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2 years ago

Which products result in a perfect square trinomial? Select three options.

Mathematics

2 answers:

Kazeer [188]2 years ago

8 0

Answer:

Second option: $(xy+x)(xy+x)$

Third option: $(2x-3)(-3+2x)$

Fifth option: $(4y^2+25)(25+4y^2)$

Step-by-step explanation:

By definition, a perfect square trinomial can be obtained by squaring binomials.

Then:

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

Knowing this, to obtain a perfect square trinomial, the binomials that you multiply must be equals.

Therefore, the products result in a perfect square trinomial are:

$(xy+x)(xy+x)=(xy+x)^2=(xy)^2+2(xy)(x)+x^2=x^2y^2+2x^2y+x^2$

$(2x-3)(-3+2x)=(2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9$

$(4y^2+25)(25+4y^2)=(4y^2+25)^2=(4y^2)^2+2(4y^2)(25)+25^2=16y^4+200y^2+625$

Setler79 [48]2 years ago

6 0

Answer:

Its Easy the answers are B, C, and E

Step-by-step explanation:

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we know that

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$V= \frac{1}{3} \pi r^{2}h$

in this problem

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$r= \frac{112}{2}= 56ft$

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Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) Find the volume before the storm

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3) Find the volume after the storm

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

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h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

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4) Find how this change affect the volume of the pile

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

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The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

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$104,358.59*80=8,348,687.2\ pounds$

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$8,348,687.2/350=23,853.39 \ lane\ miles$

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the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

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the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) Find the pounds of road salt

$4,013.79*80=321,103.20\ pounds$

9) Find the number of lane miles

$321,103.20/350=917.44 \ lane\ miles$

therefore

the answer part c) is

the number of lane miles is $917 \ lane\ miles$

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The probability that he rolls a 4 and flips a head= $\frac{\text{favorable outcome}}{\text{total outcome}}$

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Answer:

a) The simultaneous equation represented in matrix form, is

[1/3 1/4] [x] = [s]

[2/3 3/4] [y] = [w]

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[2/3 3/4]

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b) Number of sick people the preceding week = 12005

Step-by-step explanation:

x = Number of sick people in a week

y = Number of people that are well in a week

s = Number of sick people the following week

w = Number of people that are well the following week.

The relationship between these is given as

(1/3)x + (1/4)y = s

(2/3)x + (3/4)y = w

In matrix form, this is simply presented as

[1/3 1/4] [x] = [s]

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which is more appropriately written as

Ax = B

where

[1/3 1/4] = matrix A (matrix of coefficients)

[2/3 3/4]

[x] = matrix x (matrix of unknowns)

[y]

[s] = matrix B (matrix of answers)

[w]

b) Taking the current conditions as s and w, then the preceding week will be x and y

The number of sick people in this week, s = 13000

The number of people well in this week, w = total population - Number of sick people.

w = 48000 - 13000 = 35000

So, the simultaneous equation becomes

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

Then we can solve for the number of sick and well people the preceding week.

We can solve normally or use matrix solution.

Ax = B

x, the matrix of unknowns is given by product of the inverse of A (inverse of the matrix of coefficients) and B (matrix of answers)

x = (A⁻¹)B

But, solving normally,

(1/3)x + (1/4)y = 13000

(2/3)x + (3/4)y = 35000

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y = 35995.2 = 35995

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8 0

2 years ago