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tester [92]
3 years ago
10

Solve the following question

Mathematics
1 answer:
White raven [17]3 years ago
3 0

Answer:

g) u^{4}\cdot v^{-1}\cdot z^{3}, h) \frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}

Step-by-step explanation:

We proceed to solve each equation by algebraic means:

g) \frac{u^{5}\cdot v}{z}\div  \frac{u\cdot v^{2}}{z^{4}}

1) \frac{u^{5}\cdot v}{z}\div  \frac{u\cdot v^{2}}{z^{4}} Given

2) \frac{\frac{u^{5}\cdot v}{z} }{\frac{u\cdot v^{2}}{z^{4}} } Definition of division

3) \frac{u^{5}\cdot v\cdot z^{4}}{u\cdot v^{2}\cdot z}   \frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}

4) \left(\frac{u^{5}}{u} \right)\cdot \left(\frac{v}{v^{2}} \right)\cdot \left(\frac{z^{4}}{z} \right)  Associative property

5) u^{4}\cdot v^{-1}\cdot z^{3}   \frac{a^{m}}{a^{n}} = a^{m-n}/Result

h) \frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10}

1) \frac{x^{2}-16}{x^{2}-10\cdot x + 25} \div \frac{3\cdot x - 12}{x^{2}-3\cdot x -10} Given

2) \frac{\frac{x^{2}-16}{x^{2}-10\cdot x+25} }{\frac{3\cdot x - 12}{x^{2}-3\cdot x - 10} } Definition of division

3) \frac{(x^{2}-16)\cdot (x^{2}-3\cdot x -10)}{(x^{2}-10\cdot x + 25)\cdot (3\cdot x - 12)}  \frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{b\cdot c}

4) \frac{(x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2)}{3\cdot (x-5)^{2}\cdot (x-4) } Factorization/Distributive property

5) \left(\frac{1}{3} \right)\cdot (x+4)\cdot (x+2)\cdot \left(\frac{x-4}{x-4} \right)\cdot \left[\frac{x-5}{(x-5)^{2}} \right] Modulative and commutative properties/Associative property

6) \frac{(x+4)\cdot (x+2)}{3\cdot (x-5)}  \frac{a^{m}}{a^{n}} = a^{m-n}/\frac{a}{b}\times \frac{c}{d} = \frac{a\cdot c}{b\cdot d}/Definition of division/Result

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Leno4ka [110]

Equation: w×0.6p

Explanation: 4.38 dollars for a 7.30 pound watermelon, you need to divide 4.38 by 7.3 to determine the price for each pound. 4.38÷7.3=0.60. W=the watermelons weight and P= watermelons price per pound.

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3 years ago
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lyudmila [28]

Answer:

\frac{2}{3} (x+6)

Step-by-step explanation:

\frac{2}{3} x+4= \frac{2}{3} (x+4÷\frac{2}{3})

\frac{2}{3}x+4 = \frac{2}{3} (x+4×\frac{3}{2})

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\frac{2}{3}x+4 = \frac{2}{3} (x+6)

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2 years ago
Anita invested $6000, some at 5% and the rest at 6%. If the yearly income is $337.50, what is the amount invested at each rate?'
allochka39001 [22]
Is this rsm? lol okay.

x is the amount of money invested at 5%
y is the amount of money invested at 6%
the total amount of money invested is $6000, or x+y
when it says the yearly income is $337.50, it means that the 5% of x plus the 6% of y equals $337.50.

now write the two equations:

x+y =6000

0.05x + 0.06y = 337.50

now, find y for the first equations, which is y= 6000 - x. use this equation to substitute for the second equation.

0.05x + 0.06(6000 -x) = 337.50

blah, blah, blah, solve for x... you should get x = 2250, and y = 3750.

I hate money problems like this, hope it helps.


3 0
3 years ago
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kotykmax [81]

Answer:

B. \frac{60 hours}{1} \times \frac{1 day}{24 hours}

Step-by-step explanation:

Converting 60 hours to days:

24 hours = 1 day

60 hours = x day

Cross multiply

24 hours \times x = 60 hours \times 1 day

Divide both sides by 24 hours

x = \frac{60 hours \times 1 day}{24 hours}

Thus,

\frac{60 hours \times 1 day}{24 hours} = \frac{60 hours}{1} \times \frac{1 day}{24 hours}

The expression that shows how to convert 60 hours to days is:

\frac{60 hours}{1} \times \frac{1 day}{24 hours}

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3 years ago
Break the numbers 0-9 into 3 groups. Each group needs to equal the same number when added! Write out the groupsand the sum of ea
Burka [1]

we must do the following:

0

1

2

3

4

5

6

7

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select the major, the minor and the half and add, like this:

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also:

\begin{gathered} 8+4+3=15 \\  \end{gathered}

the groups are:

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