<h3>
Answer: 4(x - 1)(x^2 + x + 1)</h3>
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Work Shown:
4x^3 - 4
4(x^3 - 1)
4(x - 1)(x^2 + x + 1)
In the last step, I used the difference of cubes factoring formula which is
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
Answer:
Answer:
For converging lens
object distance u = - 2.0cm
Focal length f = 5.0cm
From lens formula
m=
m=
=3
Size of image = size of object x Magnification
= 2 x .10 = 2.0cm
For diverging lens
object distance u = 140 - 120 = 20 cm
focal length f = -30 cm
frac{1}{v}+\frac{1}{20}=-\frac{1}{30}
v = -12 cm
m = 12/20 = 0.6
size of final image = .6 x 30 = 18 cm
Answer:
14 in²; D.
Step-by-step explanation:
Hey!
To find the area of a trapezoid, we will add up both of the bases, divide by two, and then multiply the height.
In that case, we'll start by adding up 5 and 9.
5 + 9 = 14
.
7 × 2 (height) = 14.
Thus, the area of the given trapezoid is 
, or D.
Hope this helps!
Question 26)
Circumference = πD
To find the arc of a quadrant, divide the circumference by 4 = 1/4 πD
Diameter = Radius x 2 = 24 x 2 = 48
Circumference of the arc of the playground = 1/4 x π x 48 = 12π = 37.70 ft
Distance around the playground = arc + radius + radius
Distance around the playground = 37.7 + 24 + 24 = 85.70 ft (nearest hundredth)
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Answer: 85.70 ft
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