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madam [21]
3 years ago
8

Solve the equation x+3/x-4 = x-5/x+4

Mathematics
1 answer:
Serga [27]3 years ago
7 0

Answer:

\large\boxed{x=\dfrac{1}{2}}

Step-by-step explanation:

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\\\\\text{Domain:}\ x-4\neq0\ \wedge\ x+4\neq0\\\\x\neq4\ \wedge\ x\neq-4\\\\D:x\in\mathbb{R}-\{-4,\ 4\}

\dfrac{x+3}{x-4}=\dfrac{x-5}{x+4}\qquad\text{cross multiply}\\\\(x+3)(x+4)=(x-4)(x-5)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x)(x)+(x)(4)+(3)(x)+(3)(4)=(x)(x)+(x)(-5)+(-4)(x)+(-4)(-5)\\\\x^2+4x+3x+12=x^2-5x-4x+20\qquad\text{combine like terms}\\\\x^2+(4x+3x)+12=x^2+(-5x-4x)+20\\\\x^2+7x+12=x^2-9x+20\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\7x+12=-9x+20\qquad\text{subtract 12 from both sides}\\\\7x=-9x+8\qquad\text{add}\ 9x\ \text{to both sides}\\\\16x=8\qquad\text{divide both sides by 16}\\\\x=\dfrac{8}{16}\\\\x=\dfrac{8:8}{16:8}\\\\x=\dfrac{1}{2}\in D

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melamori03 [73]

The missing number is 20

<h3>How to determine the number</h3>

We can see that the values at the top must be made equal to that at the bottom

For the top, we have

30 + 11 = 41

For the bottom, we should have:

21 + x = 41

Now, let's solve for 'x' to determine the missing figure;

21 + x = 41

collect like terms

x = 41 - 21

x = 20

Thus, the missing number is 20

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2 years ago
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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable

Exact Form:

x = - 25/8 \frac{x}{y}

Decimal Form:

x = -3.125

Mixed Number Form:

x = - 3/1/8 \frac{x}{y}

Step-by-step explanation:

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2 years ago
A textile mill wishes to establish a control procedure on flaws in towels it manufactures. Using an inspection unit of 50 units,
Natasha_Volkova [10]

Answer:

•A c-chart is the appropriate control chart

• c' = 8.5

• Control limits, CL = 8.5

Lower control limits, LCL = 0

Upper control limits, UCL = 17.25

Step-by-step explanation:

A c chart is a quality control chart used for the number of flaws per unit.

Given:

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Total flaws = 850

We now have:

c' = 850/100

= 8.5

Where CL = c' = 8.5

For control limits, we have:

CL = c'

UCL = c' + 3√c'

LCL = c' - 3√c'

The CL stands for the normal control limit, while the UCL and LCL are the upper and lower control limits respectively

Calculating the various control limits we have:

CL = c'

CL = 8.5

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LCL = 8.5 - 3√8.5

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A negative LCL tend to be 0. Therefore,

LCL = 0

4 0
3 years ago
The lights go out, your bedroom is pitch dark, yet you still need to find a pair of socks, in your drawer there is 25 white sock
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If there are 25 white socks and 25 red socks, a matching pair would be picked in at most 3 times.

The first sock you pick would be either White or Red

The second sock you pick would be either white or red again which means that you now either have 2 whites, 2 reds or 1 white and 1 red.

The third sock you pick will either be white or red once more. At this point you will either have 3 whites, 3 reds, 2 whites and 1 red or 2 reds and 1 white.

You will therefore have at least a matching pair after 3 tries.

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E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).

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