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Artyom0805 [142]
2 years ago
8

Alice and Betty each want to buy the same kind of ruler. But Alice is 22 cents short and Betty is 3 cents short. When they combi

ne their money they still do not have enough money. What is the most the ruler could cost?
Mathematics
1 answer:
goblinko [34]2 years ago
7 0

Answer:

The rule could cost 24 cents at most.

Step-by-step explanation:

Let x cents be the price of the ruler.

Alice is 22 cents short, so Alice has x - 22 cents.

Betty is 3 cents short, so Betty has x - 3 cents.

When they combine their money they have

x - 22 + x - 3 = 2x - 25 cents.

This amount is still not enough, so

2x-25

Solve this inequality:

2x-x

The rule could cost 24 cents at most.

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9* 
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A property sells for $620,000 two years after it was purchased. If the annual appreciation rate was 4%, how much did the origina
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Jeff has recorded the cost of insurance premiums on his car for a particular insurance company.
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Expand (3 - 2x)6. What is the coefficient of the sixth term?
stich3 [128]
To expand (3 - 2x)^6 use the binomial theorem:

(x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + ...+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n


So, for x = 3, y = -2x , and n = 6 you get:

(3 - 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6

So, the sixth term is C(6,5)(3)(-2x)^5 =  6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.

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5 0
2 years ago
A trapezoid is 14 centimeters high and has bases that measure 13.5 centimeters and 27.5 centimeters. What is the area of the tra
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Hello!

We can find the area of the trapezoid using the formula for area of a trapezoid:

FORMULA: 

A = [(b + b) * h / 2]

SUBSTITUTE: 

A = [(13.5 + 27.5) * 14 / 2]

SOLVE: 

A = 41 * 14 / 2

A = 574 / 2 

A = 287 cm²

So, the area of the trapezoid is 287 cm².


7 0
2 years ago
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