Answer:
(x + 3) ( x - 6)
Step-by-step explanation:
x² - 3x - 18
x² - 6x + 3x - 18
x(x - 6) + 3(x - 6)
(x + 3) ( x - 6)
7 = 3/4 (3) + c
28 = 9 + 4c
4c = - 19
c = - 19/4
y = 3/4x - 19/4
5 = 3/4x - 19/4
3/4x = 39/4
x = 13
Answer:


Step-by-step explanation:
Figure of cone is missing. See attachment
Given
Radius, R = 2m
Let L = KL=LM=KM
Required:
Volume, V and Surface Area, A
<u><em>Calculating Volume</em></u>
Volume is calculated using the following formula

Where R is the radius of the cone and H is the height
First, we need to determine the height of the cone
The height is represented by length OL
It is given that KL=LM=KM in triangle KLM
This means that this triangle is an equilateral triangle
where OM = OK = 
OK = 
Applying pythagoras theorem in triangle LOM,
|LM|² = |OL|² + |OM|²
By substitution
L² = H² + (
)²
H² = L² -
²
H² = L² (1 -
)
H² = L² 
H² = 
Take square root of bot sides


Recall that 




in terms of
an d L where L = KL = LM = KM
<u><em>Calculating Surface Area</em></u>
Surface Area is calculated using the following formula


)
)





Answer:
(48.106 ; 53.494)
Step-by-step explanation:
Given the data:
X : 52 48 49 52 53
Sample mean = ΣX / n
n = 5
Sample mean, xbar = 254 / 5 = 50.8
Standard deviation, s = 2.17 (using calculator)
The standard error (SE) : s/√n =2.17/√5 = 0.970
The degree of freedom, df = n-1
df = 5 - 1 = 4
Tscore(0.05, 4) = 2.776
Confidence interval :
Xbar ± Tscore*standard error
50.8 ± (2.776 * 0.970)
50.8 ± 2.694
Lower boundary = 50.8 - 2.694 = 48.106
Upper boundary = 50.8 + 2.694 = 53.494
(48.106 ; 53.494)
Answer:
(2, 1)
Step-by-step explanation:
A line that passes through the origin and has a slope of 1/2 can be best represented as y = 1/2x
it starts at the origin
goes 2 units to the right
1 unit above
2 units to the right + 1 unit above = (2, 1)
Final Answer: (2, 1)