For what value of z would the following system of
equations be true for all real integers?
3x-2y = 14
-12x+8y = 8z

Answers

Answer 1

9514 1404 393

Answer:

  z = -7

Step-by-step explanation:

The equations will be true for all real integers when they are a dependent set. That will be the case when the second equation is a multiple of the first.

Already, we observe that the ratios of x- and y-coefficients are -4:

  -12/3 = -4

  8/-2 = -4

The equations will be dependent when the constants have that same ratio:

  8z/14 = -4 . . . . desired ratio

  8z = -56 . . . . . multiply by 14

  z = -7 . . . . makes the equations true for all real numbers

_____

Comment on the question

The system of equations can be made inconsistent (no solutions) or consistent & dependent (infinite solutions) by the choice of z.

However, integer solutions are limited to pairs of the form (2n+2, 3n-4) for integer values of n. The values of x and y are not "all real integers".

Consequently, we have interpreted the question to be asking for the value of z that will make the system of equations have an infinite number of solutions, including both rational and irrational, real and complex values of x and y. They cannot be made to be true for "all real integers" by any choice of z.

Answer 2

Answer:

z = -7 is the answer.

Step-by-step explanation:

#CarryOnLearning

Related Questions

There are 60 pupils who joined the Math Quiz Competetion. 40 were boys and 20 were girls. During the Awarding ceremony, it was found out that 20% of the boys and 15% of the girls won and received prizes. How many received prizes?

Please Answer In English
No link Kailangan ko na po ngayon!! :)​

Answers

Answer:

8 pupils received prices

Step-by-step explanation:

20% of 40 = 8 (8 boys)

15% of 20 =3  (3 girls)

8+3 = 11

Answer:

21 pupils received the prizes.

Step-by-step explanation:

20% +15% =35%

35/100 of 60 =21.

What is the prime factorization of 48?
O A. 2x3x8
OB. 2x2x3 x4
OC. 2x2x2x3
OD. 2x2x2x2x3
O E. 2x2x2x3 x3

Answers

Answer:

D

Step-by-step explanation:

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 3 = 48

What is the median?

2, 2, 1, 3, 5, 10, 2, 5

Answers

Answer:

The Miriam is 1,2,2,2,3,5,5,10

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

arrange the numbers in assending order.

perimeter and area of a rectangular figure has a perimeter of 34cm its length is 9cm​

Answers

Answer:

Perimeter of rectangle = 32

Step-by-step explanation:

32 = 2(L+B)

L+B=16

B=16-L

B=16–9

B=7

AREA = L*B

AREA = 63sq.cm

Find the surface area of the triangular prism. The base of the
prism is an isosceles triangle.
45 cm, 37cm, 35cm, 24cm

Answers

Answer:

5,250 cm²

Step-by-step explanation:

Surface area of triangular prism = bh + (s1 + s2 + s3)L

Where ,

b = 24 cm

h = 35 cm

s1 = 37 cm

s2 = 37 cm

s3 = 24 cm

L = 45 cm

Plug in the values

Surface area = 24*35 + (37 + 37 + 24)45

= 840 + 4,410

= 5,250 cm²

Can someone help me find the area of this shape.

Answers

Answer:

37 ft²

Step-by-step explanation:

The figure is composed of a triangle and a square

Therefore, area of the figure = area of the triangle + area of the square

= ½bh + s²

Where,

b = 1.5 + 4 + 1.5 = 7 ft

h = 6 ft

s = 4 ft

Plug in the values into the equation

Area of the figure = ½*7*6 + 4²

= 21 + 16

= 37 ft²

Multiply.


−3.6(−5.4)(3)

Answers

Answer:

-3.6(-5.4)(3)

=58.32

hope it helps.

Answer:

it's answer is 58.32

hope it is helpful to you

Add (-2x + 4) + (4x + 6)
A) 2x + 10
B 6x + 10
C) 2x - 2
D) 6x-2​

Answers

Answer:

A. 2x + 10

Step-by-step explanation:

In a cookie jar, 1/4 of the cookies are choclate chip, and 1/2 of the rest are peanut butter. What fraction of all the cookies is peanut butter? ( If you answer this show your work)

Answers

Answer:

4

Step-by-step explanation:

3/8 of the cookies are peanut butter

Explanation: the rest of the cookies that are not chocolate chip is 3/4 and half of that is 3/8.

Cynthia was asked to subtract 0.223 from 0.54. Which of the following is the best estimate that cynthia can make to check her answer?

Answers

I need help with this one too , can you guys please help us


In desperate need

Answer :

SOMEONE PLEASE HELP :(

Answers

Answer:

[tex](x-3)^{2} = 10[/tex]

Step-by-step explanation:

[tex]\\Question 1\\\\-2xc = -6x\\2xc = 6x\\c = \frac{6}{2} \\c = 3\\x^{2} - 6x + cx^{2} = 1 + c^{2} \\x^{2} - 6x + 3^{2} = 1 + 3^{2}\\x^{2} - 6x + 9 = 1 + 9\\x^{2} - 6x + 9 = 10\\(x - 3)^{2} = 10\\REWRITINGx^{2} - 6x = 1 is equal (x -3)^{2} = 10\\[/tex]

I hope this help!

I don't know the second one ^-^

Jorge is standing at a horizontal distance 25 feet away from the base of a building his eyes level is 5.5 feet above the ground looking up at the angle of elevation of 65 he notices a window washer on the side of the building

Answers

Answer:

59.11 ft

Step-by-step explanation:

For a certain brand of tomato seeds, the seed package claims that it takes 87 days after planting for the tomato plants to produce fruit. Sarah, a botanist, wanted to know whether the mean number of days for the plants to produce fruit where she lives is different from 87 days. She planted 40 seeds and recorded the number of days for each plant to produce fruit. With all conditions for inference met, the hypothesis test was conducted at the significance level a = 0.05, and the test resulted in a p-value of 0.0752. ?
Which of the following is a correct conclusion?
A. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
B. Sarah has convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
C. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is greater than 87 days.
D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.
E. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is equal to 87 days.

Answers

Answer:

D. Sarah does not have convincing statistical evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.

Step-by-step explanation:

The population mean, μ is given as 87

This population value is used to state the Null hypothesis ;

H0 : μ = 87

The alternative hypothesis is the opposite of the Null ; and hence, claims that the mean is different from the population mean, μ ≠ 87

H1: μ ≠ 87

The Decison level :

When Pvalue < α ; We reject the Null otherwise we fail to reject the null

The given p and α value :

P-value = 0.0752

α = 0.05

0.075 > 0.05 ; Hence ;

Pvalue > α ; We fail to reject the Null

We can thus conclude that there is not enough evidence to conclude that the population mean number of days for the plants to produce fruit is different from 87 days.

Use the graph below to find the indicated function Value. y=f(x); f(4)

Answers

From the graph at f=4
then y=3

The value of f(4) is 3 if the graph of the function is shown in the picture, the answer is 3.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The graph of the function is shown in the picture.

From the graph the value of f(4) can be evaluated as follows:

y = f(x)

Plug x = 4

y = f(4)

From the graph:

Draw a vertical line from point 3 on the x-axis and when it cuts the curve draw a horizontal line when the line cuts the y-axis note the point.

y = f(4) = 3

Thus, the value of f(4) is 3 if the graph of the function is shown in the picture, the answer is 3.

Learn more about the function here:

brainly.com/question/5245372

#SPJ2

Below is a list of equations and expressions.
1.
5(x + 3) = 25
2.
3 + x = -9
3.
X +5
3
4.
3(x + 3)
Which are examples of expressions?
A 1 and 2
B 3 and 4
с
2 and 3
D
3 only

Answers

B: 3 and 4 because they both do not have an = sign

Answer:

The answer is B.

Step-by-step explanation:

.........................................

Answers

Answer:

Whats wrong??

Step-by-step explanation:

Answer:

you ok ?

Step-by-step explanation:

I dont know what the ......... means

i put 15 i think it’s wrongs please help

Answers

Answer:

[tex] \sqrt{( {0 - 12}) {}^{2} + (1 - 10) {}^{2} } \\ = \sqrt{0 + 81} \\ = \sqrt{81} \\ = 9[/tex]

[tex] \huge\mathfrak\pink{A} \huge\mathfrak\purple{n} \huge\mathfrak\blue{s} \huge\mathfrak\red{w} \huge\mathfrak\green{e} \huge\mathfrak\orange{r}\ [/tex]

9 is the correct answer

1
3
16
Which expression is equivalent to 3/64a6b7c9?
O zabo (V4a?b°c)
4a²b2c (VD
Baºbc* (V50
Ba?b%cº (PD)

Answers

Answer:

Step-by-step explanation:

The equivalent expression is,

⇒ 4a²b²c³ ∛b

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ ∛64a⁶b⁷c⁹

Now, We can simplify the expression as;

⇒ ∛64a⁶b⁷c⁹

⇒ ∛64a⁶b⁷c⁹

⇒ ∛4³ (a²)³ (b²)³ (b) (c³)³

⇒ 4a²b²c³ ∛b

Thus, The equivalent expression is,

⇒ 4a²b²c³ ∛b

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

Jason drew a triangle to explain the Triangle Sum Theorem and labeled the angles 1, 2, and 3

He tore each angle off the triangle so he could move the three angles around.

What should Jason do next to explain the Triangle Sum Theorem?

Jason should line up the angles next to each other as adjacent angles to show that the 3 angles together form a straight angle.

Jason should create a new triangle by moving the angles closer together to show that the 3 angles can create other triangles.

Jason should fold each angle in half to show each angle with one half of the measure it had in the triangle.

Jason should stack the angles on top of each other to show that the 3 angles have the same measures.

Answers

Answer:

A

Step-by-step explanation:

Well B is strange. You might get them to make one complementary angle, but that has nothing to do with the Triangle sum theorem.

C is true. He is getting similar triangles, but that does not prove the Triangle sum theorem.  So -- don't choose C

D is just taking up space so you get 4 choices.

The answer should be A but the problem is the tips of the angles should all come to the same place. I think it does mean A, but it is a bit awkwardly worded.

Answer:A

Step-by-step explanation:

smart person above

Evan is thinking of a number that contains the digit 2 The digit 2 in Evan's number has 10 times the value of the
digit 2 in the number 328,907.
Which number could be the number that Evan is thinking of?
127,905
145,298
290,837
352,987

Answers

Answer:

C, 290,837

Step-by-step explanation:

The 2 in his number is 10x the 2 in the number 328,907

This means you need to move the number to the left once, hence it being in the hundred thousands.

290,837 is the final answer.

Question 1 of 10
Using the graph below, select all statements that are true.
.
+10
O A. (5.1) = 5
OB. This graph is one-to-one.
C. f(0.6) = 0
D. This is the graph of the greatest integer function,
E. (-3.2) = -3
SUBMIT

Answers

Answer:

the answer is going to be b

Find the measure of minor arc QN.

Answers

QN = 142°

A semicircle will always be equal to 180°, and we have two measures for semicircle QO.

[tex]QO = 180\\MN = 90\\NO = 38\\\\QM = QO - MN - NO\\QM = 180 - 90 - 38\\QM = 52\\\\QN = QM + MN\\QN = 52 + 90\\QN = 142\\[/tex]

Simplify the expression (2x- 9Xx + 6).​

Answers

Answer:

2 2 + 3 − 5 4

Step-by-step explanation:

HELP PLEASE !!

a teacher asks five students to write an equation with a solution of x= 4 . the students and their equations are shown below. which of the following students correctly wrote an equation with x= 4 as the solution ? select three that apply .

Answers

Bert, Camille, Etsuko

What is 32 divided by 4 to the second power plus 35-20 divided by 5

Answers

Because 32 divided by 4 = 8 to the 2nd power u multiply by 2 and get 16 + 35-20= 15 divided by 5? Equals 3

Which of the following points are solutions to the equation 3x - 4y - 8 = 12?
Select all that apply.
(0-5)
(82)
(-16-17)
(-1,-8)
(-40,-34)

Answers

Sorry I did it wrong.

Answer:

(0, -5) and (-16, -17)

Step-by-step explanation:

You can plug in the points into the function to test them.

(0, -5)

3(0) - 4(-5) - 8 = 12

20 - 8 = 12

12 = 12

(8, 2)

3(8) - 4(2) - 8 = 12

24 - 8 - 8 = 12

8 ≠ 12

(-16, -17)

3(-16) - 4(-17) - 8 = 12

-48 + 68 - 8 = 12

12 = 12

3(-1) - 4(-8) - 8 = 12

-3 + 32 - 8 = 12

21 ≠ 12

3(-40) - 4(-34) - 8 = 12

-120 + 136 - 8 = 12

8 ≠ 12

What is 9X plus 2Y equals -14 in slope intercept form

Answers

Answer:

y = -9/2x-7

Step-by-step explanation:

9x+2y = -14

-9x          -9x

2y= -9x-14

/2        /2

y= -9/2x-7

Please help me with this questions

Answers

He messed up step 2 he added instead of multiplying

Which is a rational function?

Answers

Answer:

C is a rational function

The answer is B. There are polynomials in the top and bottom

If anyone could help I would be so happy!

Answers

Answer: well i cant help... so dont be happy! :)

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