The surface area of the pyramid is 5,685 ft².
Solving for the surface area of the pyramid:To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:
length, l = 25 ft
width,w = 22 ft
Area = l x w
Area = 25 ft x 22 ft
Area = 550 ft².
To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of
Net dimensions of the pyramid:
length, l = 74.8 ft
width, w = 70.4 ft
h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]
h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]
h = 102.7 ft.
Now, we can use the formula for the area of a triangle:
Area = (1/2) x base x height,
where,
base,b = the length of the rectangular base (25 ft)
height = the slant height (102.7 ft).
So, the area of each triangular face is:
A = (1/2) x 25 ft x 102.7 ft
A = 1283.75 ft².
Since there are four triangular faces, the total area of all the triangular faces is:
A= 4 x 1283.75 ft²
A = 5,135 ft².
To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:
SA= 550 ft² + 5,135 ft² = 5,685 ft².
Hence, the surface area of the pyramid is 5,685 ft².
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Francesca bought a dress to wear to a wedding. The sales tax for the dress is 6%. She also paid $35, which was not taxed, to have the dress altered. If Francesca paid the store a total of $126.16. Which equation can you solve to determine the price of the dress?
The equation that can be used to determine the price of the dress
is x + 0.06x + 35 = 126.16.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Assuming the cost of the dress Francesca bought to be 'x'.
We know, 6% = 0.06 in decimal and She also paid $35 which was not taxed to have the dress altered.
Therefore, The equation to determine the cost of the dress would be,
x + 0.06x + 35 = 126.16.
1.06x = 126.16 - 35.
1.06x = 91.16.
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Temp (in "C) S -40 30 20 10 A. 10 O C. D. Ch 20 Time (in minutes) The temperature graph of freshly baked cookies after they are removed from the oven is shown in the graph. With the help of the tangent shown in the graph, estimate the rate of change of the temperature of the cookies after 20 minutes. B. -0.33 °C/minute -0.55 °C/minute 0.33 °C/minute 0.55 °C/minute 30 40 X
From the graph, it looks like the tangent line at 20 minutes has a slope that is close to 0.55°C/minute. So, the estimate of the rate of change of the temperature of the cookies after 20 minutes is approximately 0.55°C/minute.
What is rate of change?With the help of the tangent shown in the graph, it is estimated that the rate of change of the temperature of the cookies after 20 minutes is 0.55 °C/minute.This indicates that the temperature of the cookies is dropping at a rapid rate. After 40 minutes, the temperature has dropped from 40 °C to 30 °C, which shows a decrease of 10 °C in temperature.This rate of decrease in temperature is significant and it ensures that the cookies are cooked properly while also retaining their texture and flavor.This rapid decrease in temperature is a testament to the quality of the freshly baked cookies.This is called a rate of change. It is the rate at which the temperature of the cookies changes over time after being removed from the oven. The graph shows the temperature of the cookies over time in the form of a curve. The tangent to the curve at the point 20 minutes shows the rate of change of the temperature of the cookies.The tangent is sloping downwards, which implies that the temperature of the cookies is decreasing at a rate of 0.55°C per minute. This rate of change is referred to as the negative rate of change since it is a decrease in temperature over time.To learn more about rate of change refer to:
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Simplify the expression 14.33z - 3 - (6 - 5.23z).
Answer: 19.56z - 9
Step-by-step explanation: Hello! Here are the steps to solve this problem:
14.33z - 3 - (6 - 5.23z).
Firstly, you have to use the distributive property and distribute -1 to the parentheses using PEMDAS, Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
14.33z - 3 + -1(6 - 5.23z)
14.33z - 3 + (-6 + 5.23z)
14.33z + (-3) + (-6) + (5.23z)
14.33z + (5.23z) + (-3) + (-6)
(14.33z + 5.23z) + (-3 - 6)
19.56z + (-3 - 6)
19.56z + (-9)
19.56z - 9.
After Zach made a bicycle trip in Colorado, he used the equation y=1/20x+5000 to model y, his altitude in feet, in terms of x, the number of feet he bicycled. Which best describes the rate of change in altitude as he traveled
If the equation to model his altitude(y) in feet, in terms of the number of feet he bicycled(x) is y = 1/20x + 5000 , then the rate of change in altitude as he traveled is described by the fraction "1/20" .
The rate of change in altitude(y) as Zach traveled can be described as the slope of the line represented by the equation y = 1/20x + 5000. In this equation, the slope is 1/20.
The slope of a line is also called as the "rise over run", represents the change in y (altitude) per change in x (distance traveled). So in this case, the slope of 1/20 means that for every 20 feet Zach travels, his altitude changes by 1 foot.
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An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets.
The probability that Sam's first upgrade will occur after the third flight = 0.729
Let m represents the number of flights Sam must take in order to receive his first upgrade.
To find the probability that Sam's first upgrade will occur after the third flight.
i.e., to find P(m ≥ 4)
Here, 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight.
p = 0.10
q = 1 - p
q = 0.90
P(m ≥ 4) = 1 - P(m ≤ 3)
P(m ≥ 4) = 1 - [P(m = 1) + P(m = 2) + P(m = 3)]
P(m ≥ 4) = 1 - [0.1 + (0.9 × 0.1) + (0.9² × 0.1)]
P(m ≥ 4) = 1 - (0.1 + 0.09 + 0.081)
P(m ≥ 4) = 0.729
therefore, the required probability = 0.729
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The complete question is:
An airline claims that there is a 0.10
probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets.
What is the probability that Sam's first upgrade will occur after the third flight?
Determine the value of x in the figure.
The value of x in the figure is 3
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
Given;
The ratio of line segment QP=2:6
The ratio of line segment RP=X:9
Now, to find x
2/6=x/9
x=9/3
x=3
Therefore, the value of x according to given ratio will be 3
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Write this polynomial in descending order:
Photo Below
The polynomial in descending order is
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
-4[tex]x^5[/tex] + 4x³ + [tex]x^7[/tex] - 10 + 2[tex]x^4[/tex]
Arranging in descending order means arranging the terms in their descending order of power.
Now,
[tex]x^7[/tex] > [tex]x^5[/tex] > [tex]x^4[/tex] > x³
So,
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
Thus,
The polynomial is:
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
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Write an equation of the line that passes through a pair of points:
On a coordinate plane, a line goes through (0, 2) and (2, 0).
a.
y = x + 3
c.
y = -x + 2
b.
y = x - 3
d.
y = -x - 2
Answer: its d
Step-by-step explanation:
Answer:
The answer is C:
y = -x + 2
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What is the equation of the line that passes through the point (−4,8) and has a slope of −1?
Answer:
y - 8 = -1 (x + 4)
Step-by-step explanation:
I don't know if your suppose to solve it but i'll do it anyway
y - 8 = -1 (x+4)
y - 8 = -1x - 4
y - 8 +8 = -1x -4 +8
y = -1x + 4
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-4)}) \implies y -8= -1 (x +4) \\\\\\ y-8=-x-4\implies {\Large \begin{array}{llll} y=-x+4 \end{array}}[/tex]
...........................
Answer: 25.90
Step-by-step explanation:
Answer:
y = 57.2 - 7.15x
Step-by-step explanation:
Let y represent the number of gigabytes left, and let x = number of games.
Originally, y = 57.2.
Each game will occupy 57.2/8 gigabytes = 7.15 gigabytes.
x games occupy 7.15x gigabytes, so for x games loaded on his computer, the gigabytes left go down by 7.15x.
The equation is
y = 57.2 - 7.15x
The term glycol ____
indicates a lack of glucose.
Answer:The term glycol does not indicate a lack of glucose.
Step-by-step explanation:The term glycol does not indicate a lack of glucose, it refers to a specific class of organic compounds which are characterized by having two hydroxyl groups (-OH) on adjacent carbon atoms. Common examples include ethylene glycol and propylene glycol which are used in a variety of industrial and commercial applications such as antifreeze, coolants, and solvents.
Answer:
Glycopenia
Step-by-step explanation:
This is where the body lacks or shortage of glucose in the body which is properly needed.
Mrs. Hitchcock gave a test to each of her two classes and calculated the averages. Her Theater class has a standard deviation of 18. 7, and her British Literature class has a standard deviation of 1. 2.
Which class most likely larger? Why?
A the British Literature class, because the standard deviation is lower
B the Theater class, because the standard deviation is higher
C the British Literature class, because the standard deviation is higher
D the Theater class, because the standard deviation is lower
(A) The British literature class is most likely larger, because the standard deviation is lower.
A high standard deviation suggests that the observed data is very variable around the mean. This suggests that the observed data is widely dispersed. Instead, a modest or low standard deviation would suggest that the majority of the observed data is closely packed around the mean.
The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed.
Hence, when standard deviation is lower the class is most likely to be larger in number.
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Must these parallelograms be similar? Explain your reasoning.
Answer:
Yes. The two parallelograms are similar.
Step-by-step explanation:
Similarity:
Two parallelograms are said to be similar when the corresponding sides are in the same ratio.
[tex]\sf \dfrac{WX}{AB}= \dfrac{3}{2}\\\\\dfrac{XY}{BC}=\dfrac{9}{6} = \dfrac{9 \div 3}{6 \div 3}\\\\[/tex]
[tex]\sf = \dfrac{3}{2}[/tex]
[tex]\bf \dfrac{WX}{AB}=\dfrac{XY}{BC}=\dfrac{3}{2}[/tex]
Therefore, two parallelograms are similar.
what is the surface area
The surface area of the shape, can be found to be
How to find the surface area ?This is a composite shape which means you need to find the surface areas of the different shapes and then sum them up.
Area of triangle :
= 1 / 2 x base x height
= 1 / 2 x 20 x 25
= 250 cm ²
Area of rectangles :
= ∑ ( Length x Width )
= ( 20 x 15 ) + ( 25 x 15 ) + ( 15 x 30 )
= 1, 125 cm ²
The surface area is:
= 1, 125 + 250
= 1, 375 cm ²
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A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 4 inches. The vertical height between these bases is 2.3 inches. That vertical height intersects the bottom base, leaving 2.5 inches between it and the vertex to the left. The side on the right is the longest at 5.2 inches. There is a horizontal line connecting the vertex of the bottom base to the 5.2-inch side and that line is 3 inches.
Which of the following represents the total area of the figure?
The total area of the figure is 14.35 square inches
How to determine the total area of the figure?The six-sided figure is not given, however we can deduce the following parameters from the question:
The shape is made of a triangle and a trapezoid
The side lengths derived from the question are:
The triangle on top:
base: 4 inches and height: 2.3 inches
The trapezoid at the bottom:
Parallel sides: 2.5 inches and 4 inches with a height of 3 inches
So, we have the total area of the figure to be
Area of figure = 1/2 * 4 * 2.3 + 1/2 * (2.5 + 4) * 3
Area of figure = 14.35
Hence, the total area is 14.35 square inches
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Answer:
Step-by-step explanation:
dddcdcdcdc its d
2. Use a number line to show the temperature rising by 20 degrees and dropping by 20 degrees.
3. Use a number line to find the temperature if it was -7 degrees today, and rises by 20 degrees tomorrow.
Answer:
see graph attached
Step-by-step explanation:
I'LL DO ANYTHING!! PLEASE
The original length is 250 meters and the scale drawing width is 0.67 cm
The original length of the landFrom the question (see attachment), we have the following parameters that can be used in our computation:
Scale length = 0.5 meters
So, we have
Original length = 0.5/(1/500)
Evaluate
Original length = 250
This means that the original length is 250 meters
The scale drawing widthHere, we have
Scale drawing width = 335 * 1/500
Scale drawing width = 0.67 cm
Hence, the scale drawing width is 0.67 cm
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Four points B, A, E, and L are on a straight line, as shown. The point G is off the line so that angle BAG = 120 degrees and angle GEL = 80 degrees. If the reflex angle at G is x degrees, then what does x equal?
Given that the reflex angle at G is x degrees, then x is equal to
What is a reflex angle?A reflex angle is a type whose value falls within 180^o and 360^o. This implies that the value of the angle is greater than 180^o, but less than 360^o.
Considering the reflex angle given in the question, it can be deduced that;
m<AGE + m<GAE + m<GEA = 180^o
But,
i. m<GAB + m<GAE = 180^o (sum of angles on a straight line)
120 + m<GAE = 180
m<GAE = 180 - 120
= 60
m<GAE = 60^o
ii. m<GEA + m<GEL = 180^o
m<GEA + 80 = 180
m<GEA = 180 - 80
= 100
m<GEA = 100^o
Thus,
m<AGE + m<GAE + m<GEA = 180^o
m<AGE + 100 + 60 = 180
m<AGE = 180 - 160
= 20
m<AGE = 20^o
Therefore,
x + m<AGE = 360 (sum of angles at a point)
x + 20 = 360
x = 360 - 20
= 340
x = 340^o
x is equal to 340^o.
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At 6 a. M. , the temperature is 19. 4°C. Between 6 a. M. And noon, the temperature rises 3. 8°C. Between noon and 6 p. M. , the temperature falls 2. 5°C.
How much greater is the temperature at 6 p. M. Than it was at 6 a. M. ?
1. 3°C
6. 3°C
13. 1°C
20. 7°C
The temperature at 6 PM at greater than morning temperature at 6 AM by 1.3° C.
We know initially the temperature is 19.4° C.
The new temperature at noon will be = Temperature at 6 AM + temperature after noon
Keep the values
The new temperature at noon will be = 19.4 + 3.8
Performing addition
The new temperature at noon will be = 23.2° C
Temperature at 6 PM = Temperature at noon - temperature fall between noon and 6 PM
Keep the values
Temperature at 6 PM = 23.2 - 2.5
Performing subtraction
Temperate at 6 PM = 20.7° C
The difference between the temperature = 20.7 - 19.4
Performing subtraction
The difference between the temperature is 1.3° C.
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during the 1950s in the united states, married women who worked outside the home select one: a. faced social pressures to stay at home with their children. b. increased in number throughout the decade. c. accounted for nearly one-third of all married women. d. both increased in number throughout the decade, and accounted for nearly one-third of all married women. e. all these answers are correct.
The correct answer is that all the options are correct. Therefore option E is the correct option which states that all these answers are correct.
During the 1950s in the United States, married women who worked outside the home faced social pressures to stay at home with their children, but despite these pressures, the number of married women working outside the home increased throughout the decade. By the end of the 1950s, married women who worked outside the home accounted for nearly one-third of all married women.
It is worth mentioning that during that time, there were many societal expectations that women should be homemakers, and it was not as common for married women to work outside the home as it is today. Additionally, discrimination, lack of opportunities and lower wages for women further decreased the number of working women. However, during the 50s women started to participate more in the workforce, and that trend continued to increase in the following decades.
Therefore, The correct answer is that all the options are correct. Therefore option E is the correct option which states that all these answers are correct.
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please help quick!!!!!!!!!
Answer:
I believe the answer is 273
Step-by-step explanation:
The unshaded part would be an area of 273 because the base is 26 and the height 21. You times that and divide it by 2.
Along with that times the whole rectangle (26 x 21 = 546)
Subtract 546 and 273 and get 273.
Shaggy shaggy Raghu scooby boy doo ok
There are 50 bacteria present initially in a culture. In 3min., the count is 204800.
What is the doubling period?
Answer: The doubling period is the time it takes for the population of bacteria to double. To find the doubling period in this case, we need to determine how often the population doubles during the 3-minute period.
We know that the initial population is 50 and the final population is 204800, which means that the population has grown by a factor of 204800/50 = 4096. Since this is a multiplication by a factor of 4096, this means that the population has doubled 4096 times in 3 minutes.
To find the doubling period, we need to divide the total time (3 minutes) by the number of doublings (4096).
So, the doubling period is:
3 minutes / 4096 = 3/4096 minutes ≈ 0.0007 minutes ≈ 0.042 seconds
So, the population of bacteria doubles every 0.042 seconds
Step-by-step explanation:
Find the difference (-3x+8)-(x+10)
Answer: After doing the problem I got, -4x-2
•What turtle won the race?
•How long did the race take to complete?
•What speed was the Blue turtle traveling from 6-13 hours?
•Which turtle maintained a consistent speed through the entire race?
The time that it took to complete the race is the time it took for them to stop at the same position, hence it is of 16 hours.
For the Blue turtle, we have that:
At hour six, she was at a position of 10 km.At hour 13, she was at a position of 10 km.The velocity is given by the change in position divided by the change in time, hence:
v = (10 - 10)/(13 - 6)
v = 0.
The red turtle maintained a consistent speed through the entire race, as the slope of her line is constant.
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HURRY 30 POINTS
Mrs. Bready has a large bag filled with red and green cards. She tells the class that 15% of the cards are red and
85% are green. At the end of each class, she mixes the cards, reaches inside the bag, and draws out one card at
random. If a red card is drawn, the students will not be assigned homework. She shows the class the card, and
then places the card back in the bag. Carla would like to carry out a simulation to estimate the number of days it will take in order to get a "no homework" day. She assigns the digits to the outcomes.
00-14 = red
15-99 = green
Beginning at line 1 carry out one trial of this simulation. Use additional lines as needed. How many days does it take to find the first "no homework" day?
A)1
B)3
C)9
D)18
According to the concept of average it will take 3 days in order to get a "no homework" day.
The term called average in math is defined as the number you get when you add two or more figures together and then divide the total by the number of figures you added.
Here we know that Mrs. Bready has a large bag filled with red and green cards. She tells the class that 15% of the cards are red and 85% are green.
And here we need to determine the average number of days that it will take in order to get a "no homework" day based on these 5 trials,
Then the following calculation must be performed as,
=> 0.85 x 0.85 x 0.85 x 0.85 x 0.85 = X
=> x = 0.4437
Hence it will take 4.2 days in order to get a "no homework" day.
Here we have already know that the first trial is carried out then we have to subtract it from the total number then we get,
=> 4.2 - 1 = 3.2
When we round off the value then we get 3.
Therefore, option (b) is correct.
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Monomial of 9p^3 and 4p
Answer: A monomial is a polynomial with only one term. So 9p^3 and 4p are monomials.
9p^3 is a monomial with coefficient 9 and exponent 3 in the variable p.
4p is a monomial with coefficient 4 and exponent 1 in the variable p.
Step-by-step explanation:
The population of Sasquatch in a certain county can be modeled by the function P(t) = 140t t + 14 , where t = 0 represents the year 1803. What is the applied domain of P? Find P(0) and indicate the proper units. (Round your answer to the nearest whole number. ) Find P(250) and indicate the proper units. (Round your answer to the nearest whole number. )
The interpret of P(0) is 0 and P(250) = 132.58. The domain of P is [0, ∞]
The population of Sasquatch in Portage County can be modeled by the function P(t) = 140t/(t + 14) where t represents the number of years since 1803.
We have to interpret P(0).
To interpret P(0) we put t = 0 in the function then solve the function.
The function is:
P(t) = 140t/(t + 14)
Putting t = 0
P(0) = (140 × 0)/(0 + 14)
P(0) = 0/14
P(0) = 0
Now we interpret P(250) by putting t = 250.
P(250) = (140 × 250)/(250 + 14)
P(250) = 35,000/264
P(250) = 132.58
The domain of the time cannot be negative. So the domain of P is [0, ∞].
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The complete question is:
The population of Sasquatch in Portage County can be modeled by the function P(t) = 140t/(t + 14) where t represents the number of years since 1803. Find and interpret P(0) and P(250). Discuss with your classmates what the applied domain and range of P should be.
how many different paths from a to b are possible if each path must avoid the point with the circle around it?
This depends on the number of paths that exist between point a and point b. If there are more than one path, then the number of paths that avoid the point with the surrounding circle will be one less than the total number of paths.
The number of paths from point a to point b that avoid the point with the surrounding circle will depend on the total number of paths between the two points. If there are multiple paths between the two points, then the number of paths that avoid the point with the circle will be one less than the total number of paths.
For example, if there are three paths between a and b, then two of those paths will avoid the point with the circle.
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divide using synthetic division
(x^4-12x^2-6)/(x+3)
The quotient is x³-3x²-3x+9 and the remainder is -33.
What is synthetic division?Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor.
When we divide a polynomial p(x) by a linear factor (x - a) (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R is the remainder.
p(x)/q(x) = p(x)/(x- a) = Quotient + (Remainder/(x - a))
p(x)/(x - a) = Q(x) + (R/(x - a))
Given that, (x⁴-12x²-6)/(x+3)
Here, (x⁴+0x³-12x²+0x-6)/(x+3)
Now,
-3| 1 0 -12 0 -6|
| -3 9 9 -27|
________________
1 -3 -3 9 |-33
So, remainder = -33 and quotient = x³-3x²-3x+9
Therefore, the quotient is x³-3x²-3x+9 and the remainder is -33.
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