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amid [387]
3 years ago
11

Quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR

= 8. Find XY^2.
Mathematics
1 answer:
erik [133]3 years ago
3 0

Answer:

392

Step-by-step explanation:

Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.

Extend lines XQ, YR, YS and XP and mark their intersection as A and B.

Quadrilateral XAYB is a square because all right triangles PXQ, QAR, RYS and SBP are congruent (by ASA postulate) and therefore

  • all angles of the quadrilateral XAYB are right angles
  • all sides of XAYB are congruent and equal to 6 + 8 = 14 units.

Segment XY is the diagonal of the square XAYB, by Pythagorean theorem,

XY^2=XA^2+AY^2\\ \\XY^2=14^2+14^2\\ \\XY^2=196+196\\ \\XY^2=392  

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Setler [38]
Hi! :)

So a right triangle is a triangle that contains a ninety degree angle, it's not classified by side length. A scalene triangle is a triangle in which all three sides are different lengths. An isosceles triangle has two sides that are the same length. Either a scalene or an isosceles triangle could contain a right angle, so your answer is yes. 

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8 0
3 years ago
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Brainliest if you guess my age :)
LenaWriter [7]

Answer:

14

Step-by-step explanation:

or 16

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If (54)m = 512, what is the value of m?
Snezhnost [94]
The correct answer is 9.481.
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3 years ago
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The art teacher has 7 bottles of glue that are each 2/5 full. He combines them so he will have fewer bottles. How many bottles o
Katen [24]

Teacher will have 3 bottles of glue after he combines

<em><u>Solution:</u></em>

Given that,

The art teacher has 7 bottles of glue that are each 2/5 full

He combines them so he will have fewer bottles

<em><u>To find: bottles of glue does he have after he combines them</u></em>

From given,

Total bottles = 7

Each is 2/5 full

Therefore, multiply 7 with 2/5 to get total bottles of glues he will have after combining

Number\ of\ bottles\ of\ glues = 7 \times \frac{2}{5}\\\\Number\ of\ bottles\ of\ glues = \frac{14}{5} = 2.8 \approx 3

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7 0
3 years ago
Y^2 - 12y + 27 / y^2 - 6y - 27 <br> simply the rational equation.
Ulleksa [173]

The simplified rational expression is (y - 3)/(y + 3). Where y ≠ -3.

<h3>How to simplify a rational expression?</h3>

A rational expression is in the p/q form. Where p and q are polynomial functions.

To simplify this rational equation,

  • Factorize the polynomials in both numerator and denomiantor.
  • Cancel out common factors if any.
  • If the denominator and the numerator have no common factors except 1, then that is said to be the simplest form of the given rational expression.

<h3>Calculation:</h3>

The given rational equation is

\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}

Factorizing the expression in the numerator:

y² - 12y + 27 = y² - 9y - 3y + 27

⇒ y(y - 9) - 3(y - 9)

⇒ (y - 3)(y - 9)

Factorizing the expression in the denominator:

y² - 6y - 27 = y² - 9y + 3y - 27

⇒ y(y - 9) + 3(y - 9)

⇒ (y + 3)(y - 9)

Since they have (y - 9) as the common factor, we can simplify,

\frac{y^2 - 12y + 27 }{y^2 - 6y - 27}=\frac{(y-3)(y-9)}{(y+3)(y-9)}

⇒ (y - 3)/(y + 3) where y ≠ -3(denomiantor)

Here there are no more common factors except 1; this is the simplest form of the given rational expression.

Learn more about simplifying rational expressions here:

brainly.com/question/1928496

#SPJ9

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2 years ago
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