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sergij07 [2.7K]
3 years ago
14

If Colorado Springs, Colorado, has 1.4 times more days of sunshine than Boston, Massachusetts, how many days of sunshine does ea

ch city have if there are a total of 475 days of sunshine between the two in a year?
Mathematics
1 answer:
nevsk [136]3 years ago
8 0

Suppose, number of sunshine days in Boston, Massachusetts is: x

Then, number of sunshine days in Colorado Spring, Colorado will be: 1.4 x

Given that, total number of days of sunshine for both city is: 475

That is, x+1.4x = 475

Solving for x,

x=198

1.4x= 277

Therefore,

Number of sunshine days in Boston, Massachusetts is 198

and

Number of sunshine days in Colorado Spring, Colorado is 277

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Prove the divisibility:<br><br>45^45·15^15 by 75^30
garri49 [273]

Answer:

3^{75}.

Step-by-step explanation:

We have been an division problem: \frac{45^{45}*15^{15}}{75^{30}}.

We will simplify our division problem using rules of exponents.

Using product rule of exponents (a*b)^n=a^n*b^n we can write:

45^{45}=(9*5)^{45}=9^{45}*5^{45}

15^{15}=(3*5)^{15}=3^{15}*5^{15}

75^{30}=(15*5)^{30}=15^{30}*5^{30}

Substituting these values in our division problem we will get,

\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}

\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}

Using product rule of exponents (a*b)^n=a^n*b^n we will get,

\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}

\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}

Using power rule of exponents a^n*a^m=a^{n+m} we will get,

\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}

\frac{3^{105}*5^{60}}{3^{30}*5^{60}}

\frac{3^{105}}{3^{30}}

Using quotient rule of exponent \frac{a^m}{a^n}=a^{m-n} we will get,

\frac{3^{105}}{3^{30}}=3^{105-30}

3^{105-30}=3^{75}

Therefore, our resulting quotient will be 3^{75}.

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3 years ago
The point F(5, 5) is translated 7 units left.
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5 - 7 = -2. Therefore, the answer is (-2, 5).
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imagen you want to put a border around a rectangular room. summerize the steps you would use to find the length of the boarder n
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You would need to find the length of one wall then multiply it by 2 (since there are 2 walls) and then find the width and also multiply that by 2 and you would then add your to products (answers) to get the total length of your border
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3 years ago
Find the product. -2x(x2 - 3)
zalisa [80]

Step-by-step explanation:

-2x(x2 - 3)

-2x³+6x

Hope it helps ☺️

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e. Noah earned v dollars over the summer. Mai earned m dollars, which is 45 dollars more than Noah did. What's the answer?
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Step-by-step explanation:

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