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3 years ago

(8m-3n)^2 - (4m+3n)^2

Mathematics

1 answer:

natulia [17]3 years ago

4 0

Answer:

$48m^2-72mn$

Step-by-step explanation:

We need to solve $(8m-3n)^2 - (4m+3n)^2$

We know that,

$(a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab$

Using the above formula,

$(8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn$

So, the final answer is $48m^2-72mn$ .

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Can somebody plz help me

Illusion [34]

Answer: A

Step-by-step explanation:

2x²-2x-9=0

this is a quadratic equation so we will use the quadratic formula .

Δ= b²-4*a*c

b= -2
a= 2
c= -9

let's calculate Δ to khow how many solutions this equations have .

Δ= (-2)²-4*2*(-9)

= 76

we notice that 76>0

so this equation has two solutions : (-b-√76)/4 and (-b+√76)/4

let's calculte the values :
(-b-√76)/4= $\frac{-2-\sqrt{76} }{4}$ (-b+√76)/4= $\frac{-2+\sqrt{76} }{4}$

the trick here is to notice that :

$\sqrt{76}$ = $\sqrt{19*4}$

= $\sqrt{19} *\sqrt{4}$

= 2 $\sqrt{19}$

Now we will simplify Δ by factoring by 2

$\frac{2*(-1(+/-)\sqrt{19} }{2*2}$ = $\frac{-1(+/-)\sqrt{19} }{2}$

so the answer is a .

5 0

4 years ago

A service center receives an average of 0.6 customer complaints per hour. Management's goal is to receive fewer than five compla

Zolol [24]

Answer:

48.68% probability that managment is unhappy with the number of complaints in the next eight hours.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

A service center receives an average of 0.6 customer complaints per hour.

This means that $\mu = 0.6n$ , in which n is the number of hours.

Eight hours:

This means that $n = 8, \mu = 0.6*8 = 4.8$

Determine the probability that managment is unhappy with the number of complaints in the next eight hours.

They will be unhappy if they receive five or more complaints.

Either they receive less than five complaints, or they receive at least five. The sum of the probabilities of these events is 1. So

$P(X < 5) + P(X \geq 5) = 1$

We want $P(X \geq 5)$ .

Then

$P(X \geq 1) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-4.6}*4.6^{0}}{(0)!} = 0.0101$

$P(X = 1) = \frac{e^{-4.6}*4.6^{1}}{(1)!} = 0.0462$

$P(X = 2) = \frac{e^{-4.6}*4.6^{2}}{(2)!} = 0.1063$

$P(X = 3) = \frac{e^{-4.6}*4.6^{3}}{(3)!} = 0.1631$

$P(X = 4) = \frac{e^{-4.6}*4.6^{4}}{(4)!} = 0.1875$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0101 + 0.0462 + 0.1063 + 0.1631 + 0.1875 = 0.5132$

Finally

$P(X \geq 1) = 1 - P(X < 5) = 1 - 0.5132 = 0.4868$

48.68% probability that managment is unhappy with the number of complaints in the next eight hours.

6 0

3 years ago

When constructing parallel lines how can you be sure the lines you constructed are parallel

Andru [333]

They are both facing the same direction.

8 0

4 years ago

Read 2 more answers

Helpppppppppp assssaaaap

ikadub [295]

<h3>Answer: 250</h3>

==================================================

Explanation:

x = speed of the plane in mph

x-180 = speed of the car, since its 180 mph slower than the plane

For the plane, we can form the equation

distance = rate*time

d = r*t

500 = xt

t = 500/x

For the car, we can say,

d = rt

140 = (x-180)t

140 = (x-180)*(500/x)

140x = 500(x-180)

140x = 500x - 90,000

140x - 500x = -90,000

-360x = -90,000

x = (-90,000)/(-360)

x = 250

The speed of the plane is 250 mph

-----------------------------

Extra info:

The car's speed is x-180 = 250-180 = 70 mph

It takes the plane t = d/r = 500/250 = 2 hours and it takes the car t = d/r = 140/70 = 2 hours. Both vehicles travel for 2 hours, which helps to confirm the answer.

6 0

3 years ago

If 2x+13=17, then find the value of 3x+1

Aleksandr [31]

Answer: 7
2x=4
x=2
3x+1=3(2)+1=7

3 0

3 years ago

(8m-3n)^2 - (4m+3n)^2​

(8m-3n)^2 - (4m+3n)^2