Solving a system of linear equations, we conclude that the measure of side Z is 2√13
<h3>How to find the measure of side Z?</h3>
Remember the Pythagorean theorem. It says that the square of the hypotenuse is equal to the sum of the squares of the legs.
In the image, we can identify 3 right triangles, and with the Pythagorean theorem, we can write a system of 3 equations.
x^2 = y^2 + 4^2
z^2 = y^2 + 9^2
(4 + 9)^2 = z^2 + x^2
We want to solve that for z.
Now, the second equation can be rewritten to:
y^2 = z^2 - 9^2
Now let's replace the first equation into the third one, so we get:
(4 + 9)^2 = z^2 + (y^2 + 4^2)
Now we can replace y^2 by z^2 - 9^2
(4 + 9)^2 = z^2 + ((z^2 - 9^2) + 4^2)
Now we can solve this:
(13)^2 = z^2 + z^2 - 9^2 + 4^2
(13)^2 + 9^2 - 4^2 = 2*z^2
104/2 = z^2
52 = z^2
√52 = z
√(4*13) = z
√4*√13 = z
2√13 = z
We conclude that the measure of side Z is 2√13
If you want to learn more about systems of equations:
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115 degrees as 70+40=115 and that is equal to ?
23.2% of the total employees is 27,200
0.232x = 27,200
x = 27,200 / 0.232
x = 117,241 (thats rounded) <==
Answer:
12.5
Step-by-step explanation:
square root of 10^2 - 8^2 = 6 gives us missing side
sin^-1(8/10) = 53.13 gives us half of the angle
90-53.13 = 36.869 gives us the angle of the triangle on the right
tan(36.869) x 6 = 4.5
4.5 + 8 = 12.5
Hope that helps,
Good Luck! x
Answer:
1350
Step-by-step explanation:
Initially 90 squirrels were tagged out of a total population of x squirrels.
Similarly, 42 squirrels out of a sample of 630 squirrels had tag
We can use ratio equality to find the total population x.
42:90=620:x
Cross multiplying
42 X x = 630 X 90
Dividing both sides by 42
The total number of squirrels in the city park is 1350.
