The formula for arithmetic sequence is given by:
an=a+(n-1)d
where:
an=nth term
a=first term
n=number of terms
thus our first term will be:
a1=8
a2=8+(2-1)(-6)=2
a3=8+(3-1)(-6)=-4
a4=8+(4-1)(-6)=-10
a5=8+(5-1)(-6)=-16
a5=-16
thus the sequence will be:
8,2,-4,-10,-16...
Answer:
The balance after four years is $1129.27
Step-by-step explanation:
The formula for compound interest, including principal sum, is 
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit or loan amount)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
∵ $800 is deposited in an account
∴ P = 800
∵ The account pays 9% annual interest
∴ r = 9% = 9 ÷ 100 = 0.09
∵ The interest is compounded annually
∴ n = 1
∵ The time is 4 years
∴ t = 4
- Substitute the values of P, r, n, and t in the formula above
∵ 
∴ 
∴ A = 1129.265
∴ The balance after four years is $1129.27
Answer:
x= 2 and y= -1
Step-by-step explanation:
x=7 +5y
14+16y=−2
y=−1
Substitute y=-1y=−1 into x=7+5yx=7+5y.
x=2
Answer:
The ratios of the sides of a right triangle are called trigonometric ratios. We need to use trigonometric functions to find them when we don't have any angle other than 90 degree shown.
Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle.
However when we have one angle given with the 90 degree we can deduct without trigonometry but we would use all angles to find the hypotenuse or all angles to find the side of a right angle.
Alternatively, we cna do this with one given angle but if we have one, we might as well work out the other one without trigonometry and do a division with Sin = 25 (sin 35) sin 90 / sin 55
is one example when given the base 25ft that would find the hypotenuse or the length of elevation for buildings looking down or zip-wire questions.
Step-by-step explanation:
A
| \
l \
4cm| \ 5cm
| \
| \
B | - - - - \ C
3cm
Suppose we wanted to find sin( A) in△ABC
(The height of the wall in elevation questions would be used above the base shown 3cm at the start) Sin = 3 (sin 35)° sin 90° / sin 55° to find the height side (4).
Sine is defined as the ratio of the opposite to the hypotenuse
sin(A) = hypotenuse = AB/BC = 3/5
/ opposite
Answer:
Step-by-step explanation:
Given
Points:
Required
Determine the equation of line that is perpendicular to the given points and that pass through 
First, we need to determine the slope, m of FG
Where
--- 
--- 
The question says the line is perpendicular to FG.
Next, we determine the slope (m2) of the perpendicular line using:
The equation of the line is then calculated as:
Where
Multiply through by 2
Add x to both sides
Hence, the line of the equation is
