Answer:Please see answer in explanation column
Step-by-step explanation:
A
The sum of a number and 7 is not more than 10
Given answer: x + 7 < 10 , This is false
Reason :Not more than 10 means at most 10, less than or equal to 10 , " or " not greater than 10 "and therefore the correct inequality is written as
x + 7 ≤ 10
B
The product of a number and 4 is at least 20
Given answer: 4X > 20 ---- False
Reason :At least 20 means at no less than 20 " or " greater than or equal to 20 therefore the correct inequality is written as
4X ≥ 20
C
The difference between a 15 and a number is at most 12
Given answer: 15-x>12----False
Reason :At most 12 means " no more than 12 , " " less than or equal to 12 , " or " not greater than 12"therefore the correct inequality is written as
15-x ≤ 12
D
The quotient of a number and 8 is greater than or equal to
Given answer 8x <3 --False
Reason : It clearly stated greater than or equal to 3. Therefore the correct inequality is 8x ≥ 3
Answer: a) H = h( 0.5 )^n
b) H = 1.125inches
Step-by-step explanation:
Let H = height of the ball
n = number of time the ball bounces
h = initial height.
The exponential function to model the height of the ball will be:
H = h( 1 - 0.5)^n
H = h( 0.5 )^n
It's minus because the height of the ball is decreasing.
h = 36 inches
n = 5
H = 36( 1 - 0.5 ) ^5
H = 36( 0.5 )^5
H = 36 × 0.03125
H = 1.125inches
x + y = 53
x -y = 9 Adding both equations
2x = 62
x = 31 y = 22
cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>)
So if both cot(<em>θ</em>) and cos(<em>θ</em>) are negative, that means sin(<em>θ</em>) must be positive.
Recall that
cot²(<em>θ</em>) + 1 = csc²(<em>θ</em>) = 1/sin²(<em>θ</em>)
so that
sin²(<em>θ</em>) = 1/(cot²(<em>θ</em>) + 1)
sin(<em>θ</em>) = 1 / √(cot²(<em>θ</em>) + 1)
Plug in cot(<em>θ</em>) = -2 and solve for sin(<em>θ</em>) :
sin(<em>θ</em>) = 1 / √((-2)² + 1)
sin(<em>θ</em>) = 1/√(5)
Answer:the volume of a prism is the area of the base times the height of the prism. The volume of the pyramid has the same base area and height as the prism, but with less volume than the prism. The volume of the pyramid is one third the volume of the prism.
Step-by-step explanation:
i hope this helps
