9514 1404 393
Answer:
21.8 cm
Step-by-step explanation:
A useful way to write the Law of Sines relation when solving for side lengths is ...
a/sin(A) = b/sin(B)
Then the solution for 'a' is found by multiplying by sin(A):
a = sin(A)(b/sin(B)) = b·sin(A)/sin(B)
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We need to know the angle A. Its value is ...
A = 180° -75° -31.8° = 73.2°
Then the desired length is ...
a = (22 cm)sin(73.2°)/sin(75°) ≈ (22 cm)(0.9573/0.9659)
a ≈ 21.8 cm
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I like to use the longest side and largest angle in the equation when those are available. That is why I chose 75° and 22 cm.
Answer:
vertex = (3, 4 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = - (x - 3)² + 4 ← is in vertex form
with (h, k ) = (3, 4 ) ← vertex
To find the zeros set the factors on the numerator equal to zero and solve
(x - 1) = 0 x = 1
(x + 1) = 0 x = -1
Answer:
Add 1 to each side
Multiply each side by 4
Take the square root of each side
Subtract 5 from each side
Combine terms
Step-by-step explanation:
1/4(x+5)^2-1=3
Add 1 to each side
1/4(x+5)^2-1+1=3+1
1/4(x+5)^2=4
Multiply each side by 4
4*1/4(x+5)^2=4*4
(x+5)^2=16
Take the square root of each side
sqrt((x+5)^2)=±sqrt(16)
x+5 = ±4
Subtract 5 from each side
x+5-5 = -5 ±4
x = -5 ±4
Combine terms
x = -5+4 x = -5-4
x = -1 x = -9
Answer:
a= -2
b= 1
c= 5
b^2-4ac= 41
The quadratic function will have 2 real number zeros
Step-by-step explanation:
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