MATHEMATICS MIDDLE SCHOOL

(a)/(a - x) + (b)/(b - x) = ((a + b)^(2) )/(ab)
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Answers

Answer 1
Answer:

Answer:

x_1=(a(a^2+ab+b^2))/((a+b)^2)\n \nx_2=(b(a^2+ab+b^2))/((a+b)^2)

Step-by-step explanation:

First, simplify the left part:

(a)/(a-x)+(b)/(b-x)=(a(b-x)+b(a-x))/((a-x)(b-x))=(ab-ax+ab-bx)/(ab-ax-bx+x^2)

Now, cross multiply:

ab\cdot (ab-ax+ab-bx)=(a+b)^2\cdot (ab-ax-bx+x^2)\n \n2(ab)^2-a^2bx-ab^2x=(a^2+2ab+b^2)(ab-ax-bx+x^2)\n \n2(ab)^2-a^2bx-ab^2x=a^3b-a^3x-a^2bx+a^2x^2+2(ab)^2-2a^2bx-2ab^2x+2abx^2+ab^3-ab^2x-b^3x+b^2x^2\n \na^3b-a^3x+a^2x^2-2a^2bx-2ab^2x+2abx^2+ab^3-b^3x+b^2x^2=0\n \nx^2(a^2+2ab+b^2)+x(-a^3-2a^2b-2ab^2-b^3)+a^3b+ab^3=0\n \n(a+b)^2x^2-x((a+b)(a^2-ab+b^2)+2ab(a+b))+ab(a^2+b^2)=0\n \n(a+b)^2x^2-x((a+b)(a^2+ab+b^2))+ab(a^2+b^2)=0\n \n(a+b)^2x^2-x(a+b)(a^2+ab+b^2)+ab(a^2+b^2)=0

D=(a+b)^2(a^2+ab+b^2)^2-4(a+b)^2ab(a^2+b^2)\n \n=(a+b)^2(a^4+(ab)^2+b^4+2a^3b+2a^2b^2+2ab^3-4a^3b-4ab^3)\n \n=(a+b)^2(a^2-ab+b^2)^2\n \n√(D)=(a+b)(a^2-ab+b^2)=a^3-b^3

So,

x_(1,2)=((a+b)(a^2+ab+b^2)\pm (a^3-b^3))/(2(a+b)^2)\n \nx_1=(a^3+a^2b+ab^2+ba^2+ab^2+b^3+a^3-b^3)/(2(a+b)^2)=(2a^3+2a^2b+2ab^2)/(2(a+b)^2)=(2a(a^2+ab+b^2))/(2(a+b)^2)=(a(a^2+ab+b^2))/((a+b)^2)\n \nx_2=(a^3+a^2b+ab^2+ba^2+ab^2+b^3-a^3+b^3)/(2(a+b)^2)=(2b^3+2a^2b+2ab^2)/(2(a+b)^2)=(2b(a^2+ab+b^2))/(2(a+b)^2)=(b(a^2+ab+b^2))/((a+b)^2)

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Estimate the answer to 3772 ÷ 44 ?

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3772 divided by 44 is approximately 85.72 repeat. The 72 at the end is the repeat part 

Jack buys 4 / 3 pounds of
plums. martin buys 6 / 3 pounds of apples. who buys more fruit

Answers

Jack bought 1 1/3 pounds and Martin has 2 pounds so Martin has more

How do u find the scale factor of dilation

Answers

Answer:

Step-by-step explanation:

We need to understand what is dilation?

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

• A dilation that creates a larger image is called an enlargement. and its scale factor is greater than 1

• A dilation that creates a smaller image is called a reduction.and its scale factor is smaller than 1

  • The scale factor is 1, the figure and the image are congruent.

To find the scale factor of dilation, we need to identify the coordinates of one point in the original shape and the coordinates of one point in the scaled shape. Then divide the x-coordinate of the scaled point by the x-coordinate of the original point.

For example:

  • A (1 ,1) in the original shape
  • A' (2, 2) scaled shape

=> the the scale factor of dilation = 2 / 1 = 2

Hope it can find you well

Answer:


Step-by-step explanation:

Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilation with scale factor 2, multiply by 2.



or



To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides. If you begin with the smaller figure, your scale factor will be less than one. If you begin with the larger figure, your scale factor will be greater than one.

PLSSSSS help mehh..nicole walked 95 meters. ming walked 56 meters. how much further did nicole walk than ming

Answers

Answer:

95-56 = 39 meters further

Step-by-step explanation:

So, if Nicole walked 95 meters, and Ming only walked 56, this would be the simple equation of 95-56, which would equal 39 meters.

Answer:

95-56=39 more meters

Step-by-step explanation:

a gallery owner purchased a very old painting for $3,000. the painting sells at a 325% increase in price what is the retail price of the painting.

Answers

Answer:

The retail price of the painting is  $12750 .

Step-by-step explanation:

As given

A gallery owner purchased a very old painting for $3,000.

The painting sells at a 325% increase in price .

325% is written in the decimal form.

= (325)/(100)

= 3.25

Increase in the prize= 3.25 × 3000

                                 = $9750

Retail price of the painting = Purchased cost of painting + Increase in the prize

                                            = $9750 + $3000

                                            = $12750

Therefore the retail price of the painting is  $12750 .
300%= 9,000
20%= 60
5%= 15

9,000+60+15= 9,075
answer: £9,075

What's is the area of the figure below

Answers

I believe it’s 15 square units
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