The true statements are the equation of the function is y=4x+4, the relation is a function, the graph is linear.
The equation of the function start by calculating the slope (m)
The slope formula is used to calculate the inclination or steepness of a line. It finds application in determining the slope of any line by finding the ratio of the change in the y-axis to the change in the x-axis. The slope of a line is defined as the change in the "y" coordinate with respect to the change in the "x" coordinate of that line.
The formula to calculate slope is given as,
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]where, m is the slope of the line, x1, x2 are the coordinates of the x-axis, and y1, y2 are the coordinates of the y-axis.
m=[tex]\frac{12-8}{2-1}=4[/tex]
m=4
The equation is then calculated as:
y=m[tex](x-x_{1})+y_{1}[/tex]So, we have
y=4(x-1)+8
y=4x-4+8
y=4x+4
Therefore, the equation is 4x+4. Hence the statement is true.
(b) The graph is nonlinear.
A linear function forms a straight line when it is plotted on a graph. A nonlinear function does not form a straight line (it is curved in some way). The slope of a linear function is constant, whereas the slope of a nonlinear function is continuously changingBecause of (a) above, the graph is linear.
(c) The relation is a function
A linear relation is a relationship or connection between two variables that will produce a straight line when graphed. There will be times when the data points are scattered and do not form an absolutely straight line. When it appears that the scattered points resemble a straight line,
Hence, the given relation is function then the statement is true.
Therefore, the equation of the function is y=4x+4, the relation is a function, the graph is linear.
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Number of squares(x) Perimeter(y)
1 8
2 12
3 16
4 20
Complete Question: What is the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form?
Answer: The relationship between the number of squares, x, and the perimeter of the rectangles can be expressed as a y = 5.1%x. This equation states that for every one square, the perimeter will increase by 5.1%.
To calculate the perimeter of a rectangle with x number of squares, the following calculation can be used: y = 5.1%x = 0.051x. This equation can be rearranged to solve for x: x = y/0.051.
For example, if the perimeter of the rectangle is 10, the number of squares, x, can be calculated as follows: x = 10/0.051 = 196.08. This indicates that the rectangle will have 196 squares.
Therefore, the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form can be expressed as y = 5.1%x, or x = y/0.051.
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Ethan buys a video game on sale. If the video game usually costs $39.99, and it was on sale for 20% off, how much did Ethan pay?
A. $7.99
B. $14.99
C. $31.99
D. $39.74
Answer:
C
Step-by-step explanation:
1. 100% - 20% = 80%
2. 39.99*0.8 = $31.99
hope this helps!!
(-2/3)^-4, Evaluate without using a calculator
[tex]\left(-\cfrac{2}{3} \right)^{-4}\implies \left(-\cfrac{3}{2} \right)^{+4}\implies \left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\left(-\cfrac{3}{2} \right)\implies \cfrac{81}{16}[/tex]
how tall will each candle be at 11:00 PM when johnsons put the candles out for the night
Answer:
3.5 inches
Step-by-step explanation:
From the information given, it can be deduced that the length of the candle at 11:00PM will be 3.5 inches tall. Since the family lights candles
if 11011 and 11 are in binary, find their product in binary
To find the product of 11011 and 11 in binary, you can use the standard multiplication algorithm that you would use for decimal numbers.
First, you need to multiply 11011 by the rightmost digit of 11, which is 1. This gives you 11011.
Then, you need to multiply 11011 by the next digit of 11, which is 1. This gives you 100110.
Finally, you need to add these two results together to get the final answer:
11011
100110
110121
The product of 11011 and 11 in binary is 110121.
I need help with this. Could someone explain how to solve this question? A simple explanation, please. The explanations I'm seeing seem to confuse me a lot.
Step-by-step explanation:
given
a(-23) &b(5)
if you take this as a continuous graph
AB+BC =28
ATQ,
AB/BC=2/5
28-bc/BC=2/5
140-5BC=2BC
140=7BC
BC=20
B is -15
how many degrees does the minute hand of a clock turn in 45 minutes
In 45 minutes the minutes of the clock turns 270 degrees
How to find the angular measure of the hands of clockThe hands of clock while rotating is observed to be rotating 6 degree per minute
This can be calculated based on the fact that in 60 minutes a clock makes a 360 degrees rotation, using this concept we have that
if 60 minutes = 360 degrees then 1 minute will be
1 minute = 360 degrees / 60 minutes
1 minute = 6 degrees
To calculate for 45 minutes we have
number of degrees in 45 minutes = 45 * 6
number of degrees in 45 minutes = 270 degrees
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How many terms is 3xy?
Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. If Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours who will run more kilometers assuming their running pace stays the same for the entire time? How do you know?
Answer: Daren
Step-by-step explanation:
The rate for Daren is 8.55 kph, while Umberto is 9.5 kph.
Find the total miles for Daren and Umberto:
8,55 x 3,5 = 29,925
9,5 x 3 = 28,5
Daren will run more kilometers than Umberto because the distance running is more than Umberto's.
Right triangle abc is on a coordinate plane. segment ab is on the line y = 2 and is 6 units long. point c is on the line x = −3. if the area of δabc is 6 square units, then find a possible y-coordinate of point c. 3 4 5 6
Answer:
(b) 4
Step-by-step explanation:
You want the y-coordinate of point C on the line x=-3 so that ∆ABC has area 6 square units with segment AB being 6 units long.
AreaThe formula for the area of a triangle is ...
A = 1/2bh
Given the base of 6 units, and area of 6 square units, we find the height to be ...
6 = 1/2(6)h
6/3 = h = 2
The height of the triangle is 2 units.
CoordinatesPoint C is given as being on the line x=-3. Its y-coordinate must differ from the y-coordinates of A and B by 2 units. Those y-coordinates are 2, so the y-coordinate of C is ...
2 ±2 = {4, 0}
Point C may have a y-coordinate of 0 or 4. The appropriate answer choice is 4.
Does anyone know what the answer is? Thanks!
Answer:
D
Step-by-step explanation:
An obtuse angle is one over 90. They both have one of them.
A talent contest has 8 contestants. Judges must award prizes for first, second, and third places. If there are no ties,
A. In how many different ways can the 3 prizes be awarded?
B. How many different groups of 3 people can get prizes?
A. The 3 prizes be awarded in 336 different ways.
B. The 3 people can get prizes in 56 different groups.
PROBABILITY CALCULATION
A. The different ways can the 3 prizes be awarded:
There are 8 contestants, so the number of ways to award the first prize is 8. Once the first prize is awarded, there are 7 remaining contestants for the second prize, and 6 remaining contestants for the third prize. So, the total number of ways to award the 3 prizes is 876 = 336.
B. The different groups of 3 people can get prizes:
This is a combination problem. To find the number of ways to choose a group of 3 people from a group of 8, we use the formula [tex]_{n} C_{r}[/tex], where n is the total number of people and r is the number of people we want to choose. In this case, n = 8 and r = 3, so the number of ways to choose a group of 3 people from 8 is ₈C₃ = 56.
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Each situation can be modeled using a linear equation. Describe the rate of change for each situation.
1. Andre started his no-interest savings account with $1,000. He makes the same deposit each week, and there is $1,600 in the account after 6 weeks.
2. Kiran starts with $748 in his checking account. After 4 weeks of spending the same amount each week, he has $716 left.
1. The rate of change, in this case, is $100 per week.
2. The rate of change, in this case, is $-8 per week.
1. In this situation, the rate of change of Andre's savings account can be modeled using a linear equation of the form - y = mx + b
where
y represents the balance in the account,
x represents the number of weeks,
m represents the rate of change (i.e., the amount of money added to the account each week), and
b represents the starting balance.
To find the rate of change, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
In this case, y represents the balance in the account after 6 weeks (i.e., $1,600),
y1 represents the starting balance (i.e., $1,000),
x represents the number of weeks (i.e., 6), and
x1 represents the number of weeks at the starting balance (i.e., 0).
Substituting these values into the point-slope form gives 1600 - 1000 = m(6 - 0), which simplifies to 600 = 6m.
Dividing both sides of the equation by 6 gives m = 100, so the rate of change is $100 per week.
2. In this situation, the rate of change of Kiran's checking account can also be modeled using a linear equation of the form y = mx + b,
where
y represents the balance in the account,
x represents the number of weeks,
m represents the rate of change (i.e., the amount of money spent from the account each week), and
b represents the starting balance.
To find the rate of change, you can again use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
In this case, y represents the balance in the account after 4 weeks (i.e., $716),
y1 represents the starting balance (i.e., $748),
x represents the number of weeks (i.e., 4), and
x1 represents the number of weeks at the starting balance (i.e., 0).
Substituting these values into the point-slope form gives 716 - 748 = m(4 - 0), which simplifies to -32 = 4m.
Dividing both sides of the equation by 4 gives m = -8, so the rate of change is $-8 per week.
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Which action can be taken to the expression in step 3 to give an expression for step 4? divide both the numerator and denominator by sin(x)sin(y) divide both the numerator and denominator by sin(x)cos(y) divide both the numerator and denominator by cos(x)sin(y) divide both the numerator and denominator by cos(x)cos(y)
The step which is to be taken to get the required result is to divide both the numerator and denominator by cos(x)cos(y).
The given question is incomplete, I am answering as per my general knowledge.
The values of all trigonometric functions depends on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
Sides of a triangle for which we can calculate these ratios are ,
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Divide both the numerator and denominator by cos(x)cos(y) with expression is (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y))
Step 3: (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y))
Step 4: (sin(x)sin(y) + cos(x)cos(y)) / (cos(x)cos(y))
In Step 3, the expression is (sin(x)sin(y) + cos(x)cos(y)) / (sin(x)sin(y)) which is a fraction. In order to obtain the expression for Step 4, both the numerator and denominator must be divided by cos(x)cos(y). This will result in the expression (sin(x)sin(y) + cos(x)cos(y)) / (cos(x)cos(y)) for Step 4.
In order to obtain the expression for Step 4, both the numerator and denominator must be divided by cos(x)cos(y).
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Bank account starts with $10 and doubles each week.Bank account D starts with $1000 and grows by $500 each week.
When will account c contain more money than account D.
0 weeks
3 weeks
9 weeks
11 weeks
15 weeks
89 weeks
Answer:
9 weeks
Step-by-step explanation:
set y as how much money they have
set x as how many weeks spend
Bank account C:
y = 10 * 2^x
Bank account D:
y = 1000 + 500x
Set this two equations equal to find the point of two bank account have the same amount of money:
10 * 2^x = 1000 + 500x
Solve the equation:
2^x = 100 + 50x
What is the value of the product 3 2i?
The product of 3 and 2i is 6i. This means that the real component of the product is 0, and the imaginary component value is 6.
The product of two complex numbers, such as 3 and 2i, can be calculated by multiplying their real and imaginary components separately. The real component of 3 is 3 and the imaginary component of 2i is 2. So, the real component of the product is 3 x 0 = 0, and the imaginary component is 2 x 3 = 6. Therefore, the product of 3 and 2i is 0 + 6i or 6i. This means that the real component of the product is 0, and the imaginary component is 6. To calculate the product of two complex numbers, simply multiply their real and imaginary components separately and add the results together.
step by step calculations
Real component of 3 x Real component of
2i = 3 x 0 = 0
Imaginary component of 3 x Imaginary component of
2i = 2 x 3 = 6
Therefore, the product is 0 + 6i or 6i.
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Find the value of x
The value of {x} in the given geometrical figure is 7.
What are angles?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection.Given is a pair of intersected lines.
We can write, as observed from the image that -
6x + 3 = 45 {Vertically opposite angles}
6x = 42
x = 7
Therefore, the value of {x} in the given geometrical figure is 7.
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PLEASE HELP
A plumber is cutting pieces of pipe that are 3.36 meters long. The pipe must be within 0.09 meters of the required length. Write and solve an absolute value inequality to find the range of the length of pipe.
If a plumber is cutting pieces of pipe that are 3.36 meters long, and the pipe must be within 0.09 meters of the required length. The equation representing this is 3.36 / x < 0.09
the solution to the equation is x > 37 1/3
How to find the inequality equationThe inequality equation representing the condition is written as follows
length of pipe = 3.36 meters
each pipe division must be within 0.09 meters meaning < 0.09 meters
The division into say x pieces is calculated by
3.36 / x < 0.09
solving the inequality gives
3.36 / x < 0.09
3.36 / 0.09 < x
31 1/3 < x
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Segment VU is parallel to segment LM. Find the missing length.
L
M24 U
44
27
24
39
?
11
8
N
Segment VU is parallel to segment LM. The missing length is 16.
What parallel segments are there?If the matching lines formed by two segments are parallel, then the segments are parallel. In other words, two segments are considered to be parallel if they are in the same plane and do not cross even when stretched indefinitely in both directions.
Two line segments are parallel if any pair of matching angles, alternate interior angles, alternate exterior angles, or consecutive interior angles are supplementary. On a coordinate plane, parallel lines have the same slope.
If the matching lines formed by two segments are parallel, then the segments are parallel.
Segment VU is parallel to segment LM. The missing length is 16.
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Rewrite 2 and 1/5 as a decimal
Answer: 2.2
Step-by-step explanation: To find the decimal form of 2 1/5, we need to turn it into an improper fraction. That would be 11/5. Now we'd turn that into a division problem. So, we'd do 11/5, which 5 can go into 11 2 times, and would have 2 left over. I hope this helped.
What does it mean when an observational study is retrospective' When does it mean when an observational study is prospective? What does it moan when an observational study is retrospective? A retrospective study requires that individuals look back in three or require the researcher to look at existing records A retrospective study collects the data over time A retrospective study is a list of all individuals in a population along with certain characteristics of each individuals What does it mean when an observational study is prospective? A prospective study requires that individuals took hack in time or require the researcher to look at existing records A prospective study collects the data over time. A prospective study is a list of all individuals in a population along with certain characteristics of each individual.
A. Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.
A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.
In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.
On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.
In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.
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what is 53x-2=43+31x-1?
Answer:
x=2.05
Step-by-step explanation:
To solve for x, we start by adding 2 to both sides of the equation:
53x - 2 + 2 = 43 + 31x - 1 + 2
53x = 45 + 31x
Then, we subtract 31x from both sides of the equation:
53x - 31x = 45 + 31x - 31x
22x = 45
Finally, we divide both sides of the equation by 22:
22x/22 = 45/22
x = 2.05
Therefore, the value of x is 2.05.
Erin wants to buy a set of paintbrushes.
Store A sells a set for \$ 25.00$25.00 and offers a 10\%10% discount.
Store B sells a set for \$ 27.00$27.00 and offers a 20\%20% discount.
Store C sells a set for \$ 26.00$26.00 and offers a 15\%15% discount.
After calculating the discounted prices, place the stores in order from lowest price to highest price for a set of paintbrushes.
Lowest price:
Middle price:
Highest price:
Placing the stores in order from lowest price to highest price for a set of paintbrushes will be;
Lowest price: Store B
Middle price: Store C
Highest price: Store A
What is Discount?Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and it’s par value.
Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products
Store A
Discounted Price = $25 - ((10/100) x 25)
Discounted Price = $25 - $2.5
Discounted Price = $22.5
Store B
Discounted Price = $27 - ((20/100) x 27)
Discounted Price = $25 - $5.4
Discounted Price = $21.6
Store C
Discounted Price = $26 - ((15/100) x 26)
Discounted Price = $26 - $3.9
Discounted Price = $22.1
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Let f and g be differentiable functions with the following properties (i) g(x)>0 for all x (ii) f(0)=1 if h(x)=f(x)g(x) and h'(x)=f(x)g'(x) , then f(x)= :.
If h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.
Let f and g be differentiable functions such that g(x)>0 for all x and f(0)=1.
We can then write h(x) = f(x)g(x). Taking the derivative of h(x) with respect to x, we get:
h'(x) = f'(x)g(x) + f(x)g'(x)
Since h'(x) is equal to f(x)g'(x), then we can cancel out f(x)g(x) from both sides to get:
f'(x)g(x) = 0
Since g(x) is always greater than 0, this implies f'(x) = 0. This means that f(x) is a constant function. Since f(0) = 1, then f(x) = 1 for all x.
Therefore, if h(x) = f(x)g(x) and h'(x) = f(x)g'(x), then f(x) = 1.
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Why there is no AAA congruence theorem?
There is no AAA congruence theorem because it is a statement that states that if three angles of one triangle are equal to the three angles of another triangle, then the two triangles must be congruent.
The reason why there is no AAA congruence theorem is that it is not possible to determine the congruence of the two triangles based solely on the angles alone. The angles must be compared with the sides of the triangles. This means that two triangles with the same angles may not necessarily be congruent with one another. Therefore, the AAA congruence theorem does not exist.
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There is no AAA congruence theorem because it is a statement that states that if three angles of one triangle are equal to the three angles of another triangle, then the two triangles must be congruent.
The reason why there is no AAA congruence theorem is that it is not possible to determine the congruence of the two triangles based solely on the angles alone. The angles must be compared with the sides of the triangles. This means that two triangles with the same angles may not necessarily be congruent with one another. Therefore, the AAA congruence theorem does not exist.
congruence
the quality of being similar to or in agreement with something: the congruence of the two systems.
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In the ardmore hotel, 20 percent of the customers pay by american express credit card. (a) of the next 10 customers, what is the probability that none pay by american express? (b) at least two? (c) fewer than three? (d) what is the expected number who pay by american express? (e) find the standard deviation.
a) The probability that none pay by American express is 0.107.
b) The probability of atleast two is 0.8350
c) The probability of fewer than three is 0.1650
d) The expected number who pay by American Express is 4.
e) The Standard deviation is 1.788
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
In the Ardmore Hotel, 20 percent of the customers pay by American Express credit card.
Here,
Mean = μ = np = 20*0.2 = 4
Standard deviation = σ = √(npq) = √(20×0.2×0.8) = √(3.2) = 1.7889
Let A be the event in which they pay by American express.
∴ P(A) = 0.2
∴ The probability that they do not pay by American Express = 1 - P(A)= 0.8.
(a) P(none in 10) = 0.8^10 = 0.10737
(b) At least two:
P(none pay) + P(one pays) + P(at least two pay) = 1
P(at least two) = 1 - [P(none) + P(one pay)
= 1 - [0.10737 + 20C1(0.2)^1*(0.8)^19] = 1 - [0.10737+0.05765] = 0.8350
(c) Fewer than three = P(one) + P(two) = 1- 0.8350 = 0.1650
(d) The expected number who pay by American Express is:
Mean = np = 20*0.2 = 4
(e) Standard deviation:
σ = √(npq) = √(4* 0.8) = √(3.2) = √(1.6*2) = 1.788
Thus,
a) The probability that none pay by American express is 0.107.
b) The probability of atleast two is 0.8350
c) The probability of fewer than three is 0.1650
d) The expected number who pay by American Express is 4.
e) The Standard deviation is 1.788
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6. Make Sense and Persevere Glen compares the rates of
change of two linear functions represented in different forms.
a. For a linear function in the form y = mx + b,
how does Glen determine the rate of change?
b. How can Glen determine the constant rate of change of the linear
function presented in the table on the right? What is the rate of change?
The rate of change of a linear function is determined by the slope of the function and here for y = mx + b the slope is m as the funtion is in Slope intercept form.
What is Slope ?The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Slope indicates that for every unit change in the independent variable, x, the dependent variable will vary by the same amount, b. Slope indicates both direction and steepness. Positive slope causes the line to rise when it goes from left to right. When the slope is negative, the line descends when moving from left to right.
Here,
You may get the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two places. Rise divided by Run gives you the slope. Run = rise + slope Rise + run = slope.
The rate of change of a linear function is determined by the slope of the function and here for y = mx + b the slope is m as the funtion is in Slope intercept form.
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Fill in the table using this function rule.
y=6x+4
X Y
4
7
8
10
Solve (2/6)^12/7 (That's two sixths to the power of twelve sevenths.)
WRITE Math Suppose there was 1 centerpiece
for every 5 tables. Use counters to show the ratio of
centerpieces to tables. Then make a table to find the
number of tables if there are 3 centerpieces.
Answer: 15 tables.
Step-by-step explanation:
To show the ratio of centerpieces to tables using counters, we can use 1 blue counter to represent 1 centerpiece and 5 yellow counters to represent 5 tables. The ratio of centerpieces to tables can then be represented as 1:5, or 1/5.
To find the number of tables if there are 3 centerpieces, we can set up the following proportion:
3 centerpieces / 1 centerpiece = X tables / 5 tables
Cross-multiplying this proportion gives us:
3 * 5 tables = 1 centerpiece * X tables
Solving for X gives us the number of tables:
X = 15 tables
Therefore, if there are 3 centerpieces, there are 15 tables.
Rewrite 1/14x^3y + 8/14xy^2 using a common factor
Factor the polynomial.
x
y
(
x
2
14
+
8
y
14
)
i pasted this from p01nhub
