Answer:
by applying Pythagoras theorem;
the ladder(13m) acts as hypotenuse
the wall (12m) acts as height
the distance between the the two is the base
therefore
a² + b² = c²
b²= c²- a²
b²= 169 - 144
b² = 25
√b² = √25
b= 5m
the distance is 5m
Answer:
Equation: 4.90/b = 14/100
Solution: b = $35
Step-by-step explanation:
Variable b = cost of the haircut
Solve for b:
4.90/b = 14/100
490 = 14b
35 = b
Check your work:
35 × 0.14 = 4.90
Correct!
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
For the answer to the questions above,
A) Parrots are following a Geometric Progression of 15% increase.
20(1.15), 20(1.15)², 20(1.15)³,
Function = 20(1.15)^n Where n is at the end of year, n =1, 2, 3, ..
Snakes are increasing by 4.
28, 32, 36,....
Function = 24 + 4n n = number of end year, n =1, 2, 3,...
<span>B) After 10 years: </span>
Parrot = 20(1.15)¹⁰ = 80.91115471
Snakes = 24 + 4(10) = 64
<span>C) After what time they are the same: </span>
We use trial and error:
Test: n 20(1.15^n) (24 + 4n)
1 23 28
2 26.45 32
<span> 3 30.41 36 </span>
4 34.98 40
5 40.23 44
6 46.26 48
7 53.20 52
8 61.18 56
9 70.36 60
After year 7, the Parrots increases far more.
<span>At year 7 they are roughly the same.</span>
