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kakasveta [241]
3 years ago
9

What Is the nth term ruld of the quadratic sequence -5,-4,-1,4,11,20,31

Mathematics
1 answer:
nordsb [41]3 years ago
3 0
-5   - 4    -1    4     11    20    31   subtracting:-
   1       3     5    7      9      11      subtractiing:-    
       2      2     2    2      2

second row is 2 so the rule will contain n^2

so we can write the series as n^2 - 6 , n^2 - 8 , n^2 - 10 etc

the  numbers are in arithmetical sequence with  a1 = 6 and d = -2

so nth term  of our sequence is n^2 - a1 + (n - 1)d = n^2 -2n - 6 + 2
  
  = n^2 - 2n - 4   Answer
 
 
 
     
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A 5 mile jogging path diagonal divides a rectangular park in half. The park is 4 miles long. Find the width of the park.
levacccp [35]

Answer:  The required width of the park is 3 miles.

Step-by-step explanation:  Given that a 5 mile jogging path diagonal divides a rectangular park in half and the park is 4 miles long.

We are to find the width of the park.

As shown in the attached figure below, the diagonal BD divides the rectangle ABCD into two equal parts,

where length DA = 5 miles, BD = 4 miles and AB = width = ?

Since each angle of a rectangle is right-angle, so triangle ABD will be a right-angled triangle.

Using Pythagoras theorem in triangle ABD, we have

BD^2=AB^2+DA^2\\\\\Rightarrow AB=\sqrt{BD^2-DA^2}\\\\\Rightarrow AB=\sqrt{5^2-4^2}\\\\\Rightarrow AB=\sqrt{25-16}\\\\\Rightarrow AB=\sqrt{9}\\\\\Rightarrow AB=3.

Thus, the required width of the park is 3 miles.

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3 years ago
Drag each rational number to the correct location on the table.
andrey2020 [161]

Answer:

Step-by-step explanation:

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3 years ago
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Landon owns a hybrid SUV that can travel 400 miles on a 15 gallon tank of gas. Determine how many miles he can travel in 6 gallo
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Set this up as a proportion.

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3 years ago
1. What is an equation of a line, in point-slope form, that passes through (1,-7) and has a slope of -2/3?
Nookie1986 [14]

1. What is an equation of a line, in point-slope form, that passes through (1,-7) and has a slope of -2/3?


Point Slope form y − y1 = m(x − x1)


Y1: -7 x1:1 slope :-2/3


Y-(-7)=-2/3(x-1)

Y+7=-2/3(x-1)


2. What is the equation of a line, in point-slope form, that passes through (-2,-6) and had a slope of 1/3?


Y-(-6)=1/3(x-(-2))


Y+6=1/3(x+2)



3.What is an equation in point-slope form of the line that passes through the points (4,5) and (-3,-1)


SlopeM: =change in y/change in x

M= -1-5/-3-4

M= -6/-7

M=6/7


So now slope:6/7, point (4,5)

Y-y1=m(x-x1)

Equation in point slope

Y-5=6/7(x-4)



6 0
4 years ago
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