The lunch menu at Sue's Café allows the customers to choose one option from the soups & salads, one option from the entrées, and one option from the beverages. The table shows the options and their abbreviations.
Soups & Salads Entrées
Clam Chowder (C) Burger (B)
Daily Soup (D) Lasagna (L)
House Salad (H) Mac & Cheese (M)
Beverages
Soda (s)
Tea (1)
Which list shows all the possible lunch combinations for Sue's Café?
O A. C, D, H, B, L, M, S, T
O B. CB, CL, CM, CS, CT,
DB, DL, DM, DS, DT,
HB, HL, HM, HS, HT
O C. CDH, BLM, ST
O D. CBS, CBT, CLS, CLT, CMS, CMT,
DBS, DBT, DLS, DLT, DMS, DMT,
HBS, HBT, HLS, HLT, HMS, HMT

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: