4x-4y+4z=8
9x+3y+z=6
16x+4y+z=2

Answers

Answer 1

9514 1404 393

Answer:

  (x, y, z) = (-1, 3, 6)

Step-by-step explanation:

The augmented matrix for the system is ...

  [tex]\left[\begin{array}{ccc|c}4&-4&4&8\\9&3&1&6\\16&4&1&2\end{array}\right][/tex]

Your graphing or scientific calculator can tell you the solution to this system is ...

  (x, y, z) = (-1, 3, 6)

__

If you want to solve this by hand, it can work well to divide the first equation by 4 to get ...

  x -y +z = 2

This can be subtracted from the other two equations to eliminate z.

  (9x +3y +z) -(x -y +z) = (6) -(2)  ⇒  8x +4y = 4

  (16x +4y +z) -(x -y +z) = (2) -(2)  ⇒  15x +5y = 0

These two equations can be reduced to standard form:

2x +y = 13x +y = 0

Subtracting the first equation from the second, we have ...

  (3x +y) -(2x +y) = (0) -(1)  ⇒  x = -1

Substituting into the first gives y:

  2(-1) +y = 1

  y = 3 . . . . . . . add 2

Then we can find z from the reduced first equation above:

  z = 2 -x +y = 2 -(-1) +3 = 6

Then the solution is (x, y, z) = (-1, 3, 6).


Related Questions

What is the image of (−8,−8) after a dilation by a scale factor of 1/2 centered at the origin?

Answers

Answer:

(-4,-4)

Step-by-step explanation:

Since this is centered at (0,0), we have to multiply the x and the y coordinates by the scale factor.

-8 × 1/2 = -4

Solve the equation -5 m = -20.

a.m =
b.m =
c.m = -4
d.m = 4

Answers

Answer:

-5m=-20

or, m= -20 /-5

= 4

hence, d. m = 4

The angle measurements in the diagram are represented by the following expressions.
B
А
Solve for x and then find the measure of

Answers

Answer:

[tex]x = 20^{\circ}[/tex]

[tex]\angle A = 150^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle A = 8x - 10[/tex]

[tex]\angle B = 3x + 90[/tex]

See attachment

From the attachment A and B are vertically opposite.

This implies that:

[tex]\angle A = \angle B[/tex]

Substitute values for A and B

[tex]8x - 10 = 3x + 90[/tex]

Collect Like Terms

[tex]8x - 3x = 10 + 90[/tex]

[tex]5x = 100[/tex]

Solve for x

[tex]x = \frac{100}{5}[/tex]

[tex]x = 20^{\circ}[/tex]

Substitute 20 for x in [tex]\angle A = 8x - 10[/tex]

[tex]\angle A = 8 * 20 - 10[/tex]

[tex]\angle A = 150^{\circ}[/tex]

What is 42= -7 × (z - 3)?

Answers

Answer:

z=-3

Step-by-step explanation:

Answer:

z=3

Step-by-step explanation:

42=−7(z−3)

Simplify both sides of the equation.

42=−7(z−3)

42=(−7)(z)+(−7)(−3)(Distribute)

42=−7z+21

Flip the equation.

−7z+21=42

Subtract 21 from both sides.

−7z+21−21=42−21

−7z=21

Divide both sides by -7.

-7z/-7=21/7

z=3

please solve question in picture branoist to first and correct​

Answers

Answer:

The correct answer is Option 3: 12y

Step-by-step explanation:

A polynomial term is usually made of a variable and a co-efficient.

Like terms are those terms that have the same variables i.e. x and 44x are like terms.

Given expression is:

[tex]6y-2y+8y[/tex]

All the terms have only y which means that all three terms are alike.

The coefficients of like terms are added or subtracted according to their sign.

[tex]6y-2y+8y[/tex] = 12y

Hence,

The correct answer is Option 3: 12y

Suppose that Mudlark decides to sell 140 tickets for this flight. Assuming that all 140 tickets are sold and that the outcome for each ticketholder is independent, how many ticketholders should the airline expect to show up

Answers

This question is incomplete, the complete question is;

Lets consider a hypothetical airline, Mudlark Airlines. On one of its flight, previous records show that about 15% of people who had tickets for the flight did not take the flight. There are 120 seats on the plane.

Suppose that Mudlark decides to sell 140 tickets for this flight. Assuming that all 140 tickets are sold and that the outcome for each ticketholder is independent, how many ticketholders should the airline expect to show up

Answer: the airline should expect 119 ticketholders to show up

Step-by-step explanation:

Given that;

the plane contains 120 seats

Their records shows that 15% (0.15) percent of people who previously buy their flight tickets don't show up.

they sold 140 tickets,

Number of ticketholder expected to show up  = ?

Probability of showing up for flight will be;

⇒ 1 - 0.15 = 0.85

Now Expected number of ticketholders to shup will be;

⇒ 140 × 0.85

= 119

Therefore the airline should expect 119 ticketholders to show up

WILL GIVE BRAINLIEST
It takes Shayna 14 hours to pick forty
bushels of apples. Ashley can pick the
same amount in 8 hours. If they worked
together how long would it take them?

Answers

Answer: 6 hours

Step-by-step explanation: because if it takes Shayna 14 hours to pick the apples and took Ashley 8 hours  if you subtract that its 6 hours

PRE CALC ON EDGE PLEASE HELP 100 PTS!!! IM TIMED

Answers

Answer:

The last option

Step-by-step explanation:

a is the hypotenuse, x is the adjacent, h is the opposite.

a^2 = h^2 + x^2

Subtract x^2 from both sides

h^2 = a^2 - x^2

Please gimme brainliest

I think it’s the last one

!Please help!

Antoine is drawing a scale map of the park he uses a scale of 1cm : 15 paces. A pond is 75 paces from the front gate of the park how far is the pond from the gate on the map

Answers

Answer:

5

Step-by-step explanation:

i just did it

Convert the mixed number below to an improper fraction.

523

Answers

Answer:

17/3

Step-by-step explanation:

if you meant 5 2/3

Multiply the denominator by the whole number

3 x 5= 15

Add the answer above to the numerator

15 + 2= 17

Write the answer from above over the denominator

17/3

Calculate the correlation coefficient, r, for the data below.

Answers

This question is incomplete, the complete question is;

Calculate the correlation coefficient, r, for the data below.

X = -10  -8  -1  -4  -6  -7  -5  -3  -2  -9

Y = -15  -13  4  -4  -7  -11  -6  -2  1  -13

Answer: the correlation coefficient, r, for the data is 0.9896

Step-by-step explanation:

Given the data in the question;

correlation coefficient r = ?

we know that, C_Coeff is;

r = [ (Zn(∑xy) - (∑x)(∑y) ] / [ √[( n∑x² - (∑x)²) ( n∑y² - (∑y)²)] ]

so ;

       X        Y        X²        Y²        XY

     -10     -15       100      225      150

     -8      -13        64       169       104

     -1         4          1        16           -4

     -4       -4         16       16           16

     -6       -7         36      49          42

     -7       -11         49      121         77

     -5       -6         25      36         30

     -3       -2          9         4            6

     -2       1            4         1            -2

     -9      -13         81       169         117

∑   -55     -66      385     806        536

now we substitute our values into the formula

r = [ (10×536 - (-55)(-66) ] / [ √[( 10×385 - (-55)²) ( 10×806 - (-66)²)] ]

r = 1730 / √( 825 × 3704 )

r = 1730 / √3055800

r = 1730 / 1748.0846

r = 0.9896

Therefore the correlation coefficient, r, for the data is 0.9896

jester has a piece of wood measuring 1 and 2/3 m.he needs to cut in pieces measuring 3/4 m. long.how many pieces of wood did jester cut.​

Answers

Answer:

2

Step-by-step explanation:

Given that,

Jester has a piece of wood measuring 1 and 2/3 m = 5/3 m

He needs to cut in pieces measuring 3/4 m

We need to find the number of pieces. Let there are x no. of pieces.

[tex]x=\dfrac{\dfrac{5}{3}}{\dfrac{3}{4}}\\\\=\dfrac{5}{3}\times \dfrac{4}{3}\\\\=2.23\[/tex]

or

x = 2

So, he will cut it into approx 2 pieces.

1 hours 20 min : 2 hours ratio

Answers

1:20 i think sooo.Je suis américain et habite dans les montagnes vertes du vermont . Je premier apprend français il y a un an parce que c'est un beau langue . Oui, je sais mon français est mauvais, mais J'aime l'apprendre . Je suis dix-sept et j'ai un chien blanc petit . Ma famille l'appelle snowball et il est tres gentil . Mon préféré endroit en la monde est les montagnes car ils sont très beau dans tout quatre saisons . Merci pour votre temps et au revoir .

there are 36 playing tag at recess. this is 6 times as many playing hopscotch. which model shows this comparison?

i got the top one to the left (checking my answer)

Answers

Answer:

The top left one is correct.

Step-by-step explanation:

We can rewrite this as an algebraic expression simply so it's easier to read.

Let's say hopscotch is [tex]h[/tex]. Tag is 6 times [tex]h[/tex], or [tex]6h[/tex].

That means for every 1 unit of hopscotch, there are 6 units of tag.

The top left one is correct.

The ______ of a function consists of set of all output values

Answers

Domain and range :))))

Name the factors in each of the following problems

Answers

Ok sure, lol.
Can’t see anything

Consider a binomial experiment with n = 5 trials where the probability of success on a single trial is p = 0.30. (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

Answers

Answer:

0.16807 ; 0.83193

Step-by-step explanation:

Given that:

Number of trials, n = 5

Probability of success, p = 0.30

P(r = 0)

Using the binomial probability relation :

P(x =r) = nCr * p^r * (1 - p)^(n - r)

(a) Find P(r = 0).

P(r = 0) = 5C0 * 0.3^0 * (0.7)^(5- 0)

= 1 * 1 * 0.16807

= 0.16807

(b) Find P(r ≥ 1) by using the complement rule

P(r ≥ 1) = 1 - P(r = 0)

P(r ≥ 1) = 1 - 0.16807

P(r ≥ 1) = 0.83193

What is the Distance between 6+3i, 6-3i

Answers

2-8..........

ITS UR ANSWER!,

joe boght 15 tolets. 1 was pure gold 2 were pure silver and the rest were wooden. how many wooden toilets were there?

Answers

12.
It is easy all you have to do is 15-3 because 1+2=3

The value of the square root of 14 is between which two integers?

Answers

3 and 4

3x3=9
4x4=16
14 is between 9 and 16.

I think this is right but want to check need help 25 points!!!

Answers

Answer:yes your Most definitely correct

Step-by-step explanation:

SOMEONE PLEASE PLEASE HELP ME ON THIS!!

Answers

X=22

14 plus 8 gives you x

[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:

35

Step-by-step explanation:

please help me please i really need help please

Answers

Here is the solution

Pleaseee help!!!!!!!!

Answers

Answer:

no

Step-by-step explanation:

no

How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings if each topping can only be chosen once

Answers

Answer:

24,024

Step-by-step explanation:

Calculation for How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings

The 4 pizza toppings from a menu of 14 toppings will be 14,13,12,11

Hence,

14*13*12*11=24,024

Therefore the numbers of way Rudy can choose 4 pizza toppings from a menu of 14 is 24,024

3×=18 what the answer to this problem

Answers

Answer:

x=6

Step-by-step explanation:

Divide both sides by 3

Answer:

x = 6

Step-by-step explanation:

To find the answer, we must divide 18 by 3. When we do that, we get 6, meaning that x is equal to 6.

Can y’all help me solve this.
Please!!!!!!!

Answers

9514 1404 393

Answer:

  all statements are true

Step-by-step explanation:

The line 4y=-16 can be rewritten to standard form as ...

  y = -4 . . . . a horizontal line with all points having y-coordinate = -4

__

The line 3x = 27 can be rewritten to standard form as ...

  x = 9 . . . . a vertical line with all points having x-coordinate = 9.

__

All of the statements about these lines are true.

please answer asap no trolls!

Answers

Answer:

Yes.

Step-by-step explanation:

3.5 + 5.5 > 7.8

A florist sells 3 roses for a total of $10. Each rose costs the same amount. What is the cost of 12 roses?

A. $9.60
В. $10.40
C. $14.00
D. $15.00​

Answers

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

if 3 roses   costs              10 dollars

3x4=12 roses.................10x4=40 dollars

Multiply The polynomials. (3x^2+4x+4)(2x-4)

Answers

Answer:

6x^3 - 4x^2 - 8x - 16

Step-by-step explanation:

6x^3 + 8x^2 + 8x - 12x^2 - 16x - 16

combine

6x^3 - 4x^2 - 8x - 16

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