Question

BRAINLIEST ASAP & 44 Points

Answer 1

ANSWER TO QUESTION 1

A rational number is any number that can be written in the form,$\frac{a}{b}$, where $a$ and $b$ are integers and $b\ne 0$.

We can rewrite $-4=\frac{-4}{1}$.

Therefore option A is a rational number.

Option B is obviously a rational number because it is already in the form $\frac{a}{b}$.

Option C cannot be written in the form $\frac{a}{b}$ because the decimal place does not repeat or recur and it does not terminate also.

Therefore $4.51010910921...$ 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,$\frac{a}{b}$.

$0.987987987...=\frac{329}{333}$ hence it is a rational number.

ANSWER TO QUESTION 2

Yes $81$ is a perfect square.

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

If we raise $9^{2}$ we get  $81$.

In order words if we take the square root of $81$ we get a rational number.

That is $\sqrt{81} =9$

ANSWER TO QUESTION 3

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

The from Pythagoras Theorem,

$l^2+12^2=13^2$

This implies that,

$l^2+144=169$

We add the additive inverse of $144$ to both sides to obtain,

$l^2=169-144$

$l^2=25$

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

$l=\sqrt{25}$

$l=5$.

The correct answer is A.

ANSWER TO QUESTION 4

We wan to estimate $\sqrt{52}$.

The highest perfect square that can be found in $52$ is $4$.

We rewrite to obtain,

$\sqrt{52} =\sqrt{4\times 13}$.

We now split the square root sign to obtain,

$\sqrt{52} =\sqrt{4}\times \sqrt{13}$.

$\sqrt{52} =2\sqrt{13}$.

$\sqrt{52} =2(3.60)$.

$\sqrt{52} \approx 7.21$.

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  $x$ be any real number.

Then $\sqrt{x} =\frac{a}{b}$, where $a$ and $b$ are integers.

This implies that $a=b\sqrt{x}$

Base on this final equation, $a$ can only be an integer if $x$ 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 $6$ and a vertical component of $-5$.

Therefore the mapping is $(x,y)\rightarrow(x+6,y-5)$. The correct answer is D.

ANSWER TO QUESTION 7

Figure A accurately represents the Pythagorean Theorem because  

$625=576+49$

This implies that

$25^2=24^2+7^2$

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, $7,24,25$ are Pythagorean triples.