Answer:
Step-by-step explanation:
If COP and TOD are vertical angles, then they are equal to each other because vertical angles are equal.
m COP = m TOD
Given
COP = 11x - 17
TOD = 9x + 11.
Substitute:
11x-17 = 9x+11
11x-9x = 11+17
2x = 28
x = 28/2
x = 14
Get <COD
<COP = 11(14)-17
<COP = 154-17
<COP = 137
<COD = 180-<COP
<COD = 180-137
<COD = 43°
Similarly:
<POT = 180 - <TOD
<POT = 180 - [9(14)+11]
<POT = 180 - 137
<POT = 43°
Answer:
tan(a) = -4/3
sec(a) = 5/3
Step-by-step explanation:
sine is opposite over hypotenuse. so no we have a triangle with a hypotenuse of 5 and an opposite side relative to some angle a of -4. the hypotenuse is never negative.
so draw a right triangle, mark one of the non right angles as a then the side opposite to that is -4 and the hypotenuse is 5. use the pythagorean theorem to find the remaining angle. The result could be positive or negative, but the questions specifically tells us we want the positive version.
b^2 + -4^2 = 5^2
b = 3
tangent is opposite over adjacent. for a we know the opposite is 3now so tan(a) = -4/3
Now, secant is 1/cos, so lets find cos(a)
cos is adjacent over hypotenuse, and we jsut found the adjacent is 3. so cos(a) = 3/5
Now 1/cos(a) = hypotenuse over adjacent so 5/3
Answer:
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
Step-by-step explanation:
The balance in the account is given by the following exponential expression,
Exponential growth formula is
Where P is the initial amount invested
r is the rate of interest
When we compare the formula with given expression , we can see that we have 125 in the place of P
So initial amount invested is $125
Now we find out 'r'
1+ r = 1.025
Subtract 1 on both sides
r= 0.025
To get percentage we multiply by 100
0.025 * 100 = 2.5%
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
11.94 = 6 pounds
11.94/6 = 1 pound
1 pound = 1.99
8 pounds = 1.99*8
8 pounds = $15.94
Answer:
32 muffins
Step-by-step explanation:
one cup of milk will make 32 muffins
you can set up a proportion of milk/muffins = milk/muffins
let 'x' = number of muffins made from one cup of milk
5/8 ÷ 20 = 1 ÷ x
cross-multiply to get 5x = 20(8)
5x = 160
x = 32
