A & B share the cost in a ratio of 3:2. A pays £125, how much does B pay?
1 answer:
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Answer
a. 28˚
b. 76˚
c. 104˚
d. 56˚
Step-by-step explanation
Given,
∠BCE=28° ∠ACD=31° & line AB=AC .
According To the Question,
- a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°
- b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚
thus , ∠ABC=76° .
- c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,
Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°
Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)
∠DAB = 180° - 107° ⇔ 73°
& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°
Now, In Triangle ADC Sum of angles in a triangle is 180°
∠ADC = 180° - (31° + 45°) ⇔ 104˚
- d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre
For Diagram, Please Find in Attachment
Answer:
The answer that gives the best estimate is (1,1)
Step-by-step explanation:
i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y
intercept or = -1. Therefore the equation for this line can be written as
y = x +
⇒ y =
x - 1 . It can also be seen from this graph that the
line passes through the point (2 , 2). Substituting these values for x and y
respectively we get 2 = 2 - 1 ∴
=
. The equation of the first line
can be written as y = x - 1 ⇒ 2y - 3x = -2
ii) As can be seen on the other line the intercept on the y axis is at (0,2). So
the y intercept or = 2. Therefore the equation for this line can be
written as y = x +
⇒ y =
x + 2 . It can also be seen from this
graph that the line passes through the point (1 , -1). Substituting these
values for x and y respectively we get 1 = 1 + 2 ∴
= -1 . The
equation of the second line can be written as y = - x + 2 or x + y = 2
iii) Solving the two equations of the two lines respectively as found in i) and
ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and
when we add this to equation in i) we get 5y = 4 which means that y = 0.8.
If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.
iv) Therefore we get the solution of the two lines, which is the intersection
of the two lines as (1.2, 0.8). So the answer that gives the best estimate
is (1,1)