Answer:
x = 28
m∠ACD = 68°
Step-by-step explanation:
∠BAE ≅∠DAC because they are vertical angles
∠ACD = 180 - 124 = 56°
to find 'x': 56 + 2x + (180 - 4x) = 180
236 - 2x = 180
-2x = -56
x = 28
m∠ACD = 180 - 4(28) = 180 - 112 = 68°
Answer:
Step-by-step explanation:
cuz 7 is greater then 5
When setting up the equation you have the initial fee and the hourly fee. The hourly fee is what must be multiplied by the number of hours which is our unknown
Using cos addition formula:
use x for theta
cos(x+π/6)=cosx*cos(π/6)-sinx*sin(π/6)
sinx=1/4
cosx=√15/4
cos(π/6)=√3/2
sin(π/6)=1/2
cos(x+π/6)=(√15/4*√3/2)-(1/4*1/2)
cos(x+π/6)=(√45/8)-(1/8 )
cos(x+π/6)=(√45-1)/8)
STEP 1:
determine equations needed
x= # of $10 tickets
y= # of $14 tickets
QUANTITY EQUATION
x + y= 800
COST EQUATION
$10x + $14y= $9,040
STEP 2:
multiply quantity equation by -14
-14(x + y)= -14(800)
-14x - 14y= -11,200
STEP 3:
add new quantity equation in step 2 to cost equation of step 1 to solve for x using elimination
-14x - 14y= -11,200
10x + 14y= 9040
y term cancels out
-4x= -2160
divide both sides by -4
x= 540 ten dollar tickets
STEP 4:
substitute x value in step 3 into either original equation
x + y= 800
540 + y= 800
subtract 540 from both sides
y= 260 fourteen dollar tickets
ANSWER: There were 540 $10 tickets and 260 $14 tickets sold.
Hope this helps! :)
