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alexandr402 [8]
3 years ago
9

How do you solve these equations? I don't want you to answer all of them, just tell me how to solve each type of equation on the

sheet.​

Mathematics
1 answer:
miss Akunina [59]3 years ago
8 0

Answer:

8. Identify the common denominator; express each fraction using that denominator; combine the numerators of those rewritten fractions and express the result over the common denominator. Factor out any common factors from numerator and denominator in your result. (It's exactly the same set of instructions that apply for completely numerical fractions.)

9. As with numerical fractions, multiply the numerator by the inverse of the denominator; cancel common factors from numerator and denominator.

10. The method often recommended is to multiply the equation by a common denominator to eliminate the fractions. Then solve in the usual way. Check all answers. If one of the answers makes your multiplier (common denominator) be zero, it is extraneous. (10a cannot have extraneous solutions; 10b might)

Step-by-step explanation:

For a couple of these, it is helpful to remember that (a-b) = -(b-a).

<h3>8d.</h3>

\dfrac{5}{x+2}+\dfrac{25-x}{x^2-3x-10}=\dfrac{5(x-5)}{(x+2)(x-5)}+\dfrac{25-x}{(x+2)(x-5)}\\\\=\dfrac{5x-25+25-x}{(x+2)(x-5)}=\dfrac{4x}{x^2-3x-10}

___

<h3>9b.</h3>

\displaystyle\frac{\left(\frac{x}{x-2}\right)}{\left(\frac{2x}{2-x}\right)}=\frac{x}{x-2}\cdot\frac{-(x-2)}{2x}=\frac{-x(x-2)}{2x(x-2)}=-\frac{1}{2}

___

<h3>10b.</h3>

\dfrac{3}{x-1}+\dfrac{6}{x^2-3x+2}=2\\\\\dfrac{3(x-2)}{(x-1)(x-2)}+\dfrac{6}{(x-1)(x-2)}=\dfrac{2(x-1)(x-2)}{(x-1)(x-2)}\\\\3x-6+6=2(x^2-3x+2) \qquad\text{multiply by the denominator}\\\\2x^2-9x+4=0 \qquad\text{subtract 3x}\\\\(2x-1)(x-4)=0 \qquad\text{factor; x=1/2, x=4}

Neither solution makes any denominator be zero, so both are good solutions.

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Viefleur [7K]
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4 0
3 years ago
To show what he learned about the properties of volume for solids, liquids and gases, Viktor wrote the following summary.
Brrunno [24]

The wrong statement in Viktor's summary is When a round solid ball is placed in a box, the ball takes the shape of the box

The matter has three main states which are

  • Solid
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  • Gas

These states define the way we interact and manipulate materials. For instance:

  • Liquids take the shape of the container that contains them. For example water, milk, soda, among others.
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According to the above, the error in Viktor's summary is in the first phase, and the correct statement is A. because solids does not take the shape of its container.

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7 0
3 years ago
The equation of a line with slope m= - 1/4 and including point (-3, 5) is y= - 1/4 x - 4.
raketka [301]

Answer:

False

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = - \frac{1}{4}, hence

y = - \frac{1}{4} x + c ← is the partial equation

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y = - \frac{1}{4} x + \frac{17}{4} ← equation of line


8 0
3 years ago
Round to the nearest tenth: 6.932635<br> 6.9<br> 6<br> 6.8<br> 7
Lera25 [3.4K]
6.932635
   ^ This is the tenths place.

Since the number after it is less than 5, we round down.

So we round to:

6.9
7 0
3 years ago
Read 2 more answers
If f(x) =15-4(x+3), what is f(-4)?<br>​
tresset_1 [31]

Answer:

19

Step-by-step explanation:

f(-4) = 15-4((-4)+3)

       = 15-4(-1)

       = 15-(-4)

       =15+4

4 0
3 years ago
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