Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.
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To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.
What is a matrix?matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.
In computer graphics, where they have been used to describe picture transformations and other alterations.
The elements of the matrix, also known as the entry, are the numerals.
A matrix will be invertible only and only if the determinant is non-zero.
Given the matrix A.
The determinant of A is that |A| will be,
|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0
0 + 0 + -3(-4k + 8) |A| ≠ 0
-4k + 8 ≠ 0
-4k ≠ -8
k ≠ 2
Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".
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Related Questions
The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
Answers
The solution that we have that would have to do with the measurement of the unknown side would be 12.
How to solve for the unknown
The Pythagoras theorem says that the length of the suym of the square of a triangle is the same as the sum of the square of the other two sides.
From the definition that we have above.
We have the shortest side as 5.
The longest side as 13
Then we would have
13² - 5² = 25 - 169
= 144
Next we would have to take the square root of 144
= √144
= 12
Hence we would say that the length of the unknown is given as 12
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Is this correct?
Or please provide an explanation.
Answers
Answer:
The answer selected is correct
Step-by-step explanation:
When talking about balance, having -X (being X in the negative) , means owing X.
Dylan owes $19.25
Elise owes $42.75
Francesca owes $23
Jamaal owes $35.50
So naturally, Dylan owes the least.
If Omar still needs 458How much does he need after saving for 5 weeks
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(a) Setting A(w)=458, we get:
[tex]800-18w=458.[/tex]Subtracting 800 from the above equation we get:
[tex]\begin{gathered} 800-18w-800=458-800, \\ -18w=-342. \end{gathered}[/tex]Dividing the above equation by -18 we get:
[tex]\begin{gathered} \frac{-18w}{-18}=\frac{-342}{-18}, \\ w=19. \end{gathered}[/tex]Therefore Omar has been saving for 19 weeks.
(b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Evaluating A(w) at w=5 we get:
[tex]A(5)=800-18\cdot5.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A(5)=800-90 \\ =710. \end{gathered}[/tex]Answer:
(a) 19.
(b) $710.
A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 3 hrs, 14 hrs, and 10.5 hrs, respectively. Find how long it takes to fill the daily quota if all three machines are running.
Answers
Answer
It will take 2 hours to fill the daily quota if all the machines are running.
Explanation
To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:
Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines
[tex]\begin{gathered} \Rightarrow\frac{1}{3}+\frac{1}{14}+\frac{1}{10.5}=\frac{1}{x} \\ \text{Where x is the }time\text{ it takes to fill the daily quota} \\ \frac{1}{3}+\frac{1}{14}+\frac{2}{21}=\frac{1}{x} \\ \text{Multiply all through by 42x} \\ 42x(\frac{1}{3})+42x(\frac{1}{14})+42x(\frac{2}{21})=42x(\frac{1}{x}) \\ 14x+3x+4x=42 \\ 21x=42 \\ x=\frac{42}{21} \\ x=2 \\ \text{Therefore it will take 2 hours to fill the daily quota} \end{gathered}[/tex]Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
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What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is negative?
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Explanation
When the discriminant is negative, this implies that
[tex]b^2-4ac<0[/tex]Answer: In this case, the equation has no real solutions;
I’m trying to make a study guide and need step by step explanation on how to solve this question please
Answers
Given:
The dimension of square shape floor is 200 feet by 200 feet.
The area of the square is calculated as,
[tex]\begin{gathered} A=side^2 \\ A=200^2=40000 \end{gathered}[/tex]Now, given that the 1/2 bottle will cover approximately 2000 quare feet.
It gives,
[tex]\begin{gathered} \frac{1}{2}\text{ bottle=2000 square f}ee\text{t} \\ 1\text{ bottle=4000 square fe}et \end{gathered}[/tex]So, the number of bottles required are,
[tex]\frac{A}{4000}=\frac{40000}{4000}=10\text{ bottles}[/tex]Answer: option B)
The graph represents a quadratic function. Write an equation of the function in standard form.
Answers
A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (2, 0)
y = ax² + bx + c
0 = 4a + 2b + c ----------------(1)
The equation passes through (6, -4)
y = ax² + bx + c
-4= 36a + 6b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = 1/4, b = -3, and c = 5
The quadratic equation will be:
y = ax² + bx + c
y = (1/4) x² - 3x + 5
Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
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Im just needing a little bit more help with these type of problems ;/
Answers
Answer:
Expected value = 2.21
Explanation:
The formula to obtain the expected value is given by:
[tex]E\mleft(X\mright)=\mu=∑xP\mleft(x\mright)[/tex]We will proceed to calculate the given scenario as given below:
[tex]\begin{gathered} E\mleft(X\mright)=\mu=∑xP\mleft(x\mright) \\ E(X)=(1\times0.31)+(2\times0.41)+(3\times0.07)+(4\times0.18)+(5\times0.03) \\ E(X)=0.31+0.82+0.21+0.72+0.15 \\ E(X)=2.21 \\ \\ \therefore E(X)=2.21 \end{gathered}[/tex]Therefore, the expected value of this scenario is 2.21
This chart shows the cost per pound of different fruits.
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From the given data, the cost per pound of apple, CP=$1.89≈$2.
We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.
The cost of n=3 lb of apple can be calculated as,
[tex]\begin{gathered} T=CP\times n \\ =2\times3\text{ lb} \\ =6 \end{gathered}[/tex]Therefore, the cost of 3. pounds of apples is about $6.048.
How do I identify the horizontal and vertical asymptotes, find several points, and graph each function?Y=4/x+3 -2
Answers
Given:
[tex]y=\frac{4}{x+3}-2[/tex]Required:
To identify the horizontal and vertical asymptotes, and to point the graph.
Explanation:
Now the graph of the given function is
To find the horizontal asymptotes apply the limit
Blue whales can weigh as much as 150 tons. Convert the weight to pounds.
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SOLUTION:
The conversion formula from tons to pounds is;
[tex]1\text{ }US\text{ }ton=2000\text{ }pounds[/tex]Thus, converting this to pounds, the Blue whale would weigh;
[tex]150\times2000=300,000\text{ }pounds[/tex]Thus, the whale weighs 300,000 pounds
Answer:
The answer is C: 150/y
Step-by-step explanation:
The numbers of trading cards owned by 9 middle- school students are given below. ( note that these are already ordered from least to greatest.
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Given the numbers:
355, 382, 383, 427, 500, 572, 601, 638, 669
Total numbers = 9
a) We find the mean:
[tex]\begin{gathered} mean=\frac{355+382+383+427+500+572+601+638+669}{9} \\ mean=\frac{4527}{9}=503 \end{gathered}[/tex]Change 669 to 606:
[tex]\begin{gathered} mean=\frac{355+382+382+427+500+572+601+638+606}{9} \\ mean=\frac{4464}{9}=496 \end{gathered}[/tex]Then:
[tex]\begin{gathered} mean=changed\text{ mean}-original\text{ mean} \\ mean=496-503=-7 \end{gathered}[/tex]Answer: It decreases by 7
b) We find median
Median: 355, 382, 383, 427, 500, 572, 601, 638, 669
Median = 500
669 changed to 606
Median: 355, 382, 383, 427, 500, 572, 601, 606, 638
Median = 500
Answer: It stays the same
In a circle with radius 8, an angle measuring radians intercepts an arc. Find thelength of the arc in simplest form.
Answers
s = 28π/3
Explanation:The radius, r = 8
The angle, θ = 7π/6 radian
The length of the arc, s = rθ
s = 8 x 7π/6
s = 28π/3
...........................
Answers
Solution
We have the following:
5!= 5*4*3*2= 20*3*2= 60*2= 120
HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.
Answers
We have a rectangular garden.
The length L is 8 feet more than 3 times its width.
3 times the width is 3w, so we will add 8 to it and equal it to the length L:
[tex]L=8+3w[/tex]The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:
[tex]\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}[/tex]The perimeter has a value of P=16+8w.
We can draw the diagram as:
Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?
We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.
[tex]\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=\frac{72}{8} \\ w=9.75 \end{gathered}[/tex]The width is 9.75 feet.
What is the equation of the circle with endpoints (5,7) and (1,3)
Answers
Explanation:
endpoints (5,7) and (1,3)
The equation of circle formula:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ radius\text{ =r and (a, b) are the coordinates of the centre} \end{gathered}[/tex]To find the centre(a, b), we need to find the midpoint of the two given points:
[tex]\begin{gathered} \text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2) \\ \text{Midpoint = 1/2(5+1), 1/2(7+3)} \\ \text{Midpoint = 3, 5} \\ \text{centre = (a, b) =(3, 5)} \end{gathered}[/tex]The radius is the distance between the centre of the circle and any of the two points.
We will apply the distance formula:
[tex]\begin{gathered} dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ (3,5)\text{ and (1, 3)} \\ \text{Distance =}\sqrt[]{(3-5)^2+(1-3)^2} \\ \text{Distance =}\sqrt[]{4+4} \\ \text{Distance =}\sqrt[]{8}\text{ = 2}\sqrt[]{2} \\ \text{radius = distance = 2}\sqrt[]{2} \end{gathered}[/tex]Using the equation of circle:
[tex]\begin{gathered} (x-3)^2+(y-5)^2=(2\sqrt[]{2)}^2 \\ (2\sqrt[]{2)}^2=\text{ }2\sqrt[]{2)}\times2\sqrt[]{2)}\text{ = 4(}\sqrt[]{2})^2\text{ = 4(2) = 8} \\ (x-3)^2+(y-5)^2=\text{ 8} \end{gathered}[/tex]Find the exact area of a circle with a diameter of 12 in., expressed in terms of n.361 square inches61 square inches14471 square inches12 square inches241 square inches< Previous
Answers
The area of a circle is given by:
[tex]A=\pi r^2[/tex]Since the radius is half the diameter we have that r=6. Then the area is:
[tex]A=\pi(6)^2=36\pi[/tex]Therefore, the answer is the first one.
Find the vertical and horizontal lines that passes through the point (3,6).
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We have to find the vertical and horizontal lines that passes through the point (3,6).
A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.
The same goes for horizontal lines, but in this case the line is defined as y = constant.
For a point (x1,y1), the horizontal line that pass through the point will be y = y1.
Then, for point (x,y)=(3,6), the vertical and horizontal lines as:
x=3 and y=6.
Answer:
Vertical line: x = 3
Horizontal line: y = 6.
Lin is paid $90 for 5 hours of work. She used the following table to calculate how much she would be paid at this rate for 8 Hours of work. 1. What is the meaning of the 18 that appears in the table? 2. Explain how Lin used this table to solve the problem. 3. At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work. AMOUNTS EARNED ($) | TIME WORKED(hours)
Answers
Let
y ------> the amount earned
x ----> the number of hours worked
In this problem we have a direct variation
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
k=y/x
In this problem the value of k is hourly rate
so
we have
For y=$90 -------> x=5 hours
substitute
k=90/5
k=$18 per hour
substitute in the linear equation
y=18x
so
Part 1) What is the meaning of the 18 that appears in the table?
18 is the hourly rate ( amount earned by a one hour of work)
Part 2) Explain how Lin used this table to solve the problem.
using the table
For x=8 hours
the value of y=$144
Verify with the equation
y=18x
y=18(8)=144 -----> is ok
Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.
For x=3 hours
substitute in the equation
y=18x
substitute the value of x
y=18(3)=$54
For x=2.1 hours
y=18(2.1)=$37.8
What is the scale factor for AXYZ to AUVW?O A1/1O B. 1/1/20OC. 2OD. 4371620A A837-105353X 6 Z12
Answers
SOLUTION:
We want to know the scale factor of the transformation from;
[tex]\Delta XYZ\rightarrow\Delta UVW[/tex]We do this by taking ratios of corresponding sides, they should be the same in either case;
Thus , the scale factor is;
[tex]\frac{20}{10}=\frac{12}{6}=\frac{16}{8}=2[/tex]Thus, the scale factor is 2.
State the domain and range for each graph and then tell if the graph is a function(write yes or no)
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For the point 1)
- The domain will be: (note that this is not an interval, it is a set of two points)
[tex]\mleft\lbrace-3,2\mright\rbrace[/tex]-The range is the set R of all real numbers (since the line extends to infinite)
-The first graph is NOT a function
For the point 2)
-The domain will be the interval
[tex](-5,5\rbrack[/tex]-The range is the interval:
[tex]\lbrack-2,2\rbrack[/tex]-The second graph is a function.
write the following basic forms in their single form
2√3
Answers
The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.
What is the single form expression which is equivalent to the basic form expression; 2√3?It follows from the task content that the basic form expression be written as it's equivalent single form expression.
Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;
First, the square of 2, 2² is equal to 4;
Hence, by the converse;
2 = √4.
The given expression can therefore be written as; √4 • √3.
The expression above can therefore be written in its single form as; √(4 × 3) = √12.
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The problem is below, we know the man weighs 60, the cat weighs 10 but we’re having a hard time explaining how
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Given data:
The weight of man and daughter = 90
The weight of man and cat is = 70
The weight of cat and daughter = 40 .
The man weights 60 kg.
then daughter weight = 90-60 = 30.
Thus the daughter weight is 30kg.
therefore the cat weight iwith daughter, 40-30 = 10 .
also with father, 70-60 = 10 .
Thus, the father weight is 60 kg.
The daughter weight is 30 kg and
The cat weight is 10 kg.
Evaluate 2(x - 4) + 3x - x^2 for x = 2.O A. -6O B. -2O C. 6O D. 2
Answers
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
If you borrow $100 for 3 years at anannual interest rate of 9%, howmuch will you pay altogether?
Answers
We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).
You borrowed a principal amount of:
[tex]P\text{ = \$100}[/tex]The time duration for which we have borrowed the money for is:
[tex]t\text{ = 3 years}[/tex]The annual interest rate coumpounded each year is:
[tex]R\text{ = 9\% / year}[/tex]Step 1: Determine the simple interest that accumulated at the end of ( t ) years.
The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.
The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).
[tex]\text{Simple Interest ( I ) = }\frac{P\cdot R\cdot t}{100}[/tex]Use the above simple interest formula ( I ) by plugging in the respective values as follows:
[tex]\text{Simple Interest ( I ) = }\frac{100\cdot9\cdot3}{100}\text{ = \$27}[/tex]Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.
Step 2: Determine the total amount that is to be returned/paid to the lender
The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).
[tex]\begin{gathered} \text{Total amount to be paid = P + I} \\ \text{Total amount to be paid = \$100 + \$27} \\ \text{Total amount to be paid = }127 \end{gathered}[/tex]Therefore, the amount that you need to pay altogether is:
[tex]\textcolor{#FF7968}{127}\text{\textcolor{#FF7968}{ dollars}}[/tex]Select the expressions that are equivalent to 7(7f)1. 49f2. 7(f+6f)3. f+144. f+49
Answers
ANSWER :
49f and 7(f + 6f)
EXPLANATION :
From the problem, we have :
[tex]7(7f)[/tex]When multiplied, it will be 49f
When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)
The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.
So the only expressions that are equivalent to the given expression are 1 and 2
State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
Answers
D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
Jane is attending physical therapy after knee surgery. She walked 9 3/4 miles over 3 days. How many miles is this per day? (Simplify the answer and write it as a mixed number.)
Answers
She walked 3 1/4 miles per day.
Given,
Jane walked 9 3/4 miles in the course of 3 days.
If we calculate this mixed number into a fraction,
We get:
9 3/4 miles = {(9×4)+3} / 4 miles
=39/4 miles.
So, Jane walks 39/4 miles in 3 days.
Therefore, in one day she walked:
(39/4 ÷ 3) miles
= 13/4 miles per day
Let's now convert this fraction into a mixed number:
when 13 is divided by 4 we get the remainder as 1 and the quotient as 3.
So, a mixed number is given by:
quotient remainder/divisor
Hence 13/4 = 3 1/4.
So, Jane walked 3 1/4 miles per day.
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个 == CR Algebra 1 B (GP) 21-22 / 8:Radical Expressions and Equations 104 6 2 -10-8-6 -4 - 2 0 N 4 6 8 10 2 -4 6 -8 -10 Match the graph with its function by translating the graph of y = Vx. 3. O y = √x-1+7 O y = x-7+1 = 7 O O y=√x+1+7 O y = x+7+1 Search the web and Windows a
Answers
SOLUTION
The transformation of the function
[tex]y=\sqrt[]{x}[/tex]To give the graph in the question is as follows.
The graph is move to the left from the origin by 1 unit on the x-axis, which is to add 1 to x, we have
[tex]y=\sqrt[]{x+1}[/tex]Also,
The graph is the move upward along the y-axis by 7 unit, which is addition of 7 to the function
Then, the equations becomes
[tex]y=\sqrt[]{x+1}+7[/tex]Therefore
The function that produce the graph in the image is
y = (√x+1) + 7