The solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equals sign (=). The expressions on each side of the equals sign can be made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable(s) that makes both sides of the equation equal.
To find the solution of -b²+ 2b = 0, we can use algebraic manipulation as follows:
-b² + 2b = 0
Factor out -b:
-b(b - 2) = 0
From this equation, we see that either -b = 0 or b - 2 = 0:
-b = 0 or b - 2 = 0
Solving for b in each case, we get:
-b = 0 --> b = 0
b - 2 = 0 --> b = 2
Therefore, the solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.
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Working with Actual Interest Earned
Debrorah puts $300 in a CD that earns 3.0% APR, compounded
quarterly, for 1 year. She is taxed at a rate of 20% on the interest she
earns. She takes her money out after 9 months and pays the penalty
fee of 1 quarter's interest.
Deposit
PENALTY
7. What is the total amount of interest that Deborah earns, after taxes?
Type answer here.
The account has an annual interest rate of 6.80%, compounded continuously.
What is interst rate?Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.
The interest rate of the account can be calculated as follows:
Rate = ln(1,698.49/1,051)/(8×ln(1))
Rate = 0.0680 or 6.80%
This means that the account has an annual interest rate of 6.80%, compounded continuously.
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Use the given frequency distribution to find the
(a) class width.
(b) class midpoints of the first class.
(c) class boundaries of the first class.
1) Weight (in pounds)
Class Frequency, f
135 - 139 6
140 - 144 4
145 - 149 11
150 - 154 15
155 - 159 8
For the given frequency table, (a) 5 (b) 137 (c) lower class boundary is 132.5, and the upper class boundary is 141.5.
What is a frequency table ?
A frequency table is a tabular summary of data showing the frequency (i.e., the number of occurrences) of each category or value in a data set. It usually consists of two columns: one listing the categories or values and the other listing the corresponding frequencies. Frequency tables are commonly used to summarize categorical data, but they can also be used to summarize numerical data by grouping it into intervals or classes.
Now,
(a) The class width is the difference between the upper class limit and the lower class limit. For this frequency distribution, we can see that the class width is the same for each class and is equal to 5.
(b) The class midpoints are found by taking the average of the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. So, the class midpoint is (135 + 139) / 2 = 137.
(c) The class boundaries are found by adding and subtracting half of the class width to the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. The class width is 5, so half of the class width is 2.5. The lower class boundary is 135 - 2.5 = 132.5, and the upper class boundary is 139 + 2.5 = 141.5.
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center (-4, -7), tangent to x = 2
Answer:
(x + 4)^2 + (y + 7)^2 = 36
Step-by-step explanation:
The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.
The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:
d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)
In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:
d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)
d = |-6| / sqrt(1)
d = 6
Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values we have found, we get:
(x + 4)^2 + (y + 7)^2 = 36
This is the equation of the circle that satisfies the given conditions.
This pattern follows the rule add 2. What is another feature of this pattern? (4 points) An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots. a The terms appear even, odd, even, odd. b All the terms are even. c Two terms are even, then two terms are odd. d All the terms are odd.
The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.
Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.
This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.
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Question 1 of 10
cos(7)=—
О А. У
OB.
-12
O C. - 12/2
с.
OD. -√3
Go off the photo not what is typed
The value of cos(7π/6) = -√3/2
Explain values
Values are principles or beliefs that guide our behavior and decision-making. They are deeply ingrained in our personalities and are shaped by our upbringing, culture, and experiences. Values can be ethical, moral, social, or personal and influence how we prioritize our goals and interact with others. Understanding our own values can help us make better choices, build stronger relationships, and lead a more fulfilling life.
According to the given information
The cosine of π/6 is √3/2, so the cosine of 7π/6 is:
cos(7π/6) = -cos(π/6) = -√3/2
Therefore, cos(7π/6) = -√3/2.
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Answer:
-√3/2
Steps:
Rewrite the angle as a sum or difference with its reference angle:cos ([tex]\pi[/tex] + [tex]\frac{\pi }{6}[/tex])
Simplify the expression using the general reduction formula: -([tex]\frac{\pi }{6}[/tex])
Evaluate the expression: -√3/2
Find the sum of the terms. The numerator of the simplified sum is .
Answer:
I apologize, but the statement you provided is incomplete. The numerator of the simplified sum is missing. In order to find the sum of the terms, we need complete information, including the numerator and denominator of the fraction or expression. Please provide the complete statement or equation so that I can assist you accurately.
Question 1 of 10 What is the area, measured in square centimeters, of the green shape pictured below? Do not include units in your answer. Icm 1cm Answer here
21 is the area, measured in square centimeters, of the green shape pictured below.
What is square?
Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).
the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.
The rectangle:
The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared
two right triangles:
The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9
Next, we add the two areas together: 12+9 = 21
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Marcus buys a car for $45,000. If he finances it for 5
years at an annual interest rate of 8.5%, what will his
monthly payment be?
Answer:
M ≈ $933.24
Step-by-step explanation:
To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:
M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)
where:
M is the monthly payment
P is the principal (in this case, $45,000)
r is the annual interest rate (in this case, 8.5%)
n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)
Substituting the given values, we get:
M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)
Using a calculator, we get:
M ≈ $933.24
Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.
1. If it takes you 2¹/2 hours to assemble one unit, how many units will you complete in 15 hours?
(Note: Change 2¹/2 to an improper fraction before calculating.)
Answer:
Step-by-step explanation:
Make a chart.
units hours
2 5
4 10
6 15
Spring Basketball Tournament Expenses and Income Guidelines:
1. A permit for the event is required and costs $75.60. It takes 8 hours to run a tournament for 8 teams.
2. Each player will be charged a $32 entry fee.
3. There will be exactly 8 players on each team.
4. The rent for a gym in a high school is $62.50 an hour.
5. A caretaker must be present for a Saturday permit and earns $56 an hour.
Will your Spring Basketball Tournament fundraiser make money? What adjustments might you make to this tournament to ensure that it is more profitable? Show your work and explain your thinking below.
Find tan(Q).
A 1
3 9
"5
135°
P
para os a
was a s
Save and Exit
Next
Submit
The answer for the given trignomatric function is equal to tan(Q) = 1, where Q=45 degrees.
What is angle?An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "∠" is used to denote angles. The Greek letter θ can be used to represent the angle between the two beams.
What is tangent?A line that only touches a circle or an ellipse at one point is said to be tangential in geometry. Assuming a line contacts the curve at P, "P" is referred to be the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve.
according to question,
we can say that sum of a triangle is 180 degrees
so, Q=45 degrees
Tan(45) = 1
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In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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A rectangular flower bed measures 10m by 6m. It has a path 2m
wide around it. Find the area of the path
The area of the path is 80 square meters.
Given: A rectangular flower bed measures 10m by 6m. It has a path 2m wide around it.
To Find: The area of the path.
Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.
So,
The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:
A outer = 14m x 10m = 140 m²
Now,
The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.
A inner = 10m x 6m = 60 m²
Now,
The area of the path.
A path = A outer - A inner
= 140 m² - 60 m²
= 80 m²
Thus, The area of the path is 80 square meters.
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Hurry please What is the mean for the following set of data?
2,5, 7, 8, 11, 11, 12
10
11
8
Answer:
8
Step-by-step explanation:
is it right?
find the value of x
Therefore, the value of x in the right triangle is 24 cm.
What is triangle?A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.
Here,
In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.
Using the Pythagorean Theorem, we can find the missing length x:
a² + b² = c²
where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.
In this case, a = 7 cm, b = x, and c = 25 cm.
Substituting these values into the Pythagorean Theorem, we get:
7² + x² = 25²
49 + x² = 625
x² = 625 - 49
x² = 576
x = √576
x = 24
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If <2 is equivalent to (2x-8)• what is the value of c?
A 62•
B 35•
C 28•
D 18•
Reason:
[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.
Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).
[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]
20. The volume of a large crate is 84 yd³. It is 23 yd wide and 4 yd high. What is the length of the crate?
Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
The wholesale cost of a dining room table is $1,315,80. The selling price of the table is $1,776.33. What is the markup for the table?
A 10%
B 35%
C 65%
D 90%
well, the markup is 1,776.33 - 1,315,80 = 461.33.
now, if we take 1315.80(origin amount), what is 461.33 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1315.80 & 100\\ 461.33& x \end{array} \implies \cfrac{1315.80}{461.33}~~=~~\cfrac{100}{x} \\\\\\ 1315.8x=46133\implies x=\cfrac{46133}{1315.8}\implies x\approx 35[/tex]
A company is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of all their employees are women. What do you think? Test an appropriate hypothesis and state your conclusion.
To test whether the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole, we can perform a hypothesis test.
Null Hypothesis: The proportion of women in executive-level positions is equal to or greater than the proportion of women in the company as a whole.
Alternative Hypothesis: The proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole.
Using a significance level of 0.05, we can perform a one-tailed z-test for the difference in proportions.
Assuming a total sample size of 43 executives and a proportion of women in the company as a whole of 0.4, we find that the expected number of women in executive-level positions would be 43*0.4 = 17.2.
Using a z-test, we find that the test statistic is z = (13-17.2)/sqrt(0.4*0.6/43) = -1.89.
Using a z-table, we find that the p-value for z = -1.89 is approximately 0.029.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of women in executive-level positions is significantly lower than the proportion of women in the company as a whole. The company's explanation is not sufficient to account for the observed discrepancy.
~~~Harsha~~~
Christine is reviewing her credit scores form the three major credit bureaus. Her experian score is 765 her equifax score is 748, and her transunion score is 758 what is Christine’s median credit score? (Round to the nearest whole point if applicable)
Answer: To find the median credit score, we need to arrange the three scores in order from lowest to highest:
748, 758, 765
The median is the middle value in this ordered list. Since there are three scores, the median is the second score, which is 758.
Therefore, Christine's median credit score is 758.
Step-by-step explanation:
the temperature at 8 a.m. was -8.7 F. At 1 p.m. it was 9.3 F. What integer represents the change in the temperature from morning to afternoon?
The integer that represents the change in temperature from morning to afternoon is 18.
What is integer?The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.
To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:
9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F
Therefore, the integer that represents the change in temperature from morning to afternoon is 18.
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A student attempted to solve the system 5x + 2y = 10 and 10x + 2y = 1 by graphing. The graph and the conclusion are
below. What can you say about the student's work?
y
-10x + 2y = 1
5x + 2y = 10
The soluion is ().
O The solution is incorrect because the student did not correctly identify the intersection.
O The solution is correct and the lines are graphed correctly.
O The solution is correct, but the lines were graphed incorrectly.
O The solution is incorrect because the lines are not graphed correctly.
Answer:
Option A: The solution is incorrect because the student did not correctly identify the intersection.
Step-by-step explanation:
Solve by elimination method.
5x + 2y = 10; -10x + 2y = 1
Multiply the second equation by -1, then add the equations together.
(5x + 2y = 10)
-1 (-10x + 2y = 1)
Forms:
5x + 2y = 10
10x - 2y = -1
Add these equations to eliminate y.
15x = 9
Then solve 15x = 9 for x:
15x = 9
15/15 = 9/15 (Divide both sides by 15)
x = 3/5
Now that we've found x let's plug it back in to solve for y.
Write down the original equation:
5x + 2y = 10
Substitute 3/5 for x in:
5x + 2y = 10:
5(3/4)+2y=10
2y+3=10
2y+3-3=10+-3
2y=7
2y/2 = 7/2
y = 7/2
x = 3/5 and y = 7/2.
Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.
x^2+y^2+6x+2y-6=0 what is the center of this circle? what is the radius of this circle?
Answer:
center : (-3, -1) radius : 4
ixl What is the surface area of this cylinder? Use ≈ 3.14 and round your answer to the nearest hundredth. 15 cm 16 cm
We have to calculate the surface area of the cylinder.
It has a base diameter of 16 inches and a height of 15 inches.
The surface area will be equal to the sum of the area of the base, the area of the top (that is equal to the area of the base) and the lateral surface.
The area of the base can be calculated as:
[tex]\text{A}_{\text{b}}=\dfrac{\pi \text{D}^2}{4}[/tex]
[tex]\text{A}_{\text{b}}=\dfrac{3.14\times16^2}{4}[/tex]
[tex]\text{A}_{\text{b}}=\dfrac{3.14\times256}{4}[/tex]
[tex]\text{A}_{\text{b}}=200.96[/tex]
The lateral surface will be equal to the circumference of the base times the height. We then can calculate it as:
[tex]\text{A}_\text{l}}=(\pi \text{D})\text{h}[/tex]
[tex]\text{A}_\text{l}}=3.14\times16\times15[/tex]
[tex]\text{A}_\text{l}}=753.60[/tex]
Then, we can calculate the surface area of the cylinder as:
[tex]\text{A}=\text{A}_\text{b}}+\text{A}_\text{l}}+\text{A}_\text{l}}[/tex]
[tex]\text{A}=200.96+200.96+753.60[/tex]
[tex]\text{A}=1155.52[/tex]
Answer: the surface area is 1155.52 in²
Chef Lori uses 1 1/4 cup of milk for every 3/4 cup of broth in her soup recipe. This recipe will feed 4 people. Lori is making soup for a banquet that will feed 120 people. How many gallons of milk and broth combined does she need.
Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:
(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth
To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:
(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth
To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):
50/16 = 3.125 gallons of milk
30/16 = 1.875 gallons of broth
Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.
Step-by-step explanation:
4. This number line
number of minutes Diane read
week for 3 weeks.
0
200
100
300
How many minutes did she read after
the first week?
minutes
After the second week?
After the third week?
minutes
minutes
How many minutes did she read each
week? Explain how you know.
5. Diane reads the same number of minutes
each week. How many minutes does
she read after 4 weeks? After 5 weeks?
Skip count on the number line above to
find the answers.
After 4 weeks:
After 5 weeks:
minutes
minutes
4) Dane read an average of 400 minutes per week. 5) Diane will have read 2000 minutes after 5 weeks.
How to determine how many minutes did she read each week4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.
To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.
To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.
To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.
5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.
Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.
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The perimeter of the given triangle is 3x² + 2 units
and its two sides are given in the figure. Find its
third side.
Step-by-step explanation:
Perimeter is the total of all three sides added together:
2x^2 + x + 3x^2 -3 + ? = 3x^2 + 2 Simplify a bit on the L
5x^2 + x -3 + ? = 3x^2 + 2 subtract 5x^2 from both sides
x-3 + ? = - 2x^2 + 2 subtract x from both sides
-3 + ? = - 2x^2 - x + 2 finally, add 3 to both sides
? = - 2x^2 -x + 5