how do you solve 2x-3(2x-3)=45
Answers
Answer:
x = -9
Step-by-step explanation:
2x - 3(2x - 3) = 45
2x - 6x + 9 = 45
-4x + 9 = 45
-4x + 9 - 9 = 45 - 9
-4x = 36
-4x/-4 = 36/-4
x = -9
Related Questions
Simplify the expression below.
−9×(−11)×(−4)
Answers
Step-by-step explanation:
=-8×(-11)×(-4)
=22×(-4)
= -88
hope it helps.
Answer: −9×(−11)×(−4)=−396
Step-by-step explanation:
Find the largest possible domain and largest possible
range for the following real-valued function. 4 f (x) : 1 +
v9 - x2
Answers
The largest possible domain for the function is -3 ≤ x ≤ 3, and the largest possible range for the function is f(x) ≥ 1.
The given function is f(x) = 1 + √(9 - x^2). We need to find the largest possible domain and largest possible range for this function.
To find the domain of the function, we need to consider the values of x that make the expression inside the square root non-negative. In this case, 9 - x^2 must be greater than or equal to 0.
Solving the inequality 9 - x^2 ≥ 0, we can rewrite it as x^2 - 9 ≤ 0. This is a quadratic inequality, and we can solve it by factoring:
(x + 3)(x - 3) ≤ 0
Now, we need to find the values of x that satisfy this inequality. The inequality is true when either both factors are negative or both factors are zero.
When (x + 3)(x - 3) = 0, we have x = -3 and x = 3.
When (x + 3)(x - 3) < 0, we have -3 < x < 3.
Therefore, the largest possible domain for the function is -3 ≤ x ≤ 3.
To find the range of the function, we need to consider the possible values that f(x) can take. Since the function involves a square root, the expression inside the square root must be non-negative, which means 9 - x^2 ≥ 0.
Solving the inequality 9 - x^2 ≥ 0, we can rewrite it as x^2 ≤ 9. This inequality is true when -3 ≤ x ≤ 3. Therefore, the largest possible range for the function is f(x) ≥ 1, since 1 is the minimum value of the function.
Learn more about function here:
https://brainly.com/question/29631554
#SPJ11
If you are asked on a quiz to give the first (leftmost) nonzero digit of the Avogadro constant and, not knowing the answer, you make a random guess what is the probability that your answer is the correct answer of 67 8. Births Example 2 in this section includes the sample space for genders from three births. Identify the sample space for the genders from two births In Exercises 9-12, assume that 50 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high. 9. 47 girls 10.26 girls. 11.23 girls. 12. 5 girls
Answers
a) 47 girls would be considered significantly low.
b) 5 girls would be considered significantly high.
c) 26 and 23 girls would be considered neither significantly low nor significantly high.
The Avogadro constant is approximately 6.0221 x 10^23. The leftmost nonzero digit is 6.
Since there are 10 possible digits (0-9), the probability of guessing the correct leftmost nonzero digit is 1/9.
The sample space for genders from two births is:
{BB, BG, GB, GG}
(a) Significantly low: This would depend on the context, but if we assume an expected proportion of 0.5 girls per birth, then any number of girls significantly lower than 25 (i.e., 50*0.5) could be considered significantly low. Therefore, 47 girls would be considered significantly low.
(b) Significantly high: Similarly, any number of girls significantly higher than 25 could be considered significantly high. Therefore, 5 girls would be considered significantly high.
(c) Neither significantly low nor significantly high: This would be any number of girls between 32 (i.e., 500.5 rounded up) and 18 (i.e., 500.5 rounded down), inclusive. Therefore, 26 and 23 girls would be considered neither significantly low nor significantly high.
Learn more about Avogadro constant
https://brainly.com/question/14637684
#SPJ4
Suppose (a.n - - - 31(1-0}10 expresses a in base 10. Prove that. 13 | a. if
and only if 13 i (an ' ' ' (1-1)") + 4H0. (b) Use part. (a) to decide whether
20192018 is divisible by 13.
Answers
We need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.
To prove that 13 divides a number "a" if and only if 13 divides (an - (1-1)") + 4H0, we need to show that both conditions imply each other
First, let's assume that 13 divides "a". This means that "a" can be written as 13k, where k is an integer. We can express this in terms of base 10 as (13k - (1-1)") + 4H0. Simplifying further, we get (13k - 1) + 4H0. Since 13 divides 13k and 13 divides 4H0, it also divides their sum. Therefore, if 13 divides "a", it also divides (an - (1-1)") + 4H0.
Next, let's assume that 13 divides (an - (1-1)") + 4H0. This means that (an - (1-1)") + 4H0 can be written as 13k, where k is an integer. Simplifying the expression, we get an - (1-1)") + 4H0 = 13k. Rearranging, we have an = 13k + (1-1)") + 4H0. Since 13 divides 13k + (1-1)") + 4H0, it also divides their sum. Therefore, if 13 divides (an - (1-1)") + 4H0, it also divides "a".
In conclusion, we have proven that 13 divides "a" if and only if 13 divides (an - (1-1)") + 4H0.
To decide whether 20192018 is divisible by 13, we can apply the result from part (a). Let's express 20192018 as (an - (1-1)") + 4H0. Since 13 divides (an - (1-1)") + 4H0, if 13 divides 20192018, it will also divide (an - (1-1)") + 4H0. Therefore, we need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.
To know more about expression visit:
https://brainly.com/question/22468783
#SPJ11
T/F: if the slope (b) of ŷ is positive, then the correlation coefficient (r) must also be positive.
Answers
True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship. If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.
In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.
To know more about correlation coefficient visit :-
https://brainly.com/question/29978658
#SPJ11
You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
For more questions on expected value
https://brainly.com/question/14723169
#SPJ8
there are 1200 students in a school. if 2/5 are girl what is the number and percentage of boys? find it
Answers
to find the number, multiply 1200 by 60%, or 0.60, and you get 720 boys.
final answer: 720 boys, 60%
Step-by-step explanation:
Hope it will help you...
PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answers
Answer:
\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)
to what decimal place should each answer be rounded? how many significant figures does the rounded answer have?
Answers
The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.
To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.
The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.
In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
Learn more about significant figures here:
https://brainly.com/question/29153641
#SPJ4
Help please ASAP! will give brainiest and other!!!!!
No robots pls!
The level words that you are weaks is represented by the equation y = 15
A. Graph the equation.
You learn ___ new vocabulary words per week.
B. How many vocabulary words do you learn after 5 weeks? You learn ____ words.
C. How many more vocabulary words do you learn after 6 weeks than after 4 weeks? You learn___ more words.
Answers
Answer:
A is 15, B is 75, and C is 30
Step-by-step explanation:
Answer:
a.
graph this on desmos
y=15x
you learn 15 new vocab words per week
b.
75 words in 5 weeks
c.
30 more words
Step-by-step explanation:
Natalie buys organic almonds priced at
$77 from the grocery store. How much
did she pay the cashier, if she received
$23 in change? $54 or $100
Answers
Answer:
100$
Step-by-step explanation:
100$-77$=23$
If she received 23$ in change she paid the cashier 100$.
An asset is purchased on January 1 for $46,200. It is expected to have a useful life of four years after which it will have an expected residual value of $6,300. The company uses the straight-line method. If it is sold for $32,600 exactly two years after it is purchased, the company will record a:
Answers
If an asset purchased for $46,200 with a useful life of four years and an expected residual value of $6,300 is sold for $32,600 exactly two years after its purchase, the company will record a loss of $3,300.
The straight-line method is used to allocate the cost of an asset evenly over its useful life. In this case, the asset's initial cost is $46,200, and it has a useful life of four years.
The annual depreciation expense is calculated as the difference between the initial cost and the expected residual value, divided by the useful life:
($46,200 - $6,300) / 4 = $9,225 per year
After two years, the accumulated depreciation would be
2 years x $9,225 = $18,450.
If the asset is sold for $32,600, the loss on the sale would be the difference between the selling price and the book value (initial cost - accumulated depreciation):
$32,600 - ($46,200 - $18,450) = $32,600 - $27,750 = $4,850
However, since the loss ($4,850) exceeds the expected residual value ($6,300), the loss recorded would be limited to the difference between the selling price and the expected residual value:
$32,600 - $6,300 = $26,300
Therefore, the company will record a loss of $3,300 ($26,300 - $23,000) when the asset is sold two years after its purchase.
To learn more about straight-line method click here: brainly.com/question/30243743
#SPJ11
The length of a rectangle is 3 less than twice the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by 2. Show your work.
Answers
The change in the area is represented by the expression ΔA = 9 · x + 4, where x is the original width of the rectangle.
What is the change in the area of the rectangle if side lengths are changed?
By geometry we know that the area of a rectangle is equal to the product of its width (x) and length (y). Based on the statement, the original rectangle is equal to:
A = x · y
A = x · (2 · x - 3)
And the change in the area is:
A + ΔA = (x + Δx) · (y + Δy)
A + ΔA = x · y + Δx · y + Δy · x + Δx · Δy
ΔA = Δx · y + Δy · x + Δx · Δy
ΔA = (2 · x - 3) · Δx + Δy · x + Δx · Δy
ΔA = 2 · (2 · x - 3) + 5 · x + 10
ΔA = 9 · x + 4
To learn more on rectangles: https://brainly.com/question/15019502
#SPJ1
17. Which expressions contain exactly two terms? Choose ALL that is correct. A. -5 +6x +3y²B. 4xC. 7-9x D. (x + 2)(y - 4)E. 8x² + 5x
Answers
To be able to determine which among the expression contains exactly two terms, let's count how many terms each expression has.
A.) -5 +6x +3y²
The expression has the terms: -5, 6x and 3y²
Therefore, the total number of terms is 3.
B.) 4x
The expression has the terms: 4x
Therefore, the total number of terms is 1.
C.) 7-9x
The expression has the terms: 7 and -9x
Therefore, the total number of terms is 2.
D.) (x + 2)(y - 4)
Let's first expand the expression,
\(\mleft(x+2\mright)\mleft(y-4\mright)\text{ = xy -4x + 2y - 8}\)The expression has the terms: xy, -4x, 2y and -8
Therefore, the total number of terms is 4.
E.) 8x² + 5x
The expression has the terms: 8x² and 5x
Therefore, the total number of terms is 2.
Conclusion: Only the expression at C and E contains exactly two terms.
Therefore, the answer is C and E.
Find the -intercept and -intercept of the line given by the equation. If a particular intercept does not exist, enter none into all the answer blanks for that row.
Answers
Answer: Check out the image attached below
y intercept = (0,15)
x intercept = (24,0)
================================================
Explanation:
The y intercept always occurs when x = 0.
Plug in x = 0 and solve for y.
5x+8y = 120
5(0)+8y = 120
8y = 120
y = 120/8
y = 15
The y intercept is located at (x,y) = (0,15)
-------------------
On the flip side, the x intercept always happens when y = 0.
5x+8y = 120
5x+8(0) = 120
5x = 120
x = 120/5
x = 24
The x intercept's location is (x,y) = (24,0)
Refer to the diagram below to see how the boxes are filled in.
Make sure you use parenthesis when writing the ordered pairs.
what would the coordinates (4, 15) tell you about the time and position of the runner?
Answers
The coordinates (4, 15) tell us about the position of the runner on a coordinate plane, but they do not provide any information about the time the runner was at that position.
To determine information about the runner's time, additional data would be required.
A coordinate plane is a two-dimensional plane consisting of two perpendicular axes that are labeled with coordinates. These coordinates are written as (x, y), where x represents the horizontal position of a point and y represents the vertical position of the point.
The point (4, 15) represents a point that is located 4 units to the right of the origin (x-axis) and 15 units up from the origin (y-axis).
However, this coordinate alone cannot provide information about the time the runner was at that position. Additional data, such as the time the runner arrived at or departed from that position, would be needed to determine information about the runner's time.
Thus, the coordinates (4, 15) tell us about the position of the runner on a coordinate plane, but they do not provide any information about the time the runner was at that position. To determine information about the runner's time, additional data would be required.
Learn more about coordinates from the given link:
https://brainly.com/question/17206319
#SPJ11
6th grade math help me plzzz
Answers
Answer:
4. 1/5
Step-by-step explanation:
Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years in a business/professional career. In its two years of publication, the magazine has been fairly successful. Now the publisher is interested in expanding the magazine’s advertising base. Potential advertisers continually ask about the demographics and interests of subscribers to Young Professional. To collect this information, the magazine commissioned a survey to develop a profile of its subscribers. The survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers. As a new employee of the magazine, you have been asked to help analyze the survey results.what do young professional be a good advertising outlet for online brokers justify your conclusion with statistical data?
Answers
The majority of Young professional subscribers are interested in personal finance and investment opportunities.
Young Professional magazine would be a good advertising outlet for online brokers because its target audience consists of recent college graduates who are in their first 10 years in a business/professional career. This demographic is likely to have a high level of education, which means they are more likely to understand and be interested in investment opportunities. Additionally, as young professionals, they are likely to have a higher disposable income and a desire to invest and grow their wealth.
According to the survey results, the majority of Young Professional subscribers are interested in personal finance and investment opportunities. This makes the magazine an ideal outlet for online brokers to advertise their services and reach potential customers. The survey also revealed that the majority of subscribers are tech-savvy and comfortable with online transactions, which makes them more likely to be interested in using online brokers for their investment needs.
Overall, the demographics and interests of Young Professional subscribers make it a good advertising outlet for online brokers. By advertising in the magazine, online brokers can reach a highly educated, tech-savvy, and financially motivated audience that is likely to be interested in their services.
Learn more about Professional
brainly.com/question/3396195
#SPJ11
The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
Responses
A (−3, −8)(−3, −8)
B (−6, 3)(−6, 3)
C (−5, −2)(−5, −2)
D (9, 8)
Answers
The point that preserves the function is option A(-3,-8).
What do you mean by function?
A function in mathematics from a set X to a set Y assigns 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.
According to the given question,
We have four option for the answer.
Note: if f is a function then each number of the domain has an unique image.
Since (regarding the table) the image of 9 is 6 then the answer D is wrong
The same apply on answers B and C .
Therefore, the right answer is A(-3,-8).
To learn more about function, visit:
brainly.com/question/5975436?referrer=searchResults
#SPJ1
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answers
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
Someone plz help me giving brainliest
Answers
Answer:
13/20
Step-by-step explanation:
Add up all the hours and then subtract by the total hours given.
A ________ is the value of a statistic that estimates the value of a parameter a critical value b standard error c. level of confidence d point estimate Question 2 Mu is used to estimate X True False Question 3 Beta is used to estimate p True False
Answers
A point estimate is the value of a statistic that estimates the value of a parameter. Question 2 is false and question 3 is true.
Question 1: A point estimate is the value of a statistic that estimates the value of a parameter.A point estimate is a single number that is used to estimate the value of an unknown parameter of a population, such as a population mean or proportion
Question 2: False
Mu (μ) is not used to estimate X. Mu represents the population mean, while X represents the sample mean. The sample mean, X, is used as an estimate of the population mean, μ.
Question 3: True
Beta (β) is indeed used to estimate the population proportion (p) when conducting hypothesis testing on a sample. Beta represents the probability of making a Type II error, which occurs when we fail to reject a null hypothesis that is actually false. By calculating the probability of a Type II error, we indirectly estimate the population proportion, p, under certain conditions and assumptions.
Learn more about point estimate at:
brainly.com/question/30310597
#SPJ11
what kind of triangle is shown
Answers
Answer:
right isosceles triangle.
Answer:
right scalene
Step-by-step explanation:
right angle - if one angle is 90 degree
scalene triangle- if all sides are of different lengths
Please help I don't understand!
Answers
Answer:
3.8
Step-by-step explanation:
1. Use sine rule
d/sin(D) = f/sin(F) (d=EF, f=DE=3)
2. cross multiply
d=f(sin(D)/sin(F)) = 3(sin(75)/sin(50))=3.783
Answer:
(b) 3.8
Step-by-step explanation:
Often, simple relations will help you solve geometry problems. Here, you only need to know that larger angles are opposite longer sides.
__
The angle opposite side EF is angle D, which is 75°. That angle is larger than angle F, which is opposite the side marked as having length 3.
This means EF > 3.
There is only one answer choice greater than 3. Choice B is 3.8.
EF ≈ 3.8
______
The only "work" is remembering that larger angles are opposite longer sides.
Stanley runs, swims, and bikes every day. During these workouts, heruns at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ranfor half an hour longer than he swam, and his biking time was twice hisrunning time. How long did Stanley run, swim, and bike yesterday if thetotal distance he covered was 64 miles
Answers
Equations
Let's call:
x = time Stanley swam yesterday.
We know he ran for half an hour longer than he swam, thus the time he ran was:
x + 0.5 = time Stanley ran yesterday
We also know he biked for twice the time he ran, thus:
2(x + 0.5) = time Stanley biked yesterday.
The distance covered by Stanley when swimming is
2.5*x
The distance covered by Stanley when running is:
9*(x+0.5)
The distance covered by Stanley while biking is:
16*2*(x + 0.5) = 32(x + 0.5)
The total distance is 64 miles, thus:
2.5*x + 9*(x+0.5) + 32(x + 0.5) = 64
Operating:
2.5x + 9x + 4.5 + 32x + 16 = 64
Simplifying:
43.5x + 20.5 = 64
Subtracting 20.5:
43.5x = 43.5
Thus:
x = 1
Stanley swam for 1 hour, he ran for 1+0.5 = 1.5 hours and biked for 2*1.5=3 hours
Swam: 1 hour, Ran: 1.5 hours, Biked: 3 hours
what is the value of 20+30(7+4)+5+2(7+99?
Answers
Answer:
the answer is 567
Step-by-step explanation:
20+30(11)+5+2(106)
20+330+5+212
= 567
Please help! I’m stuck on this
Answers
Answer:
i don’t see anything
Step-by-step explanation:
did you write something? because i can’t see it.
Consider the following functions.f(x) = x^2 + 2x, g(x) = 3x^2 - 1
Answers
Explanation
The domain of a function is the set of all possible inputs for the function.
so
Let
\(\begin{gathered} f(x)=x^2+2x \\ g(x)=3x^2-1 \end{gathered}\)Step 1
a) (f+g)(x)
to add the function , add like terms
\(\begin{gathered} f(x)+g(x)=(f+g)(x)=x^2+2x+3x^2-1 \\ (f+g)(x)=x^2+2x+3x^2-1 \\ (f+g)(x)=4x^2+2x-1 \end{gathered}\)so
\(a)(f+g)(x)=4x^2+2x-1\)(b) domain of the function:
the domain of a quadratic function f(x) is the set of x -values for which the function is defined,so
\(\text{Domain:(-}\infty,\infty)\)Step 2
c) (f-g)(x)
subtract the functions
\(\begin{gathered} f(x)-g(x)=(f-g)(x)=x^2+2x-(+3x^2-1) \\ (f-g)(x)=x^2+2x-3x^2+1 \\ (f-g)(x)=-2x^2+2x+1 \end{gathered}\)d)Domain:For any linear function the domain and range are always all real numbers
\(\mleft(-\infty,\infty\mright)\)Step 3
e) (fg)(x)
\(\begin{gathered} f(x)=x^2+2x \\ g(x)=3x^2-1 \\ \text{then} \\ (fg)(x)=(x^2+2x)(3x^2-1) \\ \text{apply distributive property} \\ (fg)(x)=(x^2\cdot3x^2)-(1\cdot x^2)+(2x\cdot3x^2)-(2x\cdot1) \\ (fg)(x)=3x^4-x^2+6x^3-2x \\ \text{reorder} \\ (fg)(x)=3x^4+6x^3-x^2-2x \end{gathered}\)f) again we have a polynomial so, The domain of all polynomial functions is all real numbers:
\(\text{ Domain}\mleft(-\infty,\infty\mright)\)Step 4
g) (f/g)(x)
\(\begin{gathered} f(x)=x^2+2x \\ g(x)=3x^2-1 \\ \text{then} \\ (\frac{f}{g})(x)=\frac{(x^2+2x)}{\mleft(3x^2-1\mright)} \\ \end{gathered}\)
h) domain, we see this function is not definded when the denominator equals zero, we need to find that number
\(\begin{gathered} 3x^2-1=0 \\ \text{add 1 in both sides} \\ 3x^2-1+1=0+1 \\ 3x^2=1 \\ \text{divide both sides by 3} \\ \frac{3x^2}{3}=\frac{1}{3} \\ x^2=\frac{1}{3} \\ \sqrt{x^2}=\sqrt{\frac{1}{3}} \\ x=\frac{1}{\sqrt[]{3}} \\ so,\text{ the domain is} \\ (-\infty,\frac{1}{\sqrt[]{3}})\cup(\frac{1}{\sqrt[]{3}},\infty) \end{gathered}\)I hope this helps you
Find the cofactors of A, place them in the matrix C, then use ACT to find the determinant of A, where: [1 1 47 A= 1 2 2 1 2 5]
Answers
The cofactor of A is C = [-3 0; 0 -46], and the determinant of A is -3.
The cofactor of each element in a 2x2 matrix is found by switching the signs of the elements in the determinant when the sum is taken (i.e. changing the sign of one element in the determinant if it is in an odd-numbered row or column).
For a 2x2 matrix A = [a b; c d], the determinant is given by det(A) = ad - bc.
For the given matrix A = [1 1 47; 1 2 2; 2 5 1], the cofactor matrix C is found by finding the determinant of each 2x2 sub-matrix obtained by excluding one row and one column of A.
C = [(-1)(2-5) (1)(2-2); (1)(1-1) (-1)(1-47)].
C = [-3 0; 0 -46].
To find the determinant of A using the cofactor matrix C, we take the sum of the products of the elements in each row of A and the corresponding elements in each column of C.
det(A) = 1*-3 + 10 + 470 + 10 + 20 + 2*-46 = -3.
So the determinant of A is -3.
To learn more about cofactor here:
https://brainly.com/question/28207649
#SPJ4
The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax = 0?
Answers
a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.
(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.
(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:
nullity = number of columns - rank
nullity = 3 - 2 = 1
Therefore, the nullity of matrix A is 1.
(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
Know more about matrix here:
brainly.com/question/24079385
#SPJ4