answer this question pls <3

A system of equations only has a unique solution if all the equations are linearly independent (this means that we have two or more equations representing the same curve).

Here we have the system:

a*x + 2*y + 4*z = b

2*x + y + 3*z = a + 1

5*x - 2*y + (a + 1)*z = 3

Now we want to show that if a = -5 or a = 2, then the system does not have a unique solution.

To see this, we can just replace a by these values and see that the equations are not linearly independent.

for a = 2 we get:

2*x + 2*y + 4*z = b

2*x + y + 3*z = 2 + 1

5*x - 2*y + (2 + 1)*z = 3

Simplifying this:

2*x + 2*y + 4*z = b

2*x + y + 3*z = 3

5*x - 2*y + 3*z = 3

From the second and third equation we can write:

2*x + y + 3*z = 3 = 5*x - 2*y + 3*z

2*x + y + 3*z = 5*x - 2*y + 3*z

2*x + y = 5*x - 2*y

3*y = 3*x

y = x

now that we know this, we can rewrite the equations as:

4*(x + z) = b

3*(x + z) = 3

Now we can take the quotient of the two equations to get:

(4*(x + z))/3*(x + z) = (4/3) = b/3

b = 4

Then the equations become:

4*(x + z) = 4

3*(x + z) = 3

Here we can divide te above one by 4 and the below one by 3 to get:

(x + z) = 1

(x + z) = 1

So both equations represent the same line, thus, the system does not have a unique solution.

Now for a = -5:

-5*x + 2*y + 4*z = b

2*x + y + 3*z = -5 + 1

5*x - 2*y + (-5 + 1)*z = 3

Simplify it:

-5*x + 2*y + 4*z = b

2*x + y + 3*z = -4

5*x - 2*y  - 4*z = 3

Now we can rewrite the first equation as:

-5*x +2*y - b = -4*z

and the third one as:

-4*z = 3 - 5*x + 2*y

Then we can write:

-5*x +2*y - b = -4*z = 3 - 5*x + 2*y

-5*x +2*y - b = 3 - 5*x + 2*y

Now we can remove the -5*x in both sides to get:

+2*y - b = 3 + 2*y

Now we can remove the 2*y in both sides to get:

-b = 3

b = -3

Replacing this in our system we get:

-5*x + 2*y + 4*z = -3

2*x + y + 3*z = -4

5*x - 2*y  -4*z = 3

Now we can multiply the first equation by -1:

-1*(-5*x + 2*y + 4*z)= -1*(-3)

5*x - 2*y - 4*z = 3

This is the same as the third equation, so here we can see that the first and third equations represent the same line, thus, the system of equations does not have a unique solution.

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Answer:

22

Step-by-step explanation:

Answer:

948,762

Step-by-step explanation:

The greatest six digit number would have to start with 9. It is given that the four is in the ten thousand place. Since no number can be repeated. I put the next largest number to 9 in the thousands place which is 8. I then put 7 then 6.  Since the number has to be even I put 2 since 8, 6 and 4 were already used.

The greatest 6 digit even numbers with 4 in the ten thousand place and all digits different is 948,762.

An even number is an integer that can be divided by two and remain an integer or has no remainder.

Now it is given that,

greatest 6 digit even numbers with 4 in the ten thousand place and all digits different

So, the greatest will be starting from 9

Digit at the ten thousand place is fix, 4

Digit at the thousand place is 8

Digit at the hundred place is 7

Digit at the ten place is 6

Since, it is an even number then it must be divisible by 2.

So, last digit at ones is 2

Thus we get, 948,762

hence, the greatest 6 digit even numbers with 4 in the ten thousand place and all digits different is 948,762.

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Answer:

C

Step-by-step explanation:

because when you reflect it the figure A on the y-axis, it looks the same as A*, and when you move it 5 units down both figures are at the same place, showing that the shapes are congruent.

Answer:

B and C

Step-by-step explanation:

A is a non terminating number which means it isn't rational. B and C are both rational and adding 1/2 to them won't change that, since they are terminating numbers. D is not a number.

Answer:

12+1/2 (0.5 as a decimal)

Step-by-step explanation:

π +0.5 will give an irrational number.

0.314 is rational

12 is a counting number.

And 4.35889894... is an irrational number.

An irrational number plus a rational one equals an irrational number.

Hope it helps! Please mark Brainliest! :-)

Answer:

Presumably the "others time" is the quantity [tex]a[/tex], which is 28.81

Step-by-step explanation:

Let's solve for [tex]a[/tex] from

[tex]38.4-a=9.59[/tex]

Adding [tex]a[/tex] gives

[tex]a+9.59=38.4[/tex]

Then subtracting 9.59 gives

[tex]a=38.4-9.59=28.81[/tex]

Answer:

g

Step-by-step explanation:

Answer:

18 and 2

Step-by-step explanation:

18-2=16

18+2=20

Hi ;-)

[tex]\{x-y=16\\+\{x+y=20\\--------\\2x = 36 \ \ /:2\\\boxed{x=18}\\18+y=20 \ \ /-18\\\boxed{y=2}[/tex]

These numbers are 18 and 2.

Answer:

- 5°F

Step-by-step explanation:

- 3°F - 2°F

(-3) - 2

-5

- 5°F

Answer:

3  + 2 = 5

                          Thank You

Answer:

given

n=9

a=1

d=3-1=2

Step-by-step explanation:

now , by formula,

sn = n/2(2a+(n-1)d)

= 9/2(2×1+(9-1)×2)

=9/2×18

=81

The correct notation will be A∪B and it can be read as A union B

In the given Venn diagram we can deduce the following;

The shaded region in the Venn diagram includes all the elements in set A and all the elements in set B.

Thus, the correct notation will be A∪B and it can be read as A union B.

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A Venn Diagram is a diagram used to define sets.

Here we will find that the notation of the shaded region is: A ∪ B

To know this, we need to define all of the notations in the options:

So with these general notations, is easy to conclude that if we have shaded sets A and B completely, then we have the set: A ∪ B

The correct option is C.

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Answer:

1/18

Step-by-step explanation:

Probability of getting a number higher than 4=1/3

Probability of getting 2=1/6

Probability of rolling a number higher than 4 and then a 2=(1/3)*(1/6)=1/18

Answer:  1.125 miles

Step-by-step explanation:

Add the two fractions together but first rewrite the fractions with a common denominator.

4/15 = 8/30

3/10 = 9/30

8/30 + 9/30 = 17/30

Answer: 17/30

The fraction is 17/30.

fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

For example.

The following figure shows a pizza that is divided into 8 equal parts. Now, if we want to express one selected part of the pizza, we can express it as 1/8 which shows that out of 8 equal parts, we are referring to 1 part.

Given:

4/15 of the candies in a bag of Skittles are red

3/10 are yellow

So, make the denominator of both fraction same by LCM

4/15 = 8/30

3/10 = 9/30

Now,

8/30 + 9/30 = 17/30

Hence, the fraction is 17/30.

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9514 1404 393

Answer:

  1 +i√3.5

Step-by-step explanation:

In vertex form, the equation is ...

  2(x² -2x +1) +7 = 0

  2(x -1)² +7 = 0

Then the solutions are ...

  (x -1)² = -7/2

  x = 1 ±i√3.5

One solution is 1+i√3.5.

Answer:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

1936

Step-by-step

[tex][15 - (1 - 6 + 21 + \sqrt{9} )] ^{2}[/tex]

use BIDMAS

(1 - 6 + 21 + [tex]\sqrt{9}[/tex]) = (1 - 6 + 21 + 3) = (1 - 30) = -29

[15 - -29] = [15 + 29] because two minuses together make a plus

[tex]44^{2}[/tex] = 1936

Answer: I dont know

Step-by-step explanation:

Answer:

x= -y+1

y=2x+z−1

z=−x−2y+ 8 /3

Step-by-step explanation:

I honestly entered it into a algebra calculator which gave me the steps.

Answer:

f(2) = 11

Step-by-step explanation:

Plug 2 in for x

3(2) + 5

6 + 5

= 11

Answer:

CD and BE

BC and DE

...........

Answer:

6.25 or 6 2/8 or 6 R2

Step-by-step explanation:

Step-by-step explanation:

y-y1=slope (x-x1)

where x1=-6,y1=2 and slope=3÷2

y-2=3÷2{x-(-6)}

y-2=3÷2(x+6)

y-2=(3x+18)÷2 cross multiply

2y-4=3x+18 collect like terms

2y=3x+18+4

2y=3x+22....ans

Answer:

the square of a positive number is always positive

Answer:

The segment CD is a diameter . It is 15 cm long.

9514 1404 393

Answer:

  2

Step-by-step explanation:

The graphs have two (2) points of intersection. Each point of intersection is a solution to the system of equations. The coordinates of that point satisfy both equations simultaneously.

There are 2 solutions to the graphed system of equations.

Step-by-step explanation:

Additive inverse are numbers with the same number but different signs. For example, 1 and -1 are additive inverse.

An additive inverse and it original number add to zero.

For example,

[tex]1 + ( - 1) = 0[/tex]

Using this info, w is -0.8

0.8 and -0.8 are equidistant from 0.

-0.8 is 2 mark to the right of -1.

So this means that 0.8 is 2 mark to left of 1.