f(g(x))=x² + 8x +19 ; g(f(x))=x² + 7 are the value of the asked functions
explanation:-
the given functions are: f(x) = x² + 3 and g(x) = x + 4
f(g(x)) = f(x + 4) = (x + 4)² + 3 = x² + 16 + 8x +3 = x² + 8x +19
g(f(x)) = g(x² + 3) = x ²+ 3 + 4 = x² + 7
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Kiran and Clare like to race each other home from school. They run at the same speed, but Kiran's house is slightly closer to school than Clare's house. On a graph, their distance from their homes in meters is a function of the time from when they begin the race in seconds.
Answer:
Step-by-step explanation: 1. Down
2. Claire's line would go higher because she began further away from her house.
3. The lines would have the same slope , since they are going the same speed.
Initial Knowledge Check Divide. (x-2)/(3x-21)-:(5x-10)/(9x-63) Simplify your answer as much as possihlo
Dividing the fraction (x - 2) / (3x - 21) by (5x - 10) / (9x - 63) will result to 3/5.
To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is simply the fraction flipped upside down. So, the reciprocal of the second equation (5x - 10) / (9x - 63) is (9x - 63) / (5x - 10). Now we can multiply the two fractions together to get the answer.
(x - 2) / (3x - 21) × (9x - 63) / (5x - 10)
= [(x - 2)(9x - 63)] / [(3x - 21)(5x - 10)]
Now we can simplify the numerator and denominator by factoring out the common factors:
= (9x - 63)(x - 2) / (3x - 21)(5x - 10)
= (3)(3x - 21)(x - 2) / (3x - 21)(5)(x - 2)
= 3/5
So, the final answer is 3/5.
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the yearly interest on a sum of money for two consecutive years is is 400 and 440 respectively. calculate rate and principal
The principal is 50 and the rate of interest is 0.4.
The principal (P) and the rate of interest (R) can be calculated using the following equations:
P = (400*2)/(440 - 400)
R = (440 - 400)/(P*2)
Substituting the given values in the equations we get:
P = 2000/40 = 50
R = 40/100 = 0.4
To calculate the rate and principal of the sum of money, we can use the formula for simple interest: I = Prt, where I is the interest, P is the principal, r is the rate, and t is the time in years.
Given that the yearly interest for the first year is 400 and for the second year is 440, we can set up two equations:
400 = Prt
440 = Pr( t + 1)
Since the interest is for two consecutive years, the time in the first equation is t and the time in the second equation is t + 1.
We can rearrange the first equation to solve for P:
P = 400 / rt
Substituting this value of P into the second equation gives us:
440 = (400 / rt)( t + 1)
Simplifying and rearranging gives us:
440rt = 400t + 400
40rt = 400
rt = 10
Since we are looking for the rate and principal, we can substitute the value of rt back into the first equation:
400 = P(10)
P = 40
So the principal is 40 and the rate is 10 / t. To find the rate, we can substitute the value of P back into the first equation and solve for t:
400 = 40(10 / t)
t = 10
So the rate is 10 / 10 = 1.
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eady
Compare Functions-Quiz - Level H
-The equation and the table show the cost, y, for different sports programs as functions of the number
of classes, z.
) Complete the statement.
When the number of classes is ?
football is less expensive.
When the number of classes is ?
basketball is less expensive.
Football Program:
Number of Classes
1
2
3
4
Basketball Program: y
Total Cost ($)
15
30
45
60
9x + 10
X
Answer:Given that y represents the cost, and x represents the number of classes, to complete the statements, the table is given for Gymnastics while the equation, y = 18x + 20 is given for Ice-skating program.
Since the table already shows the cost for each specific number of classes for Gymnastics, find that of Ice-skating program for 1, 2, 3, and 4 classes.
For 1 class, substitute x = 1 into y = 18x + 20:
y = 18(1) + 20
y = $38
For 2 class, substitute x = 2 into y = 18x + 20:
y = 18(2) + 20
y = $56
For 3 class, substitute x = 3 into y = 18x + 20:
y = 18(3) + 20
y = $74
For 4 class, substitute x = 4 into the equation y = 18x + 20:
y = 18(4) + 20
y = $92
From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.
Ice-skating is less expensive when the classes is 3 or 4.
Step-by-step explanation:
From the given function, When the number of classes is 1 the football is less expensive.
When the number of classes is 1, the basketball is less expensive.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Four main categories can be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
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Use a linear approximation (or differentials) to estimate the given number. (Do not round your answer). (32. 03)4/5
Using linear approximation, we estimate that ([tex]32.03^{4/5}[/tex]) is approximately equal to 31.952. It's important to note that this is only an estimate and may not be exact.
To estimate the value of ([tex]32.03^{4/5}[/tex]) using linear approximation, we start by finding the differential of the function f(x) = [tex]x^{4/5}[/tex] at the point x = 32.
[tex]f(x) = x^{4/5}[/tex]
[tex]f'(x) = 4/5x^{-1/5}[/tex]
Evaluating [tex]f'(32)[/tex], we get:
[tex]f'(32) = (4/5)(32)^{-1/5} = 0.1585[/tex]
Now, using the linear approximation formula:
[tex]f(x) ≈ f(a) + f'(a)(x - a)[/tex]
where a is the point at which we are estimating the function, we have:
[tex]f(32.03) = f(32) + f'(32)(32.03 - 32)[/tex]
[tex]= 32^{4/5} + 0.1585(0.03)[/tex]
[tex]= 31.952[/tex]
Linear approximation is a useful tool for approximating values of functions near a given point, but it has limitations and may not work well for functions that are highly nonlinear or have discontinuities.
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2. For each of the following matrices \( A \in M_{n \times n}(R) \), test \( A \) for diagonalizability, and if \( A \) is diagonalizable, find an invertible matrix \( Q \) and a diagonal matrix \( D
Matrix A is diagonalizable
Yes, it is possible to test a matrix \( A \in M_{n \times n}(R) \) for diagonalizability. If \( A \) is diagonalizable, then there exists an invertible matrix \( Q \) and a diagonal matrix \( D \) such that \( A = Q D Q^{-1}\). To find these matrices, we can use the following steps:
1. Find the characteristic polynomial \( p(\lambda) \) of \( A \).
2. Find the eigenvalues of \( A \) by solving \( p(\lambda) = 0 \).
3. Find the corresponding eigenvectors for each eigenvalue of \( A \).
4. Construct the matrix \( Q \) as a matrix whose columns are composed of the eigenvectors of \( A \).
5. Construct the diagonal matrix \( D \) by placing the eigenvalues of \( A \) along the diagonal entries.
6. Check that \( A = Q D Q^{-1} \).
If these steps all check out, then \( A \) is diagonalizable.
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Ella is playing hide and seek with Dante and Mary. Dante is hiding 9 meters south of Ella, and Mary is hiding due east of Dante. If Ella is 15 meters from Mary, how far apart are Dante and Mary?
If Ella is 15 meters away from Mary and 9 meters away from Dante, then distance between Dante and Mary are 12 meters away from each other.
It is given that Ella is 9 meter away from Dante and in the Dante is in south of Ella. This means that if we consider a plane ground and mark the directions as north, south, east and west, Ella and Dante will be in north and south direction respectively. Since Mary is in the east direction of Dante, this means She will be in the South East direction of Ella and about 15 meters away from her. This creates a triangular connection between them.
Hence by applying the Pythagoras theorem, we get following equation:
ED^2 + DM^2 = EM^2
where,
ED = Distance between Ella and Dante
DM = Distance between Dante and Mary
EM = Distance between Ella and Mary
9^2 + DM^2 = 15^2
81 + DM^2 = 225
DM^2 = 144
DM = 12
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Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Answer:
33%
Step-by-step explanation:
Take the original amount and subtract to new amount.
330 -231
99
Divide this by the original amount.
99/300
.33
Change to a percent.
33%
This is the percent decrease.
In a survey, 195 consumers were asked about their buying preferences concerning a product that is sold in the market under three labels. The results were as follows.
15 buy only those sold under label A.
20 buy only those sold under label B.
28 buy only those sold under label C.
12 buy only those sold under labels A and B.
9 buy only those sold under labels A and C.
12 buy only those sold under labels B and C.
8 buy the product sold under all three labels.
How many of the consumers surveyed buy the product sold under
(a) At least one of the three labels?
consumers
(b) Labels A and B but not C?
consumers
(c) Label A?
consumers
(d) None of these labels?
consumers
104 consumers bought at least one of the three labels, 12 consumers bought labels A and B but not C 44 consumers bought label A and 91 consumers bought none of these labels because of the equations.
To find the number of consumers who buy the product sold under at least one of the three labels, we need to add up the number of consumers who buy the product under each label individually and those who buy the product under multiple labels.
However, we need to be careful not to double count those who buy the product under all three labels. Therefore, the formula for this calculation is:
At least one of the three labels = (A only) + (B only) + (C only) + (A and B only) + (A and C only) + (B and C only) + (A, B, and C)
Plugging in the given values, we get:
At least one of the three labels = 15 + 20 + 28 + 12 + 9 + 12 + 8 = 104 consumers
To find the number of consumers who buy the product sold under labels A and B but not C, we simply use the value given for those who buy only those sold under labels A and B:
Labels A and B but not C = 12 consumers
To find the number of consumers who buy the product sold under label A, we need to add up the number of consumers who buy the product under label A individually and those who buy the product under label A and one or both of the other labels. Therefore, the formula for this calculation is:
Label A = (A only) + (A and B only) + (A and C only) + (A, B, and C)
Plugging in the given values, we get:
Label A = 15 + 12 + 9 + 8 = 44 consumers
Finally, to find the number of consumers who buy the product sold under none of these labels, we subtract the number of consumers who buy the product under at least one of the three labels from the total number of consumers surveyed:
None of these labels = Total consumers - At least one of the three labels = 195 - 104 = 91 consumers
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find x. 42° 36° 113° x°
Answer:
x=35°
Step-by-step explanation:
please mark as brainliest
Check the picture below.
Select the correct answer
Answer:
Step-by-step explanation:
A.
Answer:
The answer is C
Algebra please help!
Answer:
burrito $3.00 , taco $1.50
Step-by-step explanation:
using the variables b and t for burrito and taco , then
2t + 2b = 9 → (1)
t + 3b = 10.5 → (2)
multiplying (2) by - 2 and adding to (1) will eliminate t
- 2t - 6b = - 21 → (3)
add (1) and (3) term by term to eliminate t
(2t - 2t) + (2b - 6b) = 9 - 21
0 - 4b = - 12
- 4b = - 12 ( divide both sides by - 4 )
b = 3
substitute b = 3 into either of the 2 equations and solve for t
substituting into (1)
2t + 2(3) = 9
2t + 6 = 9 ( subtract 6 from both sides )
2t = 3 ( divide both sides by 2 )
t = 1.5
1 burrito costs $3.00 and 1 taco costs $1.50
the formula used to calculate the cost to rent the ford figo is cost (in rand)=R900+R7 x n, (where n is the number of kilometers travelled) write the formulas to calculate the cost of renting the other 2 cars TOYOTA ETIOS-ONLY R15 PER KILOMETER VW POLO VIVO-THE CHEAPEST RATE PER KILOMETER ONLY R1150 BASIC FEE PLUS R3 PER KILOMETER
The formula to calculate the cost to rent Toyota Etios is R15 + R3 n.
The formula to calculate the cost to rent VW Polo Vivo is R11.50 + R3 n.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have the formula used to calculate the cost to rent the Ford Figo is cost (in rand)= R900 + R7 x n.
Now, Toyota Etios cost R15 per Km and per km charge will be R3.
So, the formula to calculate the cost to rent is
= R15 + R3 n
and, VW Polo Vivo cost R11.50 per Km and per km charge will be R3.
So, the formula to calculate the cost to rent is
= R11.50 + R3 n
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solve for x first answer gets brainliest
Answer:
The answer to your problem is, 9
Step-by-step explanation:
I can conclude that the answer is nine by the following step shown down below.
The bottom triangle the one that it on the " floor ".
It is an equilateral triangle which means that that all sides are the same length ( same with the one on top ).
So if one side is 9, the other side is also 9.
Thus the answer to your problem is, 9
Answer:
[tex]x = 6 \sqrt{3} [/tex]
Pls help me in this question
The missing numbers in the expressions are:
a. x²
b. 4x²
c. 24x
d. 36x
e. 9x²
f. 1
What are algebraic expressions?Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
Let's use the equation 5x + 7 as an example.
Now here,
We can see that by simplifying the expressions we can see that all of them are in the form of (a+b)².
So, using the same to simplify the equations we get the missing numbers.
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Arnold bought 19 gallons of milk in gallon and half-gallon jugs. if he bought a total of 24 jugs, how many of each size did he buy?
Answer:
-14 gallon jugs
- 10 half-gallon jugs
Step-by-step explanation:
I'm not an expert at solving these algebraically, so I'm going to do this the old-fashioned way: Guess and Check.
Lets sum up our information:
- He bought 19 gallons
- He bought those 19 gallons with 24 jugs
- There are half-gallon and full gallon jugs
We know that if he bought 24 full gallon jugs, he would have 24 gallons of milk, but he only has 19, so this is not the answer
We know that if he bought 23 full gallons jugs and one half-gallon jug, he would have 23.5 gallons of milk, but he only has 19 gallons of milk, so this is also not the answer.
We keep reducing the number of full gallon jugs and increasing the number of half-gallon jugs until we reach 19 gallons total.
After trying different combinations, we can figure out that he bought
-14 gallon jugs
- 10 half-gallon jugs
Let f be defined as shown.
What is f-¹(-3)?
Answer:
The notation f⁻¹(-3) refers to the value(s) of x for which f(x) = -3.
However, the function f is not given in the prompt. Therefore, we cannot determine the value(s) of x for which f(x) = -3 or find f⁻¹(-3) without knowing the definition of f.
Step-by-step explanation:
Help pls I can’t understand
In triangle ABC, measure of side BC or a is 8.8 unit
What is cosine rule?In trigonometry, the cosine rule states that the square of the length of any side of a given triangle is the sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
cosA = (b² + c² - a²)/2bc
Given,
In triangle ABC
A = 49° , b = 10, c = 11
By cosine rule
cosA = (b² + c² - a²)/2bc
cos49° = (10² + 11² - a²)/2(10×11)
0.656 = (100 + 121 - a²)/220
144.32 = 100 + 121 - a²
a² = 221 - 144.32
a² = 76.68
a = √76.68
a = 8.7567 ≈ 8.8
Hence, 8.8 unit is measure of side a in triangle ABC.
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(In the pic) why do we have to change signs?? I don’t get it pls help
Answer:
x = -2
x = 3
Step-by-step explanation:
Question 40
5
NUMBER THEORY The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 more than the original
number. Find the number.
The original number would be 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider that the 10s digit = x
And the units digit = y
x +y = 11
The Sum of the digits = 11
10x + y + 45 = 10y + x
Then Reversed number is 45 more than original,
10x - x + y + 45 = 10y
9x + y + 45 = 10y
9x + 45 = 10y - y
9x + 45 = 9y
Now, Put x + y = 11 into the equation just found.
9x + 45 = 9(11 - x)
x + 45/9 = 11 - x
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 6/2
x = 3
Therefore, we have;
x + y = 11
3 + y = 11
y = 11 - 3
y = 8
Henece, we can conclude that the original number is 38 and the new number is 83 which the digits are reversed.
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Help me. giving brainliest
Answer:
277 milliliters
Step-by-step explanation:
945 - 668 = 277
hope this helpz ya
Answer:
277 milliliters
Step-by-step explanation:
Initial volume of ice tea = 945 milliliters
Final volume of ice tea = 668 milliliters
∴Difference in the volume of ice tea = How much tea Jeffrey drank
= Final volume - Initial volume
= [tex](945 - 668)[/tex] milliliters
= [tex]277[/tex] milliliters
Sheldon has scored 6/18 of the points in a basketball game. How can you use division to simplify the fraction of the points he scored? What is 6/18 in simplest form?
Answer:
1/3
Step-by-step explanation:
6/18, divide each side by 3 and you get 1/3
Factor 10y-15 Write your answer as a product with a whole number greater than 1.
The answer is 5(2y-3).
Factorization is an easy process wherein you just need to find out the common factors and solve your question as per requirement.
To factor 10y-15, we need to find the greatest common factor (GCF) of the two terms. The greatest common factor (GFC) of 10 and 15 is 5. We can then factor out the GCF from each term to get:
10y-15 = 5(2y-3)
where 5 is a whole number greater than 1.
So the answer as a product with a whole number greater than 1 is 5(2y-3).
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Use the function value to find the indicated trigonometric value in the specified quadrant. \[ \mathrm{Fu} \] cc
The function value and the indicated trigonometric value are not specified in the question. Additionally, the specified quadrant is not mentioned. Therefore, it is not possible to provide an accurate answer to this question.
However, generally speaking, to find the indicated trigonometric value in a specified quadrant using a function value, you can use the following steps:
1. Identify the function and the quadrant in which the value is to be found.
2. Use the function value to find the reference angle in the first quadrant.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value.
For example, if the function value is sin(θ) = 1/2 and the specified quadrant is II, you can use the following steps to find the indicated trigonometric value:
1. Identify the function and the quadrant: sin(θ) and II.
2. Find the reference angle in the first quadrant: θ = 30°.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value: sin(150°) = 1/2.
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Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. a. What is the probability that none of these vehicles requires warranty service? b. What is the probability exactly one of these vehicles requires warranty service? c. Determine the probability that exactly two of these vehicles require warranty service. d.Compute the mean and standard deviation of this probability distribution.
The answer are mean and standard deviation of this probability distribution are 1.2 and 1.04403065089, respectively
Given that the probability of a new vehicle requiring warranty service within the first year is 10%, we can use the binomial probability formula to answer the questions.
The binomial probability formula is:
P(x) = nCx * p^x * (1-p)^(n-x)
Where:
n = number of trials
x = number of successes
p = probability of success
nCx = number of combinations of n things taken x at a time
a. The probability that none of these vehicles requires warranty service is:
P(0) = 12C0 * 0.1^0 * 0.9^12 = 0.282429536481
b. The probability that exactly one of these vehicles requires warranty service is:
P(1) = 12C1 * 0.1^1 * 0.9^11 = 0.35527136788
c. The probability that exactly two of these vehicles require warranty service is:
P(2) = 12C2 * 0.1^2 * 0.9^10 = 0.23622320128
d. The mean of this probability distribution is:
μ = n * p = 12 * 0.1 = 1.2
The standard deviation of this probability distribution is:
σ = √(n * p * (1-p)) = √(12 * 0.1 * 0.9) = 1.04403065089
Therefore, the mean and standard deviation of this probability distribution are 1.2 and 1.04403065089, respectively.
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1. a. Report the p-value (Sig.) Based on Mean (top row):
b. Is this statistic significant?
c. For the Levene’s Test, do we want a significant p-value? (Yes/No)
d. What does this p-value mean about the variance in the three groups?
possible medication to treat high blood pressure. They decide it would be best to have 3 groups of randomly selected male participants: • One group (n=5) will be given a high dose of HyBlox: • One group (n=5) will be given a low dose of HyBlox: • One group (n=5) will be given a placebo sugar pill. They measure participants' blood pressures on a continuous scale. Participants are blind to condition and don't know which pill they've been given. The experimenters hypothesize that the participants given the highest level of HyBlox will have the lowest mean blood pressure level, the low dose HyBlox will have the second-lowest mean blood pressure level, and that the placebo group will have the highest mean blood pressure level. QUESTIONS: 1. Is this study within-subjects, between-subjects, or mixed? 2. What are the independent and dependent variables?
This is a between-subjects study. The independent variable is the type of medication given. The dependent variable is the participants' blood pressures. The experimenters reported a p-value (Sig.) Based on Mean (top row) of 0.071. No, this is not statistic significant. No, we don't want a significant p-value for the Levene’s Test. This p-value of 0.071 indicates that the variance in the three groups is not significantly different.
1.
a. The p-value (Sig.) Based on Mean (top row): 0.071
b. This p-value indicates that the null hypothesis cannot be rejected, meaning that there is no significant difference between the three groups.
c. The Levene’s Test does not require a significant p-value for the data to be valid.
d. This p-value indicates that there is no significant difference in the variance between the three groups.
2. This is a between-subjects study.
Independent Variable: Dosage of HyBlox (high dose HyBlox, low dose HyBlox, or placebo sugar pill)
Dependent Variable: Blood Pressure on a continuous scale
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bro help me find the vol pls
Answer:
volume is L × W x
Step-by-step explanation:
15 x 12 x 6
see attached I wrote down for you.
Answer:
360 ft³
Step-by-step explanation:
Volume of a rectangular pyramid = (lwh)/3 = (12x6x15) / 3 = 1080/3 = 360 ft³
V = (length x width x height) ÷ 3
The length of a rectangle is twice its width. Find its area if its perimeter is 7 1/3 cm.
please help ive been stuck on this for a day tyy !!
Answer:
Let's start by using the information given in the problem to write an equation for the perimeter of the rectangle:
Perimeter = 2(length + width)
We know that the length of the rectangle is twice its width, so we can write:
length = 2*width
Substituting this expression into the equation for the perimeter, we get:
Perimeter = 2(2*width + width)
Simplifying this expression, we get:
Perimeter = 6*width
We are given that the perimeter is 7 1/3 cm, which we can convert to a mixed number:
Perimeter = 7 + 1/3 = 22/3
Substituting this value into the equation above, we get:
22/3 = 6*width
Solving for the width, we get:
width = 22/3 ÷ 6 = 11/9
Now that we have the width, we can use the expression for the length to find its value:
length = 2*width = 2(11/9) = 22/9
Finally, we can use the formula for the area of a rectangle, A = length * width, to find the area:
A = (22/9) * (11/9) = 242/81 square cm
Therefore, the area of the rectangle is 242/81 square cm.
Write an expression in terms of n to represent AD in rhombus ABCD.
In a rhombus, all sides are equal in length, so we can write:
AB = BC = CD = AD
Let's use n to represent the length of any of the sides, such as AB. Then, we can write:
AD = AB
Therefore, the expression in terms of n to represent AD in rhombus ABCD is simply:
AD = n
Explain all answers and show all work in order to receive full credit. 1. IfT:R4→R6is a matrix transformation defined byT(x)=Ax, what are the dimensions ofA? 2. IfS:R3→R2is a matrix transformation defined byS(x)=Bx, which of the following is true and why? Choose only one statement below. (a)Scould be onto, but it cannot be one-to-one (b)Scould be one-to-one, but it cannot be onto (c)Scould be onto, one-to-one, or both
1. The dimensions of A are 6 x 4.
2. The function is S could be onto, but it cannot be one-to-one. (C)
1. This is because T: R4 → R6 is a matrix transformation that maps from a 4-dimensional space to a 6-dimensional space. Therefore, the matrix A must have 6 rows and 4 columns in order to be able to multiply with a 4-dimensional vector x and produce a 6-dimensional vector T(x).
2. This is because S: R3 → R2 is a matrix transformation that maps from a 3-dimensional space to a 2-dimensional space.
This means that there are more input vectors than there are output vectors, so it is not possible for S to be one-to-one. However, S could be onto if every vector in R2 can be obtained from some vector in R3 through the transformation S(x) = Bx.
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