Answer:
the science fiction books and five mystery books in each package. This is because 6 is the highest common factor of both 48 and 30, and 6 x 8 = 48 and 6 x 5 = 30.
Answer:
x = 4
Step-by-step explanation:
Using cosine triangle formula, we know that;
c² = a² + b² - 2ac(cos C)
From our diagram;
a = 2x
b = x + 1
c = 7
C = 60°
Thus;
7² = (2x)² + (x + 1)² - 2(2x)(x + 1)cos 60
49 = 4x² + (x² + 2x + 1) - (4x² + 4x)(0.5)
49 = 5x² + 2x + 1 - 2x² - 2x
3x² + 1 - 49 = 0
3x² - 48 = 0
3x² = 48
x² = 48/3
x² = 16
x = √16
x = 4
To solve this problem, we need to know that
arc length = r θ where θ is the central angle in radians.
We're given
r = 6 (units)
length of minor arc AB = 4pi
so we need to calculate the central angle, θ
Rearrange equation at the beginning,
θ = (arc length) / r = 4pi / 6 = 2pi /3
Answer: the central angle is 2pi/3 radians, or (2pi/3)*(180/pi) degrees = 120 degrees
Answer:
To determine the common ratio of a geometric sequence. You just need to divide any two consecutive terms on it. You can see below that all of them have the same quotient.
1.2 / 1.5 = 0.8
0.96 / 1.2 = 0.8
0.768 / 0.96 = 0.8
.
Decimal form = 0.8
Fraction form = 4/5
.
Check:
1.5 x 0.8 = 1.2
1.5 x 4/5 = 6/5 = 1 1/5 = 1.2
Therefore, the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768 is 0.8 or 4/5.
The longest length of dowel will feet in the dimension that will give us the highest length of the hypotenuse;
given that the dimension of our box is:
15 by 20 by 30:
this will be given by:
c^2=a^2+b^2+c^2
c^2=15^2+20^2+30^2
c^2=225+400+900
c^2=1525
c=√1525
c=39.05 cm
Therefore the longest dowel will be 39 cm (to the nearest whole centimeter)<span />
