Solutions are 3 and - 5.
Step-by-step explanation:
Step 1:
Given equation is 3x² + 6x = 45. Factorize the equation to get the solutions.
⇒ 3x² + 6x - 45 = 0
⇒ x² + 2x - 15 = 0
⇒ x² + 5x - 3x - 15 = 0 (Product and Sum Method where product of coefficients = - 15 and sum = 2)
⇒ x (x + 5) - 3(x + 5) = 0
⇒ (x - 3)(x + 5) = 0
⇒ x = 3, - 5
9514 1404 393
Answer:
(9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Step-by-step explanation:
The area of the hexagon is given by the formula ...
A = (3/2)√3·s^2 . . . . for side length s
The area of the hexagonal face of this solid is ...
A = (3/2)√3·(2 ft)^2 = 6√3 ft^2
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The area of the circular hole in the hexagonal face is ...
A = πr^2
The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.
A = π(1 ft)^2 = π ft^2
Then the area of the "solid" part of the face of the figure is ...
A = (6√3 -π) ft^2
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The volume is ...
V = Bh . . . . . where B is the area of the base of the prism, and h is its height
V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3
Answer:
6
Step-by-step explanation:
The ordered pairs that satisfy the inequality are shown in the attachment. There are 6 of them.
<h3>
Answer: 100</h3>
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Explanation:
Let's add angle c to the diagram such that it's adjacent to angle b, and inside the quadrilateral. Notice how angle c is opposite the 100 degree angle of this inscribed quadrilateral.
For any inscribed quadrilateral, the opposite angles are supplementary
c+100 = 180
c = 180-100
c = 80
Angles b and c are supplementary as well, because they form a straight line.
b+c = 180
b+80 = 180
b = 180-80
b = 100
In short, angle b is the same measure as that 100 degree angle in the diagram.
