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3 years ago

Find the square root of -162 and please explain your answer

Mathematics

1 answer:

garik1379 [7]3 years ago

6 0

Answer:

12.7279221 i

Step-by-step explanation:

Round to 13 or 12.7

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Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)

emmainna [20.7K]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$(2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}$

$(3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}$

Thank you.

7 0

3 years ago

Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti

spayn [35]

Answer:

(a) $D(x)=-2,500x+60,000$

(b) $R(x)=60,000x-2500x^2$

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

$\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500$

Therefore, we have:

$y=-2500x+b$

At point (12,30000)

$30000=-2500(12)+b\\b=30000+30000\\b=60000$

Therefore:

$D(x)=-2,500x+60,000$

(b)Revenue

$R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2$

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

$R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12$

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

$R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0$

Therefore:

Optimal ticket price:$12
Maximum Revenue:$360,000

3 0

3 years ago

1. A bag contains rubber bands with lengths that are normally distributed with a mean of 6 cm of length, and a standard deviatio

romanna [79]

Roughly 1.7 percent of the bands are shorter than 3cm. We calculate the z score of the data point in standard distribution. By definition of z score, we use score minus mean divided by standard deviation. z=(3-6)/1.5=-2. A z score of -2 corresponds to approximately 1.7%, in other words, roughly 1.7 percent of data is less than 3cm.

4 0

3 years ago

a group of friends went to lunch the bill sales tax and tip was 48.60 a sales tax of 7% was added the group then tipped 18% on t

Usimov [2.4K]

Answer:

Sales tax = $2.79

Step-by-step explanation:

(18 x 48.6) /100

= 8.748 = $8.75 tip amount total

48.60-8.748 = 39.852 sales total

(39.852 x 7)/100

= 2.78964 = $2.79 sales tax

39.852 - 2.78964 = 37.06236 = $37.06 cost of bill

Sales tax was asked = $2.79

8 0

3 years ago

Read 2 more answers

Explain why the slope of line a is 2/6

nevsk [136]

Answer:

Step-by-step explanation:

Hi so 2/3

where slope means rise over run

so it means the first point or you slope(x1 y1)

and you take that point, go up 2 on Y, and move 6 unit to the left(x)

3 0

3 years ago