A direct variation suggest that the value of x in the equation would greatly affect the value of y such that when x is increasing, y also increases and the other way around. The equation for a direct variation is that,
y = kx
Substituting the given values in the ordered pair,
5 = k(4) ; k = 5/4
Step-by-step explanation:
cot x / (1 + csc x)
Multiply by conjugate:
cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)
Distribute the denominator:
cot x (1 − csc x) / (1 − csc²x)
Use Pythagorean identity:
cot x (1 − csc x) / (-cot²x)
Divide:
(csc x − 1) / cot x
Answer:
Elissa needs 4 quarts of paint, or 1 gallon.
Step-by-step explanation:
Elissa's room is in the shape of a rectangular prism. Assuming that she will only be painting the walls and not the floor or ceiling, you just need to calculate the area of the four walls - front and back and side to side. Based on the dimensions given, the area of Elissa's front and back walls are 8 ft x 9 ft or 72 ft² for each wall. Since there are two, we take that area times two: 72 x 2 = 144 ft².
Elissa's side walls are 8 ft x 13 ft or 104 ft² for each wall. Since there are two, we take this area times two: 104 x 2 = 208 ft².
To find the total area needed to paint, we add all four walls: 144 + 208 = 352 ft². Since a quart of paint covers 100 ft² and a gallon covers 400 ft², Elissa can either purchase 4 quarts of paint or 1 gallon to paint her bedroom.
Each student gets 2.5 cookies.
We know that there are 24 students there and 60 cookies, (since one ninth of 27 is 3 so 3 students are not there, and 24 are, and that 5 dozen is another way to write 60) we need to divide 60 by 24 which is 2.5.
Answer:
The solution of the given equations
x =4 , y = 1
Step-by-step explanation:
<u>Explanation</u>:-
<u>Step(l</u>):-
Given the system of equations -5x+13y = -7 ..(l)
5x+4y=24 ..(ll)
<u>Step(ll)</u>
Adding (l) and (ll) equations and cancelling '5x' terms we get
13y+4y = -7 +24
17y = 17
dividing '17' on both sides, we get
y=1
<u>Step(lll):-</u>
Substitute y=1 in equation (l) , we get
-5x+13y = -7
-5x + 13(1) = -7
subtracting '13' on both sides, we get
-5x +13 -13= -7 -13
-5x = -20
Dividing '-5' on both sides, we get
x = 4
<u>Conclusion</u>:-
The solution of the given equations
x =4 , y = 1
