Answer:
a. m<B = 100°
b. m<L = 55°
c. Scale factor = 9/11
Step-by-step explanation:
a) Similar triangles have their three corresponding angles congruent to each other, while the ratio of their corresponding sides are proportional to each other.
Since ∆ABC ~ ∆GLJ, therefore,
<A = <G,
<B = <J
<C = <L
m<J = 100° (given)
Therefore,
m<B = m<J = 100°
m<B = 100°
b) m<A = m<G
m<A = 25° (given)
Therefore,
m<A = m<G = 25°
m<G = 25°
m<L = 180° - (m<J + m<G)
Substitute
m<L = 180° - (100° + 25°)
m<L = 55°
c) scale factor of smaller triangle to the larger = side length of smaller triangle / corresponding side length of bigger triangle
Scale factor = AB/GJ
Substitute
Scale factor = 18/22
Simplify
Scale factor = 9/11
Answer:
21
Step-by-step explanation:
I shall change the pictures to letters
a + a + b = 40 --(1)
b - c = 7 --(2)
c + a = 19 --(3)
a - c + b = ?
From (1):
2a + b = 40
b = 40 - 2a --(4)
From (2):
b = 7 + c --(5)
Sub (4) into (5):
40 - 2a = 7 + c
c = 33 - 2a --(6)
Sub (6) into (3):
33 - 2a + a = 19
a = 14
Sub a = 14 into (4) and (6):
b = 40 - 2(14) = 12
c = 33 - 2(14) = 5
therefore, a - c + b = 14 - 5 + 12 = 21
Topic: simultaneous equations
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Answer:
Step-by-step explanation:
if we're going by a 24 pack of soda, 3/8 would be 9 sodas while 4/12 is a third, which would be 8 sodas
C.) x = -4 is the correct answer
Step-by-step explanation:
In order to solve the equation we have to isolate x on one side of equation
Given
7x + 6 = -22
Subtracting 6 from both sides
Dividing both sides by 7
Hence,
C.) x = -4 is the correct answer
Keywords: Linear equation
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Answer:
Number of ducks = 37
Number of pigs = 18
Step-by-step explanation:
Let,
x be the number of ducks
y be the number of pigs
According to given statement;
x+y=55 Eqn 1
2x+4y=146 Eqn 2 (As ducks will have 2 legs and pigs will have 4)
Multiplying Eqn 1 by 2
2(x+y=55)
2x+2y=110 Eqn 3
Subtracting Eqn 3 from Eqn 2
(2x+4y)-(2x+2y)=146-110
2x+4y-2x-2y=36
2y=36
Dividing both sides by 2
Putting y=18 in Eqn 1
x+18=55
x = 55-18
x = 37
Hence,
Number of ducks = 37
Number of pigs = 18
