Answer:
b = 9 ft
Step-by-step explanation:
Pythagorean Theorem:
a^2 + b ^2 = c^2
Given:
a = 12
b = ?
c = 15
Plug in values:
12^2 + b^2 = 12^2
Solve for b^2:
b^2 = 15^2 - 12^2
b^2 = 225 - 144
b^2 = 81
Take square root of both sides to find b:
sqrt(b^2) = sqrt(81)
b = 9
Hope this helps! :)
Let, the number = x
It would be: x * 0.135 = 57
x = 57 / 0.135
x = 422.23
Hope this helps!
sin^2 x + 4 sinx +3 3 + sinx
-------------------------- = -------------------
cos^2 x 1 - sinx
factor the numerator
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
cos^2 x 1 - sinx
cos^2 = 1-sin^2x
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
1- sin^2x 1 - sinx
factor the denominator
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
(1-sinx ) (1+sinx) 1 - sinx
cancel the common term (1+sinx) and (sinx +1)
(sinx +3) 3 + sinx
-------------------------- = -------------------
(1-sinx ) 1 - sinx
reorder the first term
3+sinx 3 + sinx
-------------------------- = -------------------
(1-sinx ) 1 - sinx
Name the first even integer you are looking for
. The next even number is
.
Their sum is
, so
. That means
, hence
.
So, the desired numbers are
and
.
Answer:
Principal Invested in Municipal Bonds is $16,000
Principal Invested in Corporate Bonds is $15,000
Step-by-step explanation:
If;
Principal Invested in municipal bonds = a
Principal Invested in corporate bonds = b
then we have;
a + b = $31,000
--------------------------------Equation 1
0.075a + 0.085b = $2,475 ---------------Equation 2
From equation 1 we have;
a = 31,000 - b
By putting the values of a in Equation 2 we get;
0.075 (31,000 - b) + 0.085b = 2,475
2,325 - 0.075b + 0.085b = 2,475
0.01b = 150
b = $15,000
By putting the values of b in equation 1 we get;
a = $16,000
