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FromTheMoon [43]
3 years ago
14

Help me to answer now ineed this Please...

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0
ANSWER TO QUESTION 1

\frac{\frac{y^2-4}{x^2-9}} {\frac{y-2}{x+3}}

Let us change middle bar to division sign.

\frac{y^2-4}{x^2-9}\div \frac{y-2}{x+3}

We now multiply with the reciprocal of the second fraction

\frac{y^2-4}{x^2-9}\times \frac{x+3}{y-2}

We factor the first fraction using difference of two squares.

\frac{(y-2)(y+2)}{(x-3)(x+3)}\times \frac{x+3}{y-2}

We cancel common factors.

\frac{(y+2)}{(x-3)}\times \frac{1}{1}

This simplifies to

\frac{(y+2)}{(x-3)}

ANSWER TO QUESTION 2

\frac{1+\frac{1}{x}} {\frac{2}{x+3}-\frac{1}{x+2}}

We change the middle bar to the division sign

(1+\frac{1}{x}) \div (\frac{2}{x+3}-\frac{1}{x+2})

We collect LCM to obtain

(\frac{x+1}{x})\div \frac{2(x+2)-1(x+3)}{(x+3)(x+2)}

We expand and simplify to obtain,

(\frac{x+1}{x})\div \frac{2x+4-x-3}{(x+3)(x+2)}

(\frac{x+1}{x})\div \frac{x+1}{(x+3)(x+2)}

We now multiply with the reciprocal,

(\frac{(x+1)}{x})\times \frac{(x+2)(x+3)}{(x+1)}

We cancel out common factors to  obtain;

(\frac{1}{x})\times \frac{(x+2)(x+3)}{1}

This simplifies to;

\frac{(x+2)(x+3)}{x}

ANSWER TO QUESTION 3

\frac{\frac{a-b}{a+b}} {\frac{a+b}{a-b}}

We rewrite the above expression to obtain;

\frac{a-b}{a+b}\div {\frac{a+b}{a-b}}

We now multiply by the reciprocal,

\frac{a-b}{a+b}\times {\frac{a-b}{a+b}}

We multiply out to get,

\frac{(a-b)^2}{(a+b)^2}

ANSWER T0 QUESTION 4

To solve the equation,

\frac{m}{m+1} +\frac{5}{m-1} =1

We multiply through by the LCM of (m+1)(m-1)

(m+1)(m-1) \times \frac{m}{m+1} + (m+1)(m-1) \times \frac{5}{m-1} =(m+1)(m-1) \times 1

This gives us,

(m-1) \times m + (m+1) \times 5}=(m+1)(m-1)

m^2-m+ 5m+5=m^2-1

This simplifies to;

4m-5=-1

4m=-1-5

4m=-6

\Rightarrow m=-\frac{6}{4}

\Rightarrow m=-\frac{3}{2}

ANSWER TO QUESTION 5

\frac{3}{5x}+ \frac{7}{2x}=1

We multiply through with the LCM  of 10x

10x \times \frac{3}{5x}+10x \times \frac{7}{2x}=10x \times1

We simplify to get,

2 \times 3+5 \times 7=10x

6+35=10x

41=10x

x=\frac{41}{10}

x=4\frac{1}{10}

Method 1: Simplifying the expression as it is.

\frac{\frac{3}{4}+\frac{1}{5}}{\frac{5}{8}+\frac{3}{10}}

We find the LCM of the fractions in the numerator and those in the denominator separately.

\frac{\frac{5\times 3+ 4\times 1}{20}}{\frac{(5\times 5+3\times 4)}{40}}

We simplify further to get,

\frac{\frac{15+ 4}{20}}{\frac{25+12}{40}}

\frac{\frac{19}{20}}{\frac{37}{40}}

With this method numerator divides(cancels) numerator and denominator divides (cancels) denominator

\frac{\frac{19}{1}}{\frac{37}{2}}

Also, a denominator in the denominator multiplies a numerator in the numerator of the original fraction while a numerator in the denominator multiplies a denominator in the numerator of the original fraction.

That is;

\frac{19\times 2}{1\times 37}

This simplifies to

\frac{38}{37}

Method 2: Changing the middle bar to a normal division sign.

(\frac{3}{4}+\frac{1}{5})\div (\frac{5}{8}+\frac{3}{10})

We find the LCM of the fractions in the numerator and those in the denominator separately.

(\frac{5\times 3+ 4\times 1}{20})\div (\frac{(5\times 5+3\times 4)}{40})

We simplify further to get,

(\frac{15+ 4}{20})\div (\frac{(25+12)}{40})

\frac{19}{20}\div \frac{(37)}{40}

We now multiply by the reciprocal,

\frac{19}{20}\times \frac{40}{37}

\frac{19}{1}\times \frac{2}{37}

\frac{38}{37}
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A) The length of the longer leg is x-1

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c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0

d) There is one positive real root, at x=13. A graphical solution works well.

The three sides of the triangle are 5 in, 12 in, 13 in.


_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.

6 0
3 years ago
Please help and show work!
Ierofanga [76]

Answer:

x = 3

Step-by-step explanation:

Two triangles are similar

x/(x+3) = 4/8 cross multiply expressions

8x = 4x + 12

8x - 4x = 12

4x = 12 divide both sides by 4

x = 3

8 0
2 years ago
9 cm3 divided by 3 cm2 =
Dafna11 [192]

Answer:

3m

Hope this was helpful!

4 0
2 years ago
Cheryl is buying lace for her dance costume. One foot of lace costs 3 dollars. How much does each amount cost? 3/4 of a foot?
Dima020 [189]

Step-by-step explanation:

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6 0
3 years ago
Susan Marciano invested part of her $29,000 bonus in a fund that paid a 10% profit and invested the rest in a stock that suffere
dangina [55]

Answer:The amount invested at 10% is $16000

The amount invested in stock is $13000

Step-by-step explanation:

Let x represent the amount of money that Susan invested in the fund that paid a 10% profit.

Let y represent the amount of money that Susan invested in the stock that that suffered a 4% loss.

Total amount invested is 29000. This means that

x + y = 29000

The profit made on the fund is

10/100 × x = 0.1x

The loss made on the stock is

4/100 × y = 0.04y

if her overall net profit was $1,080, it means that

0.1x - 0.04y = 1080 - - - - - - - -1

Substituting x = 29000 - y. It becomes

0.1(29000 - y) - 0.04y = 1080

2900 - 0.1y - 0.04y = 1080

- 0.1y - 0.04y = 1080 - 2900

- 0.14y = - 1820

y = - 1820/ - 0.14 = 13000

Substituting y = 13000 into x = 29000 - y, it becomes

x = 29000 - 13000

x = 16000

3 0
3 years ago
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