Mathematics, 06.07.2019 06:30 suewignall

25 points ! complete the table and pattern. determine the common difference. write the explicit rule.

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Answer from: clarissajimenez27

Look below for the answers.

Step-by-step explanation:

What I'm going to do is one of these very carefully and leave the other 2 to you. They follow exactly the same pattern and once you see one of them done, you should be able to do any of them.

Six

Step one

Find the common difference.

Two values on the second line are always together so subtract the higher number one from the lower numbered on.

n = 3 and n = 4 on this question are side by side. That is you have f(4) and f(3)

ALWAYS subrract the lower numbered one from the higher numbered one

d = f(4) - f(3) = 60 - 64 = - 4

Step Two

Find the first term.

The first term is ALWAYS f(1). Always. There is never any kind of exception. f(1) in this case is 72

Step Three

Write the general explicit term

The general formula for the explicit Formula is ALWAYS

tn = first term + (n -1)*d

first term = 72

d = - 4 from above.

Explicit formula = 72 + (n - 1)*(-4) So the fifth term is

Example

t5 = 72 + (5 - 1)*(-4)

t5 = 72 + 4*(-4)

t5 =72 - 16

t5 = 56

Step Four

Write the Recursive formula

It is always in the same formal

tn = t_(n - 1) + (common difference)

tn = t_(n - 1) - 4 in this case

Example

Find t2

t2 = t1 - 4

t2 = 72 - 4

t2 = 68

If you do the other two, you can leave them in my PM and I will mark them.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

part a

x y

0 8

1 7.5

2 7

3 6.5

4 6

5 5.5

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part c

for every x value there is only one y value

x y

0 8

1 7.6

2 7.2

3 6.8

step-by-step explanation:

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