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Anni [7]
3 years ago
10

Drag values to complete each equation.

Mathematics
2 answers:
kherson [118]3 years ago
8 0

Answer:

9^{-7} and 9^{-2}

Step-by-step explanation:

using the rules of exponents

• (a^m)^{n} = a^{mn}

• a^{m} × a^{n} = a^{(m+n)}

• \frac{a^{m} }{a^{n} } = a^{(m-n)}

given (9^{5} × 9^{-9} ) / 9^{3}

= \frac{9^{5+(-9)} }{9^{3} } = \frac{9^{-4} }{9^{3} } = 9^{-4-3} = 9^{-7}

given (9^4)^{3} × 9^{-14}

= 9^{12} × 9^{-14}

= 9^{12+(-14)} = 9^{-2}


MatroZZZ [7]3 years ago
4 0

Answer:  The required values of the given expressions are

\dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.

Step-by-step explanation:  We are given to find the values of the following expressions :

E_1=\dfrac{9^5.9^{-9}}{9^3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=(9^4)^3.9^{-14}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

We will be using the following properties of exponents :

(i)~x^a.x^b=x^{a+b},\\\\(ii)~\dfrac{x^a}{x^b}=x^{a-b}\\\\(iii)~(x^a)^b=x^{ab}.

From expression (i), we get

E_1\\\\\\=\dfrac{9^5.9^{-9}}{9^3}\\\\\\=\dfrac{9^{5+(-9)}}{9^3}\\\\\\=\dfrac{9^{-4}}{9^3}\\\\\\=9^{-4-3}\\\\=9^{-7}

and from expression (ii), we get

(9^4)^3.9^{-14}\\\\=9^{4\times3}.9^{-14}\\\\=9^{12}.9^{-14}\\\\=9^{12+(-14)}\\\\=9^{-2}.

Thus, the required values of the given expressions are

\dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.

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A movers ramp is placed on top
Salsk061 [2.6K]

Answer:

I think it would be 13 feet

Step-by-step explanation:

12*5=60

and sense it is a triangle you divide by 2 and get 30

<h3>30-12-5=13</h3><h3>this is what I think</h3>
4 0
3 years ago
Shauna spent $175 on a pair of shoes.She spent 1/9 of the remaining money on a shirt.If he still had 4/7of his moneyleft,how muc
KIM [24]

Answer:

$490

Step-by-step explanation:

Shauna spent $175 on a pair of shoes.

She spent 1/9 of the remaining money on a shirt.

If he still had 4/7 of his money left,how much did he have at first ?

Solution:

Let at first, Shauna have = x

Money spent on a pair of shoes = $175

Remaining money = x-175

<u>As she spent 1/9 of the remaining money on a shirt.</u>

Money spent on shirt = \frac{1}{9} \times(x-175)=\frac{x}{9} -\frac{175}{9}

As he still had \frac{4}{7} of his money left:-

Money left = \frac{4}{7}\ of\ his\ money=\frac{4x}{7}

Money left with Shauna = Total money, she had at first -(Money spent on a pair of shoes + Money spent on shirt )

\frac{4x}{7} =x-(175+{\frac{x}{9} -\frac{175}{9} )\\\\\\

\frac{4x}{7} =x-(\frac{175}{1} -\frac{175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7} =x-(\frac{1575-175}{9} +\frac{x}{9} )\\\\ \frac{4x}{7}=x-(\frac{1400}{9} +\frac{x}{9} )\\ \\ \frac{4x}{7}=x-\frac{1400}{9} -\frac{x}{9}

Subtracting both sides by x and adding both sides by \frac{x}{9}

\frac{4x}{7} -x+\frac{x}{9} =-\frac{1400}{9} -x+\frac{x}{9} +x-\frac{x}{9}

Taking LCM of 7 and 9, we get 63

\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ -\frac{20x}{63}=-\frac{1400}{9}

Adding both side by -

\frac{36x-63x+7x}{63} =-\frac{1400}{9} \\ \\ \frac{20x}{63}=\frac{1400}{9}

By cross multiplication:

20x\times9=1400\times63\\180x=88200\\

Dividing both sides by 180

x=490

Therefore, total $490, she had at first.

3 0
3 years ago
Find the area simply your answer
Goshia [24]
Area=base*height

A=(x+6)(2x+2)  

A=2(x+1)(x+6)  technically this is the simplified form, but they may want the expanded form...

A=2x^2+14x+12
3 0
3 years ago
Admission for a movie is $8 for children and $12 for adults. On a certain day, 3200 people attend the movie theater and $33,040
Nezavi [6.7K]
Let us assume the number of children attending the movie = x
Let us also assume the number of adults attending the movie = y
Cost of admission for a children in the movie = $8
Cost of admission of an adult in the movie = $12
Number of people going to the movie on a certain day = 3200
Total amount collected from the movie theater = $33040
Then
x + y = 3200
And
8x + 12y = 33040
2x + 3y = 8260
Let us first take the equation
x + y = 3200
x = 3200 - y
Now we will put the value of x in the equation
2x + 3y = 8260
2(3200 - y) + 3y = 8260
6400 - 2y + 3y = 8260
y = 8260 - 6400
   = 1860
Now we will put the value of y from the above deduction in the equation
x + y = 3200
x + 1860 = 3200
x = 3200 - 1860
   = 1340
So the number of children going to the movie theater is 1340 and the number of adults going to the movie theater is 1860.
5 0
3 years ago
The length of a rectangle is 5 inches less than 4 times the width. The perimeter is 110 inches. Find the length and the width.
nataly862011 [7]

Answer:

  • Length = 43 inches
  • Width = 12 inches

Step-by-step explanation:

Perimeter of a rectangle = 2 * ( L + W)

The length of a rectangle is 5 inches less than 4 times the width.

Assume the width is x. Length is:

4x - 5

Equation is therefore:

2 * (4x - 5 + x) = 110

4x - 5 + x = 110/2

5x - 5 = 55

5x = 55 + 5

x = 60/5

x = 12 inches

If width is 12 inches, then length is:

= 4x - 5

= 4 * 12 -5

= 43 inches

6 0
2 years ago
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