Answer:
Step-by-step explanation:
If AB and DE are equidistant from the center, that means that they are the same length. We set the equations equal to one another and solve for x:
3x - 7 = 5(x - 5) and
3x - 7 = 5x - 25 and
18 = 2x so
x = 9. Now we sub that into the expression for AB (or DE since they're the same length):
3(9) - 7 = 20
Both AB and DE measure 20 units.
Answer:
m∠ABG = 20 degrees
m∠BCA = 22 degrees
m∠BAC = 118 degrees
m∠BAG = 59 degrees
DG = 4
BE = 12.4
BG = 11.7
GC = 20.4
Step-by-step explanation:
The given parameters are;
m∠CBG = 20°, m∠BCG = 11°
The incenter of a triangle is the point where the three bisectors of ΔABC meets
m∠ABG = m∠CBG = 20° by definition of angle bisector
m∠ABG = 20°
m∠ACG = m∠BCG = 11° by definition of angle bisector
m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°
m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°
m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°
m∠BAG = m∠CAG by definition of angle bisector
m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG
2 × mBAG = 118°
m∠BAG = 118°/2 = 59°
m∠BAG = 59°
Given that "G" is the incenter of the triangle ABC, we have;
GF = GE = DG = The radius of the incircle of the triangle = 4
Therefore, by Pythagoras' theorem, we have;
BG = √(11² + 4²) = √137 ≈ 11.7
BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4
GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4
The result of the operations between the two functions are listed below:
- (f - g) (x) = x - 1
- (f + g) (x) = 7 · x - 1
- (f · g) (- 1) = 15
<h3>How to perform operations between real functions</h3>
In this question we find two functions defined as two linear equations, with which we must make three kinds of operations and evaluate the resulting expression in the third case. The addition, subtraction and multiplication of two functions are defined below:
Addition
(f + g) (x) = f(x) + g(x)
Subtraction
(f - g) (x) = f(x) - g(x)
Multiplication
(f · g) (x) = f(x) · g(x)
Now we proceed to find the result for each case:
(f - g) (x) = (4 · x - 1) - (3 · x)
(f - g) (x) = 4 · x - 1 - 3 · x
(f - g) (x) = x - 1
(f + g) (x) = (4 · x - 1) + 3 · x
(f + g) (x) = 7 · x - 1
(f · g) (x) = (4 · x - 1) · (3 · x)
(f · g) (x) = 12 · x² - 3 · x
(f · g) (- 1) = 12 · (- 1)² - 3 · (- 1)
(f · g) (- 1) = 12 + 3
(f · g) (- 1) = 15
To learn more on operations for functions: brainly.com/question/14996787
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