Answer:
4 1/2 tiles are needed to cover this area
Step-by-step explanation:
Mathematically, the area of a parallelogram is the product of the base and the height
We have this as;
24 * 10 = 240 cm^2
So the area of a tile is this
The number of tiles that will cover the given area will be;
1080/240 = 4.5 tiles
Is there supposed to be more of this question? Or is there supposed to be a graph?
Answer:
(0, 2 ) and (- 
, 
)
Step-by-step explanation:
Given the 2 equations
2x² + 4x - y = - 2 → (1)
x² + y = 2 → (2)
subtract x² from both sides in (2)
y = 2 - x² → (3)
Substitute y = 2 - x² into (1)
2x² + 4x - (2 - x²) = - 2
2x² + 4x - 2 + x² = - 2
3x² + 4x - 2 = - 2 ( add 2 to both sides )
3x² + 4x = 0 ← in standard form
x(3x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x = 0
3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = -
Substitute these values into (3) for corresponding values of y
x = 0 : y = 2 - 0² = 2 - 0 = 2 ⇒ (0, 2)
x = - : y = 2 - (- )² = 2 - 
= ⇒ ( - , )
This question requires us to use the cosine rule:
a^2 = b^2 + c^2 - 2bc*cos(A),
where A is the included angle between sides b and c, and a is the side of the triangle opposite to the angle.
In the context of the question, a is the length of the tunnel (let's call this t), b is 6 km, c is 7 km and A is 29°.
Given the values in the question and those we defined, we can rewrite the equation for the cosine rule as:
t^2 = 6^2 + 7^2 - 2(6)(7)cos(29)
Now, evaluating this we get:
t^2 = 36 + 49 - 84cos(29)
t^2 = 85 - 84cos(29)
t = sq.root (85 - 84cos(29))
= 3.40 km (rounded to two decimal places)
