Brainliest asap & 44 points

1.which of the following number are rational? choose any that apply
a.-4
b. 3/10
c. 4.
d.
e. none - all numbers listed are irrational.

2. is 81 a perfect square? why/why not? *
- give me an short answer.

3. determine the length from the wall to the base of the ladder. *
the triangle picture is for this one
a. 5
b.11
c. 18
d. 25

4. estimate the value of √52. explain how you use perfect squares to come up with your answer. no explanation will not receive credit! *
- short answer

5. every rational number is a square root. true or false
a. true, because the square root of a perfect square is a whole number. rational numbers are just whole numbers.
b. true, because if you get a whole number or a decimal, all rational numbers can be both.
c. false - every square root is not rational because some aren't perfect squares, meaning the result is a decimal that keeps going forever.
d. false, because all square roots give you decimal answers, and decimals are irrational.

6. how does the blue rectangle map onto the red rectangle? *
this picture is the one with the red and blue rectangles on the coordinates sheet.
a. (x-6, y+5)
b. (x-5, y-6)
c. (x+5, y-6)
d. (x+6, y-5)

7. which figure accurately represents the pythagorean theorem? explain your answer in detail!
this picture is gray and pythagorean theorem shape.
- short answer

ANSWER TO QUESTION 1

A rational number is any number that can be written in the form,, where and are integers and .

We can rewrite .

Therefore option A is a rational number.

Option B is obviously a rational number because it is already in the form .

Option C cannot be written in the form because the decimal place does not repeat or recur and it does not terminate also.

Therefore is not a rational number.

As for option D, the decimal places recurs or repeats and it does not terminate. We can rewrite in the form,.

hence it is a rational number.

ANSWER TO QUESTION 2

Yes is a perfect square.

All numbers whose square roots are perfect squares are rational numbers.

If we raise we get  .

In order words if we take the square root of we get a rational number.

That is

ANSWER TO QUESTION 3

Let the length from the wall to the base of the ladder be m.

The from Pythagoras Theorem,

This implies that,

We add the additive inverse of to both sides to obtain,

We take the positive square root of both sides to obtain,

.

The correct answer is A.

ANSWER TO QUESTION 4

We wan to estimate .

The highest perfect square that can be found in is .

We rewrite to obtain,

.

We now split the square root sign to obtain,

.

.

.

.

ANSWER TO QUESTION 5.

The statement, every rational number is q square root is false.

We only need at least a counterexample to show that, the above statement is false.

Let   be any real number.

Then , where and are integers.

This implies that

Base on this final equation, can only be an integer if is a perfect number. Hence not every rational number is a square root because some numbers aren't perfect squares.

The correct answer is C

ANSWER TO QUESTION 6.

To find the translation vector that maps the blue rectangle on the red rectangle, we draw a vector connecting any two corresponding points as shown in the diagram.

The vector has horizontal component of and a vertical component of .

Therefore the mapping is . The correct answer is D.

ANSWER TO QUESTION 7

Figure A accurately represents the Pythagorean Theorem because  

This implies that

We can see that the hypotenuse square is equal to the sum of the squares of the lengths of the  two shorter legs.

Recall that, are Pythagorean triples.

you would need to also lose 1 point for each of the other outcomes for it to be fair.

step-by-step explanation: