Answer:
a. x = 9
b. GH = 30; GK = 20
Step-by-step explanation:
An angle bisector in a triangle divides the sides proportionally.
<h3>a.</h3>
In this triangle, that means ...
(3x +3)/18 = (3x -7)/12
2(3x +3) = 3(3x -7) . . . . . . . multiply by 36
6x +6 = 9x -21 . . . . . . . . . eliminate parentheses
27 = 3x . . . . . . . . . . . . . . add 21 -6x
x = 9 . . . . . . . . . . . . . . . divide by 3
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<h3>b.</h3>
The segment lengths are found by substituting the value of 3x in each of the given expressions:
GH = 3x +3 = 27 +3 = 30
GK = 3x -7 = 27 -7 = 20
cos(2x+x)
=cos (2x)cosx-sin(2x)sinx
=(1-2sin^2x)cosx-2sinxcosx*cos x
=cos x-2 sin ^2 x cos x-2 sin^2 xcos x
=cos x-4sin^2 x cos x
=cos x {1-4(1- cos ^2 x)}
=4 cos ^3x -3 cos x
The answer isc because complementary angles add up to 90 degrees
Answer:
This means sonya moves 3 units backward 4 times
Step-by-step explanation:
4(-3) ;
4 represents the number of times a (-3) movement is executed.
-3 means a backward movement due to the presence of negative sign.
Hence, we can conclude that Sonya moves 3 units backward 4 times or can infer a direct multiplication of 4(-3) = - 12 ;
A backward movement of - 12 units.
Answer:
C. 5, 12 and 13
D. 6, 8 and 10
Step-by-step explanation:
To see if three side lengths would give you a right triangle, you have to use the Pythagoras Theorem which is a² + b² = c², where c is the hypotenuse (longest side) and a and b are adjacent to the right angle.
A. 3² + 7² ≠ 10²
9 + 49 ≠ 100
58 ≠ 100
B. 4² + 9² ≠ 10²
16 + 81 ≠ 100
97 ≠ 100
C. 5² + 12² = 13²
25 + 144 = 169
169 = 169
D. 6² + 8² = 10²
36 + 64 = 100
100 = 100