1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yarga [219]
3 years ago
5

Determine the truth value of each of these statements if thedomainofeachvariableconsistsofallrealnumbers.

Mathematics
1 answer:
hoa [83]3 years ago
5 0

Answer:

a)TRUE

b)FALSE

c)TRUE

d)FALSE

e)TRUE

f)TRUE

g)TRUE

h)FALSE

i)FALSE

j)TRUE

Step-by-step explanation:

a) For every x there is y such that  x^2=y:

 TRUE

This statement is true, because for every real number there is a square         number of that number, and that square number is also a real number. For example, if we take 6.5, there is a square of that number and it equals 39.0625.

b) For every x there is y such that  x=y^2:

 FALSE

For example, if x = -1, there is no such real number so that its square equals -1.

c) There is x for every y such that xy = 0

 TRUE

If we put x = 0, then for every y it will be xy=0*y=0

d)There are x and y such that x+y\neq y+x

 FALSE

There are no such numbers. If we rewrite the equation we obtain an incorrect statement:

                                   x+y \neq y+x\\x+y - y-y\neq 0\\0\neq 0

e)For every x, if   x \neq 0  there is y such that xy=1:

 TRUE

The statement is true. If we have a number x, then multiplying x with 1/x (Since x is not equal to 0 we can do this for ever real number) gives 1 as a result.

f)There is x for every y such that if y\neq 0 then xy=1.

TRUE

The statement is equivalent to the statement in e)

g)For every x there is y such that x+y = 1

TRUE

The statement says that for every real number x there is a real number y such that x+y = 1, i.e. y = 1-x

So, the statement says that for every real umber there is a real number that is equal to 1-that number

h) There are x and y such that

                                  x+2y = 2\\2x+4y = 5

We have to solve this system of equations.

From the first equation it yields x=2-2y and inserting that into the second equation we have:

                                   2(2-2y)+4y=5\\4-4y+4y=5\\4=5

Which is obviously false statement, so there are no such x and y that satisfy the equations.

FALSE

i)For every x there is y such that

                                     x+y=2\\2x-y=1

We have to solve this system of equations.

From the first equation it yields x=2-y  and inserting that into the second equation we obtain:

                                        2(2-y)-y=1\\4-2y-y=1\\4-3y=1\\-3y=1-4\\-3y=-3\\y=1

Inserting that back to the first equation we obtain

                                            x=2-1\\x=1

So, there is an unique solution to this equations:

x=1 and y=1

The statement is FALSE, because only for x=1 (and not for every x) exists y (y=1) such that

                                         x+y=2\\2x-y=1

j)For every x and y there is a z such that

                                      z=\frac{x+y}{2}

TRUE

The statament is true for all real numbers, we can always find such z. z is a number that is halway from x and from y.

You might be interested in
Which expression shows the prime<br> factorization of 66?<br> A 32 x 11<br> B 2x 3 x 11<br> C 6 x 11
lesya [120]

Answer:

B 2x 3 x 11

Step-by-step explanation:

good luck have a nice day

5 0
3 years ago
Read 2 more answers
Anybody down to help?
vova2212 [387]

Answer:

A to D E to B C to F F to 216

This ez

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Jada's sister works in a furniture store.
Bingel [31]

Answer:

1) $16.35

2) 75%

3) $245  

Step-by-step explanation:

1) Jada earns = $15 per hour

  9% increase = 15 * 9/100 = $1.35

  Increased Jada's pay = 15+1.35 = $16.35

2) Markup = selling price - cost= $350 - 200= $150

   Markup % = \frac{sale price - cost }{cost}*100 \

                      = \frac{150}{200}*100 = 75%

3) Jada's sister commission is 3.5% of $7000

          = \frac{3.5}{100}* 7000

           = $245  

5 0
2 years ago
Solve for x, given the equation square root of x + 9 -4 = 1
saveliy_v [14]

Answer:

x = -4

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Simplify the product. 8p(-3p2+6p-2)
Temka [501]

Answer:

9

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Guys HALP meh with this one
    5·1 answer
  • Find two numbers whose sum is 0 and who's difference is 8
    11·2 answers
  • Mateo is constructing an equilateral triangle inscribed in a circle with center P. He draws the diameter of the circle through c
    7·2 answers
  • What is 72 divided by 4
    10·2 answers
  • 60÷5(7-5) what is the answer to this math equation?
    11·2 answers
  • Get correct for brainleist!
    11·1 answer
  • Suppose a sample of 256 was taken from a population with a standard deviation of 64 centimeters. What is the margin of error for
    12·2 answers
  • Is 3:2 and 10:5 equvalent?
    8·1 answer
  • Solve for y. 3/2x-3y=6
    5·2 answers
  • Convert 7 grams into ounces. Round your answer to the nearest hundredth.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!