If X = then what is XY?<br> (Please see images)

Solve. Write the solution in interval notation. -2x>-8 and -5x<20.

Novosadov [1.4K]

Answer:

The interval notation of the solution is (-4 , 4)

Step-by-step explanation:

* Let us explain a very important point in solving inequality

- When you multiply or divide an inequality by negative number we

must reverse the symbol of the inequality

- Ex:

∵ 2 < 3

- If we multiply the both sides of the inequality by -1, then the

inequality will be -2 < -3 and this is completely wrong, so we must

reverse the symbol of the inequality

∴ -2 > -3

* Now let us solve the problem

∵ -2x > -8

- Divide both sides by -2 and remember to reverse the symbol of the

inequality

∴ x < 4

∵ -5x < 20

- Divide both sides by -5 and remember to reverse the symbol of the

inequality

∴ x > -4

- From both solutions

∴ -4 < x < 4

∴ The solution is {x : -4 < x < 4}

- Interval notation is a way of writing the solutions of inequalities

( , ) if x does not equal the end numbers

[ , ] if x equals the end numbers

[ , ) , ( , ] if x equals one of the two end numbers

* The interval notation of the solution is (-4 , 4)

4 0

3 years ago

Help me please !<br> 4,5 and 6

andreev551 [17]

9514 1404 393

Answer:

4a. ∠V≅∠Y

4b. TU ≅ WX

5. No; no applicable postulate

6. see below

Step-by-step explanation:

a. When you use the ASA postulate, you are claiming you have shown two angles and the side between them to be congruent. Here, you're given side TV and angle T are congruent to their counterparts, sides WY and angle W. The angle at the other end of segment TV is angle V. Its counterpart is the other end of segment WY from angle W. In order to use ASA, we must show ...

∠V≅∠Y

__

b. When you use the SAS postulate, you are claiming you have shown two sides and the angle between them are congruent. The angle T is between sides TV and TU. The angle congruent to that, ∠W, is between sides WY and WX. Then the missing congruence that must be shown is ...

TU ≅ WX

__

The marked congruences are for two sides and a non-included angle. There is no SSA postulate for proving congruence. (In fact, there are two different possible triangles that have the given dimensions. This can be seen in the fact that the given angle is opposite the shortest of the given sides.)

"No, we cannot prove they are congruent because none of the five postulates or theorems can be used."

__

The first statement/reason is always the list of "given" statements.

1. ∠A≅∠D, AC≅DC . . . . given

2. . . . . vertical angles are congruent

3. . . . . ASA postulate

4. . . . . CPCTC

8 0

3 years ago

What is the mathematical relationship between the atomic radius (r) and the lattice parameter (a0) in the BCC structure? a. b. c

ryzh [129]

Answer: Lattice parameter, a = (4R)/(√3)

Step-by-step explanation:

The typical arrangement of atoms in a unit cell of BCC is shown in the first attachment.

The second attachment shows how to obtain the value of the diagonal of the base of the unit cell.

If the diagonal of the base of the unit cell = x

(a^2) + (a^2) = (x^2)

x = a(√2)

Then, diagonal across the unit cell (a cube) makes a right angled triangle with one side of the unit cell & the diagonal on the base of the unit cell.

Let the diagonal across the cube be y

Pythagoras theorem,

(a^2) + ((a(√2))^2) = (y^2)

(a^2) + 2(a^2) = (y^2) = 3(a^2)

y = a√3

But the diagonal through the cube = 4R (evident from the image in the first attachment)

y = 4R = a√3

a = (4R)/(√3)

QED!!!

8 0

3 years ago

Read 2 more answers

3 pizzas for $ 16.50 what is the unit rate for one pizza

o-na [289]

The answer is 5.50$ you have to divide 16.50/ 3

8 0

3 years ago

Read 2 more answers

What is the slope of the following 12x - y = 30<br> -12

antiseptic1488 [7]

Answer:

12

Step-by-step explanation:

Rearrange into the form y = mx + c, where m is the slope.

12x - y = 30

y = 12x - 30

m = 12

4 0

4 years ago

If X = then what is XY? (Please see images)