PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST
For a certain value of k, the system
x + y + (k-1) = 2,
6x + 2y - 3z = 1
kx - z = -3
has no solutions. What is this value of k?

Answers

Answer 1

In matrix form, the given system is written as

[tex]\begin{bmatrix}1&1&0\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3-k\\1\\-3\end{bmatrix}[/tex]

and the system has no solution is the coefficient matrix is singular. The determinant is

[tex]\begin{vmatrix}1&1&0\\6&2&-3\\k&0&-1\end{vmatrix} = -3k+4[/tex]

and this is zero when k = 4/3.

On the other hand, in case you are missing a factor of z in the first equation, so that the system should read

x + y + (k - 1) z = 2

6x + 2y - 3z = 1

kx - z = -3

reframing it as a matrix equation gives

[tex]\begin{bmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2\\1\\-3\end{bmatrix}[/tex]

Then the determinant of the coefficient matrix is

[tex]\begin{vmatrix}1&1&k-1\\6&2&-3\\k&0&-1\end{vmatrix} = -2k^2-k+4[/tex]

and the determinant is zero at two values, k = (-1 ± √33)/4.


Related Questions

x-(x-(x-y³)) use x=9, and y=1

Answers

9-(9-(9-1))
9-(9-8)
9-1
8

Answer:

The answer: 8

Step-by-step explanation:

x-(x-(x-y³))

x=9 , y=1 —> 9 - (9-(9-1³)) —> 9 - (9-(8))—> 9 - ( 1) —> =8

which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2?

Answers

the answer is on the photo

What is the slope of a line that is perpendicular to the line: -4x + 6y = -1 ?

A. -3/2
B. -2/3
C. 1/4
D. 3/2

Answers

Your answer should be 2/3

How much less is 17km than 24.6km?​

Answers

24.6-17= 7.6 (km) i think so

Answer:

[tex]7.4km[/tex]

Step-by-step explanation:

[tex]24.6km - 17km \\ = 7.4km[/tex]

hope this helps you.

Complete the equations below. 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths}\div 2 hundredths÷2start text, space, h, u, n, d, r, e, d, t, h, s, end text, divided by, 2 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals \text{ hundredths} hundredths start text, space, h, u, n, d, r, e, d, t, h, s, end text 1.86 \div 2 =1.86÷2=1, point, 86, divided by, 2, equals

Answers

Answer:

[tex]1.86 \div 2 = 0.93[/tex]

Step-by-step explanation:

The correct form of the question is:

Complete the equations below.

[tex]1.86 \div 2 =[/tex]

Required

Solve

Start from left to right

[tex]1 \div 2 = ??[/tex] --- this will give a fraction.

So, we append the next digit

[tex]1.8 \div 2 = 0.9[/tex]

Next:

[tex]0.06 \div 2 = 0.03[/tex]

Bring the results together:

[tex]1.86 \div 2 = 0.9+ 0.03[/tex]

[tex]1.86 \div 2 = 0.93[/tex]

draw the Venn diagram of b union b
A=(2 4 6 8 10 12)
B=(1 3 5 7 9 11)​

Answers

Step-by-step explanation:

Explanation is in the attachment

hope it is helpful to you ☺️

Factor the following polynomial 9x2 + 21x – 18

Answers

Answer:

factors are

21 and x

Step-by-step explanation:

equation 9 × 2 + 21x - 18

terms 9 , 2, 21x, -18

factors 21x = 21 and x

Answer:

3(x + 3)(3x - 2)

Step-by-step explanation:

Given

9x² + 21x - 18 ← factor out 3 from each term

= 3(3x² + 7x - 6) ← factor the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 6 = - 18 and sum = + 7

The factors are + 9 and - 2

Use these factors to split the x- term

3x² + 9x - 2x - 6 ( factor first/second and third/fourth terms )

3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term

(x + 3)(3x - 2)

Then

9x² + 21x - 18 = 3(x + 3)(3x - 2) ← in factored form

9. Choose the equation that represents the graph below:

Answers

Answer:

y= -4/3 x + 4

Step-by-step explanation:

i guess

Which r-value represents the weakest correlation?

–0.75
–0.27
0.11
0.54

Answers

Answer:

0.11

Step-by-step explanation:

Strongest correlation:

The strongest correlations happen for [tex]r = -1[/tex] and [tex]r = 1[/tex], that is, when r has the higher absolute value.

In this question:

The value of r with the lowest correlation is the one with the lowest absolute value(absolute value of -0.75 is 0.75 for example), so it is 0.11, which is the answer.

Answer:

it's C on edg

Step-by-step explanation:

.11

please help. i need this done today

Answers

Answer:

herlojffhgdxvjdxhyeb olis the tim view on the euros 2020 final

Patricia has $34,000 to invest. She invests some at 17% and the balance at 20%. Her total annual interest income is $6245. Find the amount invested at each rate

Answers

Answer:

she invest $18,500 at the 17% rate and $15,500 at the 20% rate.

Step-by-step explanation:

Suppose that you invest some quantity A to an invest rate of x%

At the end, the amount you will have is given by:

Amount = A + A*(x%/100%)

Where:

A*(x%/100%)  is the interest income

So, here she initially has $34,000

And she invest some quantity X to a 17% and a quantity Y to 20%

Then we have:

X + Y = $34,000

And we know that her total anual income is $6245

X*(17%/100%) + Y*(20%/100%) =  $6245

Then we have a system of two equations:

X + Y = $34,000

X*(17%/100%) + Y*(20%/100%) =  $6245

First we can rewrite the second one to a more simpler form:

X*(0.17) + Y*(0.20) =  $6245

Now we can isolate one of the variables in the first equation to get:

X = $34,000 - Y

Now we can replace that in the other equation to get:

( $34,000 - Y)*0.17 + Y*0.20 = $6245

Now we can solve this for Y:

$34,000*0.17 + Y*(0.20 - 0.17) = $6245

$5,780+ Y*0.03 =  $6245

Y*0.03 = $6245 - $5,780 = $465

Y = $465/0.03 = $15,500

And X = $34,000 - Y = $34,000 - $15,500 = $18,500

So she invest $18,500 at the 17% rate and $15,500 at the 20% rate.

For each function, state whether it is linear, quadratic, or exponential.

Answers

Answer:

Step-by-step explanation:

Table for function 1,

         x                      y              Difference 1          Difference 2        

         2                    10                      -                             -

         3                     1                 1 - 10 = -9                     -

         4                    10                10 - 1 = 9                9 - (-9) = 18

         5                    37               37 - 10 = 27            27 - 9 = 18

         6                    82               82 - 37 = 45          45 - 27 = 18

Since, difference 2 is common as 18,

Table will represent a quadratic function.

Table for function 2,

        x                    y               Difference 1            Difference 2

        5                    16                       -                               -

        6                    19              19 - 16 = 3                        -

        7                    28             28 - 19 = 9                  9 - 3 = 6

        8                    43             43 - 28 = 15              15 - 9 = 6

        9                    64             64 - 43 = 21              21 - 15 = 6

Since, difference 2 is common as 6,

Table will represent a quadratic function.

Table for function 3,

        x                    y                   Ratio

        1                   112                     -

        2                  56               56 ÷ 112 = [tex]\frac{1}{2}[/tex]  

        3                  28               28 ÷ 56 = [tex]\frac{1}{2}[/tex]

        4                   14               14 ÷ 28 = [tex]\frac{1}{2}[/tex]

        5                    7                7 ÷ 14 = [tex]\frac{1}{2}[/tex]

Since, ratio is common as [tex]\frac{1}{2}[/tex].

Table will represent an exponential function.

50 POINTS!!!! If you were on a rocket ship for a month that sat in between the moon and earth, how might moon phases be different? (need quickly!!!) also at least 2-4 sentences

Answers

Answer:I would sayif the planet earth was making a shadown on it. when u on other side

Step-by-step explanation:

That is the best i got

Answer:

Different times

Step-by-step explanation:

The closer you could get to the moon, the faster the phases will move. If you are about half way it should cut the time it takes to get through a season. Since you get closer to the object.

Write an equation of the line that passes through the point (6, -9) with the given slope m = 3.

Answers

Answer:

y = 3x - 27

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (6, - 9) into the partial equation

- 9 = 18 + c ⇒ c = - 9 - 18 = - 27

y = 3x - 27 ← equation of line

Answer Y=3x - 27 step by step

What should be done first to evaluate the expression?

4 + 8 ÷ 4 - 2 × 5

Add 4 and 8.
Divide 8 by 4.
Subtract 2 from 4.
Multiply 2 by 5.

Answers

Divide 8 by 4

Because is PEDMAS, division comes first.

Answer:

divide 8 by 4

Step-by-step explanation:

PEMDAS or BODMAS

Solve for the triangle: ABC
A: 90 degrees
B: 6 feet
C: 10 feet

Answers

I would say A degrees, bc it’s an angle, but I would need more information

what is (2x9)- (15 divided by 3)

Answers

Answer:

13

Step-by-step explanation:

We can simplify it:

(2x9)-(15/3)

(18)-(5)

18-5

13

Today only, a desk is being sold at a 33% discount. The sale price is $268. What was the price yesterday?

Answers

Discount percent = 33%

Sale price = $268

Let the original price be $x.

So,

[tex]x - (33\% \: of \: x) = 268 \\ = > x - ( \frac{33}{100} \times x) = 268 \\ = > x - ( \frac{33x}{100}) = 268 \\ = > \frac{100x}{100} - \frac{33x}{100} = 268 \\ = > \frac{(100x - 33x)}{100} = 268 \\ = > \frac{67x}{100} = 268 \\ = > 67x = 268 \times 100 \\ = > 67x = 26800 \\ = > x = \frac{26800}{67} \\ = > x = 400[/tex]

So, yesterday the price was $400.

Mr. Serpe started with $200. He has a hole in his pocket and he lost $2 every day for a week. He then found $150. How much money does he have?

Answers

Answer:

336

Step-by-step explanation:

2x7=14, so 200-14=186, then 186+150=336

2. The parameter "b": Compare the graphs of several different exponential growth functions in
Mathematica to discover the significance of the parameter "b". Explain in detail what the
parameter "b" tells you about the graph of an exponential growth function.

Answers

Answer:

See explanation

Step-by-step explanation:

Required

The significance of "b" in exponential function

An exponential function is represented as:

[tex]y = ab^x[/tex]

In the above equation, parameter "b" is the rate of the function

In other words, the constant multiplier of the function.

Take for instance;

[tex]y = 2*4^x[/tex]

By comparison:

[tex]b = 4[/tex]

Another instance is:

[tex]y = 2(-4)^x[/tex]

By comparison

[tex]b = -4[/tex]

Other significance of parameter b are:

If [tex]b > 0[/tex] then b represents a growth factor

If [tex]b < 0[/tex] the b represents the factor of decay

[tex]b \ne 0[/tex] i.e. b is never 0

HELP QUICK ILL GIVE BRAINLIEST

Answers

Answer:

A=35 degrees, B=55 degrees, C=110 degrees

Step-by-step explanation:

The 35 degree given angle is vertical angles with A, so they are congruent

The sum of angles in a triangle is 180, and we already have 2 angles (35 and 90) so subtract those and you get 55

angle c and the other given angle (70 degrees) are supplementary so subract 70 from 180

Been on this math problem for almost an hour will mark most brainly(just the bottom part)

Answers

Answer:

5. (8,33) (-1, -21) (5, 15)

6. (-5, 29) (2, 1) (4, -7)

7. (-4, -9) (0, -1) (7, 13)

8. (-9, 0) (1, 8) (5, 4)

Step-by-step explanation:

Since X is given, you plug it into the equations.

Then put the answers into the Y. hope it helps!!

Find the missing side length

Answers

Answer:

35

Step-by-step explanation:

Since the triangles are similar, we can write a ratio

25      ?

---- = -----

5       7

Using cross products

25*7 = 5 ?

Divide each side by 5

25*7/5 = 5?/5

35 = ?

16:32:12
Which linear inequality is represented by the graph?
O x < 2 x + 3
Oy> x+3
O y>x+3
O y<{x+3
-3 -2 -1

Answers

It’s y>x+3 the third one

The linear inequality that represents the graph is y > (2/3)x + 3.

Option C is the correct answer.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y < (2/3)x + 3

y > (3/2)x + 3

y > (2/3)x + 3

y < (3/2)x + 3

The graph is on the positive side of the y-coordinate so,

We can consider:

y > (3/2)x + 3

y > (2/3)x + 3

Now,

Plotting in a graph we see that,

We need to have the y-intercept at y = 3 and the x-intercept at x = 4.5.

So,

y > (2/3)x + 3 satisfied.

Thus,

y > (2/3)x + 3 represents the graph.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ7

The wind is blowing opposite to leg AB. Given the fact that you’re traveling in a wind-powered boat, which leg of the course will take you the longest? Why? (4 points)

Answers

Answer:

The leg of the course that will take longest is from A to B

The reason is that the leg of the course, A to B is slowed by the wind

Step-by-step explanation:

The direction of the wind is opposite to leg AB

The starting and finishing point is point A, and the course is from A to B to C and back to point A

The leg of the course that will take the longest is course in which th motion is against the wind which is from B to A

The motion from B to C and from C to A are partly in the wind ward direction, because the wind would be behind the sales and will therefore be aided by the wind, leading to rapid motion

However, the starting motion on the leg from A to B is opposite the wind and will be slowed down by the wind, and would therefore, take the longest.

There are 25 rows of seats in the high school auditorium with 20 seats in the first row, 21 seats in the second
row, 22 seats in the third row, and so on. How many total seats are in the auditorium?
OA) 800 seats
OB) 860 seats

Answers

Answer:

A) 800 seats

Step-by-step explanation:

Notice that an arithmetic sequence is formed with the number of seats. Since we're adding one seat each row, the last (25th) row will have 44 seats since the first row has 20 seats.

The sum of an arithmetic sequence is given by:

[tex]S_n=n\left(\frac{a_1+a_n}{2}\right)[/tex], where [tex]n[/tex] is the number of terms, [tex]a_1[/tex] is the first term, and [tex]a_n[/tex] is the last term

Therefore, substituting [tex]a_1=20[/tex], [tex]a_n=44[/tex], and [tex]n=25[/tex], we get:

[tex]S_n=25(\frac{20+44}{2}),\\s_n=25\cdot 32=\boxed{800}[/tex]

8. A juice container shaped like a cylinder has a base area of 100 cm2 and can hold 1500 cm3 of juice. The height of the juice container is

Answers

Answer:
15 cm

Explanation:
The cylinder’s volume can be found by multiplying base by height. The formula for this would be base*height=volume. The base and volume are given, so plug the values in and solve for height.

base*height=volume
100*height=1500
height=15 cm

The height of a juice cylinder container with base area of 100 cm² and volume of 1500 cm³ is 15 cm

Base area of a cylinder

Base area = πr²

base area = 100 cm²

100 = π × r²

r² = 100 / π

r = √100 / π

Volume of a cylinder  

volume = πr²h

1500 = π (√100 / π)² × h

1500 = π(100 / π) × h

1500 = 100h

divide both sides by 100

h = 1500 / 100

h = 15 cm

learn more on cylinder here: https://brainly.com/question/27342403

Can someone help me with this math homework please!

Answers

The answer is A and C
A and c hope this helps!!

The midpoint of AB is M(1,1). If the coordinates of A are (3, 3), what are the coordinates of B?​

Answers

Answer:

The answer in (-1,-1) because it goes down by x-2 and y-2

What are the steps to this problem (and the answer?)

Answers

Answer:

[tex](25 {x}^{2} + 20xy + 16 {x}^{2} )(5x - 4y) = \\ 125 {x}^{3} + 100 {x}^{2} y + 80x {y}^{2} - 100 {x}^{2} y \\ - 80x {y}^{2} - 64 {y}^{3} = \\ 125 {x}^{3} - 64 {y}^{3} \\ please \: give \: brainliest[/tex]

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