Answer:
The answer to your question is 14° and 76°
Step-by-step explanation:
Data
leg 1 = x
leg 2 = x/4
angle 1 = ?
angle 2 = ?
Process
To solve problem use trigonometric functions. We must use the trigonometric function that relates both legs (tangent).
tangent Ф = Opposite side / Adjacent side
-Substitution
tan Ф = (x/4) / x
-Simplification
tan Ф = x / 4x
tan Ф = 1/4
- Find Ф
Ф = tan⁻¹(1/4) = 14°
- Find the other acute angle
The sum of the internal angles in a triangles equals 180°
Ф + Ф₁ + 90° = 180
-Solve for Ф₁
Ф₁ = 180 - 90 - 14
-Result
Ф₁ = 76°
Answer:
(- 4, 27 )
Step-by-step explanation:
Equate the right sides of both equations, that is
x² - 2x + 3 = - 2x + 19 ← subtract - 2x + 19 from both sides
x² - 16 = 0 ← in standard form
(x - 4)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 4 = 0 ⇒ x = - 4
Substitute these values into f(x) = - 2x + 19
f(4) = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )
f(- 4) = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )
Step-by-step explanation:
The area of a rectangle is 171 m²
Let l is the length and b is the width of the rectangle
It width is 10 m less than the length. So,
b = l-10 ...(1)
Area of a rectangle is given by :
or
l = 9 m or l = 19 m
If l = 9 m,
b = 9-10 = -1 m (can't be possible)
If l = 19 m
b = 19-10 = 9 m
So, the length an the breadth of the rectangle is 19 m and 9 m respectively.
<u>Answer:</u> 5 years!
<u>Reasoning:</u>
Year 1: 2700 x .70=1890
Year 2: 1890 x .70= 1323
Year 3: 1323 x .70= 926.1
Year 4: 926.1 x .70= 648.27
Year 5: 648.27 x .70=453.79
Use the identity:-
a^2 + b^2 = (a + b)^2 - 2ab
Plugging in the given values;-
a^2 + b^2 = 6^2 - 2*7 = 36-14 = 22 Answer
