If Alonso pays the monthly payment each month for the full term. Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.
How to find the total amount?To calculate the total amount that Alonzo will repay over the 6-year term of the loan, we need to use the formula for the monthly payment on an amortized loan:
M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)
where:
M is the monthly payment
P is the principal amount
r is the monthly interest rate (which is the annual interest rate divided by 12)
n is the total number of payments (which is the number of years multiplied by 12).
Using the values given in the problem, we have:
P = $49,000
r = 6.55% / 12 = 0.005458333 (monthly interest rate)
n = 6 years * 12 months/year = 72
Substituting these values into the formula, we get:
M = $49,000 * 0.005458333 * (1 + 0.005458333)^72 / ((1 + 0.005458333)^72 - 1)
= $824.85 (rounded to the nearest cent)
To find the total amount he will repay, we can simply multiply the monthly payment by the number of payments:
Total amount =$824.85 * 72
Total amount = $59,389.2
Therefore, Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.
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The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.
There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
How to test for the evidenceTo test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.
Let p be the true proportion of mathematics research published by U.S. authors.
The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).
sample proportion, x/n = 62/130 = 0.477
The test statistic for a two-tailed test is given by:
z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)
= 2.41
Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.
Since 0.016 < 0.05
, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
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3. How many different numbers can be created by selecting 4 of the digits from the number 8712395?
840 different numbers can be created selecting 4 of the digits from the number
How many different numbers can be created selecting 4 of the digits from the numberFrom the question, we have the following parameters that can be used in our computation:
Number = 8712395
Digits = 4
The count of digits in the number is 7
Using the above as a guide, we have the following:
First digit = any of the 7second digit = any of the remaining 6Third digit = any of the remaining 5Fourth digit = any of the remaining 4So, we have
Numbers = 7 * 6 * 5 * 4
Evaluate
Numbers = 840
Hence, 840 numbers can be formed
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How would I solve this?
Answer:
f(1) = 1
Step-by-step explanation:
Open holes on a graph means that the function is not defined at that point, so we ignore the open hole.
At f(1), there is both an open hole at y=-2 and a closed hole at y=1
We ignore the open hole as it is not defined so the answer would be the closed hole, y = 1
So f(1) is 1
. Evaluate
11! 11!
24!
.
The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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Evaluate this limit without using L'Hopital's Rules
The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1
Evaluate this limit without using L'Hopital's RulesFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]
By substitution, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]
So, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]
Evaluate the exponents
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]
Evaluate the sum
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]
Hence, the solution is 1
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Given: mzA+m/B=m/B + mzC
Prove: m₂C=m/A
Write a paragraph proof to prove the statement.
We have proven that m∠C = m∠A.
We have,
We are given that m∠A + m∠B = m∠B + m∠C.
We want to prove that m∠C = m∠A.
Using algebra,
We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.
This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.
We can also use the transitive property of equality to show that
m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that
m∠A = m∠C.
Therefore,
We have proven that m∠C = m∠A.
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factor the expression
7x^2+12x+5
Hi again
I did it wrong
I'm here to redeem
When you have to factor these types of equations, you have to use a method called slide divide and bottoms up.
First you have to slide the a value to the end and mutiply with the c value so it is easily factorable
x^2+12x+35
Then you solve it like always
(x+7)(x+5)
Now, don't forget our buddy 7
7 is coming back
we divide 7 by 7 and 5 by 7
so
(x+1)(x+5/7)
7 has to move
So we move the 7 to the front
Therefore the answer is
(x+1)(7x+5)
If you have questions please ask me
Answer:
(7x + 5) (x + 1)
Step-by-step explanation:
7x² + 12x + 5
general form ax² + bx + c
a = 7
b = 12
c = 5
we have to find number that, if
... × ... = a . c = 7 . 5 = 35
... + ... = b = 12
and it would be
7 × 5 = a . c = 7 . 5 = 35
7 + 5 = b = 12
7x² + 7x + 5x + 5
= 7x (x + 1) + 5 (x + 1)
= (7x + 5) (x + 1)
#CMIIWplease hurry thats all i ask
The value of A, B, C,D are 33, 36,25 and 16 respectively
What is word problem?A word problem is a math problem written out as a short story or scenario. We use this word problem to solve the unknowns.
The total number of students is 60 and 24 students prefer volley ball. therefore the number of students that prefer basketball = 60-24 = 36 students
Since 11 student are girls that prefer basketball, therefore the number of boys that prefers basketball = 36-11 = 25
C = 25
and B = 36
55% of the students are boys, therefore the number of boys = 55/100 × 60 = 33
A = 33
therefore the number of boys that prefer volley ball= 33-25 = 8
Number of girls = 60-33 = 27
therefore number of girls that prefer volley ball = 27-11 = 16
D= 16
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Law if sines math question
Question: What are the two possible angles of a triangle with sides of 100 and 75 with a 40° as marked in the triangles above? Solution: Use the law of sines formula where the 75 length is opposite of 40°, and 100 is opposite of θ. Answer: The two possible angles for this triangle is 58.97° and 121.03°.
A 45-year-old man puts $2500 in a retirement account at the end of each quarter until he reaches the age of 66, then makes no further deposits. If the account pays 4% interest compounded quarterly, how much will be in the account when the man retires at age 71? There will be $ in the account.
Answer: The man will make deposits for 66 - 45 = 21 years, or 21 x 4 = 84 quarters.
The quarterly interest rate is 4% / 4 = 1%.
Let's use the formula for the future value of an annuity:
FV = PMT x ((1 + r)^n - 1) / r
where FV is the future value of the annuity, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, PMT = $2500, r = 1%, and n = 84. Substituting these values into the formula, we get:
FV = $2500 x ((1 + 0.01)^84 - 1) / 0.01
FV = $2500 x (5.409 - 1) / 0.01
FV = $2500 x 540.9
FV = $1,352,250
Therefore, there will be $1,352,250 in the account when the man retires at age 71.
The Problem Rodeos have long been a part of the culture in the southernmost part of the country and the growing popularity of the annual Easter event across South America prompted the Rupununi Development Corporation to construct a luxury resort with 60 two-bedroom suites for the visiting cultural troupes (troupe leaders and artistes). Capacity is ten troupe leaders and fifty artistes. Each suite is equipped with a small kitchenette, which contains a 7.3 cu ft. refrigerator, a microwave, and a coffee maker. A Drystan 6-piece bedroom set and the Ashley stationary sofa and love seat (all imported from Manaus at considerable cost) are also part of the furnishings. Each accommodation also has an excellent view if the Kanuku Mountains and nearby savannahs. The facility cost the Corporation $1,920,000 to build and equip and depreciation $160,000 per year (a fixed cost). Other operating costs include: Labor $320,000 per year plus $5 per suite per day Utilities $158,000 per year plus $1 per suite per day Miscellaneous $100,000 per year plus $6 per suite per day In addition to these costs, costs are also incurred on food and beverage for each guest. These costs are strictly variable, and (on average), are $40 per day for troupe leaders and $15 per day for artistes. Required Part A Assuming that the facility can maintain an average annual occupancy of 80% in both troupe leader and artistes suites (based on a 360 -day year), calculate the following: i. the annual fixed costs ii. the variable cost per guest by type of guest iii. the annual number of guest days by type of guest
Fully factorise 27t² + 15t
Answer: 3t(9t + 5)
Step-by-step explanation:
Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.
To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.
So we start by factoring out the 3t:
27t² + 15t = 3t(9t + 5)
Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:
3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t
Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).
algebra hw I will give brainlyest
The other value of x where g(x) = 15 is 16 in the absolute value function
Finding the value of xSince the vertex of the absolute value function is at (10,0), the equation for the function can be written as:
g(x) = a|x - 10|
To find the value of a, we can use the fact that the function passes through the point (4,15):
15 = a|4 - 10|
15 = 6a
a = 2.5
So the equation for the absolute value function is:
g(x) = 2.5|x - 10|
To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:
2.5|x - 10| = 15
|x - 10| = 6
x - 10 = 6 or x - 10 = -6
x = 16 or x = 4
Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.
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There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box. What is the probability that the marble is not green?
A) 92
B) 10
C) 85
D)20
We have 20 marbles in the bag. The probability of a marble that is not green is 20/20.
So the probability of the randomly that the marble is not green is 20/20 or just 20.
Help I have to turn this in tmw!!
Answer:
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the area of a 2D Rectangle.}[/tex]
[tex]\large\underline{\textsf{What is Area?}}[/tex]
[tex]\textsf{Area for 2D shapes is how much space is inside between edges. Consider edges}[/tex]
[tex]\textsf{as the sides of a shape.}[/tex]
[tex]\underline{\textsf{How are we able to find Area?}}[/tex]
[tex]\textsf{Many shapes require different formulas to find the area. Some have the same}[/tex]
[tex]\textsf{formulas however it depends on how many sides the shape has, and the number of}[/tex]
[tex]\textsf{dimensions shown in the shape. For a Rectangle it's simple. Because a Rectangle}[/tex]
[tex]\textsf{has 2 Dimensions (Length and Width), to find the area we should multiply}[/tex]
[tex]\textsf{the dimensions together, hence resulting in the amount of space inside the shape.}[/tex]
[tex]\large\underline{\textsf{Formula;}}[/tex]
[tex]\large\boxed{\tt Area = Length \times Width}[/tex]
[tex]\large\underline{\textsf{Plug in Values;}}[/tex]
[tex]\textsf{The Length and Width aren't mentioned in the question, but it doesn't matter}[/tex]
[tex]\textsf{since we're still going to get the same answer no matter which place they're in.}[/tex]
[tex]\large\boxed{\tt Area = 8.6 \ cm. \times 3 \ cm.}[/tex]
[tex]\large\underline{\textsf{Solving for the Area;}}[/tex]
[tex]\textsf{We have our formula, now multiply the dimensions together.}[/tex]
[tex]\large\boxed{\tt Area = 25.8 \ cm.^{2}}[/tex]
A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal area?
The dimensions of the region which enclose the maximal area will be 40.5 feet in length by width 27 feet.
How to find the dimensions of the areaGiven that the farmer has 162 feet of fencing, we will have:
2L + 3W = 162 feet
2L = 162 - 3W
L = 162 - 3W\2
L = 81 -3/2W Eqn 1
Given that the area of a rectangle is A = L × W we will call this equation 2
Now we substitute the first equation in the second one to give
A = (81 -3/2W) × W
A = 81W -3/2W²
When we take the derivative W will equal
81/3 = 27
Now we substitute in the second equation, we will have:
= 81 - 3/2(27)
= 81 - 40.5
= 40.5.
So the length will be 40.5 feet while the width will be 27 feet.
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Overview
Question Progress
1/3 Marks
11
12
13
14
Homework Progress
27/30 Marks
At a school there are five lessons in a day.
In total, the five lessons last for 4 hours.
a) Assume that each lesson lasts the same amount of time.
How many minutes long is the final lesson?
Optional working
+ Answer:
b) In fact, the first lesson of the day is shorter than the other lessons.
The other lessons last the same amount of time.
What does this tell you about the length of the final lesson?
A It is shorter than the answer to part a)
B It is the same as the answer to part a)
C It is longer than the answer to part a)
minutes
Submit Answering
Time taken by final lesson is 48 minutes and time consumption will not be affected if first lesson takes less time to finish.
Given that;
The time to finish five lessons = 4 hours
Then one lesson takes = 4/5 hours to finish
(a) Since each lesson takes equal amount of time
Therefore,
The time taken by final lesson in minutes = (4/5)x60
= 48 minutes
(b) Since each lesson has own capacity of time so the time consumption for other lesson is not affected if first lesson takes less time.
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Find the slope of the tangent to f(x)=x^2 at the point (3,9).
Answer:
f'(x) = 2x, so f'(x) = f'(3) = 2(3) = 6.
I need help please
here is the picture is about Row Ops
The given operation of the matrix is expressed as: -9y + 2z = 12
How to use Matrix to solve simultaneous Equations?Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.
The simultaneous equations formed by the matrix are:
x + 2y + z = -5
4y - 2 = 3
4x - y + 6 = -8
We are told to Multiply row 1 by -4 and this gives us:
-4x - 8y - 4z = 20
Adding it to row 3 gives us:
-9y + 2z = 12
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How many more sunflowers with a height of 27 1/2 inches or more were there than sunflowers with a heigh less than 27 1/2 inches?
The number of sun flowers with a height of 27¹/₂ inches or more are 4 more than those with a height of less than 27¹/₂ inches
How to Interpret Dot Plots?A dot plot, which is also known as a strip plot or dot chart, is a simple form of data visualization that comprises of data points plotted as dots on a graph with an x- and y-axis. These types of charts are used to graphically depict certain data trends or groupings.
The number of heights below 27¹/₂ inches that exists in the given dot plot is seen to be 8 in number.
Similarly, the number of dot plots that exists above or equel to 27¹/₂ inches from the given dot plot are 12 in number.
Therefore, we can say that:
Difference in total number for both parameters = 12 - 8= 4
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Which of the following represents vector w = ❬–27, 35❭ in linear form?
w = –27i + 35j
w = 27i – 35j
w = –35i + 27j
w = 35i – 27j
Answer: w = –27i + 35j
Step-by-step explanation:
Line n is perpendicular to the x-axis and passes through the point (–3,–7).
Write the equation for line n.
What is the slope of line n?
The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.
Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.
To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:
x = -3
This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.
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Given that a function, g, has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could true for g.
A. g(-4)= -11
B. g(-13)= 20
C. g(0) = 2
D. g(7) = -1
The statement that could be true for the domain of g is g(-4) = -11.
option A.
Which statement is true for domain of g?
The function g has a domain of -20 s × s 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6.
The given statements that could be true for g is calculated as follows;
Option A: g(-4) = -11
Since the range of g is -5 s g(x) s 45, it is possible for g(-4) to be -11.
Therefore, this could be true.
Option B: g(-13) = 20
Since the domain of g is -20 s × s 5, it is not possible for g(-13) to be defined. Therefore, option B is not true.
Option C: g(0) = 2
We are given that g(0) = -2, so option C is not true.
Option D: g(7) = -1
Since the domain of g is -20 s × s 5, it is not possible for g(7) to be defined. Therefore, option D is not true.
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Find the area and central angle of the polygons given the apothem or side length. Thank you.
The missing parameters of the regular polygons are listed below:
Case 1: θ = 45°, a = 10.864 cm
Case 2: θ = 72°, s = 5.812 cm
How to compute parameters of regular polygons
In this problem we must determine missing parameters of regular polygons, that is, polygons with sides of equal length. All parameters are summarized below:
Central angle
θ = 360 / n
Relationship between apothema and side length
a = s / [2 · tan (180 / n)]
Where:
n - Number of sidesa - Apothemas - Side lengthNow we proceed to find missing parameters:
Case 1: s = 9 cm, n = 8
θ = 360 / 8
θ = 45°
a = (9 cm) / [2 · tan (180 / 8)]
a = 10.864 cm
Case 2: a = 8 cm, n = 5
θ = 360 / 5
θ = 72°
s = 2 · a · tan (180 / n)
s = 2 · (8 cm) · tan (180 / 5)
s = 5.812 cm
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Please help me i dont get this. PLEASE I GIVE 20 points. And I give BRAINLIEST
Answer:
A B
Step-by-step explanation:
Is between A or B
Answer: A yes
Step-by-step explanation:
The answer is A because they divided both sides by 5
Not by variable and they didn't add/sub
This equations are equivalent
an expression that is equivelent to 12x-3x
Answer:
it would be 9x
Step-by-step explanation:
because subtract 3 from 12 and leave the x
Find f(-1).
Provide your answer below:
f(t)=-3t²-2t+1
Answer:
f(-1)=0
Step-by-step explanation:
To evaluate the function f(t) = -3t² - 2t + 1, we will start by plugging in -1 everywhere t occurs in the function :
[tex]\star \phantom{t-u} f(-1)=-3(-1)^2-2(-1)+1\\\\\\\star\phantom{t-u} f(-1)=-3*1+2+1\\\\\star\phantom{t-u} f(-1)=-3+3\\\\\underline{\star\phantom{t-u}f(-1)=0}[/tex]
[tex]\bigstar[/tex] Therefore the answer is f(-1) = 0
A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, then compiles the results into a probability distribution as shown in the table:
a.) There is a 25% chance that a party will contain 5 or more people. b.) There is a 50% chance that a party will contain 4 or more people. c.) There is a 50% chance that a party will contain 2 or fewer people.
d.) There is a 75% chance that a party will contain 3 or more people.
There are 25% chance of 5 more people in the party.
Hence option (a) is correct.
Relative frequency = (number of times of occurrence of an event )/ (number of trials)
For the given table
relative frequency for 1 people = 0.05 = 5%
relative frequency for 2 people = 0.46 = 46%
relative frequency for 3 people = 0.18 = 18%
relative frequency for 4 people = 0.22 = 22%
relative frequency for 5 people = 0.06 = 6%
relative frequency for 6 people = 0.03 = 3%
Since relative frequency for 1 people is 5%
Therefore,
Relative frequency for 5 people is = 5x5%
= 25 %
Hence,
Relative frequency of 5 more people 25%.
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Find the perimeter of each figure
The perimeter of the composite figure is 46 metres.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the 2 dimensional figure. Therefore, the perimeter of the composite figure is the sum of the whole sides.
Therefore, the perimeter of the figure can be found as follows:
perimeter of the shape = 5 + 6 + 9 + 11 + 3 + 12
perimeter of the shape = 11 + 9 + 11 + 15
perimeter of the shape =20 + 11 + 15
perimeter of the shape = 31 + 15
perimeter of the shape = 46 metres
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Factor the polynomial completely. If the polynomial is prime, so state.
15y2 - 19y + 6
Answer: 15y2 - 19y + 6 = 0
Step-by-step explanation:
The first term is, 15y2 its coefficient is 15 .The middle term is, -19y its coefficient is -19 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 15 • 6 = 90 Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -19 .
