Answer:
c. 108.4
Step-by-step explanation:
cos theta = (u dot v)/ (||u|| ||v||)
where dot stands for dot product and || || is the magnitude
u = (1,5) v= (7,-4)
u dot v = (1*7 + 5*-4) = 7-20 = -13
||u|| = sqrt( 1^2 +5^2) = sqrt(1+25) = sqrt(26)
||v|| = sqrt(7^2 + (-4)^2) = sqrt(49+16) = sqrt(65)
cos theta = -13/ sqrt(26) sqrt(65)
cos theta = -13 /sqrt(1690)
theta = arccos (-13/sqrt(1690))
theta = 108.43
Answer:
The total interest to pay back on the loan is $122.40
Step-by-step explanation:
Here. we want to get the amount of interest on the loan
We are going to use the compound interest formula here
A = P(1 + r/n)^nt
where A is the amount to be paid back
P is the amount borrowed called the principal which is $1,500
r is the interest rate which is 4% annually
This is same as 4/100 = 0.04
n is the number of times the interest will be compounded per year ; annually means yearly and so for this case, n = 1
t is the number of years = 2
So we have;
A = 1500(1 + 0.04/1)^(2)(1)
A = 1500(1.04)^(2)
A =$ 1,622.40
So the amount of interest is the difference between the amount borrowed and the value to pay back
That will be;
$1,622.40 - $1,500
= $122.40
Answer
x≤3/17 or x≥-10
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
substitute x = f(x) into g(x)
g(f(x))
= g(x² + 2)
= 4(x² + 2) - 1
= 4x² + 8 - 1
= 4x² + 7
