Answer:
28
Step-by-step explanation:
Average of first 6 scores is 12, so the total of those 6 scores is 6 × 12 = 72.
Average of next 12 scores is 36, so the total of those 12 scores is 12 × 36 = 432.
Total of all 18 scores is 72 + 432 = 504.
Overall average is 504 ÷ 18 = 28.
What series of transformations would carry the rectangle onto itself?
O(x+0,y-4), 180° rotation, reflection over the y-axis
O(x+0, y-4), 180° rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis
O (x-4, y+0), 90° counterclockwise rotation, reflection over the y-axis
The answer of the given question based on the graph transformations is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
What is Reflection?Reflection is a transformation that flips an object over a line, plane, or point. The line, plane, or point is called the "line of reflection", the "plane of reflection", or the "point of reflection", respectively. Reflection is a fundamental concept in geometry, and it has applications in various fields of mathematics, physics, and engineering. It is often used in symmetry analysis, transformation geometry, and computer graphics.
The series of transformations that would carry the rectangle onto itself is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.
To see why, we can analyze each transformation and its effect on the rectangle:
(x-4, y+0) translates the rectangle left by 4 units.
90° counterclockwise rotation preserves the right angles and parallel sides of the rectangle.
Reflection over the x-axis preserves the right angles of the rectangle and also preserves the orientation of its parallel sides.
Therefore, the final image after all three transformations would be congruent to the original rectangle, i.e., the rectangle would be carried onto itself.
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What are the solutions to 3(x-10)2=243?
x=1 and x=19
x=-1 and x=-19
x=343/3 and x=-343/3
x=1 and x=19
x=50.5 and x=30.5
Answer:
1 and 19
Step-by-step explanation:
3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300
If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0
Divide by 3 to get x^2 - 20x + 19 = 0
use the quadratic equation (-b±√(b²-4ac))/(2a) to get
(20±√324)/2 = (20±18)/2 = 1 and 19
What is measurement angle S to the nearest degree?
The unknown angle in the triangle is as follows;
m∠S = 38 degrees
How to find the angle measure of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
In the triangle QRS,
m∠Q = 4m∠R
m∠R = 3 / 4 m∠S
Therefore, let's find the angle m∠S in the triangle as follows:
Therefore,
m∠Q + m∠R + m∠S = 180°
let
m∠R = x
4x + x + 4 / 3 x = 180
5x + 4 / 3 x = 180
15x + 4x / 3 = 180
19x / 3 = 180
19x = 180 × 3
19x = 540
x = 540 / 19
x = 28.42
Therefore,
m∠S = 4 / 3 (28.42)
m∠S = 37.8947368421
m∠S = 38 degrees
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The graph above shows quadrilateral ABCD. Which set of vertices represents a rotation? a glide reflection? a translation? a similarity transformation? Write a rule for each of these transformations. 1. A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) 2. A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) 3. A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) 4. A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) 5. A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) 6. A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3)
Note that the transformation for the above vertices are given as follows.
What is the transformation for the above vertices ?From the given graph, we can determine the transformations as follows:
A'(-3, 1), B'(-1, 4), C'(-3, 6), D'(-6, 3) - This set of vertices represents a reflection across the line y = 3. Rule: (x, y) -> (x, 6 - y)A'(-5, -5), B'(-3, -8), C'(-5, -10), D'(-8, -7) - This set of vertices represents a glide reflection. Rule: (x, y) -> (x - 2, -y)A'(-8, 0), B'(-4, -6), C'(-8, -10), D'(-14, -4) - This set of vertices represents a translation. Rule: (x, y) -> (x - 4, y - 4)A'(1, -3), B'(4, -1), C'(6, -3), D'(3, -6) - This set of vertices represents a rotation of 270 degrees counterclockwise about the origin. Rule: (x, y) -> (y, -x)A'(-1, -3), B'(-4, -1), C'(-6, -3), D'(-3, -6) - This set of vertices represents a reflection across the line y = -2. Rule: (x, y) -> (x, -4 - y)A'(6, 1), B'(8, 4), C'(6, 6), D'(3, 3) - This set of vertices represents a similarity transformation (rotation and dilation). Rule: (x, y) -> (2x - 9, 2y + 1)Learn more about transformation at:
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
Mr.jibril is four times as old as his son. four years,he was seven times as old as his son. In how many years will Mr.Jibril's age be twice his son's age
Answer:
After 16 years Mr. Jibril will be twice as old as his son.
Step-by-step explanation:
t - age Mr. Jibril
s - son age
t=4s (father is 4 times older than son)
t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)
t=7s-28+4
t=7s-24
7s-24=4s
3s=24
s=8
t=32
x- years after Mr. Jibril will be twice as old as his son.
32+x=2(8+x)
32+x=16+2x
16=x
x=16
Martin is a hair stylist. He averages a weekly wage of $240 and
usually gets another $356 in tips. What is his average total
income?
To find Martin's average total income, we need to add his average weekly wage to his average weekly tips:
$240 (weekly wage) + $356 (weekly tips) = $596 (average total income)
Therefore, Martin's average total income is $596 per week.
The most appropriate measure of center for this data is the .
The mean is the most appropriate measure of center for the given data. While the median and mode were also calculated, the mean provides the best representation of the data's central tendency. The geometric mean was not applicable in this case.
Option A) Mean: To calculate the mean, we add up all the values and divide by the total number of values.
Mean = (20 + 6 + 42 + 13 + 15 + 10 + 9 + 12 + 12) / 9
Mean = 16.222
Option B) Median: To calculate the median, we need to arrange the values in order and find the middle value.
After arranging the values in ascending order: 6, 9, 10, 12, 12, 13, 15, 20, 42
The median is 12.
Option C) Mode: To calculate the mode, we need to find the most frequently occurring value. In this case, there is no value that occurs more than once, so there is no mode.
Option D) Geometric Mean: The geometric mean is used to calculate the average rate of change or growth. It is not suitable for this data set.
Therefore, option A) mean is the most appropriate measure of center for this data.
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Complete question:
The most appropriate measure of center for this data is the.
20, 6, 42, 13, 15, 10, 9, 12, 12
A) mean
B) median
C) mode
D) geometric mean
Answer:
median, A, 65
Step-by-step explanation:
.....
PLEASE HELPPP!!!
Solve the system of equations using elimination
Answer:
the answer is 3,9
Step-by-step explanation:
-3x+2y=9
3(x+y=12)
-3x+2y=9
3x+3y=36
5y=45
_ __
5 5
y=9
x+y=12
x+9=12
-9 -9
_______
x=3
Find the area and circumference of a circle with diameter 7 feet use the value 3.14 for pi
Answer:
Circumfrance= 21.991
area= 38.48
Step-by-step explanation:
2piR
R=3.5
:)
Two groups of volunteers are cleaning up the football stadium after the Homecoming game. Volunteers from the Band Booster Club have already cleaned 5 rows of bleachers and will continue to clean at a rate of 3 rows per minute. The leadership class has completed 6 rows and will continue working at 2 rows per minute. Once the two groups get to the point where they have cleaned the same number of rows, they will take a break and decide how to split up the remaining work. How long will that take? How many minutes will each group have cleaned by then?
1) The time it will take for both to have cleaned the same number of rows is: 1 minute
2) The number of rows cleaned by then is: 16 rows
How to solve Algebra word problems?We are told that Volunteers from the Band Booster Club have already cleaned 5 rows of bleachers and will continue to clean at a rate of 3 rows per minute. If the number of minutes is x, then the equation here is:
3x + 5
Similarly, the leadership class has completed 6 rows and will continue working at 2 rows per minute. If the number of minutes is x, then the equation here is:
2x + 6
The point at which they have cleaned the same number of rows will be:
3x + 5 = 2x + 6
3x - 2x = 6 - 5
x = 1 minute
Thus, after 1 minute they would have cleaned 8 + 8 = 16 rows of bleachers
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Erik just found an old set of reference books his grandfather gave him years ago. There are 12 same-sized books in the set, each being 6 inches long and 3 4 of an inch wide. The books are packed in a case shaped like a rectangular prism that fits them perfectly. The case has a volume of 432 cubic inches. How tall are the books?
Thus, each book has an 8-inch height.
What are some math examples of volume?
The quantity of space taken up by a three-dimensional object can also be used to describe volume. By determining the number of units cubes it contains, the volume of such a solid like such a cube or cuboid can be determined.
Get the volume of a single book in cubic centimeters to get things started. We can accomplish this by multiplying a book's length, width, and height:
Volume of one book = 6 inches x 3/4 inches x height
Volume of one book = 4.5 cubic inches x height
Since the 12 books are all the same size, their combined volume is:
Total volume of books = 12 books x Volume of one book
Total volume of books = 12 books x 4.5 cubic inches x height
Total volume of books = 54 cubic inches x height
Since we are aware that the case has a total volume of 432 cubic inches, we can construct the following equation:
Total volume of case = Total volume of books
432 cubic inches = 54 cubic inches x height
When we solve for height, we obtain:
height = 432 cubic inches / 54 cubic inches
height = 8 inches
Thus, each book has a height of 8 inches.
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I don't understand this could someone help I will give brainliest!
Answer: c
Step-by-step explanation:
3x − 2y = –17
–x − 9y = –4
Answer: x = -5, y = 1
Step-by-step explanation:
These are simultaneous equations
I will use the substitution method
BTW [1] means the top equation, and [2] the bottom equation
Rearrange [2] for x
-x = -4 + 9y
x = 4 - 9y
Substitute 4 - 9y into [1]
3(4 - 9y) - 2y = -17
Expand the bracket
12 - 27y - 2y = -17
Simplify
12 - 29y = -17
Rarrange for y
12 = 29y - 17
29y = 12 + 17 = 29
y = 1Now substitute y into either equation to solve for x
I will use [2] as it looks easier
-x - 9(1) = -4
Expand the bracket
-x -9 = -4
-x = 5
x = -5Now lets substitute x and y into [1] to check our answer
3(-5) - 2(1) = -17
-15 - 2 = -17
Help! I have a take home test due Tommorow please give me answers
This is the simplified ratio of lengths DE:EF as (2/√(29))√(34) : 1.
What is ratio?A ratio is a relationship between two or more quantities that indicates how many times one quantity is contained in another. It is a way of comparing quantities of the same kind, such as lengths, areas, volumes, or numbers. A ratio is usually expressed as a fraction or a colon (:). Ratios can be simplified by dividing both terms of the ratio by their greatest common factor (GCF). Ratios are used in many fields such as mathematics, finance, science, engineering, and statistics, among others. They are used to compare different quantities, to express proportions or rates, and to solve various mathematical problems.
Here,
We can use the distance formula to find the lengths DE and EF, and then calculate their ratio:
Length DE = √[(xE - xD)² + (yE - yD)²]
= √[(10 - 4)² + (15 - 4)²]
= √(6² + 11²)
= √(136)
= 2√(34)
Length EF = √[(xF - xE)² + (yF - yE)²]
= √[(12 - 10)² + (20 - 15)²]
= √(2² + 5²)
= √(29)
Therefore, the ratio of lengths DE:EF is:
DE:EF = (2√(34)) : (√(29))
We can simplify this ratio by dividing both sides by √(29):
DE:EF = (2√(34))/√(29) : (√(29))/√(29)
= (2/√(29))√(34) : 1
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Write the equation of the hyperbola using the given information, The hyperbola has vertices (-2,9) and (-2,3) and foci (-2,13) and (-2,-1)
The center of the hyperbola is the midpoint between the vertices, which is (-2,6).
The distance between the center and each vertex is 3, so the distance between the center and each focus is c = 7.
The distance between each vertex and focus is a = 4.
The equation of the hyperbola with center (h,k) is:
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
where b^2 = c^2 - a^2.
Plugging in the values we have:
- Center: (h,k) = (-2,6)
- a = 4
- c = 7
- b^2 = c^2 - a^2 = 49 - 16 = 33
So the equation of the hyperbola is:
(x + 2)^2 / 16 - (y - 6)^2 / 33 = 1
The nineteenth term in an arithmetic
sequence is 243, and the eleventh term is 147.
What is the value of the eighty-sixth term?
Answer:
1047
Step-by-step explanation:
a_n = a_1 + (n - 1)d
a_19 = 243
a_11 = 147
243 = a_1 + (19 - 1)d
147 = a_1 + (11 - 1)d
243 = a_1 + 18d
147 = a_1 + 10d
a_1 = 243 - 18d
a_1 = 147 - 10d
243 - 18d = 147 - 10d
-8d = -96
d = 12
a_1 = 147 - 10d
a_1 = 147 - 10(12)
a_1 = 27
The first term is 27. The common difference is 12.
a_86 = a_1 + (n - 1)d
a_86 = 27 + 85(12)
a_86 = 1047
Using the quadratic formula, solve 0 = 2x² 2x² - 10x + 7 Give each of your answers to 2 d.p.
Answer:
x1 ≈ 0,84; x2 ≈ 4,16
Step-by-step explanation:
Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)
a cylinder is leaking water at an unknown rate. the cylinder has a height of 6 meters and a radius of 5 meters. find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters.
The rate at which the volume of water in the tank is changing is 58π(dr/dt).
To find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters, we need to use the formula for the volume of a cylinder, which is given by:
V = πr²hwhere V is the volume of the cylinder, r is the radius, and h is the height.
We also need to differentiate the formula for the volume of a cylinder with respect to time to get an equation for the rate of change of the volume of the cylinder. Differentiating the formula for the volume of a cylinder with respect to time, we get:
dV/dt = πr²dh/dt + 2πrhdr/dt
where dV/dt is the rate of change of the volume of the cylinder, dh/dt is the rate of change of the height of the cylinder, and dr/dt is the rate of change of the radius of the cylinder.
Substituting the given values into the formula and simplifying, we get:
dV/dt = π(5²)(-8/100) + 2π(5)(6)(dr/dt) = -2π + 60π(dr/dt) = 58π(dr/dt)
Therefore, the changes in water volume in the tank is 58π(dr/dt).
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Select the equation that correctly describes the following real-world situation. 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.
(s x 10) ÷ 5 = 225
(s x 10) = 225 ÷ 5
225 ÷ (s + 10) = 5
(225 − 5) ÷ 10 = s
The arithmetic equation that correctly describes the following real-world situation is (s x 10) ÷ 5 = 225.
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.
We have to find the equation that correctly describes the following real-world situation.
(s x 10) ÷ 5 = 225
2s = 225
s = 112.5
Hence, the value of s is 112.5
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Answer: ( s x 10 ) `-. = 225
Step-by-step explanation:
The radius of a circle is 5 in. Find its circumference in terms of pi
The formula for the circumference of a circle is C = 2πr, where "C" is the circumference, "π" is pi (approximately equal to 3.14), and "r" is the radius.
Given that the radius of the circle is 5 inches, we can substitute this value into the formula to find the circumference:
C = 2πr
C = 2π(5)
C = 10π
Therefore, the circumference of the circle is 10π inches.
Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit. Over a fixed distance, the speed R varies inversely with the time T. In one
particular pair of markings, R is 41 mph when Tis 8 seconds. Find the speed of a car that travels the given distance in 5 seconds.
R= ? mph (Round to the nearest whole number.)
The the speed of a car that travels the given distance in 5 seconds from the information is 65.6 mph.
How can the speed be calculated?Speed and time are two fundamental concepts in physics and mathematics that are often used together to describe the motion of objects.
Speed refers to how fast an object is moving, and is typically measured in units of distance per unit of time, such as meters per second (m/s) or miles per hour (mph). Speed can be either constant, meaning the object is moving at the same speed throughout its motion, or variable, meaning the object's speed changes over time.
Given that the speed R varies inversely with the time T
R = 41 mph T = 8 seconds
The distance can be calculated as( speed * time)
Distance = ( speed * time)
= 41 * 8 = 328miles
The total distance travel can now bw seen as 328miles, the speed of a car that travels the given distance in 5 seconds can now be calculated as
Speed =Distance / time.
= 328miles/ 5 seconds
= 65.6 mph.
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A recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt write the ratio of baking soda to salt then find the value of the ratio
Answer:
Step-by-step explanation:
To write the ratio of baking soda to salt, we need to compare the amount of baking soda to the amount of salt in the recipe.
The recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt, so the ratio of baking soda to salt is:
3/4 : 3
To simplify this ratio, we can divide both numbers by the greatest common factor (GCF) of 3 and 4, which is 1.
3/4 divided by 1 = 3/4
3 divided by 1 = 3
So the simplified ratio of baking soda to salt is:
3/4 : 3 = 3: 12
To find the value of the ratio, we can divide both the numerator and denominator by 3:
3/3 : 12/3 = 1: 4
Therefore, the value of the ratio of baking soda to salt is 1:4.
USE PEDMAS
What is the correct numerical expression for "subtract the sum of 2 and 9 from the product of 4 and 3?"
2 + 9 − 4 x 3
(2 + 9) − 4 x 3
(4 x 3) − (2 + 9)
4 x (3 − 2) + 9
Answer:
The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:
4 x 3 - (2 + 9)
Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:
= 4 x 3 - 11
= 12 - 11
= 1
Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.
Step-by-step explanation:
A certain set of plants were constantly dying in the dry environment that was provided. The plants were moved to a more humid environment where life would improve. (a) Before moving all of the plants, the rescarchers wanted to be sure the new environment was promoting lfe. The study found that 21 out of 50 of the plants were alive after the first month. What is the point estimate? 42 (b) What Is the95 confldence Interval for the population proportlon? (Use a table or technology.Rud your answers to three decimal places.) X ,1555 (c what is the 99% confidence interval for the population proportion? Use a table or technology. Round your answers to three decima places.
The 99% confidence interval for the population proportion is (0.257, 0.583).
(a) The point estimate of the population proportion of plants alive after the first month in the more humid environment is:
point estimate = x/n = 21/50 = 0.42
So, the point estimate is 0.42.
(b) To find the 95% confidence interval for the population proportion, we can use the formula:
confidence interval = point estimate ± z√(point estimate(1-point estimate)/n)
where z is the z-score corresponding to the desired confidence level, n is the sample size, and √ represents the square root.
For a 95% confidence level, z = 1.96 (from a standard normal distribution table).
Plugging in the values, we get:
confidence interval = 0.42 ± 1.96√(0.42(1-0.42)/50)
= 0.42 ± 0.127
= (0.293, 0.547)
So, the 95% confidence interval for the population proportion is (0.293, 0.547).
(c) To find the 99% confidence interval for the population proportion, we can use the same formula but with a different z-score.
For a 99% confidence level, z = 2.58 (from a standard normal distribution table).
Plugging in the values, we get:
confidence interval = 0.42 ± 2.58√(0.42(1-0.42)/50)
= 0.42 ± 0.163
= (0.257, 0.583)
So, the 99% confidence interval for the population proportion is (0.257, 0.583).
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As the demand for the products grew, a manufacturing company decided to hire more employees. For which they want to know the mean time required to complete the work for a worker
We can conclude after answering the presented question that Use the equation data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
The procedures that a manufacturing organisation might take to undertake a time study analysis are as follows:
List the tasks performed by the workers and describe what constitutes a complete unit of labour.
Choose a representative sample of employees to observe. The sample size should be high enough to be statistically significant, but not so large that observing all workers becomes unfeasible.
Use the data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.
By doing a time study analysis, the manufacturing organisation may acquire useful insights into their workers' productivity and find chances for process changes that will help them fulfil the rising demand for their products.
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Measure angels level D. Please help
Answer: What is the measure of ∠ D?
By using the angle sum property of quadrilateral, we get the measure of angle ∠D is 76.765°.
Step-by-step explanation:
Somebody please please please help me
Answer:
a₅ = 11
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 2 , with a₁ = 3 , then
a₂ = a₁ + 2 = 3 + 2 = 5
a₃ = a₂ + 2 = 5 + 2 = 7
a₄ = a₃ + 2 = 7 + 2 = 9
a₅ = a₄ + 2 = 9 + 2 = 11
24 ÷ (5 + a) when a = 3
Answer:
3
Step-by-step explanation:
do the brackets first
(5+3) = 8
24÷8=3
so the answer is 3
1. An ant walks from center A, to point
B, clockwise to point C, and then
back to center A. What is the total
distance of her walk?
B
2cm
90°
A
C
let g be a function such that g(4)=8 and g’(4)=-3
let h be the function h(x)=sqrt
Answer:If (2t+1)is a factor then t=2−1 must be one of the zeroes of the given polynomial. Substituting in the given equation.
q((2−1))=4(2−1)3+4(2−1)2−(2−1)−1=4(8−1)+4(41)+(21)−1=(2−1)+1+(21)−1=0
Hence(2t+1) is a common factor of q(t)
Step-by-step explanation: