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romanna [79]
1 year ago
5

I f x ≠ – 2 a n d x ≠ 32 , w h a t i s t h e s o l u t i o n t o

Mathematics
1 answer:
Juliette [100K]1 year ago
3 0

x=5,x=3

1) The restraint that x ≠2 and x≠3/2 is the condition that prevents that to have a zero on the denominator. 0 on the denominator makes an undefinition.

2) So now, let's solve it:

\begin{gathered} \frac{5}{x+2}=\frac{x}{2x-3} \\ 5(2x-3)=x(x+2) \\ 10x-15=x^2+2x \\ -x^2+10x-2x-15=0 \\ -x^2+8x-15=0 \\ x^2-8x+15=0 \end{gathered}

Note that cross multiplying we get a quadratic equation. So let's solve it:

\begin{gathered} x^2-8x+15=0 \\ Sx=-5-3=8_{}_{}_{} \\ Px=-5\cdot-3=15 \end{gathered}

Note that the sum of two numbers that yield -8x is -5 and -3 as well as -5 x -3 yields 15 as their product. But to find the answers via this method, we need to switch signs, so the answer is:

x_1=5,x_2=3

A quadratic equation yields two roots. And that's the answer.

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aliina [53]

Answer:

lines are perpendicular

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

Where c is the value of the x- coordinates the line passes through

x = - 1 ← is the equation of a vertical line

The equation of a horizontal line parallel to the x- axis is

y = c

Where c is the value of the y- coordinates the line passes through

y = - 1 ← is a horizontal line

Since lines are vertical and horizontal they are perpendicular to each other.

4 0
3 years ago
Read 2 more answers
Which equation listed below, when solved, shows how to find the circumference of a circle if the diameter is 6 inches? Use 3.14
siniylev [52]
The pertinent formula for the circumference of a circle with diameter d is

C =pi*d.

Thus, if the dia. is 6 inches, the circumf. is C = 6pi inches.  Alternatively, if we let pi = 3.14, the circumf. is   C = 6*3.14   (answer A).
6 0
3 years ago
Read 2 more answers
Find the sum of the arithmetic sequence. 5,7,9,11,...,23
eduard

Answer:

140

Step-by-step explanation:

The arithmetic series is 5, 7, 9, 11, ........., 23.

First u have to determine the no. of terms that can be done by using

Tₙ = [a + (n - 1)d]

Tₙ-------nth term

a---------first term

n---------no.of terms in the series

d---------common difference

here a = 5,d = 2.

let it contain n terms Tₙ= [a + (n-1)d]

Substitute Tₙ, a, and d in the equation

23 = 5 + (n - 1)2

Subtract 5 from each side.

18 = (n-1)2

Divide each side by 2

(n - 1) = 9

Add 1 to each side

n = 9 + 1 = 10

The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]

Substitute Sₙ, a, n and d in the equation

Sₙ= (10/2)[2(5) + (10-1)2]

Sₙ= (5)[10 + (9)2]

Sₙ= 5[10 + 18]

Sₙ= 5[28] = 140

Therefore the sum of the arithmetic sequence is 140.

6 0
3 years ago
Rosie Belin worked these total weekly hours in four weeks of work: 45, 38, 42, and 43. Her job pays $14 for each hour worked. Wh
MatroZZZ [7]

Answer:

Add the total number of hours in the four weeks and multiply that with the hourly pay rate to find the total gross pay. Divide the total gross pay by 4 to find the weekly average gross pay. An employee may earn income from various sources. The total income is the sum of all the earnings and is called as.

=727

5 0
3 years ago
Plz help me.
Vlad [161]
Assuming you want to find x?
You know that the angles at C and B have to be the same (6x) because it’s an isosceles triangle (as indicated by the lines going through AC and AB), and angles in a triangle add to 180*

So 3x + 6x + 6x = 180*
15x = 180*
x = 180*/15
x = 12*
4 0
3 years ago
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