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Tcecarenko [31]
3 years ago
12

Solve the rational equation 4/x=3x+2/x^2, and check for extraneous solutions.

Mathematics
1 answer:
Aleks [24]3 years ago
4 0

Answer:

x = 2 is a solution

x = 0 is an extraneous solution

(Option 2)

Step-by-step explanation:

4/x = (3x + 2)/x²

4x² = 3x² + 2x

x² - 2x = 0

x(x - 2) = 0

x = 0, x = 2

Verification:

4/x = (3x + 2)/x²

At x = 2

4/2 = [3(2) + 2]/2²

2 = 8/4

2 = 2

At x = 0

4/0 = [3(0) + 2]/0²

Is undefined

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Show work and Factor 4x^2+xy-18y^2
grigory [225]

Answer:

4x^2+xy-18y^2=(4x+9y)\,(x-2y)

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2

so we want the following to happen:

a\,c = 4\\ad+bc=1\\bd--18

Notice as well that ad+bc =1 means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product bd=-18, then we can consider the case in which one of this  (b or d) is the negative factor. So let's then assume that a\,\,and \,\,c are positive.

We can then try combinations for  a\,\,and \,\,c  such as:

a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4

Just by selecting the first one (a=4;\,\,c=1)

we get that 4d_b=1\\b=-4d-1

and since

bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

d=-18/(-2)\\d=9

Now we have a good combination of parameters to render the factoring form of the original trinomial:

a=4; \,\,b=9;\,\,c=1;\,\,d=-2

which makes our factorization:

(4x+9y)\,(x-2y)=4x^2+xy-18y^2

6 0
3 years ago
NEED HELP ASAP!<br> find the volume of the cylinder
denpristay [2]

Answer:

V = 314.2 ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h    r is the radius (5) and h is the height (4)

Using the pi button for pi

V = pi (5^2) (4)

V =314.1592654

Rounding to the nearest tenth

V = 314.2 ft^3

3 0
3 years ago
For non zero X and Y if X + Y = 0 then​
S_A_V [24]
Either X or Y is negative. One has to be
7 0
3 years ago
Plz answer the below question u will be awarded brainliest and will get points too..
brilliants [131]

Answer:

x=0.6241

Step-by-step explanation:

Square both sides and end up with

75.24+x=75.8641

isolate x

x=75.8641 - 75.24

x=0.6241

6 0
4 years ago
PLSSSSSSS HELPPPPPppppp
icang [17]

Answer:

20 units

Step-by-step explanation:

The polygon has 4 vertices as indicated by the 4 coordinate points given.

(3, 1) and (8, 1) is a horizontal side of length 8 - 3 = 5

Similarly

(3, 6) and (8, 6) is the opposite horizontal side of length 8 - 3 = 5

Points (3, 1) and (3, 6) is a vertical side of length 6 - 1 = 5

(8, 1) and (8, 6) is the opposite side of length 6 - 1 = 5

The polygon is therefore a square of side 5 units.

Perimeter = 4 × 5 = 20 units

5 0
3 years ago
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