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marshall27 [118]
3 years ago
6

Select THREE expressions equivalent to –81x + 27.

Mathematics
1 answer:
Ivahew [28]3 years ago
5 0

Answer:

A, C, and D

Step-by-step explanation:

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rollercoaster can accommodate 1600 passengers per hour. If you are number 346 in line, how many minutes do you have to wait?
Effectus [21]

Answer:

13.31 minutes  

Step-by-step explanation:

800 in 30min

400 in 15 min

26 passengers in an min

346/26

13.31 minutes  

8 0
3 years ago
Tan x + sqrt(3) = - 2 tan x
Svet_ta [14]

9514 1404 393

Answer:

  nπ -π/6 . . . for any integer n

Step-by-step explanation:

  tan(x) +√3 = -2tan(x) . . . . . given

  3tan(x) = -√3 . . . . . . . . . . . add 2tan(x)-√3

  tan(x) = -√3/3 . . . . . . . . . . divide by 3

  x = arctan(-√3/3) = -π/6 . . . . use the inverse tangent function to find x

This is the value in the range (-π/2, π/2). The tangent function repeats with period π, so the set of values of x that will satisfy this equation is ...

  x = n·π -π/6 . . . . for any integer n

8 0
2 years ago
I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP
aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

  • 0+1 = 1
  • 1+3 = 4
  • 3+6 = 9
  • 6+10 = 16
  • 10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

==========================================================

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

8 0
2 years ago
PLEASE HELP!! 25 POINTS !!! Graphing
Sunny_sXe [5.5K]
A = 6, 2
B = 3, 4
C = -10, 3
D = -4, 5
E = -5, -3
F = -4, -2
G = 3, -8
4 0
2 years ago
Read 2 more answers
Find mzP<br><br> A 50<br> B. 60<br> C. 70<br> D. 120
marishachu [46]

Answer:

d.120

Step-by-step explanation:

p=70

m=120

z=120

8 0
3 years ago
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