Answer:
29 miles
Step-by-step explanation:
a²+b²=c²
√a²+b² =c
√21²+20²=29
29miles
Answer:
The required explicit formula is A(n)= 4-4n
10th term of arithmetic sequence is (-36)
Step-by-step explanation:
Given arithmetic sequence is 8,4,0,-4,-8......
The arithmetic sequence is given by a,a+d,a+2d.......a+(n-1)d
Comparing both the sequence we get,
a=8 and a+d=4
For value of d:
d+a=4
d=4-8=(-4)
The explicit formula is given by : A(n)= a+(n-1)d
A(n)= a+(n-1)d
A(n)= 8+(n-1)(-4)
A(n)= 8-4n+4
A(n)= 4-4n
Therefore, The required explicit formula is A(n)= 4-4n
To find value of 10 th term:
Take n=10 in explicit formula
A(10)= 4-4(10)
A(10)= -36
Therefore, 10th term is (-36)
The length = 6W + 7. 2L + 2W = 70. This is a system of equations. To get L by itself in the second problem, -2W from both sides to get 2L = 70 - 2W. Divide by 2 to get L = 35 - W. Now put them together. 6W +7 = 35 - W. Add W to both sides to get 7W + 7 = 35. Subtract 7 from both sides to get 7W = 28. Divide 7 to both sides to get W = 4. Now replace W with 4. 6(4) + 7 = L. 24 + 7 = 31. The length is 31. To check, do the second equation. 2(31) + 2(4) = 62 + 8 = 70. Your answer is 31.
Answer:
$2000 is invested at 8%
$2000 is invested at 14%
Step-by-step explanation:
A total of $4000 is invested part at 8% and the remainder at 14%
Annual interest is $440.
Simple interest formula;
I = P × R × T
Where I is the interest, P is the principal, R is the rate and T is the time.
P = $4000
R = 8% and 14%
T = 1 year
I = $440
Let's say $a is invested at 8% and;
$b is invested at 14%
Then,
($a × 
× 1 ) + ($b × 
× 1) = $440
and
$a + $b = $4000
This forms a simultaneous equation;
0.08a + 0.14b = 440 ... (i)
a + b = 4000 ... (ii)
Multiplying (i) by 1 and (ii) by 0.08 we get;
0.08a + 0.14b = 440 ... (i)
0.08a + 0.08b = 320 ... (ii)
Subtracting (i) - (ii) we get;
0 + 0.06b = 120
0.06b = 120
b = 120 ÷ 0.06 = 2000
So amount invested at 14% ($b) = $2000 and,
The amount invested at 8% ($a) = $4000 - $2000 = $2000
