We have proved that a set containing three non-zero vectors in V cannot be linearly independent if {v1, v2} is a spanning set for V.
To prove that a set containing three non-zero vectors in V cannot be linearly independent, we will use the definition of linear independence and the fact that {v1, v2} is a spanning set for V. Here are the steps:
Let {v1, v2, v3} be a set containing three non-zero vectors in V.
Since {v1, v2} is a spanning set for V, any vector in V can be written as a linear combination of v1 and v2. In particular, v3 can be written as v3 = a*v1 + b*v2 for some scalars a and b.
Now, consider the linear combination 0 = c1*v1 + c2*v2 + c3*v3, where c1, c2, and c3 are scalars. Substituting v3 = a*v1 + b*v2, we get 0 = (c1 + a*c3)*v1 + (c2 + b*c3)*v2.
Since {v1, v2} is a spanning set, the only way for this linear combination to be equal to 0 is if both coefficients are 0, i.e., c1 + a*c3 = 0 and c2 + b*c3 = 0.
If c3 = 0, then c1 = 0 and c2 = 0, which means that the set {v1, v2, v3} is linearly independent. However, if c3 is not 0, then we can solve for c1 and c2 in terms of c3, and we get c1 = -a*c3 and c2 = -b*c3.
This means that there are infinitely many solutions to the linear combination 0 = c1*v1 + c2*v2 + c3*v3, and therefore the set {v1, v2, v3} is not linearly independent.
we have proved that a set containing three non-zero vectors in V cannot be linearly independent if {v1, v2} is a spanning set for V.
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If the pattern below follows the rule starting with two every consecutive line has a number that is one less than twice the previos line how many marbles must be in the sith line
Answer:
The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:
1st line: 2
2nd line: 2(2) - 1 = 3
3rd line: 2(3) - 1 = 5
4th line: 2(5) - 1 = 9
5th line: 2(9) - 1 = 17
6th line: 2(x) - 1 (unknown)
To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:
2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)
2x - 1 = 33
2x = 34
x = 17
Therefore, the 6th line of the pattern would have 17 marbles
Step-by-step explanation:
The pattern is described as having a number in each line that is one less than twice the previous line.
Write out the first few lines of the pattern, starting with 2 as the first line:
1st line: 2
2nd line: 2(2) - 1 = 3
3rd line: 2(3) - 1 = 5
4th line: 2(5) - 1 = 9
5th line: 2(9) - 1 = 17
To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:
6th line: 2(x) - 1
Substitute 17 for x (the value in the 5th line):
2(x) - 1 = 2(17) - 1
Simplify the right-hand side:
2(x) - 1 = 33
Add 1 to both sides:
2(x) = 34
Divide both sides by 2:
x = 17
Therefore, the 6th line of the pattern would have 17 marbles.
The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.
How to solve for the complete pattern?To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.
Starting with two, we can apply the rule to generate the next few numbers:
First line: 2
Second line: 2(2) - 1 = 3
Third line: 2(3) - 1 = 5
Fourth line: 2(5) - 1 = 9
Fifth line: 2(9) - 1 = 17
Now we can apply the rule again to find the sixth number:
Sixth line: 2(17) - 1 = 33
Therefore, the sixth line must have 33 marbles.
The pattern starts with two, which is the first line.
The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.
To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.
Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.
We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.
Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.
So, the complete pattern is: 2, 3, 5, 9, 17, 33.
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Jason jumped off of a cliff into the ocean in Acapulco while vacationing with same friend. His height could be modeled by the equation [tex]h= -16x^{2}+16x+480[/tex] , where t is the time in seconds and h is the height in feet.
After how many seconds, did Jason hit the water? Step by step.
Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.
After how many seconds, did Jason hit the water?We know that the height of Jason is modeled by the quadratic function:
h = - 16x² + 16x + 480
The water is at h = 0, so we need to solve the quadratic equation:
0 = - 16x² + 16x + 480
If we divide all the right side by 16,we will get:
0 = (- 16x² + 16x + 480)/16
0 = -x² + x + 30
Now we can use the quadratic formula to get the solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]
We only care for the positive solution, which is:
x = (-1 - 11)/-2 = 6
Jason will hit the water after 6 seconds.
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calculate the ground distance if the map distance is 20 cm write your answer in kilometers
The ground distance, given the map distance and the scale, would be 5 kilometers.
How to find the distance?If the scale on a map is 1:25,000, it means that one unit of distance on the map represents 25,000 units of distance on the ground. If the map distance is 20 cm, we can find the ground distance as follows:
Convert the map distance from centimeters to kilometers:
20 cm = 0.2 m = 0. 0002 km
Find the ground distance using the scale:
Ground distance = Map distance / Scale
Ground distance = 0. 0002 km / ( 1 / 25,000 )
Ground distance = 0.0002 km x 25,000
Ground distance = 5 km
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The full question is:
The scale on a map is 1:25,000. Calculate the ground distance if the map distance is 20 cm write your answer in kilometers
The cost to repair a computer was $190. This included $115 for parts and $25 per hour for labor. How many hours of labor were required to fix the computer? hr
Total 3 hours of labor were required to fix the computer.
To find the number of hours of labor required to fix the computer, we can use the following equation:
Total cost = Cost of parts + (Cost of labor per hour × Number of hours of labor)
We can rearrange this equation to solve for the number of hours of labor:
Number of hours of labor = (Total cost - Cost of parts) ÷ Cost of labor per hour
Plugging in the given values:
Number of hours of labor = ($190 - $115) ÷ $25
Number of hours of labor = $75 ÷ $25
Number of hours of labor = 3 hr
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sandra contributed $400, jaclyn $600 and alecia $1000. they agreed that the profit would be divided among them based on how each person give as capital.how much percentage of the capitol did jacklyn contribute
The total percentage of capital contributed by Jacklyn is 30%
The total capital contributed by Sandra, Jaclyn, and Alecia is:
$400 + $600 + $1000 = $2000
To find the percentage of capital contributed by Jacklyn contributed,
Percentage contributed by Jaclyn = (Jaclyn's contribution / Total capital) x 100
= ($600 / $2000) x 100
= 30%
Therefore, Jacklyn contributed 30% of the capital.
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On the standard (x, y) coordinate plane below, which of the following quadrants contain all of the points found on the line –3x + 5y = 15 ?
The quadrants that contain all the points found on the linear function -3x + 5y = 15 are given as follows:
Quadrant 1.Quadrant 2.Quadrant 3.How to obtain the quadrants of the linear function?The linear function for this problem is defined as follows:
-3x + 5y = 15.
In slope-intercept format, it is given as follows:
5y = 3x + 15
y = 0.6x + 3.
The features of the line are given as follows:
Increasing line due to the positive slope -> passes through the first quadrant.Positive intercept -> Means that the line passes though the 2nd quadrant and the 3rd quadrant.More can be learned about linear functions at https://brainly.com/question/24808124
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It! Add and Subtract Polynomials idd or subtract the polynomials. ((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5)) (2a^(2)b^(2)+3ab^(2)-5a^(2)b)-(3a^(2)b^(2)-9
The polynomial that need to be added is
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
To add or subtract polynomials, we need to combine like terms. Like terms are terms that have the same variable and the same exponent.
First, let's add the first two polynomials:
((2)/(5)a^(4)-6a^(3)-(5)/(6)a^(2)+(a)/(2)+1)+((9)/(4)a^(3)+(2a^(2))/(3)+(5)/(3)a-(8)/(5))
= (2/5)a^(4) + (-6 + 9/4)a^(3) + (-5/6 + 2/3)a^(2) + (1/2 + 5/3)a + 1 - 8/5
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5
Now, let's subtract the third polynomial from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - (2a^(2)b^(2)+3ab^(2)-5a^(2)b)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b
Finally, let's subtract the last term from this result:
(2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 2a^(2)b^(2) - 3ab^(2) + 5a^(2)b - (3a^(2)b^(2)-9)
= (2/5)a^(4) + (-15/4)a^(3) + (1/6)a^(2) + (11/6)a - 3/5 - 5a^(2)b^(2) - 3ab^(2) + 5a^(2)b + 9
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Estimate the quotient 5,692 divided by 5
Christopher needs to order some new supplies for the restaurant where he works. The restaurant needs at least 775 spoons. There are currently 355 spoons. If each set on sale contains 10 spoons, write and solve an inequality which can be used to determine
�
s, the number of sets of spoons Christopher could buy for the restaurant to have enough spoons.
According to the inequality, Christopher would need to purchase 35 + 10s 75 sets of spoons to ensure that the restaurant has enough of them.
Why does inequality matter?According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller proportion of what they earn than do poorer households, concentrated earnings lower the amount of demand for goods and services. The economy may suffer if low-income families have fewer possibilities.
There are already 355 spoons available, but the eatery needs at least 75. Each set that is for sale includes 10 spoons.
Let s be the representation of each set. It will be demonstrated by:
35 + (10 × s) ≥ 75
35 + 10s ≥ 75
Collect like terms
10s ≥ 75 - 30
10s ≥ 45
Divide
s ≥ 45/10
s ≥ 4.5
The restaurant must have at least 5 sets.
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Answer: 10s + 355 >=755
s>=42
Step-by-step explanation:
A rectangular region has an area of 299 square miles. The length of the region is 10 miles longer than its width. Find the length and width of the region.
Answer:
Let's represent the width of the region by "w". According to the problem, the length of the region is 10 miles longer than the width, so we can represent the length as "w + 10".
The formula for the area of a rectangle is:
Area = Length x Width
So we can write an equation for the area of this region:
299 = (w + 10) x w
Expanding the right side, we get:
299 = w^2 + 10w
Now we can rearrange this equation into standard quadratic form:
w^2 + 10w - 299 = 0
We can solve for "w" by using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 10, and c = -299. Plugging in these values, we get:
w = (-10 ± sqrt(10^2 - 4(1)(-299))) / 2(1)
w = (-10 ± sqrt(1180)) / 2
w = (-10 ± 34.351) / 2
We can ignore the negative solution, since the width of the region cannot be negative. So the width is:
w = (-10 + 34.351) / 2
w = 12.176
We can round the width to the nearest mile, since we can't have a fractional width. So the width is approximately 12 miles.
Now we can use the equation we derived earlier to find the length:
299 = (w + 10) x w
299 = (12 + 10) x 12
299 = 22 x 12
So the length is 22 miles.
Therefore, the width of the region is approximately 12 miles and the length is 22 miles.
A car travels 1 mile every
minute, what is its speed in
mi/hr?
Answer:
Step-by-step explanation:
60mi/hr
Find two numbers that multiply to -24 and adds to 2
Answer:
6 and -4
Step-by-step explanation:
Let the first number be n.
Other number= [tex]\frac{-24}{n}[/tex]
Their sum= 2
n + [tex]\frac{-24}{n}[/tex]= 2
[tex]\frac{n^{2-24} }{n}[/tex]= 2
n²-24= 2n
You can solve this problem in either of these 2 ways:
i) Square Completion method:
n²-2n = 24
Half of the coefficient= [tex]\frac{2}{2}[/tex] =1
Its square= 1²= 1
n²-2n+1= 24+1
(n-1)²= 25
n-1= [tex]\sqrt{25}[/tex]
n-1= ±5
If n-1= 5,
n= 5+1
n= 6
If n-1= -5,
n= -5+1
n= -4
∴ the numbers are 6 and -4
ii) Equation Method:
n²-24= 2n
n²-2n-24= 0
a= 1,
b= -2,
-b= 2,
c= -24
n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a
n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1
n= 2±[tex]\sqrt{4+96}[/tex]/2
n= 2±[tex]\sqrt{100}[/tex]/2
n= 2±10/2
If n= [tex]\frac{2+10}{2}[/tex],
n= [tex]\frac{12}{2}[/tex]
n= 6
If n= [tex]\frac{2-10}{2}[/tex],
n= [tex]\frac{-8}{2}[/tex]
n= -4
∴ the numbers are 6 and -4
The sum of Eli's age and Cecil's age is 15 Eli is twice as old as Cecil
eli=e
Cecil=c
e+c=15
e=2c
2c+c=15
3c=15
c=5
e=10
Rewrite the quadratic function in standard form. f (x) = x2 - 8x + 23 Get Hint Enter Your Step Here 7 4
The quadratic function in standard form of f (x) = x2 - 8x + 23 is (x) = (x - 4)2 + 7.
The quadratic function given is f (x) = x2 - 8x + 23. To rewrite this function in standard form, we need to complete the square for the x terms. Standard form for a quadratic function is f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
f (x) = 1(x2 - 8x) + 23
Step 2: Take half of the coefficient of the x term, square it, and add it inside the parentheses. In this case, half of -8 is -4, and -4 squared is 16.f (x) = 1(x2 - 8x + 16) + 23 - 16
Step 3: Simplify the constant term outside of the parentheses.f (x) = 1(x2 - 8x + 16) + 7
Step 4: Factor the quadratic inside the parentheses.f (x) = 1(x - 4)2 + 7
Step 5: Simplify the coefficient of the quadratic term, if necessary. In this case, the coefficient is 1, so there is no need to simplify further.The final answer is f (x) = (x - 4)2 + 7, which is the standard form of the given quadratic function.
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Please answer this question
The value of x, given the equation, can be found to be 2 .
How to find the value of x ?We are given the equation:
( 5x + 4 ) / 2 = 7
The first step is to remove the denominator using cross - multiplication :
2 x ( 5x + 4 ) / 2 = 7 x 2
5 x + 4 = 14
Solving directly for x then gives:
5 x + 4 = 14
5 x = 14 - 4
x = 10 / 5
x = 2
In conclusion, the value of x in the equation which needed to be simplified to 5 x + 4 = 14 , and then solved, is 2.
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An investment company provides strategies for improving return on your investment. It believes that it can increase a customer’s returns by 2. 3%. Which statistical method would be best to use in this situation?
A statistical method would be best to use in this situation - Hypothesis testing
We know that the hypothesis testing is nothing but a form of statistical inference that uses data from a sample to draw conclusions about a population probability distribution. Here, first we made a tentative assumption about the distribution. This assumption is called the null hypothesis , which is denoted by H₀. An alternative hypothesis is the opposite of the null hypothesis. It is denoted by [tex]H_a[/tex]
Hypothesis testing is used for confirming a business claim or idea. It is useful for investors who trying to decide what to invest in and whether the it would provide a satisfactory return.
In this case, an investment company provides strategies for improving return on your investment. It believes that it can increase a customer’s returns by 2. 3%.
Here, hypothesis testing which is one of the statistical method that would be best to use.
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Determine the quotient and remainder when (2a^(3)+7a^(2)+2a+9) is divided by (2a+3). Use long division or synthetic division
The remainder is -21 and the quotient is 6a2-18a+21.
What is synthetic division?Synthetic division is a method for dividing polynomials by monomials. It is a simplified form of the long division of polynomials, and is useful when the divisor is a monomial. The method involves arranging the coefficients of the dividend in a row, and then dividing each term by the divisor .
To determine the quotient and remainder when (2a3+7a2+2a+9) is divided by (2a+3), you can use either long division or synthetic division.
Using long division:
÷2a+3
2a3+7a2+2a+9
-6a2 (2a3 ÷ 2a = 6a2)
-18a (7a2 ÷ 2a = 3a2 = 18a)
-21 (2a+9 ÷ 2a+3 = -2a+12 ÷ 2a+3 = -21)
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A recipe calls for mixing 8/5 cups of blueberries and 7/5
cups of strawberries. The mix is divided equally among 18 items. What fraction of a cup is used for each item?
3 cups of fruit mix is divided equally among 18 items.
Each item will contain 1/6 cup of fruit mix.
How to find out what fraction of a cup is used for each item ?First we need to divide the total amount of fruit mix by the number of items.
The total amount of fruit mix is :
8/5 cups of blueberries + 7/5 cups of strawberries
= (8/5 + 7/5) cups
= 15/5 cups
= 3 cups
So, 3 cups of fruit mix is divided equally among 18 items.
To find the fraction of a cup used for each item, we need to divide 3 cups by 18:
Copy code
3 cups ÷ 18 = 1/6 cup
Therefore, each item will contain 1/6 cup of fruit mix.
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Manuel’s final exam has true/false questions, worth three points each, and multiple choice questions, worth four points each, let x be the number of true/false questions he gets correct, and let y be the number of multiple choice questions he gets correct. He needs more than 82 points on the exam to get an A in the class. Using the values and variables given, right in equality describing it.
Answer: Let T be the number of true/false questions on the exam, and let M be the number of multiple choice questions on the exam.
Then, the total number of points Manuel can earn on the exam is:
3T + 4M
We know that Manuel needs more than 82 points on the exam to get an A in the class. Therefore, we can write the following inequality:
3x + 4y > 82
where x is the number of true/false questions Manuel gets correct, and y is the number of multiple choice questions Manuel gets correct.
Step-by-step explanation:
Mipl Analyze a Problem Without calculating, is the product of 7 and 5(3)/(4) greater than or less than 35 ? Explain.
The product is less than 35.
To analyze this problem without calculating, we can look at the factors involved in the product. The first factor is 7, and the second factor is 5(3)/(4).
The second factor, 5(3)/(4), is less than 5 because it is the product of 5 and a fraction less than 1.
When we multiply 7 by a number less than 5, the result will be less than 35.
Therefore, the product of 7 and 5(3)/(4) is less than 35.
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Does $10,000 invested at 6% interest double its value in half the time as $10,000 invested at 3% interest? Show your work.
The answer is $21,989.34 and Yes, $10,000 invested at 6% interest will double its value in half the time as $10,000 invested at 3% interest.
Now, For the 6% investment:
$10,000 invested at 6% interest will double in 12 years:
$10,000 × (1.06)^12 = $21,989.34
For the 3% investment:
$10,000 invested at 3% interest will double in 24 years:
$10,000 × (1.03)^24 = $21,989.34
Therefore, it will take half the time (12 years) for the 6% investment to double its value compared to the 3% investment (24 years).
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Which image shows a pair of similar polygons? A. An image showing pair of Similar Polygons with an X-axis showing the Value range from 0 to 16 and Y-axis values from 0 to 16. B. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. C. Graphic Image showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. D. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. Reset Next
The correct answer is option C. A graphic image showing a pair of similar polygons with an X-axis showing the value range from 0 to 16 and a Y-axis values from 0 to 16.
What are polygons?Polygons are two-dimensional shapes with straight sides that are joined together. They are closed shapes, meaning all the sides are connected. Polygons can have anywhere from three sides to an infinite number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, and octagons.
This correct image is showing two polygons that are similar, or which have the same shape. This means that the sides of the two polygons are equal in length and each angle is the same. In other words, they are exactly the same shape, but can be different sizes. The X-axis and Y-axis values shown in the image are the coordinates of the points that make up the polygons. The X-axis values indicate the horizontal distance from the origin, while the Y-axis values indicate the vertical distance from the origin. By looking at the coordinates of the points that make up the polygons, we can see that the two polygons are similar.
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HELP PLS HURRY...............................................................................
Answer:
C) - 1/10--------------------------------
Given two points:
[tex](-3, -7/2}) \ and \ (2, -4)[/tex]Find the slope of the line containing these points.
Slope equation:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]Substitute coordinates and find the slope:
[tex]m=(-4-(-7/2))/(2-(-3))=(-4+7/2)/(2+3)=(-1/2)/5=-1/10[/tex]Answer:
-1/10
Step-by-step explanation:
To find:-
The slope of the line passing through the points (-3,-7/2) and (2,-4) .Answer:-
We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;
[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]
where ,
(x1,y1) and (x2,y2) are the coordinates of the two points.Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .
So on substituting the respective values, we have;
[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]
[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]
[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]
[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]
[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]
Hence the slope of the line is -1/10 .
e synthetic division and the Remainder Theorem to evaluate P(C). P(x)=3x^(3)+15x^(2)-10x+9,c=2
P(2) = 73.
To evaluate P(C) using synthetic division and the Remainder Theorem, we will follow the following steps:
Set up the synthetic division table with the value of C on the left and the coefficients of P(x) on the right.
Bring down the first coefficient to the bottom row.
Multiply the value of C by the first coefficient in the bottom row and place the result in the next column.
Add the values in the second column and place the result in the bottom row.
Repeat steps 3 and 4 for the remaining columns.
The last value in the bottom row is the remainder. According to the Remainder Theorem, this is the value of P(C).
Therefore, P(2) = 73.
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True or False with explanation (e.g. a piece of the Invertible Matrix Theorem) or a counterexample. All matrices aren×n. - (a) If the equationAx=0has only the trivial solution, thenAis row equivalent to the identity matrix. - (b) If the columns ofAspanRn, then they are linearly independent. - (c) IfATis not invertible, then neither isA. - (d) If there is a matrixDwithAD=I, thenDA=Ialso.
(a) If the equation Ax=0has only the trivial solution, then A is row equivalent to the identity matrix is True.
(b) If the columns of Aspan Rn, then they are linearly independent is True.
(c) If AT is not invertible, then neither is A is True.
(d) If there is a matrix D with AD=I, then DA=I also is True.
If the equation Ax=0 has only the trivial solution, then the matrix A has a pivot in every column and is therefore row equivalent to the identity matrix.
If the columns of A span Rn, then they are linearly independent because if they were not, there would be a nontrivial linear combination of the columns that equals the zero vector, which would contradict the fact that they span Rn.
If AT is not invertible, then it has a nontrivial null space, which means that there is a nonzero vector x such that ATx=0. This implies that xTA=0, which means that x is in the null space of A. Since A has a nontrivial null space, it is not invertible.
If there is a matrix D with AD=I, then DA=I also because the inverse of a matrix is unique and both AD and DA must be equal to the inverse of A.
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A family buys 6 airline tickets online. The family buys travel insurance that costs $18 per ticket. The total cost is $1,128. Let x represent the price of one ticket. Then find the price of one ticket.
Answer: $170
Step-by-step explanation:
6x + 18(6) = 1128.
6x + 108 = 1128
6x = 1020
x = 170
The price of one ticket is 170
HELP THIS IS DUE TOMMOROW USE ANY STRATEGIE
Answer: what is ur questions?
Step-by-step explanation:
The y-intercept of f(x)=3(12)x
is ____________________ the y-intercept of the function in the graph. is it greater than less than or equal to
The y-intercept of the given function is 0.
What is y-intercept?A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.
Given is a function f(x) = 3(12)x, we need to find the y-intercept.
The general equation of a line is given by
y = mx+c
Where m is the slope and the c is the y-intercept,
But in our equation, the y-intercept is not available that means it is zero,
We can write the equation as ;-
f(x) = 3(12)x + 0
Hence, the y-intercept of the given function is 0.
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Anyone help wit this
The value of x is equal to 10.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a line segment is intersected by a straight line which is parallel to the third (3rd) side of the line segment, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
21/(x - 3) = 27/(x - 1)
By cross-multiplying, we have the following:
21(x - 1) = 27(x - 3)
21x - 21 = 27x - 81
27x - 21x = 81 - 21
6x = 60
x = 60/6
x = 10.
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Subtract the ratiunal expressi answer in its fully factored for (m^(2)+4m-12)/(m^(2)-64)-(m^(2)+11m+24)/(2m^(2)-128)
The fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
To subtract the rational expressions and find the answer in its fully factored form, we first need to find a common denominator for the two expressions.
The denominators of the two expressions are (m^(2)-64) and (2m^(2)-128). We can factor both of these to find the common denominator.
(m^(2)-64) = (m+8)(m-8)
(2m^(2)-128) = 2(m^(2)-64) = 2(m+8)(m-8)
The common denominator is 2(m+8)(m-8).
Now we can rewrite the two expressions with the common denominator and subtract them:
[(m^(2)+4m-12)(2) - (m^(2)+11m+24)(m+8)(m-8)] / [2(m+8)(m-8)]
= [(2m^(2)+8m-24) - (m^(3)+11m^(2)+24m+8m^(2)+88m+192)] / [2(m+8)(m-8)]
= [m^(3)-17m^(2)-104m-216] / [2(m+8)(m-8)]
= (m-9)(m^(2)-8m-24) / [2(m+8)(m-8)]
= (m-9)(m-12)(m+2) / [2(m+8)(m-8)]
So the answer in its fully factored form is (m-9)(m-12)(m+2) / [2(m+8)(m-8)].
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