Answer:
see explanation
Step-by-step explanation:
(a)
the sum of the 3 angles in the triangle = 180° , then
∠ A = 180° - 90° - 48° = 180° - 138° = 42°
(b)
using the tangent ratio in the right triangle
tan48° =
=
( multiply both sides by 10 )
10 × tan48° = y , then
y ≈ 11.1 units ( to the nearest tenth )
(c)
using the cosine ratio in the right triangle
cos48° =
=
( multiply both sides by x )
x × cos48° = 10 ( divide both sides by cos48° )
x =
≈ 14.9 units ( to the nearest tenth )
Answer:
![y=-1(x-2)^2+1](https://tex.z-dn.net/?f=y%3D-1%28x-2%29%5E2%2B1)
Step-by-step explanation:
The parabola has the vertex (2, 1) and goes through the point (4, -3).
We will use the vertex form, given by:
![f(x)=a(x-h)^2+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%5E2%2Bk)
Where (h, k) is the vertex and a is the leading coefficient.
Line 1)
So, by substitution:
![\text{Vertex}=(h,k)=(2,1)\Rightarrow y=a(x-2)^2+1](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%28h%2Ck%29%3D%282%2C1%29%5CRightarrow%20y%3Da%28x-2%29%5E2%2B1)
Lines 2-4)
Since (4, -3) is a point, y = -3 when x = 4:
![-3=a(4-2)^2+1](https://tex.z-dn.net/?f=-3%3Da%284-2%29%5E2%2B1)
![-3=a(2)^2+1](https://tex.z-dn.net/?f=-3%3Da%282%29%5E2%2B1)
![-4=4a\Rightarrow a = -1](https://tex.z-dn.net/?f=-4%3D4a%5CRightarrow%20a%20%3D%20-1)
Line 5)
By substitution, we acquire our equation*:
![y=-1(x-2)^2+1](https://tex.z-dn.net/?f=y%3D-1%28x-2%29%5E2%2B1)
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of ∠1 is 30°, while the measure of ∠2 is 60°.
<h3>What are Complementary Angles?</h3>
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
Since the two angles together form a 90° angle. The angles are complementary to each other, therefore, we can write,
∠1 + ∠2 = 90°
x + x + 30 = 90°
2x = 60°
x = 30°
Thus, the measure of the angles can be written as,
∠1 = x = 30°
∠2 = x+30° = 60°
Hence, the measure of ∠1 is 30°, while the measure of ∠2 is 60°.
Learn more about Complementary Angles:
brainly.com/question/5708372
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Answer:
120 nails.
Step-by-step explanation:
80 x 1.5 = 120.
80 x 1 = 80
80 x 0.5 = 40
80 + 40 = 120
$81.60
( 20% of $68 is 13.60, so you add $68 and $13.60 and it’s $81.60 )