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Normally we want

where m = slope and b = y-intercept.
in our example we have

which means

or m = 0 and b = -8/5.
to graph
first plot -8/5 on the y-axis.
second move up 0 and over 1 (rise / run) and place a dot.
connect the dots to find a long horizontal line.

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the problem is
Given G(t) = 4 − 7t, write G(5 + h) − G(5) in simplest form.
step 1 - replace t with 5+h to get
G(5+h) = 4 - 7(5+h)
distribute to get
G(5+h) = 4 - 35 -7h
combine like terms to get
G(5+h) = -7h - 31
---
G(5) = 4 - 7*5 = 4 - 35 = -31
---
G(5+h) - G(5) = -7h - 31 - (-31) = -7h

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We
(i) a + b = 35
(ii) a = 3b - 5
substituting (ii) into (i), we get
(iii) 3b-5 + b = 35
combine like terms to get
(iv) 4b - 5 = 35
adding 5 we get
(v) 4b = 40
dividing, we get
b = 10
so
a = 25

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This is a mixture problem with out mixture information. Here is a table based on the given information
alloy . . . . . .% . . . . . .g . . . . . . .%g
70 . . . . . . . 70 . . . . 30 . . . . . .2100
15 . . . . . . .15 . . . . .50 . . . . . .750
mix . . . . . . x . . . . . .80 . . . . . .80x
looking at the third column, we get

adding we get

dividing, we get
x = 35.625
which is
35.63% = 35.6%

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I think you are looking for a linear equation to model this data. We have two coordinates here
(0, 66.2) and (5, 69.9). Let 1992 = 0 and 1997 = 5.
step 1 - find the slope using

to get

which is

---
step 2 - using y = mx + b, and a coordinate, we get


so,

---
we have our answer as

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Lets take these one at a time:
Determine whether the system is consistent, inconsistent, or dependent.
(i)
(ii)
step 1 - multiply (i) by -3 to get
(iii)
step 2 - add (ii) and (iii) to get
(iv)
Here we have dependent , consistent
Determine whether the system is consistent, inconsistent, or dependent.
(i)
(ii)
step 1 - multiply (i) by -3 to get
(iii)
step 2 - add (ii) and (iii) to get
(iv)
Here we have dependent , consistent

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This is a mixture problem. Here is a table based on the given information
fat . . . . . . .% . . . . . . pounds . . . . . . . . %-pounds
29. . . . . . . 29 . . . . . . . .p . . . . . . . . . . .29p
15 . . . . . . .15 . . . . . . . .63-p. . . . . . . . .945 -15p
17 . . . . . . .17 . . . . . . . .63. . . . . . . . . . .1071
set the third column equal to get

combine like terms to get

subtract 945 to get

p = 9 pounds @ 29 %
63-p = 54 pounds @ 15%

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This is an RTD problem. Here is a table based on the given information
location . . . . . rate . . . . .time . . . . . distance
resort . . . . . . . .22 . . . . .t. . . . . . . . . . 22t
harbor . . . . . . .10 . . . . .4-t. . . . . . . . . 40-10t
total. . . . . . . . . . . . . . . . 4
since distances are =, set

add 10t to get

divide by 32 to get
hours
we want distance, so
22*1.25 = 27.5 miles

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This is an RTD problem. Here is a table based on the given information
travel . . . . . rate . . . . . .time . . . . . .distance
horse . . . . . . 4 . . . . . . . .t . . . . . . . . .4t
speech . . . . . 5 . . . . . . . t-1 . . . . . . . 5t - 5
set

subtract 5t to get

so
t = 5.
distance = 4t = 20 miles

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The original equation was

step 1 - rewrite the left side as

and then using difference of cubes, we get

set each part = 0 and solve to get

add 2^(5/3) to get

divide by 4^(1/3) to get

the other parentheses, trinomial, will generate imaginary answers. so we get
x = 2.

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This is a working together problem.
The rate of the 8 hp pump = 1/8
the rate of the 3 hp pump is 1/12
The time together will be 4 hours.
The time that the 3 hp pump works alone is x hrs.
We want to fill only 1 tank
-----
we use the formula

we get

adding the fractions, we get

subtract 5/6 to get

multiply by 12 to get

So, the 3 hp pump must work and additional 2 hours.

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The general parabola formula is

or

in either case to determine up or down, look at the "a" value
If "a' is positive, then it opens up
if "a" is negative, then it opens down

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Perimeter formula is

area formula is

---
from the given information, we get
}

P = 70 m
---
from the given information, we get

A = 66 meters squared.

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If I understand the question correctly, we have two equations
(i)
(ii)
setting them equal, we get

distribute to get

combine like terms to get

subtract 10m and add 900 to get

divide to get

So, at 68 mph,
city A fine will be $120
city B fine will be $120

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Here is the given equation

step 1 - add 250 to get

step 2 - divide by 2 to get

step 3 - take a cube root of both sides to get

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Here is our original system
(i)
(ii)
step 1 - multiply (ii) by -2 to get
(iii)
add (ii) and (iii) to get
(iv)
this mans that we have the same equations but in disguise.
These equations are "dependent"

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here is the given equation

step 1 - subtract 64 to get

step 2 - take a cube root of both sides to get

this is the only "real" solution.
There are 2 imaginary solutions.

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We use the permutation formula:
nPr and get
9P6 = 60,480

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The 234 occur in the millions period.

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here is the original question

step 1 - subtract 3 to get

step 2 -factor to get

step 3 we need to create 3 number line graphs. Make sure the 0 marker is aligned in all three.
number line graph #1:
x+3> 0
this means open circle above -3 and then + signs to the right and - signs to the left.
number line graph #2:
x-1> 0
this means open circle above +1 and then + signs to the right and - signs to the left.
number line graph #3:
(x+3)(x-1) > 0
we place open circles above -3 and then +1.
To the left of -3, we have - signs for both lines. - x - = + so in the third number line place a + to the left of -3.
Between -3 and +1 we have different signs, so place a - sign on the third number line between -3 and +1.
To the right of +1, we have + signs for both lines. + x + = +, so in the third number line place a + to the right of +1.
we want where the signs are > 0 or the + regions.
Our final answer is
open circles above -3 and +1 and then arrow from the -3 to the left and arrow from the +1 to the right.

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Using our volume formula as

and our given information, we get

notice I didn't use 3. D = 3, so r = 1.5

by division, we get
yrds

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Let x be the length of each equal side and then 2x - 4 is the length of the base.
p = a + b + c
24 = a + b + c

step 1 - combine like terms to get

step 2 - add 4 to get

step 3 - divide by 4 to get

the three sides are
{7, 7, 10}

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here is the original equation

step 1 - multiply by the common denominator of (x+1)(x+2) to get

step 2 - combine like terms to get

step 3 - subtract 3 to get

step 4 - divide to get

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To determine the domain of any function, we ask 2 questions
(1) is the variable in a square root of any type?
if "yes" set the stuff under the root >= 0 and solve for x.
if "no" go to question 2.
(2) is the variable information in the denominator?
if "yes" set the denominator stuff not = 0 and solve for x.
if "no" then you say "all reals"
-----
Using these questions on the given problem., we get
(1) NO
(2) YES
so

solving for x, we get
x = 8.
This means we cannot use x = 8 as a domain number.

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The answer is yes. By completing the square you convert the quadratic equation into the vertex form of a parabola. After the process is done you end up with the following:

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we can use synthetic division to verify. This will generate another equation that we will factor.
-2 // . . . 2 . . . . 1 . . . . -10 . . . . . -8
. . . . . . . . . . . . -4 . . . . .6 . . . . . . .8
. . . . . . . 2 . . . . -3 . . . . -4 . . . // . 0
So, we have verified by getting a 0 remainder. We now have a new equation of the form

By quadratic, we get

and then

we have two answers and rounded, we get
x ~ 2.35
x ~ -0.85

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here is the original problem
/
step 1 - multiply by 1/(x-3) to get
/
notice the denominator x-3 parts drop out, so we get

which is

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here is the original equation

step 1 - using quadratic, we get

and then

simplifying the radical, we get

and canceling, we get

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here is the original equation

step 1 - multiply by 2x to get

step 2 - subtract x and subtract 8 to get

by division, we get

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here is our original equation:

step 1 - multiply by z to get

using the quadratic, we get

which becomes

and then

canceling, we get

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the e and ln drop out and we are left with