Answer:
Step-by-step explanation:
x = cost of drink
y = total cost
First information: "one large pizza and 3 medium drinks cost $21.96":
3a + b = 21.96
Second information: "one large pizza and 6 medium drinks cost $30.93":
6a + b = 30.93
{3a + b = 21.96
{6a + b = 30.93
{- 3a - b = - 21.96
{6a + b = 30.93
3a = 8.97
a = 2.99
3a + b = 21.96
3•2.99 + b = 21.96
8.97 + b = 21.96
b = 21.96 - 8.97
b = 12.99
Each drink costs $2.99 and each pizza costs $12.99. The linear function rule is:
y = 2.99x + 12.99
I hope I've helped you.
Step-by-step explanation:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ)
Multiply by the reciprocal:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)
(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]
(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]
Distribute and simplify:
(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)
[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)
(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)
Use Pythagorean identity:
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)
(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)
Factor:
(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))
(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))
(1 + sin θ) / cos θ
1. 2/100 as a percent is 2% and as a decimal it is 0.02
3. 9/10 as a percent is 90% and as a decimal it is 0.9
5. 48% as a decimal is 0.48 and as a fraction is 48/100
7. 0.04 as a percent is 4/100 and as a percent of is 4%
Hope I helped you
Follow PEMDAS.
You would first do your distributive property which is, -5(z+2). You would multiply -5 to z and -5 to 2 which will give you -5z + -10.
so now you have 2z-5z+ -10= -8 - 2z. Now you must isolate the variable. So subtract -8 to -10 which will give you -18.
Now you have the equation 2z-5z-18=-2z
Now combine like terms. 2z-5z= -3z
Now you have the equation -3z-18=-2z
Now you must move the -3z to the other side of the equal sign by adding the opposite which is +3z to -2z which will give you +1z
Now you have -18= 1z
Now you divide. -18 divided by 1 is -18.
So your final answer will be -18=z
