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

How in the world do I set this up?

The formula

c = 75 + 30(n - 5) is used to find the cost, c, of a taxi ride where n represents the number of [tex]\frac{1}{5}[/tex] miles of the ride. Find the cost of a taxi ride of 2/frac{2}{5}


Thanks

Answers

Answer:

Step-by-step explanation:

The 2 2/5 is not showing up correctly, but I think it means that you are going 2 miles + 2/5 of a mile. If that is not true, leave me a note and I'll correct it.

So 75 and 30(n - 5) represent cents (I think) per 1/5 of a mile.

1 mile has 5 fifths.

2 miles has 10 fifths

2/5 has 2 fifths.

the total is 17 fifths so n = 17

C = 75 + 30(17 - 5)

C = 75 + 30(12)

C = 75 + 360

C = 435

That means you pay 4 dollars and 35 cents.

If 12 out of 30 fruits are oranges, how many oranges fruits will there be per 100 fruits total?​

Answers

Answer:

40 oranges are there in 100 fruites.

Two cards are drawn from a deck of 52 playing cards. The first card is NOT replaced into the deck before the 2nd card is drawn What is the probability of drawing a King and then another King?​

Answers

Answer:

probability that 2 cards drawn from a deck of 52 cards are both kings.

is probability that first card is a king times probability that second card is a king

with replacement 4/52*4/52 =0.592%

without replacement 4/52*3/51=0.452%

Step-by-step explanation:

Solve for x. Round to the nearest tenth, if necessary

Answers

Answer:

20.4

Step-by-step explanation:

cos(74) = x/74

x = 74×cos(74)

x = 20.4

Answered by GAUTHMATH

Ive never really understood 8th-9th grade volume, could use some help

Answers

The answer is B

Eplanation:

V = pi * r² * (h/3)

Then from here you just make h the subject of the formula:

h = (V * 3)/(pi * r²)

h = (393*3)/[3.14* (10/2)²]

h = 15.01910828 ft

which is rounded to 15 ft...B

:)


A water bottling company has purchased the rights to bottle 960 liters of spring water a month from the local spring.
How many 4-liter bottles can they produce a month?

Answers

Answer:

becouse 4×960 will give you

3840

Cual es el resultado de la siguiente división (– 1/3 a^2 b^5 – 1/2 a^5 b^4 + 2/5 a^3 b – 5a^2 b^7) / ( – 5a^2 b^2)

Answers

Answer:

dont understand clearly

Step-by-step explanation:

Find the length of BW
A.132.59
B.134.24
C.21.26
D.3.33

Answers

Answer:

BW = 132.59

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 9 = 21 / BW

BW tan 9 = 21

BW = 21/ tan 9

BW = 132.5887818

BW = 132.59

Answer:

Step-by-step explanation:

Side BW is the height, aka as the side adjacent to the reference angle of 9 degrees. We have the side opposite the reference angle (21) and we are looking for the side adjacent to the reference angle. The trig ratio that we use for this, the one that relates the sides opposite and adjacent, is the tangent ratio, namely:

[tex]tan(9)=\frac{21}{BW}[/tex] and solving for BW:

[tex]BW=\frac{21}{tan(9)}[/tex] so

BW = 132.59

2( 5 1 ​ m− 5 2 ​ )+ 5 3 ​ 2, left parenthesis, start fraction, 1, divided by, 5, end fraction, m, minus, start fraction, 2, divided by, 5, end fraction, right parenthesis, plus, start fraction, 3, divided by, 5, end fraction

Answers

Answer:

2/5m - 1/5

Step-by-step explanation:

Given the equation :

2(1/5m - 2/5) + 3/5

First step:

Open the bracket by multiplying values in the bracket by 2

2/5m - 4/5 + 3/5

-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5

Hence,

2/5m - 4/5 + 3/5 = 2/5m - 1/5

= 2/5m - 1/5

Dorothy put $470 into a savings account for one year. The rate of interest on the account was 5.5%. Find the interest earned on the amount.

Answers

Answer: $25.85 assuming annual compounding.

Step-by-step explanation:

PV=470

I/Y=5.5

N=1

CPT_FV

In the picture below, which lines are lines of symmetry for the figure?

A. 1 and 3
B. 2 and 4
C. 1, 2, and 3
D. none

Answers

Answer:

None

Step-by-step explanation:

No lines can be folded over to match up with the opposite side

How do I solve this: 12v + 10v + 14 = 80

Answers

Answer:

v = 3

General Formulas and Concepts:

Pre-Algebra  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

12v + 10v + 14 = 80

Step 2: Solve for v

Combine like terms:                                                                                         22v + 14 = 80[Subtraction Property of Equality] Subtract 14 on both sides:                       22v = 66[Division Property of Equality] Divide 22 on both sides:                               v = 3

Quadrilateral A'B'C'D' is a dilation of quadrilateral ABCD about point P Is this dilation a reduction or an enlargement? O reduction enlargement​

Answers

Answer: reduction

Step-by-step explanation:

ABCD-> 'ABCD

its bc 'ABCD got smaller compared to ABCD

Answer:

It is a reduction.

Step-by-step explanation:

Hope this helped.

Determine the 3 digit chopping and rounding approximately of the number 0.9

Answers

Answer:

We want to "chop and round" the periodic number 0.9 at 3 digits.

First, remember that we can write our periodic number as:

0.9 = 0.9999...

Such that the nine repeats infinitely.

Now we want to chop it at the third digit, and then round.

To chop at the third digit we just "cut" the number at the third digit after the decimal point, we will get:

0.9 ≈ 0.999

Now we round.

Remember that to round a number, we need to look at the last digit after the decimal point.

If the last digit is 5 or larger, we round up, adding 1 to the previous decimal.

If the last digit is 4 or smaller, we round down, don't adding anything to the previous decimal.

in our number:

0.999

The last digit is a 9, so we round up.

Then we add "1" to the previous decimal

but the previous decimal is a 9, so when we add 1, it will transform into a 10.

So it also adds one to the previous decimal, which also is a 9, so the process repeats, this time adding 1 to the decimal to its left, in this case, that decimal will be the first decimal at the left of the decimal point.

So after rounding, we will get:

0.999 ≈ 1

Then we can conclude that:

he 3 digit chopping and rounding approximately of the number 0.9 is 1"

Find the measure of the indicated arc.

Answers

It should be 102 degree

factor and solve the problems in the photo ……….. pleaseeeee help i haven’t done algebra in 2 years

Answers

Answer:

30. 2x²-x-1=0

or, 2x²-2x+x-1=0

or, 2x(x-1)+1(x-1)=0

or, (x-1)(2x+1)=0

so, x-1 = 0 or, x = 1

and 2x+1 = 0 or, 2x = -1 or, x = -1/2

so, x = 1 and 1/2

31. 3x²-14x=5

or, 3x²-14x-5=0

or, 3x²-15x+x-5=0

or, 3x(x-5)+1(x-5)=0

or, (x-5)(3x+1)=0

so, x-5=0 or, x=5

and 3x+1=0 or, 3x=-1 or, x=-1/3

so, x = 5 and -1/3

Answered by GAUTHMATH

Solve the compound inequality 7x > –35 and 3x ≤ 30.

Answers

Answer:

x>-5 x ≤10

Step-by-step explanation:

-35/7=-5

7x/7=x

3x/3=x

30/3=10

Answer: -5 < x _< 10

Step-by-step explanation:

4.
A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work

Answers

Answer:

x is 3.[tex]\overline{72}[/tex]

Step-by-step explanation:

The given points on the line are;

R(-5, -6), S(1, 5) and T(x, 10)

The number of points required to find the equation of the line = 2 points

The slope, m, of the line using points R(-5, -6) and S(1, 5) is given as follows;

m = (5 - (-6))/(1 - (-5)) = 11/6

The equation of the line in slope and point form, using point S(1, 5) is therefore;

y - 5 = (11/6)·(x - 1) = 11·x/6 - 11/6

y - 5 = 11·x/6 - 11/6, given that the x-value is required, we have;

x = (y - 5 + 11/6) × 6/11 = 6·y/11 - 19/11

x = 6·y/11 - 19/11

At point T(x, 10), y = 10, therefore, we have;

x = 6×10/11 - 19/11 = 41/11 = 3.[tex]\overline{72}[/tex]

x = 3.[tex]\overline{72}[/tex].

find the inequality represented by the graph​

Answers

Answer:

y < 5/2x + 5

Step-by-step explanation:

slope goes up 5, then over 2 ( 5 on top, 2 on bottom --> 5/2)

y intercept is +5

Answer:

Plug your slope and a point into the formula y = mx + B, in which "m" is the slope, (x, y) is a point on the line and "b" is the y-intercept, to find the equation governing the inequality line. Plugging in (0, 0), you obtain 0 = 0 + b, so b = 0. Rewriting the equation, you obtain y = x/2

What is the slope of a line parallel to line B?

Answers

The slope to line B is 5/2 so a line parallel would have a slope of 5/2.

Please help me ASAP!! Please write answer in inequalities form! Thanks so much! :)

Answers

Answer:

.5 < 2 - sqrt(2) < .6

Step-by-step explanation:

sqrt() is larger than 1.4 and less than 1.5

2 - sqrt(2)    2 -1.4 = .6

2 - sqrt (2) 2 - 1.5 = .5

.5 < 2 - sqrt(2) < .6

[tex]1.4 < \sqrt{2} <1.5 \\ - 1.5 < - \sqrt{2} < - 1.4 \\ 2 - 1.5 < 2 - \sqrt{2} < 2 - 1.4 \\ 0.5 < 2 - \sqrt{2 } < 0.6[/tex]

Exercise A Rewrite each of the following expressions. Use the
words divided by. Then set up the division problem. Look at the
examples on the top of this page.

Miles per hour

Answers

Answer:

gansjehensjhebebsbbvevbeb

Step-by-step explanation:

bebbdnxnbahwv sbbhw €6%×:nbbe

v2 = u2 + 2as

u = 12
a = -3
s = 18

work out v

Answers

[tex] {v}^{2} = {u}^{2} + 2as \\ {v}^{2} = 144 - 108 \\ {v}^{2} = 36 \\ v = 6 , -6 \: [/tex]


Use the figure to find the Total Area.

Answers

Answer:

60

Step-by-step explanation:

Multiply length times width times height

Answer:

C or 104

Step-by-step explanation:

I assume this is surface area, and I don't know what kinda sadist person would make everyone learn in "Total Area," but it is what it is.

So, to find total area, we need to literally multiply every different number with the other.

(You should not do it the way I did, as I did it in the easiest and simpliest way to understand possible.)

Actually, you get the length, width, and height of a figure and do what is below pretty much.

You multiply the length by the width, the length by the height, and the width by the height (doesn't have to be in this order, this is just to make it easy to remember which ones you did.)

We multiply the

5 * 6

5 * 2

and then the

6 * 2

This accounts for every possible case, as multiplying 2 * 5 gives the same thing as the second expression anyways.

So we then solve these three expressions.

5 * 6 = 30

5 * 2 = 10

and then the

6 * 2 = 12

And we add them to get

30 + 10 + 12

= 52.

Then we multiply by 2, because there are two cases of each face of the shape.

You need to remember that there is 3 other faces on the shape you are looking at, it's just that the shape/figure is facing you in a way that you can't see them.

After multiplying by 2, we get

52 * 2

= 104, which is C.

TAKE A SCREENSHOT NOT A PICTURE AS WE DON'T NEED TO SEE SOME 420P MONITOR FROM 1987 THAT SHOWS EVERY PIXEL PLEASE AND THANK YOU :D

14. Peter needs to buy a package of pencils to write his final exam. The store offers two packages.
Package 1: pack of 6 pencils for $1.68
Package 2: pack of 9 pencils for $2.34
Determine the cost per pencil. Which is the better deal? Round to 2 decimal places. Show all your work for full marks. (3 marks) REPOST

Answers

Answer:

Step-by-step explanation:

peter can buy pack of nine pencils

6 divided by 1.68 =3.5

9 divided by 2.34=3.8

package 2 is just 0.3 more

it give 3 more pencils for 0.3

I need help to find m =

Answers

Answer:

hlo buddy

are u free now.. nhjm....

13. The Cyclone Coaster has 16
cars. Some of them hold 2
passengers and some hold 3
passengers. If there is room for
36 people altogether, how many
cars hold 3 passengers?

Answers

Answer:

Four cars that can hold 3 passengers

Step-by-step explanation:

The number of cars on the Cyclone Coaster = 16 cars

The number of passengers some cars hold = 2 passengers

The number of passengers the other cars hold = 3 passengers

The number of people altogether the Cyclone Coaster has room for = 36 people

Let x represent the number of cars that can hold 3 passengers, and let y represent the number of cars that can hold 2 passengers, we have;

3·x + 2·y = 36...(1)

x + y = 16...(2)

The value of x can be found by making y the subject of equation (1) and equation (2) and equating both values of y given in x as follows;

The value of y from equation (1) is, y₁ = (36 - 3·x)/2 = 18 - 3·x/2

∴ y₁ = 18 - 3·x/2

The value of y from equation (2) is, y₂ = 16 - x

Equating both y values, to find the coordinates of the common point to both equations, gives;

At the common point y₁ = y₂

By the substitution property of equality

∴ 18 - 3·x/2 = 16 - x

3·x/2 - x = 18 - 16 = 2

x/2 = 2

∴ x = 4

The number of cars that can hold 3 passengers, x = 4

(From y₂ = 16 - x, we have

y₁ = y₂ = 16 - 4 = 12

y = 1

The number of cars that can hold 2 passengers, y = 12).

The tangent ration! helpp!!

Answers

Answer:

13.5

Step-by-step explanation:

Given

tan34° = [tex]\frac{x}{20}[/tex] ( multiply both sides by 20 )

20 × tan34° = x , then

x ≈ 13.5 ( to the nearest tenth )

please help me in this questions....​

Answers

Part (i)

I'm going to use the notation T(n) instead of [tex]T_n[/tex]

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

Answers: -1, -4

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

Answer:  21st term

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

Answer: 8

Can someone please exlpain how to do this???

Answers

Answer:

40. A c=60

41 B z= 40

Step-by-step explanation:

The sum of the angles in a triangle is 180

40.  61+59+c = 180

Combine like terms

120+c = 180

c = 180-120

c =60

41.  90+50+z = 180

140 +z = 180

z = 180-140

z = 40

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