Let the medium angle be B degrees
the small angle be A degrees
the large angle be C degrees
Then
C = 2 B + 20 ..................X
5 B = A + C ..................Y
Sum of all angles
A + B + C = 180 .............Z
Applying Y in Z
5 B + B = 180
6 B = 180
B = 30
From X C = 2 x 30 + 20 = 60 + 20 = 80
From Y 5 x 30 = A + 80
150 = A + 80
150 - 80 = A = 70
Hence medium angle B = 30 degrees
the small angle A = 70 degrees
the large angle C = 80 degrees
Every 56 seconds, the radioactive substance is divided in half.
224 / 56 = 4
We need to cut the substance in half 4 times.
896 / 2 = 448
448 / 2 = 224
224 / 2 = 112
112 / 2 = 56
After 224 seconds, there will be 56 grams of the radioactive substance left over
Answer:
Let the width of the Rectangle be x inches
Then, length is (3x-5) inches
Perimeter of the Rectangle= 46 inches (given)
According to the above problem,
Equation :---- Perimeter=2(length+breadth)
<u>2{(3x-5)+x}=46</u>
2(4x-5)=46
(4x-5)=46/2=23
4x=(23+5)=28
x=28/4
<u>x=7</u>
So, length of the Rectangle is {(3×7)-5}=16 inches
and width is= 7 inches
Answer:
x = 12
m(QS) = 52°
m(PD) = 152°
Step-by-step explanation:
Recall: Angle formed by two secants outside a circle = ½(the difference of the intercepted arcs)
Thus:
m<R = ½[m(PD) - m(QS)]
50° = ½[(12x + 8) - (4x + 4)] => substitution
Solve for x
Multiply both sides by 2
2*50 = (12x + 8) - (4x + 4)
100 = (12x + 8) - (4x + 4)
100 = 12x + 8 - 4x - 4 (distributive property)
Add like terms
100 = 8x + 4
100 - 4 = 8x
96 = 8x
96/8 = x
12 = x
x = 12
✔️m(QS) = 4x + 4 = 4(12) + 4 = 52°
✔️m(PD) = 12x + 8 = 12(12) + 8 = 152°
