Answer:x=1/24
Step-by-step explanation:
To find 9x(x+6)-(3x+1)^2=1
Open the brackets
9x^2+54x-(3x+1)(3x+1)=1
9x^2+54x-(9x^2+6x+1)=1
9x^2+54x-9x^2-6x-1=1
54x-6x-1=1
Collect like terms
48x=1+1
48x=2
Divide through by 48
x=2/48
x=1/24
Answer:
H < 8
Step-by-step explanation:
-9+6h>39
Add 9 to the -9 and the 39
6h>48
Divide the 6 and the 48 by 6, then flip the > to a <
h = 8
I hope this helps you out!
Answer:
Assuming that 
is a diameter.
Given that 
And that point O is the center of the circle
Explanation:
Because angle AOB is subtended by arc AB from point O.
Arc AB is equal to the measure of that angle.
Since arc ABC is subtended by the diameter, the arc is 180°.
Answer:
a) 3.507
b) 75.48
c) 78.41
Step-by-step explanation:
Problem A
The opposite side of the angle and the hypotenuse are involved in the question. Therefore you will be using the sine.
sin(26) = x / 8 Multiply both sides by 8
8*sin(26) = x Sin(26) = 0.4384
8*0.4384 = x Do the multiplication
3.507 = x
Problem B
The side adjacent and the hypotenuse are used in this problem. The angle is given, so you are working with the cosine.
Cos(58) = adjacent / hypotenuse
Cos(58) = 0.5299
0.5299 = 40/x Multiply both sides by x
0.5299 x = 40 Divide both sides by 0.5299
x = 40 / 0.5299
x = 75.48
Problem C
The opposite side and the adjacent side are involved and the angle is given.
Tan(71) = opposite / adjacent
tan(71) = 2.904
2.904 = x / 27 Multiply both sides by 27
2.904 * 27 = x Combine
x = 78.414
Answer: $5100
Step-by-step explanation:
Given, The prize money starts at $20 for the first question.
Let a= 20,
Also, Each question is tougher than the one before it, and the station doubles the prize money from the previous amount.
i.e. the sequence prize willbe : $20 , 2 x ($20) , 2² x ($20)x ....
That is its is an geometric progression with the common ratio r= 2,
Since the sum of n terms in GP is given by :-
So the total money will it hand out in prizes after 8 questions would be :
Hence, the total money it will hand out in prizes = $5100
