under his eye. praise be. i welcome u to geometry land

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 ...

  [tex]f(n)=an^2+bn+c[/tex]

We can substitute values for n and f(n) to get 3 equations in 3 unknowns:

  [tex]1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c[/tex]

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

__

b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26

__

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.

__

d. Terms 5 and 6 are 15 and 21.

17 is not the value of one of the terms in this sequence.

Answer:

=2574+1287i

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a Geometric System, describe how postulates differ from theorems. Postulates are statements that require proof, while theorems cannot be proven.

Answer:

Exact Form:

x = √ 3 , − √ 3

Decimal Form:  x = 1.73205080 … , − 1.73205080 …

Step-by-step explanation:

Answer:350 Trouts

Step-by-step explanation:To determine the number of trouts the conservationist expect to be in the lake, you add 120+120 that equal to 240.Then you add 240+40 that equals to 284.Then you add 284+44 that equals to 328.Then you add 328+11 that equals to 339.Finally, you add 339+11 to get your answer:350.

Answer:

(x+1)(x-1)(x-5)

The roots are 1, -1, 5

Step-by-step explanation:

x³-5x²-x+5

(x³-5x²) - (x-5)

x²(x-5) - (x-5)

(x²-1)(x-5)

(x+1)(x-1)(x-5)

The roots are 1, -1, 5

Answer:

Least common multiple

Step-by-step explanation:

Just try and see which number is divisible by both values

ex: What is the LCM of 10 and 12

Your answer would be 2 because thats the lowest number it is divisble by.  

[tex]x = \frac{12}{5}[/tex] or the x-intercept coordinates, [tex](\frac{12}{5},0)\\[/tex].

[tex]y = -6[/tex] or the y-intercept coordinates, [tex](0,-4)[/tex].

Simplifying the equation into standard form:

[tex]4y = 10x - 24 \\ 4y - 10x = - 24[/tex]

Finding the x-intercept by evaluating (x,0):

[tex]4(0) - 10x = - 24 \\ - 10x = - 24 \\ x = \frac{ - 24}{ - 10} \\ x = \frac{12}{5} [/tex]

Finding the y-intercept by evaluating (0,y):

[tex]4y - 10(0) = - 24 \\ 4y = - 24 \\ y = \frac{ - 24}{4} \\ y = - 6[/tex]

Answer:

Since:

a^2-2ab+b^2 = (a-b)^2

and

a^2+2ab+b^2 = (a+b)^2

We need to find value of * which is 2ab

In your equation = [tex]\sqrt{6.25} = 2.5 and \sqrt{1/4} = 0.5\\Now 2ab = 2 * 2.5 * 0.5\\ = 2.5\\\\\\* = 2.5ab[/tex]

Answer:

[tex]y=\frac{1}{5}x[/tex]

Step-by-step explanation:

We want to write an equation of a line that passes through the point P(0, 0) and is perpendicular to the line y=-5x+3.

First, let's figure out the slope of our new line. Remember that slopes of perpendicular lines are negative reciprocals of each other.

So, to find our new slope, we need to flip our old slope and multiply by -1. So, our new slope is:

[tex]-5[/tex]

Flip:

[tex]-\frac{1}{5}[/tex]

Multiply by a negative:

[tex]=\frac{1}{5}[/tex]

So, the slope of our new line is 1/5.

To find our equation, we can use the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

As previously determined, our slope is 1/5.

Note that (0, 0) is our y-intercept (and also our x-intercept). So, substitute 0 for b. Therefore, our new equation is:

[tex]y=\frac{1}{5}x+0[/tex]

Simplify:

[tex]y=\frac{1}{5}x[/tex]

And we're done!

Answer:

its the way it goes from minus 4

Answer:

52° 86' 65"

Step-by-step explanation:

20° + 30° + 2° = 52°

15' + 41' + 30' = 86'

18" + 32" + 15" = 65"

Answer:

yes its X-squadrant

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

2x + 9y + 5

Step-by-step explanation:

Combine like terms:

(6x - 4x) + (4y + 5y) + 5

2x + 9y + 5

Answer:

2, 9, 5

Step-by-step explanation:

These are the numbers to plug into this equation.

Answer:

-(1+7x)-6(-7-x)=26

-1-7x+42+6x=26

-x+41=26

-x=26-41

-x=-15

x=15

hope it helps you!

Answer:

x=15

Step-by-step explanation:

-1 - 7x + 42 + 6x = 26

41 -7x + 6x = 26

41 - x =26

-x = 26 - 41

-x = -15

x = 15

Answer:

(4x+1)(4x-3)

4x(4x-3)+1(4x-3)

16x²-12x+4x-3

16x²-8x-3

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1) \\ [/tex]

where

m is the slope

( x1 , y1) is the point

From the question the point is (5, -6) and slope - 3/5

The equation of the line is

[tex]y + 6 = - \frac{3}{5} (x - 5) \\ y + 6 = - \frac{3}{5} x + 3 \\ y = - \frac{3}{5} x + 3 - 6[/tex]

We have the final answer as

[tex]y = - \frac{3}{5} x - 3 \\ [/tex]

Hope this helps you

Answer:

y = -3/5x - 3

Step-by-step explanation:

Slope intercept form is [ y = mx + b ] where m = slope and b = y-intercept.

We know the slope so we need to find the y-intercept.

y = -3/5x + b

-6 = -3/5(5) + b

-6 = -3 + b

-3 = b

Put everything we know/solved for into the formula shown above.

y = -3/5x - 3

Best of Luck!

Answer:

D

Step-by-step explanation:

4x - 2(x + 3) = 8

Use distributive property

4x -2x - 6 = 8

2x - 6 = 8

2x = 8 + 6

2x = 14

x = 14 ÷ 2

x = 7

Answer:

Step-by-step explanation:

Given

Functions:

Finding the difference between S(5) and H(5)

Answer is 35.875 grams

Answer:

153.94

Step-by-step explanation:

Answer:

-11,589

Step-by-step explanation:

|3a| − 54b

|3(-7)| − 54(215)

|-21| - 11610

21 - 11610

-11589

Best of Luck!

Hey there!☺

[tex]Answer:\boxed{a<\frac{-1}{6}}[/tex]

[tex]Explanation:[/tex]

[tex]a+\frac{5}{6}<\frac{2}{3}[/tex]

We only have one step in this inequality which is subtract 5/6 from both sides:

[tex]a+\frac{5}{6}-\frac{5}{6}<\frac{2}{3}-\frac{5}{6}\\a<\frac{-1}{6}[/tex]

[tex]a<\frac{-1}{6}[/tex] is our answer.

Hope this helps!☺

Answer:

mk,  eee

Step-by-step explanation:

Answer:

-54

Step-by-step explanation:

plug (-4) in for t and solve for k(t)

Answer:

x=13.4

Step-by-step explanation:

x=v_i(t)+1/2(at^2 )

x=11(23)+12(-4.5)(2.3)^2

x=25.3-11.9

x=13.4

The stopping distance for the car in this situation will be x = 13.4 meters.

Equations of motion are used to describe how a physical system behaves in terms of how its motion changes over time.

The behavior of a physical system is described in more detail by the equations of motion as a collection of mathematical functions expressed in terms of dynamic variables.

Given that the school zone in front of your school has a posted speed limit of 25mi/h which is about 11 m/s. The car moves at a constant velocity of 11 m/s for 2.3 seconds while the driver reacts, then slows down at a constant rate of -4.5 m/s.

The distance will be calculated as below:-

x=v(t)+1/2(at² )

x=11(23)+12(-4.5)(2.3)²

x=25.3-11.9

x=13.4 meters

Therefore, the stopping distance for the car in this situation will be x = 13.4 meters.

To know more about an equation of motion follow

https://brainly.com/question/25951773

#SPJ2

Answer:

Step-by-step explanation:

dived the figure into 3 areas (see attached image)

1. area of a triangle = 1/2 b h   where b=6 , h=3

A1 = 1/2 (6) 3 = 9

2. area of  trapezoid = a + b * (h/2)  here a = 4, b = 6, h = 5

A2 = (4 + 6 ) * 5/2  =  25

3. area of a triangle = 1/2 b h   where b=8 , h=6

A3 = 1/2 (8) 6  =  24

total  area = 9 + 25 + 24

                 = 58 in²