Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule:
Answer:
Breadth = 8 cm
Length = 17 cm
Step-by-step explanation:
Given rectangle:
Breadth = x cm
Length = x + 9 cm
Area = length * breadth
= x * (x + 9)
= x² + 9x
Rectangle with length and breadth increased:
Breadth = x + 3 cm
Length = x + 9 + 3 = x + 12 cm
Area = 84 + (x² + 9x) cm²
(x +3) * (x +12) = 84 + x² + 9x
Use FOIL method
x*x + x*12 + 3*x + 3*12 = 84 + x² + 9x
x² + 12x + 3x + 36 = 84 + x² + 9x {add the like terms}
x² + 15x + 36 = 84 + x² + 9x
x² + 15x + 36 - 84 - x² - 9x = 0
6x - 48 = 0
6x = 48
x = 48/6
x = 8
Breadth = x = 8 cm
Length = x + 9 = 8 +9 = 17 cm
Answer:
Step-by-step explanation:
The interval notation is (-12, 12).
Answer:
Senior citizen ticket: $3
Student ticket: $9
Explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
