Complete the equations

The denominator of the simplified expression will be (9n² + 4).

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given below.

[(2 / 6n + 4)] [(3n + 2) / (3n – 2)]

On multiplication, we have

(6n + 4) / (18n² + 8)

(3n + 2) / (9n² + 4)

The denominator of the simplified expression will be (9n² + 4).

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Answer:

[tex](x^{2} +2)-3\\x^{2} +2-3\\x^{2} -1\\(x+1)(x-1)[/tex]

Answer:

x^2+4x+1

Step-by-step explanation:

(x+2)^2-3

(x+2)(x+2)-3

x^2+2x+2x+4-3

x^2+4x+4-3

x^2+4x+1

Answer:

14.3 km  (1 d.p.)

Step-by-step explanation:

To find the mean, divide the sum of all data values by the total number of data values.

If Mark ran a mean distance of 13.2 km in five days, we can use the mean distance for each of the 5 days in our calculation.

[tex]\begin{aligned}\implies \sf mean\:distance & = \sf \dfrac{13.2+13.2+13.2+13.2+13.2+20}{6}\\ & \sf =\dfrac{86}{6}\\\\ & = \sf 14.3\:km\:\:(1\:d.p.)\end{aligned}[/tex]

Answer:

A=30

B=35

C=44

Step-by-step explanation:

It has been proved that the 5 star vertices have their sum of angles as A + B + C + D + E = 180°

The adjoining star contains a regular pentagon. Thus;

Sum of interior angles of the pentagon = (5 - 2) * 180 = 540°

Thus;

Each interior angle of the pentagon = 540/5 = 108°

Thus, each exterior angle = 180 - 108 = 72°

Then measure of the angle at the vertex = 180 - 72 - 72 = 36°

Thus, each angle at the vertices of the star have an angle of 36°.

There are 5 star vertices and so;

Sum of angles of 5 star vertices = 5 * 36 = 180°

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Answer:

Length = 30

Width = 17

Step-by-step explanation:

Let L = length of rectangle and W = Width

The first sentence gives the equation

W = L/2 + 2 ==>

2W = L +4 ==>

L = 2W - 4 ....  (1)

The perimeter of the rectangle is 2(L+W) = 2L +2W

Second sentence gives us the equation

4L = 2L + 2W + 26 ===>
2L = 2W + 26 ......   (2)

(2) - (1) ==> L = 30   (2W cancels out)

From (1), W = 30/2 + 2 = 15 + 2 = 17

Check:
Using these values and substituting in equation 2 gives us
2 * 30 = 2* 17 + 26
60 = 34 + 26
which matches

Answer:

f(1) = 2

f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

the point of coordinates (1 , 2) is on the graph

Then

f(1) = 2

…………………………

We notice that :

f(2) = 4

f(3) = 8

f(4) = 16

16/8 = 8/4 = 4/2 = 2/1 = 2

________________________

This means the common ratio

of the geo sequence = 2

Hence ,

f(n) = 2 × f(n - 1)

Answer: f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

The graphed that represents the new function with the same slope and y-intercept is: graph Y.

Slope = rise/run along a line.

Y-intercept is the y-value of the point on the y-axis that the line intercepts.

Slope of the function given = rise/run = 2/1 = 2

2 multiplied by 1/2 = 2/2 = 1.

Y-intercept of the given function is: 1

1 increased by 3 units is: 1 + 3 = 4

The slope of graph Y = rise/run = 2/2/ = 1

The y-intercept is also 4

Therefore, the answer is: Graph Y

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Answer:

D. 41

Step-by-step explanation:

To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:

The only solution for 22x=901 is 41

Answer: x=41

Step-by-step explanation:

Hii!

Do you need to know the solution set of 22x=902? No problem! (:

We just need to divide both sides by 22 to solve for "x".

x=41; this equation has one solution only

--

Hope that this helped! Best wishes.

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Answer: 4 blue chips (brochure), 6 yellow chips (news article), and 10 red chips (computer presentation).

Step-by-step explanation: If you have 20 colored chips, then 20% of the people that chose the brochure will be 20% of 20 of the chips. That is 20 * 0.2 = 4. Now, to find how to model the people who chose the news article, it will be 30% of the 20 chips. That is 20 * 0.3 = 6. Thus, 6 chips can be modeled for the news articles. Lastly, we add 6 + 4 and that is 10. The rest is another ten out of the 20. Thus, we can use 10 red chips to model the computer presentation.

The teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

A division is a process of splitting a specific amount into equal parts.

To model this situation using colored chips, we can use the following approach:

Divide the total number of chips (20) into five equal parts, each representing 20% of the total number of students.

For the making a brochure option, use four blue chips to represent the 20% of students who choose this option.

For the writing a news article option, use six yellow chips to represent the 30% of students who choose this option.

For the designing a computer presentation option, use ten red chips to represent the remaining 50% of students who choose this option.

So, the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

Hence,  the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

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Answer:

The team won 144 gold medals

Step-by-step explanation:

A fraction tells us how many parts of a whole we have

144 / 360 translated into words is 144 out of 360

144 is the part and the 360 is the whole (total)

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Answer:

y = 4x - 17

Step-by-step explanation:

y - 3 = 4(x - 5) ← distribute parenthesis by 4

y - 3 = 4x - 20 ( add 3 to both sides )

y = 4x - 17

Step-by-step explanation:

As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:

letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).

▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.

▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.

▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.

Answer:

y=160

Step-by-step explanation:

y=90+14(x)

x=5

y=90+14(5)

y=90+70

y=160

Hope this helps!

If not, I am sorry.

Answer:

409

Step-by-step explanation:

296 = 200 + 90 + 6
The value of the 9 is 90 in 296.
1/10 of 90 is 9. The only number that has a 9 in the units digit is 409.

See attached images for work.

Answer:

I'm not sure what the question is.    I'll offer one simplification that might help.

Step-by-step explanation:

[tex]\sqrt{3} - 3(4*\sqrt{8})[/tex]

One can convert the [tex]\sqrt{8}[/tex] to [tex]\sqrt{2} *\sqrt{4}[/tex] and then that becomes [tex]\sqrt{2} *\2}[/tex]2 or 2[tex]\sqrt{2}[/tex]

[tex]\sqrt{3} - 3(4*\sqrt{2}\sqrt{4})\\[/tex]

[tex]\sqrt{3} - 3(4*2*\sqrt{2})\\[/tex]  See above explanation.

[tex]\sqrt{3} - 24*\sqrt{2})\\[/tex]

[tex]\tan(90^{\circ}-A)\\ \\ =\frac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}\\ \\ =\frac{\cos A}{\sin A}\\\\=\boxed{\frac{1}{\tan A}}[/tex]

Answer: [tex]\sqrt[4]{64}[/tex]

Step-by-step explanation:

[tex]64^{\frac{1}{4} }= \sqrt[4]{64}[/tex]

Step-by-step explanation:

please mark me as brainlest

1. The value of x is 40

m ∠2x + 10 = 90

m ∠3x = 120

m ∠2x +5 = 85

m ∠2x -15 = 65

2. The value of x is 15

m ∠5x = 75

From the question, we are to determine the value of x and the given angles

Since sum of angles is 360°

3x + 2x + 10 + 2x + 5 + 2x -15 = 360°

Collect like terms

3x + 2x + 2x + 2x  = 360° - 10° - 5° + 15°

9x = 360

x = 360 / 9

x = 40

∴ x = 40

Then,

m ∠2x + 10 = 2(40) + 10

m ∠2x + 10 = 80 + 10

m ∠2x + 10 = 90

m ∠3x = 3(40)

m ∠3x = 120

m ∠2x +5 = 2(40) + 5

m ∠2x +5 = 80 + 5

m ∠2x +5 = 85

m ∠2x -15 = 2(40) - 15

m ∠2x -15 = 80 - 15

m ∠2x -15 = 65

Hence, the measure of angle 2x-15 is 65

2.

Since sum of angles is 180°

Then,

5x° + x° + 90° = 180°

6x° = 180° - 90°

6x° = 90°

x = 90/6

x = 15

m ∠5x = 5(15)

m ∠5x = 75

Hence, the measure of angle 5x is 75

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Answer:

b

Step-by-step explanation:

eq y=x+4 is for x>=2 inclusive

Answer:

x+5 (under assumption you meant to do -3x

Step-by-step explanation:

you can use long division.

Take the leading coefficient x^4 and divide it by x^3. This results in x which is going to be the first part of you quotient. Now take that x and multiply it by the divisor (x^3 - 3). This gives you x(x^3 - 3) = x^4 - 3x. Now subtract that x^4 - 3x from the original polynomial and repeat this until you can't divide anymore

[tex]x^4+5x^3-3x-15 - (x^4-3x) = 5x^3-15\\x^3/5x^3=5\\5(x^3-3) = 5x^3-15\\5x^3-15-(5x^3-15) = 0\\\\x+5[/tex]

Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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which of the following sets are discrete?

Answer: C. {2,4,6,8}

Step-by-step explanation:

because constituting a separate entity : individually distinct several discrete sections. 2a : consisting of distinct or unconnected elements : noncontinuous. b : taking on or having a finite or countably infinite number of values discrete probabilities a discrete random variable.

The value obtained by doing the operation are ,a=0.11,b=11,c=(111/250)d=44,e=(1/8),f=(83/500),h=0.375,i=37.5%,j=(111/125),k=0.888,i=(777/1000),m=77%,n=0.2,o=20%,p=(777/1000),q=66.6%.

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The procedure of changing the basis of a number is known as number conversion. A binary number is made up of only two numbers: 1 and 0. A decimal number is made up of ten digits ranging from 0 to 9.

The values obtained from the table the decimal and the percentage form are solved as;

[tex]\frac{1}{9} \\\\ 0.3111 \\\\\ 0.1111 \times 100 \\\\ 11.11 \%[/tex]

The other missing values are;

a=0.11

b=11

c=(111/250)

d=44

e=(1/8)

f=(83/500)

h=0.375

i=37.5%

j=(111/125)

k=0.888

i=(777/1000)

m=77%

n=0.2

o=20%

p=(777/1000)

q=66.6%

Hence all the missing values are given above.

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The choice trigonometric ratio is tangent and the distance is 3. 98 meters.

The given angle is 86

The opposite side is given as 57 meters

The distance is in the adjacent

Thus, trigonometric ratio to use is the tangent

Tangent = opposite/ adjacent

We have,

tan 86 = 57/x

14. 300 = 57/x

x = 57/ 14. 300

x = 3.i 98 meters

Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.

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