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2 years ago

9

How many axes of symmetry has a rhombus

1 answer:

Kitty [74]2 years ago

3 0

Rhombus has 2 axes of symetry (they contain diagonals).

If rhombus is a square then has 4 axes of symetry.

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Which is the best interpretation of the solution set for the compound inequality? 3(2x + 1) > 21 or 4x + 3 4 D. all real numb

loris [4]

D

I just had the same test

5 0

3 years ago

The sum of the squares of two numbers is 8 . The product of the two numbers is 4 . Find the numbers.

fenix001 [56]

Hello there.

First, assume the numbers $x,~y$ such that they satisties both affirmations:

The sum of the squares of two numbers is $8$ .
The product of the two numbers is $4$ .

With these informations, we can set the following equations:

$\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}$

Multiply both sides of the second equation by a factor of $2$ :

$2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}$

Make $(1)-(2)^{\ast}$

$x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0$

We can rewrite the expression on the left hand side using the binomial expansion in reverse: $(a-b)^2=a^2-2ab+b^2$ , such that:

$(x-y)^2=0$

The square of a number is equal to $0$ if and only if such number is equal to $0$ , thus:

$x-y=0\\\\\\ x=y~~~~~~(3)$

Substituting that information from $(3)$ in $(2)$ , we get:

$x\cdot x = 4\\\\\\ x^2=4$

Calculate the square root on both sides of the equation:

$\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2$

Once again with the information in $(3)$ , we have that:

$y=\pm~2$

The set of solutions of that satisfies both affirmations is:

$S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}$

This is the set we were looking for.

7 0

2 years ago

Determine whether the triangles are similar. if so, write a similarity statement and name the postulate ot theorem you used. if

Gekata [30.6K]

Answer: Explained.

Step-by-step explanation: The explanations are as follows :

(7) Since GF is parallel to JK and FK and GJ are tranversals, so we have

∠GFK = ∠JKH,

∠FGK = ∠KJH (pairs of alternate interior angles) and

∠GKF = ∠JHK (vertically opposite angles).

Therefore, both the triangles are similar by AAA similarity rule.

(8) Here,

$\dfrac{AN}{MP}=1,~\dfrac{AD}{PR}=\dfrac{4}{5}.$

Since the ratio of the corresponding sides are not proportional, so the triangles are not similar.

(9) Here,

$\dfrac{PS}{RS}=\dfrac{SQ}{ST}=\dfrac{PR}{QT}=\dfrac{2}{3}.$

So, the triangles are similar by proportionality rule.

(10) Here,

$\dfrac{RQ}{JK}=\dfrac{11}{16},~\dfrac{PR}{KL}=\dfrac{30}{45}=\dfrac{2}{3},~\dfrac{PQ}{JL}=\dfrac{2}{3}.$

Since all the ratios are not equal, so the triangles are not similar.

(11) Here , no angle of one triangle matches with the angle of the other triangle, so the given triangles are not similar.

(12) Here,

$\dfrac{GH}{AC}=\dfrac{GK}{AB}=\dfrac{KH}{BC}=\dfrac{1}{2}.$

So, the triangles are similar by the proportionality rule.

Hence explained.

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2 years ago

There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced

leonid [27]

Answer:

The question is an incomplete question

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Jada went to the mall yesterday with $30.

stealth61 [152]

Im pretty sure she should have $13 left.

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2 years ago