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Sedaia [141]
3 years ago
5

Which expressions are equivalent to 1/36?

Mathematics
2 answers:
Aleks04 [339]3 years ago
7 0

Answer:

b) 6^{-2}

c) \frac{6^3}{6^5}

f) 6^{-9} . 6^{7}

Step-by-step explanation:

The given expression is \frac{1}{36}

36 can be written as 6*6 = 6^{2}

So the given expression can be written as \frac{1}{6^2}

We can use the following exponent rules and write the given equation in different forms.

i) a^{-m} = \frac{1}{a^m}

ii) a^m *a^n = a^{m + n}

\frac{1}{6^2} = 6^{-2}

\frac{1}{6^2} = \frac{6^3}{6^5}

\frac{1}{6^2} = 6^{-9} . 6^{7}

Kamila [148]3 years ago
5 0
6^-2 , 6^3/6^5 , 6^-9 • 6^7. I believe these are the expressions that are equivalent to 1/36.
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Fill in the Blanks
tatyana61 [14]

Answer: This would fill 4 and 4/9 containers.

Explanation:

Since we have given that

Quantity of walnuts in a container is given by

6\frac{2}{3}=\frac{20}{3}\ pounds

Quantity of walnuts which divided equally into containers is given by

1\frac{1}{2}=\frac{3}{2}\ pounds

Now, number of containers they would fill is given by

\frac{\frac{20}{3}}{\frac{3}{2}}=\frac{20\times 2}{3\times 3}=\frac{40}{9}

When we change it into mixed fractions we get,

\frac{40}{9}=4\frac{4}{9}

So, blank will be filled with '4'.


7 0
3 years ago
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The city of Orlando’s building a dog park in downtown Orlando dog park will be triangular shaped as shown on the coordinate plan
kiruha [24]

Answer:

Perimeter of the dog park = 15.4 yards

Step-by-step explanation:

Coordinates of the vertices of the given triangle are,

P(1, 2), Q(1, 6), R(-4, 2)

Since distance between the two points (x_1, y_1) and (x_2,y_2) is,

d = \sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

Length of PQ = \sqrt{(1-1)^2+(2-6)^2}

PQ = 4

Length of PR = \sqrt{(1+4)^2+(2-2)^2}

PR = 5

Length of QR = \sqrt{(1+4)^2+(6-2)^2}

QR = \sqrt{25+16}

     = \sqrt{41}

     = 6.4 yards

Therefore, perimeter of the given triangle = PQ + QR + PR

                                                                       = 4 + 6.4 + 5

                                                                       = 15.4 yards

4 0
3 years ago
Calculate the area of the triangle
Artemon [7]

Answer:

30

Step-by-step explanation:

3 0
3 years ago
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What is the solution to the system of equations below?
kifflom [539]

Answer:

(-5,-14)

Step-by-step explanation:

To find the solution of the system of two equations

\left\{\begin{array}{l}y=4x+6\\y=2x-4\end{array}\right.

equate right sides of these two equations:

4x+6=2x-4

Rewrite terms with x into the left side and without x into the right side:

4x-2x=-4-6\\ \\2x=-10\ [\text{divide by 2}]\\ \\x=-5

Substitute x=-5 into the first equation:

y=4\cdot (-5)+6=-20+6=-14

The solution is (-5,-14)

4 0
3 years ago
Taylor purchased 9 pints of ice cream for a party. If each guest will be served exactly 1 2 2 1 ​ pint of ice cream, how many gu
Neporo4naja [7]

Complete question :

Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pint of ice cream, what is the greatest number of gusts that Carly can serve

Answer:

15 guests

Step-by-step explanation:

Given that:

Total pints of icecream = 9 1/2

Fraction of ice cream pints per guest = 3/5 pints

Number of guest that can be served :

Total pints / fraction per guest

9 1/2 ÷ 3/5

19/2 * 5/3

95 / 6

= 15.8 guest

Hence, greatest Number of guest that can be served = 15

8 0
2 years ago
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