
If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height, then find the ratio of the
Oduvanchick [21]

<u>Given</u><u> </u><u>info:</u><u>-</u>If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.

Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?

<u>Explanation</u><u>:</u><u>-</u>

Let the radius of the right circular cylinder be r units

Let the radius of the right circular cylinder be h units

Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)

If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units

The height of the new right circular cylinder

= (1/4)×h units

⇛ h/4 units

Curved Surface Area of the new cylinder

= 2π(2r)(h/4) sq.units

⇛ 4πrh/4 sq.units

⇛ πrh sq.units --------(ii)

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder

⇛ πrh : 2πrh

⇛ πrh / 2πrh

⇛ 1/2

⇛ 1:2

Therefore the ratio = 1:2

The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2

6 0
2 years ago
Find the distance between the points (9,3) and (–5,3).
Nutka1998 [239]

Answer:

The answer to the question provided is 14.

Step-by-step explanation:

》The Distance Formula:

d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}  }

》Plug in.

d =  \sqrt{( - 5 - 9)^{2} + (3 - 3) ^{2}  }  \\ d =  \sqrt{( - 14)^{2}  + (0) ^{2} }  \\ d =  \sqrt{196 + 0}  \\ d =  \sqrt{196}  \\ d = 14

6 0
3 years ago
Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers u
Crank

The intervals on which the graph is increasing:   ]-∞,-3[ U ]0.5,-∞[ . On the other hand, the graph is decreasing:  ]-3,0.5[

<h3>Function</h3>

A function can be classified as increasing or decreasing. Thus, a function is increasing when the y-values increase, on the other hand, a function is decreasing when the y-values decrease.

From the image, you can see that the y-values increase in the following x-intervals: from -∞ to -3 and from 0.5 to ∞. Using interval notation, you can write that the function is increasing in:

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From the graph, you can see that the y-values decrease in the following x-intervals: from -3 to 0.5. Using interval notation, you can write that the function is decreasing in:

                                         ]-3,0.5[

Learn more about function here:

brainly.com/question/2649645

3 0
2 years ago
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