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2 years ago

Counter example. The sum of three fractions with odd numerators is never 1/2

Mathematics

2 answers:

kolbaska11 [484]2 years ago

8 0

1/6 + 1/6 + 1/6 = 3/6 = 1/2

tia_tia [17]2 years ago

5 0

One <em>possible counterexample</em> is:

1/4 + 1/5 + 1/20 = 1/2.

In this problem, we would find the least common denominator for 4, 5 and 20. The first thing all 3 numbers will divide into is 20:

1/4 = 5/20; 1/5 = 4/20; 1/20 = 1/20

This gives us: 5/20 + 4/20 + 1/20

Adding the numerators, we get (5+4+1)/20 = 10/20 = 1/2.

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2 years ago

Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year

kramer

Answer:

(a) $-3x^2+150x-10000$

(b) $-\$16,863,760,000$

Step-by-step explanation:

Alphaville's Budget Surplus Model is $-2x^2+ 500x$

Betaville's Budget Surplus Model is $x^2- 100x + 10000.$

We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.

To do this, we subtract Betaville's Model from Alphaville's model.

$-2x^2+ 500x-(x^2- 100x + 10000)\\$

Opening the brackets

$-2x^2+ 500x-x^2+100x - 10000\\$

Collect like terms and simplify

$-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000$

The expression that shows how much greater Alphaville's Budget is:

$-3x^2+150x-10000$

(b) If the tax revenue that year in each town is $75,000

We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000

$-3x^2+150x-10000\\=-3(75000)^2+150(75000)-10000\\=-\$16,863,760,000$

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2 years ago

What type of function can approach zero as x decreases without end?

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Answer: c. Exponential

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2 years ago

Solve for x if 2(5x+2)^2=48

likoan [24]

2(5x + 2)^2 = 48
divide both sides by 2
(5x + 2)^2 = 24
square root both sides to clear the power of two.
5x + 2 = + - sqrt24
subtract 2 from both sides
5x = -2 + - sqrt 24
divide both sides by 5
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2 years ago

Read 2 more answers

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