Given the figure below, find the values of x and z. (10x - 65) (9x - 49)

Mathematics

1 answer:

nexus9112 [7]2 years ago

5 0

(10x - 65) degrees is equal to (9x - 49) degrees, therefore you can set them into an equation.

(10x - 65) = (9x - 49)

By subtracting 9x in both sides,

(10x - 9x) - 65 = (9x -9x) - 49

x - 65 = -49

By adding 65 in both sides,

x - 65 + 65= -49 + 65
x = 16

Next, to find the value of z, it’s important to know that the straight line has 180 degrees. Then you would substitute the x value you found into one of your equation and subtract it from 180.

10 (16) - 65 = 160 - 65 = 95

Now you know that (10x - 65) degrees is equal to 95 degrees,

180 - 95 = z = 85

Answer: x = 16
z = 85

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Find the values of x and y.

vova2212 [387]

Look at the picture.

We have the equation (1) 12x + 4y = 40.

We know, the sum of the acute angles in a right triangle is 90°.

Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90

Substitute (1) to (2):

40 + 17x - y = 90 <em>subtract 40 from both sides</em>

17x - y = 50 (3)

We have the system of equations:

$\left\{\begin{array}{ccc}12x + 4y = 40&|:4\\17x-y=50\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x + y = 10\\17x-y=50\end{array}\right}\ \text{add both side of equations}\\.\qquad20x=60\qquad|:20\\.\qquad x=3$