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veneciaconton347
03.11.2019 •
Mathematics
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
Solved
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Ответ:
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,
.
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![\sqrt{81} =9](/tpl/images/0357/5121/59a29.png)
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![a=b\sqrt{x}](/tpl/images/0357/5121/d8711.png)
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.
Ответ:
Please mark me brainliest. Rly wanna rank up!