Prove that the natural number x is prime if and only if x>1 and there is no positive integer greater than 1 and less than or equal to [tex]\sqrt{x}[/tex] that divides x.

Check the picture below.

Mind you that we have four 30-60-90 triangles.

The area of given rectangle before the piece was removed is 65 cm² approximately.

The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.

In Δ DEF,

∠EDF + ∠DEF + ∠DFE = 180° (angle sum property)

30° + 90° + ∠DFE = 180°

∠DFE = 60°

[tex]cos F = \frac{EF}{FD}(\frac{base}{hypotenuse}\\ \\ cos(60) = \frac{5}{FD}\\ \\FD = 5 * 2= 10[/tex]

[tex]cos D = \frac{ED}{FD}(\frac{base}{hypotenuse}\\ \\ cos(30) = \frac{ED}{10}\\ \\ED = \frac{\sqrt{3} }{2} * 10= 5\sqrt{3}[/tex]

In Δ AED,

∠AED + ∠EAD + ∠EDA = 180° ( angle sum property)

∠AED + 90° + 30°= 180°

∠AED = 60°

[tex]sinE = \frac{AD}{DE} (\frac{perpendicular}{hypotenuse}\\ \\sin(60) = \frac{AD}{5\sqrt{3} } \\\\AD= \frac{\sqrt{3} }{2}*5\sqrt{3} \\\\AD = 7.5[/tex]

In Δ DFC,

∠FDC + ∠DCF + ∠DFC = 180° (angle sum property)

30° + 90° + ∠DFC = 180°

∠DFC = 60°

[tex]sinF = \frac{DC}{DF} \\\\sin(60) = \frac{DC}{10}\\ \\\frac{\sqrt{3} }{2} *10 = DC\\\\DC = 5\sqrt{3}[/tex]

Area of rectangle = length * breadth = xy = AD * DC = [tex]7.5 * 5\sqrt{3} = 64.95[/tex]

Learn more about area of rectangle here

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Answer:

Step-by-step explanation:

→ [tex]\left(6x\:+\:9x\right)^3[/tex]

→ [tex]\left(15x\right)^3[/tex]      [ add the x inside the bracket ]

→ [tex]15^3x^3[/tex]       [ remove the bracket ]

→ [tex]3375x^3[/tex]     [ final answer ]

Answer:

3x(3x² + 2x)

Step-by-step explanation:

6x + 9x³

rearrange tribe

9x³ + 6x

factor by grouping

3(3x³ + 2x)

3x(3x² + 2x)

Step-by-step explanation:

out of the first equation we get

x = 2y - 3z - 1

this we use in the second equation

-3(2y - 3z - 1) + 6y - 9z = 3

-6y + 9z + 3 + 6y - 9z = 3

0 = 0

this is the same equation as the first one, just multiplied by -3.

and we see the third equation is again the same one as the first just multiplied by 2.

so, there are infinite solutions.

this has not a single solution, as in the end this is just one equation with 3 variables.

Step-by-step explanation:

a² + b²

difference of two square

= (a + b)(a - b)

Answer:

see explanation

Step-by-step explanation:

(a + b)(a - b)

each term in the second factor is multiplied by each term in the first factor, that is

a(a - b) + b(a - b) ← distribute parenthesis

= a² - ab + ab - b² ← collect like terms

= a² - b²

Answer:

Ans=B.1

Step-by-step explanation:

hope this helps

Answer:

16.81

Step-by-step explanation:

P = 4a.

then the length of a side is 16.4 /4 = 4.1.

A = a * a = 4.1 * 4.1 = 16.81

Answer:

45.1 cubic inches

Step-by-step explanation:

16.4 divided by 4 is 4.1 and 4.1 multiplied by 4.1 is 45.1.

Yes, adding the matrices would give a meaningful result as it provides a measure of the total number of nutrient and calorie intake throughout the day.

Yes, subtracting the matrix from each other gives a measure of the surplus or deficit of nutrients and calorie intake between any pair of meals.

A matrix can only be added to (or subtracted from) another matrix if the two matrices are of the same dimensions .

Hence, it follows that to add or subtract two matrices, just add or subtract the corresponding entries, and place this sum or difference in the corresponding position in the matrix which results accordingly.

Read more on matrix addition and subtraction;

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Total cards signed:-

[tex]\\ \tt\longmapsto \dfrac{1}{4}+\dfrac{3}{5}[/tex]

[tex]\\ \tt\longmapsto \dfrac{5+12}{20}=\dfrac{17}{20}[/tex]

Cards left:-

[tex]\\ \tt\longmapsto 80-17/20(80)=80-68=12[/tex]

Answer:

42 cm squared

Step-by-step explanation:

base times height, divided in half

Answer:

Step-by-step explanation:

1 pound of potato salad costs 2.96

0.75 pounds of potato salad costs x

1/0.75 = 2.96/x            Cross multiply

x = 0.75 * 2.96

x = 2.22  

0.75 pounds of potato salad costs 2.22 dollars.

Answer:

listed below.

Step-by-step explanation:

So basically its 420x420 which is 176400 which applies to all of these.

SO insert 1600 into Data Set 1.

For Data set II will be 69x69=4761

That is all you need. STAY SAFE!

Answer:

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

Step-by-step explanation:

Answer:

x = 7, y = 2

Explanation:

equations given:

x + 7y = 21

x + 4y = 15

make "x" the subject:

x + 7y = 21

x = 21 - 7y .........equation 1

x + 4y = 15

x = 15 - 4y .......equation 2

Solving both the equations simultaneously:

15 - 4y = 21 - 7y

-4y + 7y = 21 - 15

3y = 6

y = 6 ÷ 3

y = 2

If y is 2

Then x = 21 -7y;

x = 21 - 7(2)

x = 21 - 14

x = 7

x + 7y= 21

7 goes to RHS = X+ y = 21/7-3

x + 4y = 15

4 goes to RHS= x+y = 15/4 = 3.75

Answer:

1 1/2

Step-by-step explanation:                                                                                    15x2/4x-5   =30/-20        =1 1/2                                                                                          First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:                                                                                             Applying the fractions formula for division,                                                                Simplifying 30/-20,                                                                        

Answer:

The answer is C I can't explain it but maybe someone else can, I'm sorry.

Answer:

do u mean factorization​?

if so, In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number. When you split a number into its factors or divisors, that's factorization. For example, factorization of the number 12 might look like 3 times 4.

Step-by-step explanation:

Hope this helps!

Answer:  it   an operation of resolving a quantity into factors; also : a product obtained by factorization

Step-by-step explanation:  hope i help

Answer:

-5

Step-by-step explanation:

Answer:

−5a+6

Step-by-step explanation:

hope this is right

Answer:

1/2  in fraction each kid will get 0.50 in decimal and 50% in percent

Step-by-step explanation:

Answer:

500 times

Step-by-step explanation:

Divide 10,000,000,000 by 20,000,000 to determine how many 20 millions can go into 10 billion.

10,000,000,000 ÷ 20,000,000 = ?

Eliminate 7 zeros:

1,000 ÷ 2 = 500.

20,000,000 can go into 10,000,000 500 times.

Using an inequality, it is found that the maximum number of desks that Bella can assemble is of 4.

We consider that:

Hence:

[tex]35.5 + 45.5x < 240[/tex]

Then, solving the inequality:

[tex]x < \frac{240 - 35.5}{45.5}[/tex]

[tex]x < 4.49[/tex]

Considering the number of desks has to be an integer, maximum number of desks that Bella can assemble is of 4.

More can be learned about inequalities at https://brainly.com/question/25235995

I already answered this as B

You also already asked this question

Answer:

a-24, b-36, c-36

Step-by-step explanation:

a) 4(6)=24

b) 5(6)+6=36

c) (6)^2=36

Answer:

a) c -24

b) a - 36

c) d - 36

Step-by-step explanation:

a) When x = 6, what is the value of 4x?

4x

4(6) = 24

b) When x = 6, what is the value of 5x + x

5x + x

5(6) + 6

30 + 6

36

c) When x = 6, what is the value of x^2?

x^2

6^2

36

Hope this helps!

Exact Answer:   2*sqrt(5)

Approximate Answer:  4.4721

====================================================

Explanation:

Original set = {1,3,4,5,7}

Square each value to get {1,9,16,25,49}. This is the list of squares.

Add up those squares: 1+9+16+25+49 = 100

Next, divide that over n = 5 which is the number of items in the set

100/n = 100/5 = 20

The value 20 is the mean of the list of squares above.

Lastly, apply the square root to get sqrt(20) = sqrt(4*5) = sqrt(4)*sqrt(5) = 2*sqrt(5)

This approximates to roughly 4.4721

--------------------

Side note: The term "root mean square" is often abbreviated to "RMS".

If we reversed the order of the three words, then we get "square mean root". In this reversed order, we see that the squaring operation is done first, then the mean next, and finally the square root is done last.

The value of the root mean square which is having sets of 1, 3, 4, 5, and 7 is 4.472.

It is the square root of the mean square, which is the arithmetic mean of the squares of the group of values.

The formula of root mean square is given as

[tex]\rm X_{RMS} = \sqrt{\dfrac{x_1^2+x_2^2+x_3^2+....+x_n^2}{N}}[/tex]

N be the total number of observations.

The sets 1, 3, 4, 5, and 7.

Then the root mean square will be

[tex]\rm X_{RMS} = \sqrt{\dfrac{1^2+3^2+4^2+5^2+7^2}{5}}\\\\X_{RMS} = \sqrt{\dfrac{1+9+16+25+49}{5}}\\\\X_{RMS} = \sqrt{\dfrac{100}{5}}\\\\X_{RMS} = \sqrt{20}\\\\X_{RMS} = 4.472[/tex]

More about the root mean square link is given below.

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Given :-

To Find :-

Solution :-

Given equation is ,

[tex] 3x + 6y = 24 [/tex]

To find the y intercept set x = 0 , we have ,

[tex] 3(0) +6y = 24 [/tex]

Simplify ,

[tex] 6y = 24[/tex]

Divide both sides by 6 ,

[tex] y = 4 [/tex]

Hence the y intercept is 4 .

[tex]\rule{200}2[/tex]

Now again to find x intercept , set y = 0

[tex] 3x +6(0)= 24[/tex]

Simplify ,

[tex] 3x = 24 [/tex]

Divide both sides by 3 ,

[tex] x = 8 [/tex]

Hence the x intercept is 8 .

Domain:-

Range:-

Yes it's a function as domains have unique range

Answer:

Domain = Planet

Range = number of solar congress reps

Function = YES (many-to-one)

Step-by-step explanation:

Domain : input values ⇒ planet

Range : output value ⇒ number of solar congress reps

Function : A function relates each element of a set with exactly one element of another set (possibly the same set).

One-to-many is not a function.

Many-to-one is a function.

From inspection, we can see that every element in the domain is related to exactly one element in the range.  Both Venus and Neptune are related to 18.  So this is a many-to-one function.

Answer:

19/31

Step-by-step explanation:

since there are 15 squares and 4 circles, both is 19

and since the total pieces 31

so the probability that he will grab a square or circle is 19/31

Answer:

M>22

Step-by-step explanation:

Answer:

[tex]\boxed{\sf{m > 22}}[/tex]

Step-by-step explanation:

To solve this problem, first, you have to isolate it on one side of the equation.

First, divide by -1 from both sides.

[tex]\Longrightarrow: \sf{\dfrac{-m}{-1} < \dfrac{-22}{-1} }[/tex]

Solve.

Divide the numbers from left to right.

⇒ -22/-1=22

[tex]\Longrightarrow: \boxed{\sf{m > 22}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

[tex]\frac{3}{4}n>27[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}n>27[/tex]

[tex]\implies n > 36[/tex]