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
x(t) = 20t
y(t) = 40t - 5t^2
Since we are only interested in comparing the two at time t = 5 seconds, we plug in 5 everywhere we see the variable t and then compare x and y
x(5) = 20(5) becomes x(5) = 100
y(5) = 40(5) - 5(5)^2 becomes y(5) = 200 - 125 and then y(5) = 75
The ratio of y to x can be expressed as: y/x, so we can say the ratio is equal to 75/100 or 0.75
Answer: 0.75
ok so for the 2 ft pillows the perimeter would be 8 ft and for the 1 ft pillows the perimeter would be 3 ft. So you would need 8(2)+3(3)=16+9=25 so she needs 25 feet of trimming.
Let
x---------> amount of money saved by Mark
x---------> amount of money saved by Neil
we know that
x=y+258-------> equation 1
x/y=(7/4)-------> equation 2
substitute equation 1 in equation 2
(y+258) /y=7/4--------> 4*(y+258)=7*y------> 4y+1032=7y
7y-4y=1032--------> 3y=1032------> y=$344
x=344+258------>x=$602
the answer is
$602
You mulitply 25 by .2 to get 5 and you add that to 25 to get $30