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3 years ago

Which expressions are equivalent to 7x-14?

Mathematics

1 answer:

Sholpan [36]3 years ago

4 0

7x+(-14)
-14+7x
These two equations are both equal to 7x-14.
Hope this helps and please give brainliest!

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BRAINLIEST ASAP & 44 Points

Marta_Voda [28]

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 $-5$ .