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2 years ago

9

3 Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ: ●

(a + b)^2, ●(a – b)^2, and ●(a - b)(a + b).

1 answer:

Pavel [41]2 years ago

4 0

<span>●(a + b)^2 = (a +b) (a +b)

(a + b) (a + b) = a*a + a*b + b*a+ b*b = a^2 + 2ab + b^2

●(a – b)^2 (a - b) (a -b)

(a - b) (a -b) = a*a + -ab - ba + b*b = a^2 - 2ab + b^2

●(a - b)(a + b). =

= (a - b) (a + b) = a*a + ab - ba - b*b = a^2 - b^2
</span>

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The area of a small pond is 78.5 yds. What is the diameter of the pond?

Zolol [24]

Answer:

Diameter of pound = 10 yd

Step-by-step explanation:

Given area of circular pond = 78.5 square yd

To find the diameter of the pond.

Solution:

The pond being circular in shape, the area of pond can be given as:

⇒ $\pi\ r^2$

where $r$ represents radius of the pond.

Thus, we have:

⇒ $\pi\ r^2=78.5$

Using $\pi=3.14$

⇒ $3.14r^2=78.5$

Solving for $r$

Dividing both sides by 3.14

⇒ $\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}$

⇒ $r^2=25$

Taking square root both sides.

⇒ $\sqrt{r^2}=\sqrt{25}$

⇒ $r=\pm5$

So, radius = 5 yd, as distances are always positive.

Diameter = $2\times radius=2\times 5\ yd= 10\ yd$

Thus, diameter of pound = 10 yd

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2 years ago

Janie ordered boxed lunches for a student advisory committee meeting. Each lunch costs $4.25. The total cost of the lunches is $

andriy [413]

Answer:

11 boxed lunches

Step-by-step explanation:

Full question

Janie ordered boxed lunches for a student advisory committee meeting. Each lunch cost 4.25. The total cost of the lunches is 53.75, including a 7$ delivery fee. Write and solve an equation to find x the number of boxed lunches Janie ordered

First of all subtract the delivery feesince it was inckuded in the total cost, this will now be the total cost of all the noxed lunches ordered by Janie, then divide the balance of the total cost by the cost of one boxed lunch to get thd total boxed kunches

X= 53.75-7/4.25

X= 53.75-7= 46.75/4.25

X=11

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2 years ago

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Daisy works at an ice-cream parlor. She is paid $10 per hour for the first 8 hours she works in a day. For every extra hour she

andre [41]

Answer:

80+(15x)

Step-by-step explanation:

10 times 8=80

1.5 times 10=15

so she gets 80 dollars for the first 8 hours then for every extra hour she gets 15 dollars

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2 years ago

Megan wants to build a fence around her pool. The pool is 28 feet long by 23 feet wide. The fence is to be 15 feet from the edge

ASHA 777 [7]

23 +30 (15 feet each way) = 53

28 + 30 = 58

58 x 53 = 3074ft

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2 years ago

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The editor of a textbook publishing company is deciding whether to publish a proposed textbook. Information on previous textbook

kogti [31]

Answer:

34.86% probability that it will be huge success

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Receiving a favorable review.

Event B: Being a huge success.

Information on previous textbooks published show that 20 % are huge successes

This means that $P(B) = 0.2$

99 % of the huge successes received favorable reviews

This means that $P(A|B) = 0.99$

Probability of receiving a favorable review:

20% are huge successes. Of those, 99% receive favorable reviews.

30% are modest successes. Of those, 70% receive favorable reviews.

30% break even. Of those, 40% receive favorable reviews.

20% are losers. Of those, 20% receive favorable reviews.

Then

$P(A) = 0.2*0.99 + 0.3*0.7 + 0.3*0.4 + 0.2*0.2 = 0.568$

Finally

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.2*0.99}{0.568} = 0.3486$

34.86% probability that it will be huge success

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