Are these 2 triangles congruent? 0 If no, type "not congruent" If yes, state what postulate or theorem proves it.

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

hoa [83]

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.

5 0

3 years ago

A square is made up of an L-shaped region and three transformations of the region. If the perimeter of the square is 40 units, w

Mila [183]

Answer:

20 units

Step-by-step explanation:

This implies that the square can be divided into four equal L-shaped regions. These regions with respect to transformation forms a square.

Perimeter of the square is 40 units. Since a square has equal length of sides, thus each side of the square is 10 units.

Thus, each L-shape region has dimensions; 8 units, 5 units, 5 units and 2 units.

Perimeter of each L-shape region = the addition of the length of each side of the shape

Perimeter of each L-shape region = 8 + 5 + 5 + 2

= 20 units

3 0

3 years ago

Which numbers have a digit in the ones place that is 1/10 the value of the digit in the tens place

liq [111]

Answer:

4,099 and 5,011

Step-by-step explanation:

This problem can be solved by taking options one by one.

Option (1) : 4,099

Digit in ones place = 9

The value of the digit in tens place = 90

$\dfrac{9}{90}=\dfrac{1}{10}$ . It is correct.

Option (2) : 4,110

Digit in one places = 0

The value of the digit in tens place = 10

It is incorrect.

Option (3) : 5,909

Digit in one places = 9

The value of the digit in tens place = 0

It is again incorrect.

Option (4) : 5,011

Digit in one places = 1

The value of the digit in tens place = 10

$\dfrac{1}{10}$ . It is correct.

Hence, in option (a) and (d), the he ones place is 1/10 the value of the digit in the tens place.

7 0

3 years ago

In the Holiday Shop the manager wants 20% of the total inventory in the stockroom and the rest displayed on the floor. After mee

Lilit [14]

Answer:

Total inventory: $175,000

Inventory in the stockroom: $35,000.

Inventory on the selling floor: $140,000.

Step-by-step explanation:

Let x be the the total inventory.

We have been given that in the Holiday Shop the manager wants 20% of the total inventory in the stockroom. You placed $35,000 of inventory in the stockroom.

We can set an equation such that 20% of x equals $35,000.

$\frac{20}{100}\cdot x=\$35,000$

$0.20x=\$35,000$

$\frac{0.20x}{0.20}=\frac{\$35,000}{0.20}$

$x=\$175,000$

Since $35,000 of inventory in the stockroom, so we will subtract $35,000 from $175,000.

$\text{Amount of the inventory on the selling floor}=\$140,000$

Therefore, $140,000 of the inventory on the selling floor.

7 0

3 years ago

Sanjay read 56 pages of his book this weekend. This is 35% of the pages in the book. How many total pages are in the entire book

sukhopar [10]

I don't know if I did this right.
There are 1097.6 pages in the book. I multiplied .35 by 56 and got 19.6. I multiplied 19.6 by 56 and got 1097.6. Therefore, there are 1097.6 pages in the book.

7 0

3 years ago

Are these 2 triangles congruent? 0 If no, type "not congruent" If yes, state what postulate or theorem proves it.​

Are these 2 triangles congruent? 0 If no, type "not congruent" If yes, state what postulate or theorem proves it.