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3 years ago

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Kacey is making a bracelet that is 8 inches long. She uses 1 green bead at each end of the bracelet. She also uses 1 green bead

every 2 inches
between the two ends. How many green beads does she use?
A. 16
B. 7
C.5
D.4

1 answer:

Effectus [21]3 years ago

5 0

Answer:

The answer would be C. 5

Step-by-step explanation:

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Let x,y \epsilon R. Use mathmatical induction to prove the identity.

mariarad [96]

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}$

We will prove our base case (when n=1) to be true:

Base case:

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=(x-y)(x^{1}+y^{1})=x^2-y^2=x^{1+1}-y^{1+1}$

Inductive hypothesis:

Given a natural n,

$x^{n+1}-y^{n+1}=(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})$

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that, for y=0 the conclusion is clear. Then we will assume that $y\neq 0.$

$(x-y)(x^{n+1}+x^{n}y+...+xy^{n}+y^{n+1})=(x-y)y(\frac{x^{n+1}}{y}+x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+(x-y)y(x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+y(x^{n+1}-y^{n+1})=(x-y)x^{n+1}+y(x^{n+1}-y^{n+1})=x^{n+2}-yx^{n+1}+yx^{n+1}-y^{n+2}=x^{n+2}-y^{n+2}\\$

With this we have proved our statement to be true for n+1.

In conlusion, for every natural n,

$(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}$

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2 years ago

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Rzqust [24]

Answer:

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Step-by-step explanation:

-3/8(-4y)-3/8z

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2 years ago

Melissa earns a 2% commission on the first $750 of sales she makes each week. She earns a 3% commission on the amount of her sal

gizmo_the_mogwai [7]

Answer:

0.02(750)+0.03(x−750)=37.5

Step-by-step explanation:

Given data

Melissa earns a 2% commission on the first $750 of sales

= 0.02(750)

She earns a 3% commission on the amount of her sales that are greater than $750 each week

let the amount of her sales be x

= 0.03(750-x)

Melissa earned $37.50 in commissions last week.

= $37.5

Her total earnings is $37.5

37.5= 0.02(750)+ 0.03(x-750)

37.5= 15+0.03x- 22.5

37.5-15+22.5= 0.03x

45= 0.03x

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Answer:

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2 years ago

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