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Alborosie
3 years ago
7

Rita is thinking of two numbers. Adding 4 times the first number and 9 times the second number gives a total of 1. Also, adding

4 times the first number and 6 times the second number gives -2. What are the two numbers?
Mathematics
1 answer:
charle [14.2K]3 years ago
6 0

Answer:

first number is negative 2, second is 1

Step-by-step explanation:

-2×4= -8 1×9=9

-8+9=1

-2×4= -8 1×6=6

-8+6= -2

hope this helped

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two points on the same side of a tree are 65 feet apart. the angles of elevation of the top the tree are 21 19 from one point an
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The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are  21° 19' and 16°20'.

1) Convert the angles to decimal form:

19' * 1°/60' = 0.32° => 21° 19' = 21.32°

20' * 1°/60' = 0.33° => 16° 20' = 16.33°

2) Deduce the trigonometric ratios from the verbal information.

You can form a triangle with

- horizontal leg  x + 65 feet
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=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)

You can form a second triangle with:

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=> trigonometric ratio: tan(21.32) = h / x  => h = x * tan(21.32)

Now equal the two expressions for h:

(x+65)*tan(16.33) = x*tan(21.32)

=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet

=> h = 195.73 * tan(21.32) = 76.39 feet.

Answer: 76.39 feet
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