Answer:4x>2+3x+5
Step-by-step explanation:
12x>3+8x>2+9x>2+21x+10
12x>3+8x>2+9x>2+6x+15×10
4x^2(3x+2)+9x^2×6x
4x^2(3x+2)+3x(3x+2)+15x+10
4x^2(3x+2)3x(3x+2)+5(3x+2)
Cancel
3x+2(4×^2+3x+5)
_____________
3x+2
4x^2+3x+5
Answer:
Dimension => 10 m × 9.6 m
Step-by-step explanation:
From the question given above, the following data were obtained:
Area (A) = 96 m²
Circumference (C) = 39.2 m
Dimension =.?
Next, we shall determine the Lenght and breadth of the rectangle. This can be obtained as follow:
Let L be the Lenght
Let B be the breadth
Area of a rectangle = L × B
96 = L × B ..... (1)
Circumference of rectangle = 2(L + B)
39.2 = 2(L + B) .... (2)
From equation 2, make L the subject
39.2 = 2(L + B)
Divide both side by 2
39.2 /2 = L + B
19.6 = L + B
Rearrange
L = 19.6 – B ....(3)
Substitute the value of L in equation 3 into equation 1
96 = L × B
L = 19.6 – B
96 = (19.6 – B ) × B
Clear bracket
96 = 19.6B – B²
Rearrange
B² – 19.6B + 96 = 0
Solving by factorisation
B² – 10B – 9.6B + 96 = 0
B(B – 10) – 9.6(B – 10) = 0
(B – 9.6)(B – 10) = 0
B – 9.6 = 0 or B – 10 = 0
B = 9.6 or B = 10
Substitute the value of B into equation 3:
L = 19.6 – B
B = 9.6
L = 19.6 – 9.6
L = 10
Or
L = 19.6 – B
B = 10
L = 19.6 – 10
L = 9.6
Since the length is always longer than the breadth,
Length (L) = 10 m
Breadth (B) = 9.6 m
Finally, we shall determine the dimension of the rectangle. This can be obtained as follow:
Length (L) = 10 m
Breadth (B) = 9.6 m
Dimension =?
Dimension = L × B
Dimension = 10 m × 9.6 m
Answer:
a) m arc AD = 145
b) D = 10
Step-by-step explanation:
a) mAD can be found because triangle OCM can be shown to be congruent to triangle ODM.
The angle AOD is supplementary to DOB which we just showed to be congruent to the known 35° angle COB. Therefore AOD = 180 - 35 = 145°
The arc length is identical to the arc angle when measured between radii.
b) The radius OC = √(OM² + (CD/2)² = √(3² + 4²) = 5.
Diameter is twice radius = 10
L = -4,4
E = -2, -3
N = 2,1
I = 4,3
E = 1,3
-18 +15x = y
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