The rate per hour of Carrie's reading is 27.5 pages per hour
How to determine the rate per hourFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as:
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.This means that the rate of reading is
Rate = 5 ½ pages per 12 minutes
Express as decimal
This gives
Rate = 5.5 pages per 12 minutes
Convert minute to hours
So, we have the following representation
Rate = 5.5 pages per 0.2 hour
Evaluate the quotient
Rate = 27.5 pages per hour
Hence, the rate is 27.5 pages per hour
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Complete question
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.
At what rate, in pages per hour, did Carrie read?
2
In Prodigy, Luigi's inventory weighs 3 grams. He is collecting old
2
4
socks, each sock weighs - grams.
3
Let the total weight of his inventory be represented by i.
Let the number of old socks collected be represented by s.
An equation that represents this scenario is:
4
i = −(s) + 3
3
~IN
2
2
What is the total weight of his inventory if he
collects 27 socks?
138 is the total weight of his inventory if he collects 27 socks.
What is the total weight ?Luigi's inventory in Prodigy weights 18/6 grams. Each sock he is gathering weighs 20/4 grams.
Let I indicate the whole weight of his stock.
Let s indicate the quantity of used socks that have been gathered.
This situation is represented by the equation I = 20 / 4 * s + 18 / 6.
when s = 27 :
= 20 / 4 s + 18 / 6 = 5 s + 3
therefore i = 5 * 27 + 3 = 138 {Substitute).
138 is the total weight of his inventory if he collects 27 socks.
The complete question is In Prodigy, Luigi's inventory weighs 18/6 grams. He is collecting old socks, each sock weighs 20/4 grams.
Let the total weight of his inventory be represented by i.
Let the number of old socks collected be represented by s.
An equation that represents this scenario is:
i = 20/4 * s + 18/6
What is the total weight of his inventory if he collects 27 socks?
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What is the value of m?
10
30
70
150
what is the value of m
10 (the answer)
30
70
150
Which method is used for fraction?
Answer:
You can divide fractions in one of two ways: the cross multiplication method or the inverse multiplication method.
Step-by-step explanation:
The vertices of ADEF are D(2,5), E(6,3), and F(4,0)
Graph ADEF and its image when you translate ADEF using the vector (-2,-4).
Answer:
The resulting coordinate of △ D'E'F' is translated by the vector is (8, 5), (12,3), and (10, 0)
Given the coordinates of vertices of △ DEF as D (2, 5), E (6, 3), and F (4, 0).
If the coordinate of the vertices is translated by the vector (6, 0), the resulting coordinates of △ D'E'F' will be expressed as:
D'= (2+6, 5 + 0) = (8, 5)
E' = (6 + 6, 3 + 0) = (12, 3)
F' = (4 + 6, 0 + 0) = (10, 0)
The graph of both triangles is as attached;
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Step-by-step explanation:
Mackenzie borrowed some money from her
friend in order to help buy a new video game
system. Mackenzie agreed to pay the friend back
some amount every week until her loan was paid
off. Let L represent the amount Mackenzie owes
her friend after t weeks. The table below has
select values showing the linear relationship
between t and L. Determine how many weeks
when the amount of money Mackenzie owed her
friend was $100.
The equation that represent the amount Mackenzie owes her friend after t weeks is L = -6t + 90
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let L represent the amount Mackenzie owes her friend after t weeks
From the table, using the points (1, 84) and (3, 72):
[tex]L-L_1=\frac{L_2-L_1}{t_2-t_1} (t-t_1)\\\\substituting:\\\\L-84=\frac{72-84}{3-1} (t-1)\\\\L= -6t+ 90l[/tex]
The equation is y = -6x + 90
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In a small-group discussion, Leo is trying to explain to his classmates the purpose of the analogy in the following excerpt from an article:
To build a strong debate team, Mr. Gonzalez starts with a strong foundation: He recruits students who are interested in current events and are willing to put in the necessary time and effort. He then forms the framework by providing students with the tools they need to construct solid arguments.
The accurate statement based on the information is that B. The author compares building a debate team to building a house to help readers understand the importance of each step in the process.
How to illustrate the information?From the information, to strong debate team, Mr. Gonzalez starts with a strong foundation: He recruits students who are interested in current events and are willing to put in the necessary time and effort. He then forms the framework by providing students with the tools they need to construct solid arguments.
Based on the analogy, the author compares building a debate team to building a house to help readers understand the importance of each step in the process. The correct option is B.
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Complete question
In a small-group discussion, Leo is trying to explain to his classmates the purpose of the analogy in the following excerpt from an article:
To build a strong debate team, Mr. Gonzalez starts with a strong foundation: He recruits students who are interested in current events and are willing to put in the necessary time and effort. He then forms the framework by providing students with the tools they need to construct solid arguments.
Which of the following statements is accurate?
A.
The author compares building a debate team to building a house to help readers understand the challenge of recruiting eligible students.
B.
The author compares building a debate team to building a house to help readers understand the importance of each step in the process.
C.
The author compares building a debate team to building a house to help readers understand the similarities between building and debating.
D.
The author compares building a debate team to building a house to help readers understand the contrast between literal tools and figurative tools
Coby sells apples and bananas at his fruit store. He charges $6 for a pound of bananas, and $8 for a pound of apples. If a customer buys a total of 13 pounds of fruit and is charged $92, how many pounds of bananas did he buy? Also, how many pounds of apples did he get?
Answer:
6 bunches of bananas7 pounds of applesStep-by-step explanation:
We have to assume that a "piece of fruit" is either a bunch of bananas or a pound of apples. Without that assumption, there is insufficient information to work the problem.
Let B represent the number of bunches of bananas. Then 13-B is the number of pounds of apples. The total cost is ...
6B +8(13 -B) = 92
-2B + 104 = 92 . . . . . eliminate parentheses
B = -12/-2 = 6 . . . . . . subtract 104, then divide by the coefficient of B
13-B = 7 . . . . . . . . . . . the number of pounds of apples
The customer bought 6 bunches of bananas and 7 pounds of apples.
Hoped This Helped!
Can someone answer this question really quick
Simplify the expression by combining like terms.
43a−12b+13a+52b
Enter your answer as an expression, like this: 42x+53
Answer:
[tex]56a+40b[/tex]
Step-by-step explanation:
[tex]43a+13a-12b+52b=56a+40b[/tex]
Point z is the circumcenter of δlmn. point z is the circumcenter of triangle l m n. lines are drawn from each point of the triangle to point z. lines are drawn from point z to each side to form right angles and line segments z a, z b, and z c. which must be true?
The true about all of these statements are:
The lines drawn from each point of the triangle (L, M, N) to point Z will be perpendicular to each side of the triangle. The distance from each vertex of the triangle (L, M, N) to the circumcenter Z will be equal to the distance from the circumcenter to the midpoint of the opposite side of the triangle. The lengths of the segments ZA, ZB, and ZC will be congruent. The segments ZA, ZB, and ZC are the perpendiculars from the circumcenter to each side of the triangle. The circumcenter Z lies on the intersection of the perpendicular bisectors of the sides of the triangle.All three angle bisectors of triangle L,M,N intersect at circumcenter Z.THE CIRCUMCENTER OF TRIANGLEThe lines drawn from each point of the triangle (L, M, N) to point Z will be perpendicular to each side of the triangle. This is because the circumcenter of a triangle is the point that is equidistant from the three vertices of the triangle. When the distance from a point (in this case, the circumcenter Z) to each vertex of the triangle is the same, the line connecting the point to each vertex is perpendicular to the line containing the side opposite the vertex.The distance from each vertex of the triangle (L, M, N) to the circumcenter Z will be equal to the distance from the circumcenter to the midpoint of the opposite side of the triangle. By the definition of circumcenter, the distance from circumcenter to the midpoint of the opposite side is the same as radius of the circumcircle. and it is also the same distance from each vertex of the triangle to the center.The lengths of the segments ZA, ZB, and ZC will be congruent. The segments ZA, ZB, and ZC are the perpendiculars from the circumcenter to each side of the triangle. Since the circumcenter is equidistant from each vertex of the triangle, the lengths of these segments will be the same.The circumcenter Z lies on the intersection of the perpendicular bisectors of the sides of the triangle. The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of a triangle. This center is equidistant from the three vertices of the triangle, and it lies on the intersection of the perpendicular bisectors of the sides of the triangle. The perpendicular bisectors are lines that pass through the midpoint of a side of a triangle and are perpendicular to that side. So, the circumcenter is located at the intersection point of the three perpendicular bisectors of a triangle, which is also the point equidistant from all three vertices of the triangle.All three angle bisectors of triangle L,M,N intersect at circumcenter Z. It's important to notice that in this statement is referring to the incenter and not the circumcenter, and as such they are different properties and have different properties, location and constructions.Learn more about circumcenter here:
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Jen collects survey data which indicates that students who spend more time preparing for the AP test tend to do better than other students. Jen can now conclude that:
Preparing more for the AP test is associated with higher scores on the AP test.
The Relationship Between AP Test Preparation and PerformanceJen's data suggests that there is a correlation between the amount of time spent preparing for the AP test and the score that a student receives. This implies that there is a relationship between the two variables, and that increased preparation for the AP test is associated with higher scores. It is important to note, however, that this correlation does not necessarily imply causation. It is possible that students who are more likely to do well on the test are also more likely to put in more effort into preparing for it. Additional research would be needed to determine the exact nature of the relationship between the two variables.
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what is 1+2????
PLS HELP I will give brainliest
Answer:
3
Step-by-step explanation:
2+1 = 3
Answer:
3 ( 1 + 2 = 3)
Step-by-step explanation:
How did i get the answer 3?
Simple for example if you have 1 cookie's and your other two friend's have cookie's to. but they decide they don't want them so they give it to you well if you have 1 cookie and you get 2 more your adding more cookies to you collection.
what does it look like in problem form?
It look's like this:
1 + 2 = 3
in total you will have 3 cookies.
Find the values of the variables
Answer:
W = 59 degree
Y = 59 degree
Z = 53 degree
x = 121 degree
v = 121 degree
Step-by-step explanation:
W = 59 degrees because a triangle has a total of 180 degrees, and we know 2 of the angles, one is 31 degrees and the other is 90 degrees, so
90 + 31 = 121
180 - 121 = 59 degrees
So, W = 59 degrees
Y = 59 degrees because w and y are vertical angles.
z = 53 degrees because
68 + 59 = 127
180 - 127 = 53 degree
So, z = 53 degree
x = 121 degree, y = 121 degree because w, x, y, v add up to 360 degree
59 + 59 = 118
360 - 118 = 242
242 / 2 = 118 degree
So, x and y equal to 118 degrees.
If you can, please give me a Brainliest; thank you!
Your quality ratings for this week are 88, 93, 70, 62 and 100 My average is
My average from the given data sets is 82.6
What is the average mean of a data set?The average or mean of a data set is a measure of the data's central tendency. It is computed by the summation of all of the values in the dataset and then dividing the sum by the total number of values of the dataset.
The average or the mean of a data set is a good representation of the data as a whole because it takes into consideration all of the values in the data set.
From the given information:
My average = (88 + 93 + 70 + 62 + 100)/5
My average = 413/5
My average is 82.6
Therefore, we can conclude that from the quality ratings, the average mean is 82.6
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GEOMETRY PLEASE HELPP
Answer:
what do you need help on?
Mrs. Bowlin organized the markers into sets. If there were 9 markers
in each set, how many sets of markers did Mrs. Bowlin create? ANSWER QUICKLY
Based on the information provided, it can be concluded Mrs. Bowlin created a total of 63 sets each set with 9 markers.
What mathematical operation should be used to find the number of sets?The recommended mathematical operation in this case is division as the focus of this problem is distributing a total of markets or grouping them in sets of 9 markets.
What is the total number of sets Mrs. Bowlin created?First, let's identify the information that we already know:
Total number of markers: 567 markers
Number of markers in each set: 9 markers per set
567 / 9 = 63This means the total number of sets that Mrs. Bowlin created were 63 sets. You can verify this answer by multiplying the number of sets and the markets per set.
63 x 9 = 567Note: This question is incomplete; here is the complete question:
Mrs. Bowlin organized the markers into sets. If there were 9 markersin each set, how many sets of markers did Mrs. Bowlin create? there are 567 markers
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Which statements are true of the given function?
Check all that apply.
A) f[-1/2] = -2
B) f(0) = 3/2
C) f(1) = -1
D) f(2) = 1
E) f(4) = 7/2
(B and E are the answers)
Answer:
Option B (3/2) and E (7/2)
Step-by-step explanation:
Given function [tex]f(x) = \frac{x}{2} + \frac{3}{2} = \frac{(x + 3)}{2}[/tex]
so,
(A) [tex]f(\frac{-1}{2}) = \frac{\frac{-1}{2}+3 }{2} = \frac{\frac{5}{2} }{2} = \frac{5}{4}[/tex] (Incorrect)
(B) [tex]f(\frac{-1}{2}) = \frac{0+3 }{2} = \frac{3}{2}[/tex] (Correct)
(C) [tex]f(\frac{-1}{2}) = \frac{1+3 }{2} = \frac{4}{2} = 2[/tex] (Incorrect)
(D) [tex]f(\frac{-1}{2}) = \frac{2+3 }{2} = \frac{5}{2}[/tex] (Incorrect)
(E) [tex]f(\frac{-1}{2}) = \frac{4+3 }{2} = \frac{7}{2}[/tex] (Correct)
if three points are coplanar, they are also collinear
If three points are coplanar, they are also collinear is referred to as a false statement.
What are Collinear points?This is referred to as the points that lie on the same straight line or in a single line.
Coplanar points on the other hand are three or more points which all lie in the same plane. Any three points not on the same line, there is exactly one plane, but three points on the same line could be in separate planes which is why false was chosen as the correct choice.
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What is a rectangle circle called?
A rectangle circle is not a real shape; it is a figure of speech.
The Impossibility of a Rectangle CircleA rectangle-circle is an expression used to describe something that is impossible or illogical. It is used to emphasize the absurdity of something that could never exist in reality.
For example, someone might say that it's like trying to “fit a square peg into a rectangle circle.”
This expression conveys the idea that the task is impossible and that it is foolish to even attempt it. It is an example of a figure of speech used to make a point, rather than to describe a real shape.
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The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home. 60-69 70-79 Over 79 Total Male 1 9 5 Female 19 2 4 Total What is the probability that a resident is female ? Round your answer to three decimal places if necessary. a. 0.635 c. 0.62 b. 0.629 d. 0.625
The probability that a resident is female is 0.625.
Probability is a method for determining how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
We know that the probability of a function is the ratio of favorable cases to the total number of cases possible.
Given that,
Total number of females = 19+2+4 =25
total number of males=1+9+5 = 15
The probability that a resident is female is the Total number of females / total number of people
Hence total number of people = 25+15 = 40
So, Probability = 25/40 = 0.625
Therefore, the probability that a resident is female is 0.625.
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The probability that a resident is female = 0.625
The correct answer is an option (d)
The complete contingency table would be:
60-69 70-79 Over 79 Total
Male 1 9 5 15
Female 19 2 4 25
Total 20 11 9 40
Here, sample space i.e., the total number of residents = 40
So, n(S) = 40
Let event A: a resident is female
From the contigency table, the number of favourable outcomes of the event A are 25
So, n(A) = 25
Using the definition of probability, the probability of event A would be,
p(A) = n(A)/n(S)
p(A) = 25/40
p(A) = 0.625
Therefore, the required probability is 0.625
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A juice stand sells two types of fresh juice in 12 oz cups, the Refresher and the Super-Duper. The Refresher is made from 3 oranges, 2 apples and a slice of ginger.
The Super Duper is made from one slice of watermelon, 3 apples and one orange. The owners of the juice stand have 50 oranges, 40 apples, 10 slices of watermelon
and 15 slices of ginger. Let x denote the number of Refreshers they make and let y denote the number of Super-Dupers they make. Which would be correct
constraints for the oranges
The correct constraints for the oranges would be 3x + y <= 50.
What is the linear equality in two variables?
Linear equality in two variables is an equation that uses a linear function to describe a relationship between two variables (x and y). A linear function is of the form:
ax + by = c
Where a, b, and c are constants, and x and y are the variables.
The correct constraint for the oranges used in the Refresher and Super-Duper juice would be:
3x + y <= 50
This represents the maximum number of oranges that can be used, given the number of Refreshers (x) and Super-Dupers (y) that the juice stand is making. It says that the total number of oranges used in the Refreshers (3 oranges per Refresher) plus the total number of oranges used in the Super-Dupers (1 orange per Super-Duper) must be less than or equal to the total number of oranges the juice stand has on hand (50 oranges).
Hence, the correct constraints for the oranges would be 3x + y <= 50.
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if lim x→0 f(x) = [infinity] and lim x→0 g(x) = [infinity], then lim x→0 [f(x) − g(x)] = 0. true or false
If lim x→0 f(x) = [infinity] and lim x→0 g(x) = [infinity], then lim x→0 [f(x) − g(x)] , this statement is False.
What is limit ?
limit, mathematical concept based on the idea of closeness, used primarily to assign values to certain functions at points where no values are defined, in such a way as to be consistent with nearby values.
If limx→0 f(x) = ∞ and limx→0 g(x) = ∞,
then limx→0 [f(x) - g(x)] = 0, is false.
limx→0 [f(x) - g(x)]
= limx→0 f(x) - limx→0 g(x)
= ∞ - ∞
This is in-determinant.
Since the numerators are different, 4/0 and 8/0 cannot be equal to the same infinity,We have different types of in- determinant forms: 0/0, ∞/∞, 1∞ , 0⁰, etc,
If lim x→0 f(x) = [infinity] and lim x→0 g(x) = [infinity], then lim x→0 [f(x) − g(x)] ,this statement is False.
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5. Which of the following triangle side lengths will form a triangle?
• 6 cm, 7 cm, 13 cm
• 2 cm, 5 cm, 6 cm
• 3 cm, 6 cm, 10 cm
•cm, 4 cm, 7 cm
in an arthmrtic sequence beggining with 36 and ending with 405, how many integers are divisibe by 9?
The number of integers that are divisible by 9, given the arithmetic sequence beginning with 36 and ending with 405, is 42 integers
How to find the integers ?To find the integers that would be divisible by 9, in an arithmetic sequence beginning with 36 and ending with 405, find the multiples of 9 between 36 and 405.
This is because only the multiples of 9 are divisible by 9 and so the multiples of 9 between 36 and 405 would be the integers divisible by 9.
The multiples of 9 between 36 and 405 are :
36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405
This means that the number of integers divisible by 9 in the sequence would be :
42 integers
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evaluate the integral. (use c for the constant of integration.) ∫ tan^3(x)sec^6(x)dxI am stuck on the first step.According to my book, it says "if the power of the secant is even, save a factor of sec^2(x) and use sec^2(x) = 1 + tan^2(x) to express the remaining factors in terms of tan(x)If the power of tangent is odd, save a factor of sec(x)tan(x) and use tan^2(x) = sec^2(x) - 1 to express the remaining factors in terms of sec(x).The power of tangent is odd and the power of secant is even, what should I do next? Can I apply both rules to the equation? Or will it be wrong? Please show steps and help guide me.
Answer:
[tex]\displaystyle {\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}[/tex]
Step-by-step explanation:
[tex]\displaystyle \int {\tan^3(x)\sec^6(x)} \, dx\\\\=\int {\tan^2(x)\sec^5(x)\tan(x)\sec(x)} \, dx\\=\int {\bigr(\sec^2(x)-1\bigr)\sec^5(x)\tan(x)\sec(x)} \, dx\\[/tex]
Now let [tex]u=\sec(x)[/tex] and [tex]du=\tan(x)\sec(x)dx[/tex]:
[tex]\displaystyle \int {\bigr(u^2-1\bigr)u^5} \, du\\\\=\int {u^7-u^5} \, du\\\\=\frac{u^8}{8}-\frac{u^6}{6}+C\\\\=\bold{\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}[/tex]
So, because the tangent term was odd and the secant term was even, we had to break it up so we could have the factor sec(x)tan(x), and then turn tan²(x) into sec²(x)-1. Also, because the derivative of sec(x) is sec(x)tan(x), the substitution becomes really simple as you see above.
PLS HELP RN PLSSS
I NEED THIS DONE BY RN
Answer: It has to be 61 feet because you have to convert 20 yards to feet. It will 10980 dollars. And the area is 5490
Step-by-step explanation:
Write an equation for the line of best fit and then predict how much money travelers will spend in 2008. a. y = 2 x 380; travelers will spend about $410 billion in the year 2008. b. y = 2 x 320; travelers will spend about $350 billion in the year 2008. c. y = 20 x 320; travelers will spend about $620 billion in the year 2008. d. y = 20 x 380; travelers will spend about $680 billion in the year 2008.
The line of the equation should be y = 20x + 320 and travelers will spend about $620 billion in the year 2008. So, the option c is correct.
In the given question, we have to write an equation for the line of best fit and then predict how much money travelers will spend in 2008.
The graph of the question is given below:
From the graph the points are (1.5, 350) and (4, 400)
As we know that the formula of the equation of line is:
y-y(1) = {y(2)-y(1)}/{x(2)-x(1)} (x-x(1))
x(1) = 1.5, y(1) = 350, x(2) = 4 and y(2) = 400
Now putting the values
y-350 = (400-350)/(4-1.5) (x-1.5)
y-350 = 50/2.5 (x-1.5)
y-350 = 20(x-1.5)
y-350 = 20x-30
Add 350 on both side, we get
y = 20x + 320
So, the line of the equation should be y = 20x + 320.
So that travelers will spend about $620 billion in the year 2008.
Hence, the option c is correct.
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if event a and event b cannot occur at the same time, then events a and b are said to be : (a) mutually exclusive
(b) statistically independent
(c) collectively exhaustive
(d) none of the above
The correct option is option a) mutually exclusive.
Mutually exclusive events are events that cannot occur simultaneously. They are also referred to as disjoint or incompatible events. In probability theory and statistics, mutually exclusive events have a probability of zero occurring together.
For example, in a coin flip, getting "heads" and getting "tails" are mutually exclusive events because a coin cannot land on both "heads" and "tails" at the same time.
Another example would be the events "rolling a six on a dice" and "rolling an even number on a dice", these events are mutually exclusive because a dice can't land on a six and an even number at the same time.
In general, mutually exclusive events have no intersection, meaning that they don't share any outcomes.
Therefore, The correct option is option a) mutually exclusive.
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Use the distributive property with factoring to find the equivalent expression.
48d + 96g = (d + 2g)
Answer:
48d + 96g = 48(d + 2g)
Step-by-step explanation:
Between the numbers 48 and 96, the highest common factor(HCF) of these two numbers is 48 as 96/48 is exactly 2.
48/48 = 1
96/48 = 2
48d + 96g = 48(d + 2g)
hey can someone please help me with this math problem? thank you so much if possible :)
The solution for each system of equations is given as follows:
1. x = -4, y = 0.
2. x = 7, y = -2.
How to solve the system of equations?The first system of equations is defined as follows:
2x - y = -8.-3x + 4y = 12.By the substitution method, using the first equation, we have that:
y = 2x + 8.
Replacing in the second, we have that:
-3x + 4(2x + 8) = 12.
-3x + 8x + 32 = 12
5x = -20
x = -20/5
x = -4.
Hence the solution for y is given as follows:
y = 2(-4) + 8 = -8 + 8 = 0.
The second system of equations is defined as follows:
-3x - 6y = -9.-3x - 5y = -11.Multiplying the first equation by -1, we have that:
3x + 6y = 9.-3x - 5y = -11.Adding the two equations, the solution for y is obtained as follows:
y = -2.
Then the solution for x is calculated as follows:
3x + 6(-2) = 9
3x = 21
x = 21/3
x = 7.
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Find the product. (3a4 4)2 6a4 8 9a8 16 9a8 24a4 16 9a16 24a4 16
The product of expression (3a⁴ + 4)² is 9a⁸ + 24a⁴ + 16
In this question we have been given an expression (3a⁴ + 4)²
We need to find the product (3a⁴ + 4)².
Consider given expression
(3a⁴ + 4)²
We use the formula (a + b)² = a² + 2ab + b²
So, (3a⁴ + 4)²
= (3a⁴)² + 2(3a⁴)(4) + (4)² ...............(1)
We know that the exponents property that, for any non-zero numbers p, q, r;
[tex](p^q)^r = p^{(q \times r)}[/tex]
So, from expression (1),
(3a⁴)² + 2(3a⁴)(4) + (4)²
= 9a⁽⁴ ˣ ²⁾ + (2 × 3 × 4)a⁴ + 16
= 9a⁸ + 24a⁴ + 16
Therefore, the product (3a⁴ + 4)² = 9a⁸ + 24a⁴ + 16
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