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Furkat [3]
2 years ago
7

Solve for x and y

Mathematics
1 answer:
bekas [8.4K]2 years ago
7 0

Answer:

x = 2√2

y = 2√6

Step-by-step explanation:

Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)

These will be equal since the triangles are similar

shorter leg : longer leg

(blue triangle = red triangle)

⇒ x : 4 = 2 : x

⇒ x/4 = 2/x

⇒ x² = 8

⇒ x = √8

⇒ x = 2√2

Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)

⇒ 4² + (2√2)² = y²

⇒ y² = 24

⇒ y = √24

⇒ y = 2√6

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a millionaire leaves 4/17 of his estate to his son, 7/13 to his wife, 2/3 to his daughter and the remaining 2 million to his dog
ss7ja [257]
Comment
I'm going to do this two ways, one using a calculator and one not.
Let the total amount of his estate be x.

Equation and Solution
If you have a calculator with an a b/c key on it you can do this problem easily, or at least the fractional part will be easy.

First: develop the  equation
(4/17) x + (7/13)x + 2/3 x + 2 000 000  

Solve the equation
Use the a b/c key on your calculator if you have one. If not go down the second solution part. Put a fraction in as follows.
4 a b/c 17 + 7 a b/c 13 + 2 a b/c 3 = 
You should get 1 r 16 r 51 
What this translates into is 1 292 / 663 of x
or 955/663 x + 2000000

So the total of fhis estate is
(955/663) x + 2000000 <<<< answer In decimal form you get
1,44 x + 2000000 <<<< answer in decimal.

Note: you cannot solve this to the exact amount of his estate because the fractional amount exceeds x which assumed to be the total amount of his estate.

By hand
Find the ;lowest common denominator of 13 17 and 3. Since all of them are prime numbers the lowest common denominator is 13 * 17 * 3 = 663
\
Next set up the 3 fracttions so the denominator = 663
4 / 17 =( 4 * 13 * 3) / 663 = 156 / 663

7/13 = 7 * 17*3 / 663 = 357 / 663

2/3 = 2*13 * 17 / 663 = 442 / 663

Now add these up 156/663 + 357/663 + 442/663 = 955 / 663 This is irreducible
This fraction is over 1 so it cannot represent the total amount in his estate. It is too large.    

(955/663)x + 2000000 <<<<<< fractional answer
1.44x + 2000000 < decimal answer.
3 0
3 years ago
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Black_prince [1.1K]

Answer:

64

Step-by-step explanation:

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Answer:

y = x -3

Step-by-step explanation:

From the graph we see the line goes from point (0, -3) to point ( 3, 0), so we can find the slope as m= rise ( go up 3)  / run ( go to the right 3)  = 3/ 3 = 1

From the graph we can also see the y-intercept ( where the line intersects the y axis is at b = -3

The general equation of the line is y= mx+ b

Our line's equation is y = x -3, because m=1 and b= -3

5 0
3 years ago
Need help asap <br> x=4 and y= -9<br> 2xy+15x
ohaa [14]

Answer:

12

Step-by-step explanation:

2xy+15x

Let x=4 and y= -9

2(-4)(-9) + 15(-4)

Multiply

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Subtract

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8 0
3 years ago
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What is the hypothenuse of a right triangle with bases 13cm and 5cm?
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To find the hypothenuse use Pythagorean theorem: 13²+5²=h²,
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