All categories

3 years ago

Which formula defines the sequence f(1)=2, f(2)=6, f(3)= 10, f(4)= 14,f(5)=18

Mathematics

1 answer:

lianna [129]3 years ago

7 0

Answer:

y=4x-2

Step-by-step explanation:

for every 1 unit increase in x, y values change by a factor of four units

slope=4x

f(x)=y

y=mx+b

2=4(1)+b

b=-2

equation= y=4x-2

CHECK

6=4(2)-2

6=8-2

6=6

CORRECT

10=4(3)-2

10=10

CORRECT

alternatively... (y2-y1)/(x2-x1)

(6-2)/(2-1)= (4)/(1)

slope=4

You might be interested in

-19x + 23x = 44 what is x

matrenka [14]

Step-by-step explanation:

- 19 x + 23 x = 44

4x = 44

x = 44/ 4

x = 11

Hope it will help :)

6 0

3 years ago

Read 2 more answers

Given x – 5 < One-fourth (y – 8)2, which graph represents the inequality?

Annette [7]

Step-by-step explanation:

x - 5 < 2 (y - 8) • 1/4

x - 5 < (y - 8) / 2

2 (x - 5) < y - 8

2x - 10 < y - 8

2x - 10 + 8 < y

y > 2x - 2

graph 2x - 2 and shade the section above

5 0

3 years ago

Please help asap!!! i dont understand it

pshichka [43]

Answer:

Step-by-step explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m = $\frac{13-1}{9-(-7)}$ = $\frac{12}{9+7}$ = $\frac{12}{16}$ = $\frac{3}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{4} }$ = - $\frac{4}{3}$ ← slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

midpoint = ( $\frac{-7+9}{2}$ , $\frac{1+13}{2}$ ) = ( $\frac{2}{2}$ , $\frac{14}{2}$ ) = (1, 7 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{4}{3}$ , then

y = - $\frac{4}{3}$ x + c ← is the partial equation

To find c substitute the midpoint (1, 7) into the partial equation

7 = - $\frac{4}{3}$ + c ⇒ c = $\frac{21}{3}$ + $\frac{4}{3}$ = $\frac{25}{3}$

y = - $\frac{4}{3}$ x + $\frac{25}{3}$ ← equation of perpendicular bisector

7 0

3 years ago

The sum of the digits in a two digit number is 14. If you reverse and double the original number, and then add the result to the

gtnhenbr [62]

Answer:

Step-by-step explanation:

Let the two digits be x and y, where x is the tens digit and y is the units (ones) digit.

Then the number is 10x + y.

From the question,

The sum of the digits in a two digit number is 14,

That is, x + y = 14 ....... (1)

Also, from the question,

If you reverse and double the original number, and then add the result to the original number, the sum is 222

If the number is reversed, the new number will be 10y + x; and if this is doubled, we will get 2(10y + x).

Now, if this is added to the original number (10x + y), the sum is 222.

That is,

2(10y + x) + (10x + y) = 222

Then,

20y + 2x + 10x + y = 222

12x + 21y = 222 ........ (2)

Now, we will bring the two equations together and solve simultaneously.

x + y = 14 ....... (1)

12x + 21y = 222 ........ (2)

From equation (1)

x + y = 14

Then, x = 14 - y ...... (3)

Substitute the value of x in equation (3) into equation (2)

12x + 21y = 222

12(14 - y) + 21y = 222

168 - 12y + 21y = 222

168 + 9y = 222

9y = 222 - 168

9y = 54

∴ y = 54/9

y = 6

To determine x, substitute the value of y into equation (3)

x = 14 - y

∴ x = 14 - 6

x = 8

∴ x = 8 and y = 6

Recall that, the two digits are x and y, where x is the tens digit and y is the units (ones) digit.

Hence, the original number is 86.

8 0

3 years ago

Solution to <br> -7+3w=4w-8

Contact [7]

-7 + 3w = 4w - 8

-7 = 4w - 8 - 3w

-7 = w - 8

-7 + 8 = w

1 = w

hope this helped, blessings! :)

8 0

3 years ago