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nirvana33 [79]
3 years ago
11

Show that any number of the form ABCABC (e.g. 356356) is divisible by 13.

Mathematics
1 answer:
Shtirlitz [24]3 years ago
8 0

We could write such a number as

10^5a+10^4b+10^3c+10^2a+10b+c

=10^2(10^3+1)a+10(10^3+1)b+(10^3+1)c

=(10^3+1)(100a+10b+c)

10^3+1=1001=13\cdot77 so we're done.

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Find the lowest common denominator of and . A. x3y4 B. x2y3 C. xy4 D. x4y5
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Lowest Common Denominator refers to lowes t common multiple. These expressions have two terms 'x' and 'y' and we want to choose the expression that has the highest power such that the other expressions can be multiplied into the common denominator.

For the 'x' term, the highest power is x⁴ and for the 'y' term, the highest power is y⁵

Common denominator of A, B, C, and D: x⁴y⁵




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Read 2 more answers
Consider the isosceles triangle. left side (2x+8)units bottom of triangle (4x-10)units right side of triangle (2x+8) units Part
Blizzard [7]

Complete Question

Consider the isosceles triangle. left side (2z+8)units, bottom of triangle (4z-10)units, right side of triangle (2z+8) units Part A Which expression represents the perimeter of the triangle? a.(4z+16) units b.(6z−2)units c.(8z−16) units d.(8z+6) units

Answer:

d. (8z + 6) units

Step-by-step explanation:

The formula for the Perimeter of a Triangle is :Side A + Side B + Side C

Hence,

(2z + 8)units + (4z - 10) units + (2z + 8)units

= (2z + 8 + 4z - 10 + 2z + 8)units

Collect like terms

= 2z + 4z + 2z + 8 - 10 + 8

= 8z + 6 units

The expression that represents the perimeter of the triangle is (8z +6) units

3 0
2 years ago
Otis has saved $18,500 so far to buy a house. He can put this amount into account that earns 5.1% simple interest, or another wi
Troyanec [42]

Answer:

J Compound interest; $298.65

Step-by-step explanation:

Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.

For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...

  1.051^4 = 1.22024337

and the effective multiplier for simple interest is ...

  1 +0.051·4 = 1.204

Then the difference in interest rate multiplier for the 4-year period is ...

  1.22024337 -1.204 = 0.01614337

That fraction of the $18500 principal is $298.65.

Compound interest earns $298.65 more than simple interest in this scenario.

Hope this helps, have an amazing day!

8 0
2 years ago
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