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Katena32 [7]
3 years ago
7

1 . a sequence in which a fixed amount is added on to get the next term arithmetic sequence 2 . an individual quantity or number

in a sequence common difference 3 . a set of numbers that follow a pattern, with a specific first number sequence 4 . the fixed amount added on to get to the next term in an arithmetic sequence term
Mathematics
1 answer:
Dmitry [639]3 years ago
6 0
T_n = a_1 + d(n-1)

If a = 4 and d = 3,

T_n = 4+ 3(n-1)

T_n = 4+ 3n-3

T_n = 3n + 1

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Answer: The general equation for the nth term is 3n + 1.
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Find the value of y.
Leno4ka [110]

Answer:

\sqrt{55}

Step-by-step explanation:

Based off of what we do know, if we can find length DB we can use the pythagorous theorem (I will be assigning the variable z)

x^{2} =36+z^{2} \\\\y^{2}=25+z^2\\\\x^{2} +y^2=121\\\\

First equation is for triangle ABD

Second is for BCD

And the last one is for ACD

Substitute x^{2} and y^2

36+z^2+25+z^2=121\\\\61+2z^2=121\\\\2z^2=60\\\\z^2=30\\\\z=\sqrt{30}

As discovered before

y^2=25+z^2\\\\y^2=25+30\\\\y^2=55\\\\y=\sqrt{55}

8 0
3 years ago
On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph t
natulia [17]

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway d_1 = 60 mph

Let the time taken to travel on highway = t_1 hours

Distance traveled = 60t_1 miles

Speed in the city = 40 mph

Let the time taken = t_2 hours

Distance traveled in the city = 40t_2 miles

Speed on the construction = 20 mph

Let the time spend on the construction = t_3 hours

Distance traveled on the construction = 20t_3 miles

Since, total distance covered = 380 miles

d_1+d_2+d_3=60t_1+40t_2+20t_3

He spends one half the time on the highway as he does on the construction,

t_3=2t_1

Total time spent in the trip = 11 hours

Therefore, t_1+t_2+t_3=11

t_1+t_2+2t_1=11

t_2=11-3t_1

From equation (1),

60t_1+40(11-3t_1)+20(2t_1)=380

60t_1-120t_1+40t_1+440=380

440-20t_1=380

20t_1=440-380

t_1=\frac{60}{20}

t_1=3 hours

t_2=11-3t_1=2 hours

t_3=2t_1=6 hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

3 0
3 years ago
A city manager made a scatter plot of the number or retail store in a certain city over the years. the scatter plot had a trend
Fiesta28 [93]

Answer:

155

Step-by-step explanation:

The problem sounds complicated, but it's not. Let's analyse.

The city manager have come up with an equartion y=11x +12, with Y is the total number of the stores and X stands for how long it has been since 2003.

We can't explain how the manager came up with this equation, so iwe don't need to think of if the equation is real or not. Let's just base on what we have.

Because the equation aboce is a trendy line, it means that it would likely to be true with any X ( number of years since 1990).

In Tracy's case, the year is 2003, so it has been 2003 - 1990 = 13 years since 1990. This is the X in the equation. Now we only need to find Y in the equation, which is the number of retail stores there were in 2003, exactly what the problem asks.

y= 11x + 12

=> In Tracy's case: y= 11*13 + 12= 155

So the number of retail stores there were in 2003 was 155

5 0
3 years ago
What Is 9+10? Please Tell Me. Is It 19 Or 21!?
mrs_skeptik [129]
9+10=19
proof, 9=1 plus 1 9 times (to lazy to write it out)
10=1 plus 1 10 times(to lazy)
so 1+1+1+1+1+1+1+1+1 + 1+1+1+1+1+1+1+1+1+<span>1 = 19</span>
5 0
3 years ago
Read 2 more answers
Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared
alisha [4.7K]

Answer:

The least squares method results in values of the y-intercept and the slope, that minimizes the sum of the squared deviations between the observed (actual) value and the fitted value.

Step-by-step explanation:

The method of least squares works under these assumptions

  • The best fit for a data collection is a function (sometimes called curve).
  • This function, is such that allows the minimal sum of difference between each observation and the expected value.
  • The expected values are calculated using the fitting function.
  • The difference between the observation, and the expecte value is know as least square error.
7 0
3 years ago
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