Find the measure of b, given m∠A = 38o m ∠ A = 38 o , m∠B = 74o m ∠ B = 74 o and a = 31.
1 answer:
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Answer:
B, C, E
Step-by-step explanation:
Elena’s aunt pays her $1 for each call she makes to let people know about her aunt’s new business. The table shows how much money Diego receives for washing windows for his neighbors.
Select all the statements about the situation that are true.
A. Elena makes more money for making 10 calls than Diego makes for washing 10 windows.
Elena:
$1 = 1 call
$10 = 10 calls
Diego:
27 windows = $30
10 windows = $x
Cross product
27*x = 30*10
27x = 300
x = 300/27
x = $11.11
Statement A not true
B. Diego makes more money for washing each window than Elena makes for making each call.
Diego:
10 windows = $11.11
Each window = $11.11/10
= $1.11
Statement B is true
C. Elena makes the same amount of money for 20 calls as Diego makes for 18 windows
Elena:
20 calls = $20
Diego:
18 windows = 18 × $1.11
= $19.98
Approximately $20 to the nearest whole dollar
Statement C is true
D. Diego needs to wash 35 windows to make as much money as Elena makes for 40 calls.
Diego
35 × $1.11 = $38.85
Approximately $39
Elena:
40 calls = $40
Statement D is not true
E. The equation y = x, where y is the number of dollars and x is the number of calls, represents Elena’s situation.
Statement E is true
Answer:
a. f(n) = n(n+1)/2
b. 351
c. 19
d. no; n would not be an integer for f(n) = 17.
Step-by-step explanation:
a. The terms are 1, 3, 6, 10, ...
Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.
When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.
For the polynomial ...
We can substitute values for n and f(n) to get 3 equations in 3 unknowns:
Solving these equations by your favorite method gives ...
(a, b, c) = (1/2, 1/2, 0)
That is, the function representing the relationship is ...
f(n) = n(n+1)/2 . . . . the function describing the relationship
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b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26
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c. The number of the term having 190 squares can be found by solving ...
n(n +1)/2 = 190
n(n +1) = 380 = 19(20)
The 19th term will have 190 squares.
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d. Terms 5 and 6 are 15 and 21.
17 is not the value of one of the terms in this sequence.