A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
Answers
A small order coffee company charges $12 for each bag of coffee +3 dollars shipping no matter how many bags are ordered. Describe the function that this situation gives rise to. make a table for this function, sketch a graph for this function, and find an equation for this function. Is the function linear or not? How can you tell?
Step 1
Describe the function,
.
Let
x, the number of bags
shipping = 3 dollars
Charges=$12 for each bag, then
charges=12*x
Now, the total is
total=charges + shipping
total=12x +3
now, we have a function ( the total (y) depends on the number of bags)
[tex]y=12x+3[/tex]where
y is the total charge, and x is the numbers of bags
Step 2
assume values for x, replace and find y
x=-3
then y=12(-3)+3, y=-36+3, y=-33
so, when x=-3, y=-33
2
then y=12(-2)+3, y=-24+3, y=-21
so, when
x=-2, y=-21
1
then y=12(-1)+3, y=-12+3, y=-9
so, when
x=-1, y=-9
0
then y=12(0)+3, y=+3, y=3
so, when
x=0, y=3
1
then y=12(1)+3, y=12+3, y=15
so, when
x=1, y=15
the table is
x y
-3 -33
-2 -21
-1 -9
0 3
Step 3
, just sepick two cooridnadinates from the table mak, then mark those pintsoints, and finally, dwr in the planeaaw a line conceeecting he connectingnts
Step 4
as you can see, when we take the points of the table and we unite them, a line appears
so , this is a linear function
Also, the exponent of the variable ( x) is cero, which means it is a linear function.
Related Questions
The stockholders’ equity section of TVX Company on February 4 follows. Common stock—$25 par value, 150,000 shares authorized, 62,000 shares issued and outstanding $ 1,550,000 Paid-in capital in excess of par value, common stock 426,000 Retained earnings 551,000 Total stockholders’ equity $ 2,527,000 On February 5, the directors declare a 2% stock dividend distributable on February 28 to the February 15 stockholders of record. The stock’s market value is $36 per share on February 5 before the stock dividend. 1. Prepare entries to record both the dividend declaration and its distribution.
Answers
The journal entries to record both the dividend declaration and its distribution is : Dr Retained earnings $44,640, Cr Common stock dividend distributable $31,000, Cr Paid-in capital in excess of par value, Common stock $13,640 .
Journal entriesTVX Company Journal entries
Feb 05
Dr Retained earnings $44,640
[ (62,000 shares × 2%) ×$36 ]
Cr Common stock dividend distributable $31,000
[ (62,000 shares × 2%) ×$25 ]
Cr Paid-in capital in excess of par value, Common stock $13,640
($44,640 - $31,000)
(To record dividend declaration)
Feb 28
Dr Common stock dividend distributable$31,000
[ (62,000 shares × 2%) ×$25 ]
Cr Common stock, $25 par value $31,000
(To record dividend distribution)
Therefore the entry is Dr Retained earnings $44,640, Cr Common stock $31,000, Cr Paid-in capital $13,640.
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Find a polynomial with real coefficients that has the given zeros -1 and 2-3i
Answers
Using the Factor Theorem, the polynomial with real coefficients that has zeros -1 and 2 - 3i is given by:
f(x) = x³ - 3x² + 9x + 13.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).
Considering a leading coefficient of a = 1, the zeros of the polynomial are given as follows:
Zero at x = -1, hence [tex]x_1 = -1[/tex].Zero at x = 2 - 3i, hence [tex]x_2 = 2 - 3i[/tex].Zero at x = 2 + 3i, which is the conjugate of x = 2 - 3i, since if a complex number is a root of a polynomial, it's conjugate also is, hence [tex]x_3 = 2 + 3i[/tex].Hence the polynomial is given by:
f(x) = (x + 1)(x - 2 + 3i)(x - 2 - 3i)
f(x) = (x + 1)[(x - 2)² - (3i)²]
f(x) = (x + 1)(x² - 4x + 13), as (3i)² = 9i² = 9(-1) = -9, -(-9) = 9.
f(x) = x³ - 3x² + 9x + 13.
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devin prepares for a multi day hike by packing his backpack with food,water,bedding, and emergency supplies. the tracks how many pounds of each he's carrying and find the ratio of their respective weights 2:3:1:4 f the total weight of his supplies is 35 pounds how many pounds of water is devin carrying
Answers
The amount in pounds of water that's been carried by Devin as described by the ratio given in the task content is; 10.5 pounds.
How many pounds of water is Devin carrying as described in the task content?It follows from the task content that the amount of water Devin is carrying is to be determined.
On this note, since the backpack contains food, water, bedding, and emergency supplies are in the ratio; 2 : 3 : 1 : 4.
It therefore follows from proportion that the ratio representation of total of all supplies is; (2 + 3 + 1 + 4) = 10.
Therefore, since the total weight is; 35 pounds, it follows that the amount of water Devin is carrying can be of help as follows;
w/35 = 3/10.
w = (3 × 35)/10
w = 105/10
w = 10.5 pounds.
Ultimately, the total weight of water Devin is carrying is therefore; 10.5 pounds.
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The base of a monument at Veterans Park is shaped like a rectangular prism with a base of 5 meters by5 meters and a height of 3.2 meters. What is the surface area, in square meters, of the prism?3.2 m5 m5 m
Answers
The rectangular prism has the following dimensions;
[tex]\begin{gathered} \text{height}=3.2m \\ \text{length}=5m \\ \text{width}=5m \end{gathered}[/tex]The total surface area of
[tex]\begin{gathered} TSA_{rec\tan gular\text{ prism}}=2(lw+lh+wh) \\ \text{Where l= length} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} TSA_{rec\tan gular\text{ prism}}=2((5\times5)+(5\times3.2)+(5\times3.2)) \\ TSA_{rec\tan gular\text{ prism}}=2(25+16+16) \\ TSA_{rec\tan gular\text{ prism}}=2(57) \\ TSA_{rec\tan gular\text{ prism}}=114m^2 \end{gathered}[/tex]The total surface area of the rectangular prism is 114 square meters
Two distinct lines, & and m, are each perpendicular to the same line n.
a. What is the measure of the angle where line / meets line n?
b. What is the measure of the angle where line m meets line n?
A. The measure of the angle where line | meets line n is ___ degrees
B. The measure of the angle where line meets line n is ____ degrees
Answers
The two distinct lines, line l and line m, have the following relationship with line n
A. The measure of the angle where line | meets line n is 90 degrees
B. The measure of the angle where line meets line n is 90 degrees
What are perpendicular lines?This is a term used to refer to lines that intersect at angle 90 degrees. perpendicular lines are also found in right angle triangle. Hence it is right to say that two sides of a right angled triangle are perpendicular to each other.
The features of perpendicularity also helps in defining a squire and rectangles. This is true because the sides meet at angle 90 degrees
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PLS HELPPPP IVE ASKED THIS 3 TIMES (3y + 11) (7x - 30) (5x + 14)Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
Answers
Answer: 2x + 3y = 33
PLEASE HELP ME 1. A different pool had an area that is of the form
▢ × 102 + ▢ × 101 + 6
and that can be written in the form x3 ,
where x is a whole number.
A) Decide what your number could be.
B) What is the perfect square number that is closest to the number you chose? What would the side length of a square pool with that area be?
C) Estimate the side length of a square pool with the area you chose in part a).
Answers
The solutions to the questions are
The number we are using is 5The perfect square number closest to the area is 1024The estimated side length is 32What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
The number to useThe area expression is given as
Area = ▢ × 102 + ▢ × 101 + 6
From the question, we can use any number
However, this number must be positive
Assume the number is 5
So, we have
Area = 5 × 102 + 5 × 101 + 6
The perfect square number closest to the resultIn (a), we have:
Area = 5 × 102 + 5 × 101 + 6
Evaluate
Area = 1021
The perfect square number closest to this is
Closest = 1024
The estimated side lengthIn (b), we have
Closest = 1024
Rewrite as
Area = 1024
Take the square roots
Length = 32
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Please fill in the blanks so that the following statement is true
Answers
In general, given a function g(x), a transa
Can you please explain this to me?
Answers
The amplitude is determined as the distance from the midline of the cosine function.
From the graph provided, the depth is shown as 3 units (between 5 units and 2 units) which puts the midline at 3.5 units. The amplitude therefore is 1.5
Write an equation of each line with the given characteristics.
1. slope = 3;
y-intercept = -1
Answers
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{3}x\stackrel{\stackrel{b}{\downarrow }}{-1}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
An average male lion in captivity requires
8 pounds of food per day. The equation y = 8x
can be used to represent this situation. What is
the constant of proportionality? What does the
constant of proportionality represent in the
context of the problem? (Example 1)
4.
Answers
Answer: 8 is actually the constant of proportionality, since it is the number that stays the same regardless of the change in x and y.
Step-by-step explanation:
Let's say you want to know how many pounds of meat a male lion would eat in a month in order to purchase for the zoo the correct amount of food needed. Let's assume the month was 30 days. we know that 8 is the amount of food per day (that number will not change because it is a constant.
so 30 x 8 = 240 which is what y is for the 30 days.
if you needed two weeks, 14 days. 14 x 8 = 112 pounds for the 14 days.
So you see 8 stays the same for each scenario, so it is the constant that is used for all values of x to find y.
The owner of A Ranch wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a
fence down the middle, parallel to one side.
What is the shortest length of fence that the Ranch owner can use?
Length of fence =
feet.
Answers
In linear equation, 3464.1016 feet is the shortest length of fence that the Ranch owner can use.
What is linear equation definition and example?
An equation in which there is only one variable is known as a linear equation in one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Let L represent the length of the field.
Let W represent the width of the field.
Let F represent the length of fence needed.
L*W=500000
2L+3W=F Both length sides+both width sides+ fence across the width.
Let's look at the first equation again:
L*W=500000
W=(500000/L)
Now we can substitute (500000/L) for W in the second equation.
2L+3(500000/L)=F
2L+1500000/L=F
Now we have a function. We can input any length, and we'll know length needed. But how can we find the length needed so that F is as small as it can be? If you know derivatives, there's an exact way. The next easiest way to do it is to graph.
Manner 1: Derivative
Set the derivative to zero...when the length stops going down and starts coming back up, it'll be at it's lowest point.
2L+1500000^-1=F
F'=2-1500000^-2
0=2-1500000^-2
1500000/(L^2)=2
1500000=2L^2
1500000=L^2
L=866.025
Now, we know that L=500000/W
so 866.025=500000/W
W=500000/866.025
W=577.35027 feet.
Now,
2L+3W=2(866.025)+3(577.35027)
Minimum fencing needed: 3464.1016 feet.
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If Katie Pittman earns a $60,840 annual salary, what is her weekly gross salary?
$2,340
$2,530
$1170
$1,216.80
Answers
If Katie Pittman earns a $60,840 annual salary, her weekly gross salary is $1170.
What is weekly gross salary?
The number of hours worked multiplied by the hourly wage of an employee is how gross wages are determined for hourly workers. For instance, an employee making $12 per hour and working 25 hours per week would earn a gross weekly salary of $300 (25 x 12 = 300).
What is annual salary?
The gross pay (before tax deductions) divided by the number of pay periods in a year yields the yearly salary. For instance, a worker making $1,500 each week would make $78,000 a year (1,500 multiplied by 52).
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Complete the calculation
5 5 5
5 + 5 + 5 = x 5 = 5 x
Answers
Answer:
29
Step-by-step explanation:
=5+5×5–1(5÷5=1)
Multiplication
=5+25–1(5×5=25)
Addition
=30–1
(25+5=30)
Subtraction
=29
(30-1=29)
Which of the following is an inequality which involves one or more rational
expressions?
a. Exponential inequality
b. Linear inequality
c. Logarithmic inequality
d. Rational inequality
Answers
The inequality in which involves one or more rational expressions is Rational inequality.
What is inequality?
Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.
An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.
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The answer is d. Rational inequality, which includes fractions with polynomials. Other options involve exponential, linear, or logarithmic functions, without rational expressions as in inequalities.
The right choice is d. Rational inequality. An objective disparity includes at least one sane articulations, which are portions with polynomials in the numerator and denominator. These disparities can be settled by finding the basic places where the normal articulation is indistinct or changes sign.
The arrangement includes deciding the stretches where the disparity turns out as expected in view of the indication of the judicious articulation in those spans. Interestingly, dramatic, direct, and logarithmic disparities include various kinds of numerical capabilities.
Remarkable imbalances contain dramatic terms, direct disparities incorporate straight capabilities, and logarithmic imbalances contain logarithmic capabilities. Each kind of imbalance has its own qualities and strategies for settling, however just objective disparities straightforwardly manage levelheaded articulations including parts of polynomials.
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In ΔLMN, \overline{LN} LN is extended through point N to point O, \text{m}\angle MNO (5x+2)^{\circ}m∠MNO(5x+2)∘,\text{m}\angle NLM = (x+10)^{\circ}m∠NLM=(x+10) ∘,and \text{m}\angle LMN = (x+16)^{\circ}m∠LMN=(x+16)∘. What is the value of x?x?
Answers
Using the exterior angle theorem, the value of x in the triangle is: x = 8.
What is the Exterior Angle Theorem?The exterior angle theorem states that the measure of the angle formed outside a triangle when a side is extended through one of the points of the triangle is equal to the sum of the remote interior angles of the triangle.
Triangle LMN is shown in the diagram attached below, where:
The measure of angle MNO = (5x + 2)°
The measure of angle NLM = (x + 10)°
The measure of angle LMN = (x + 16)°
Therefore:
Measure of angle MNO = measure of angle NLM + measure of angle LMN [based on the exterior angle theorem]
Substitute
(5x + 2)° = (x + 10)° + (x + 16)°
Solve for x
5x + 2 = x + 10 + x + 16
Combine like terms
5x + 2 = 2x + 26
5x + 2 - 2x = 2x - 2x + 26 [subtraction property of equality]
3x + 2 = 26
3x + 2 - 2 = 26 - 2 [subtraction property of equality]
3x = 24
3x/3 = 24/3 [division property of equality]
x = 8
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There are 18 boys and 46 girls in class. 87.5% of the students in the class take the
bus to school. How many students do not take the bus to school?
Answers
Reason:
87.5% of the students take the bus to school
100% - 87.5% = 12.5% of the students do not take the bus to school
The info about the "18 boys and 46 girls" is put there as a distraction since it's never used.
If f(x)=√x-3, which inequality can be used to find the domain of f(x)?
square root of x - 3 over or equal to zero, x minus three over or equal to zero, square root of x-3 under or equal to zero; x-3 under or equal to 0
Answers
The inequality that can be used to find the domain of f(x) is x - 3 ≥ 0.
The correct answer is the second one i.e.x minus three over or equal to zero.
What is the Domain of a Square Root Function?Fundamentally, the square root function has the form f(x) = √x. In other words, f(x) = √x is the parent square root function.A negative number's square root is not a real number. Therefore, negative values cannot be put into the square root function.That is, the set of all real numbers that are not negative constitutes the domain of the square root function, f(x) = √x.Consequently, [0,∞ ) is the square root function domain. It should be noted that the domain also contains 0.Given:
Function f(x) = √x-3
The fact that a negative number cannot be used as the term in the root square, so
x - 3 ≥ 0 which implies that, x ≥ 3.
From the inequality, we can tell that the domain of the function is the interval [3,∞).
Hence the inequality is x - 3 ≥ 0.
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Which of the m-values satisfy the following inequality? 5m + 1 <_ 4Choose all answers that apply: A.) m = 0B.) m = 1C.) m = 2
Answers
We want to know which values of m satisfy ≤
5m + 1 4
Substracting 1 both sides:
-1 - 1
+03
5m ≤ 3
Dividing by 5 both sides
/5/5
m ≤ 3/5
m ≤ 0.6
Since 1 and 2 are higher than 0.6 and 0 ≤ 0.6
Then if m=0 it is satisfied
Answer: AWill give you brainliest
Answers
The simplified form of 13√5 + 3√5 is option c 16√5
Given,
The expression : 13√5 + 3√5
We have to simplify the above given expression.
Lets see the simplification of numbers with square roots.
1. Addition: a√b + c√b = (a + c) √b
2. Subtraction: a√b - c√b = (a - c) √b
3. Multiplication: a√b × c√b = a × c × b
4. Division: a√b ÷ c√b = a ÷ c
So here,
We can use addition:
That is,
a√b + c√b = (a + c) √b
Where,
a = 13, b = 5 and c = 3
Now,
13√5 + 3√5 = (13 + 3) √5 = 16√5
Therefore, the simplified form of 13√5 + 3√5 is option c 16√5
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Using point P, which point would form a line parallel to line AB?
(-6,4)
(3,2)
(1,1)
(-2,3)
Answers
Answer:
(3,2)
Step-by-step explanation:
The equation of the line graphed is
y = 2/3x + 2
Parallel lines have the same slope.
y = mx + b
y = 2/3x + 0 P tells me that the y-intercept is 0
y = 2/3 x Which point would make this true?
Point (3,2) We plug in 3 for x and 2 for y
2 = 2/3(3)
2 = 2 This is a true statement, so the point (3,2) is on the line.
what is the converse of t > r
Answers
The converse of t > r is r > t
What is a converse statement?A converse statement is determined when both the hypothesis and conclusion are reversed or interchanged.
In this condition, the hypothesis is written as the conclusion and the conclusion is changed to be the hypothesis.
If a conditional statement is written as: x → y
The converse is then written as y → x
Where;
x is the hypothesisy is the conclusionGiven the expression as;
t > r
We can see that;
The variable 't' is the hypothesisThe variable 'r' is the conclusionThe converse will be;
r > t
Hence, the converse is r > t
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graph and label each figure and its image under the translation along the given vector. identify the coordinates of the image.
Answers
The transformations are
Transformation 1: The image of the transformation are P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)Transformation 2: The image of the transformation are E'(1, -4), F'(6, 0) and G'(7, -4)How to perform the transformationTransformation 1
Here, we have
The coordinates are given as
P(-5, 4), Q(2, 8), R(6, 1) and S(-1, -3)
The transformation is given as
<2, -4>
This is represented as
(x, y) ⇒ (x + 2, y - 4)
This means that the translation is (x + 2, y - 4)
When this rule is applied on the coordinates, we have
P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
Transformation 2
Here, we have
The coordinates are given as
E(-7, -7), F(-2, -3), G(-1, -6)
The transformation is given as
<8, 3>
This is represented as
(x, y) ⇒ (x + 8, y + 3)
This means that the translation is (x + 8, y + 3)
When this rule is applied on the coordinates, we have
E'(1, -4), F'(6, 0) and G'(7, -4)
Next, we plot the image of the transformation on a coordinate plane
See attachment for the image of the transformation
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A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total
possible outcomes are there when choosing a marble from the bag?
Answers
Answer: 14
Step-by-step explanation: https://brainly.com/question/15694490
Classify the following
sequence:
1, 4, 9, 16, 25, ...
A. neither
B. geometric
C. arithmetic
Answers
FOR ARITHMETIC
[tex]lhs = 9 - 4 \\ lhs = 5 \\ rhs = 4 - 1 \\ rhs= 3 \\ \\ lhs \: not = rhs[/tex]
SINCE THERE IS NO COMMON DIFFERENCE LET US TEST FOR A GEOMETRIC SEQUENCE.
[tex]lhs = \frac{9}{4} \\ \\ rhs = \frac{4}{1} \\ rhs = 4 \\ \\ lhs \: not = rhs[/tex]
THERE IS NO COMMON DIFFERENCE NOR A COMMON RATION THIS MEANS THAT THE SEQUENCE IS NEITHER AN ARITHMETIC NOR A GEOMETRIC SEQUENCE.
THE OPTION IS A.NEITHER.
Hoover Electronics has a beginning inventory of 15,500 units, will sell 53,000 units for the month, and desires to reduce ending inventory to 40 percent of beginning inventory.
How many units should Hoover produce?
Answers
Based on the beginning inventory to Hoover Electronics and the units to be sold, the number of units that Hoover should produce is 43, 700 units
How many units should Hoover produce?First, find the ending inventory that Hoover Electronics would prefer which is 40% of the beginning inventory:
= Percentage of beginning inventory
= 40% x 15, 500
= 6, 200 units
The amount that Hoover should produce in units is:
= Amount to be sold + Ending inventory - Beginning inventory
= 53, 000 + 6, 200 - 15, 500
= 43, 700 units
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It’s helpful to know the background of how much you owe in federal taxes by calculating by hand. What is another way that people can look up how much they owe?
Answers
Another way that people can look up how much they owe in tax is by looking it at IRS.gov/account.
What is the tax about?A tax that you pay to the federal government in the US as opposed to a state government If income is used to pay for college, it could not be subject to federal taxes. Federal taxes are collected by the federal government.
The marginal tax rate should be used to calculate federal taxes. It only applies to taxable income. Make changes to gross revenue to arrive at a determinable Taxable income before computing Taxable income. Deductions must then be made. After deductions, taxable income is available. There is no tax due if there is no taxable income.
At IRS.gov/account, you can securely log in to access your federal tax account. Once you've logged into your account, you can see your balance and the amount you owe, as well as 18 months' worth of payment history, access Get Transcript, and see the most important data from your most recent tax return.
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what is the value of the x variable in the solution to the following system of equations? 4x-3y=3 5x-4y=3
Answers
Answer: 3.
Step-by-step explanation:
[tex]\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.[/tex]
Please help I’ll mark you as brainliest if correct!!
Answers
The value of A in the digit is 6.
How to find the value of A when any consecutive number digit sum is equals to 20?The 14 digit numbers are written in the boxes.
The sum of any three consecutive digits is 20.
Therefore, from the last three digits,
5 + 9 + x = 20
14 + x = 20
subtract 14 from both sides of the equation
14 - 14 + x = 20 -14
x = 6
There the value of A is 6.
If you notice the pattern, it follows the same pattern forward and backward as follows:
69569569569569
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Prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.
Answers
It is proved that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7 because on solving it results in 7(n² + 2n -1).
To prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.
When an algebraic expression is a multiple of 7 it should be divisible by 7.
Now, solve the algebraic expression.
12n - n²+ 8n² + 6n - 4n -3 - 4 (combine the like terms)
7n² + 14n - 7 (take out the common factor 7)
7(n² + 2n -1)
Therefore, the algebraic expression has a factor of 7 and is always a multiple of 7 for all positive integer values of n.
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