You are choosing between two plans at a discount warehouse. plan a offers an annual membership fee of $ 90and you pay 30 %of the manufacturer's recommended list price. plan b offers an annual membership fee of $ 40and you pay 80 %of the manufacturer's recommended list price. how many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? what will be the cost for each plan?

Step-by-step explanation:

We have 2 linear equations, and in both, the amount of merchandise you would have to purchase is "x", the unknown.  We are asked to find that value of x.

The first equation is

C(x) = .30x + 90, which says that the cost of this plan is a fixed $90, and you pay 30% of the manufacturer's cost, x.

The second equation is

C(x) = .80x + 40, which says that the cost of this plan is a fixed $40, and you pay 80% of the manufacturer's cost, x.

If we want to know when the cost of these 2 are equal to each other, we set the equations equal to each other and solve for x:

.3x + 90 = .8x + 40 so

-.5x  = -50 so

x = $100

The cost for each plan will be the same at this value of x, but we will plug in 100 for x in each just to make sure we did it right:

C(100) = .3(100) + 90

C(100) = 30 + 90

C(100) = 120  and

C(100) = .8(100) + 40

C(100) = 80 + 40

C(100) = 120

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841