Answer:
A)58cm
B)
C)125.55square cm
Step-by-step explanation:
AB is a line is symmetry
Total length of left half part=12cm+9cm+3cm+5cm
Total length of left half part=29 cm
Length of left half part=Length of right half part
Therefore, length of right half part=29 cm
A) Perimeter of the shape=29cm+29cm=58cm
B)
Pythagoras theorem

Hypotenuse=12 cm
Base=5+3=8cm
In triangle ADC
Now, using Pythagoras theorem




C)
Area of shape=Area of triangle+ area of rectangle
Area of shape=
Where l=9cm
breadth=3+3=6cm
h=
base=2(5)+3(2)=16cm
Area of shape=
Area of shape=125.55 square cm
1,800 socks
Johnny has 800 and John has 1000 more, so you would add the two numbers to get the answer of 1,800 socks.
4x + 7x = 33
11x = 33
x = 3
4x = 4(3) = 12
7x = 7(3) = 21
12 and 21 are how you split 33 in to a ratio of 4 to 7.
Answer:
The correct option is C.
C) ellipse, -30°
Step-by-step explanation:
General form of equation for a conic section is:
(A)x² + (B)xy + (C)y² + (D)x + (E)y + F = 0
The equation of the conic section is given:
21x² - (8√3)xy + 13y² = 225
21x² - (8√3)xy + 13y² - 225 = 0
Which can be rewritten as:
(21)x² + (-8√3)xy + (13)y² + (0)x + (0)y + (-225) = 0
where
A = 21
B = -8√3
C = 13
D = 0
E = 0
F = -225
Consult the table below.
As A ≠ C and and AC > 0 , the equation represents an ellipse
The angle of rotation can be found by following equation:
cot(2θ) = (A - C)/B
cot(2θ) = (21 - 13)/(-8√3)
2θ = cot⁻¹(8/-8√3)
2θ = 120°
θ = 60° (from x-axis)
As the major axis of ellipse lies on y-axis, axis of rotation from y-axis is
θ = -30°
You need to list the statements