I don't understand this factorisation
a2+ 4a+3​

Answer:

[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n + 15

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₆ = 18 and d = [tex]\frac{1}{2}[/tex] , then

a₁ + 5d = 18 , that is

a₁ + [tex]\frac{5}{2}[/tex] = 18 ( subtract [tex]\frac{5}{2}[/tex] from both sides )

a₁ = [tex]\frac{31}{2}[/tex]

Thus

[tex]a_{n}[/tex] = [tex]\frac{31}{2}[/tex] + [tex]\frac{1}{2}[/tex] (n - 1) = [tex]\frac{15}{2}[/tex] + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + 15

Answer:

Choice A

Step-by-step explanation:

First, let's simplify the equation. We get [tex]\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }[/tex] . Then, we can simplify. We now have [tex]\frac{3^{-3}m^{5} }{6n}[/tex] . To get rid of the negative exponent, we multiply the top and bottom by 3^3 to get [tex]\frac{m^{2} }{6nx3^{3} }[/tex]. Note that the x in the denominator stands for multiplication. 3^3 = 27, so we have [tex]\frac{m^{5} }{6n(27)} = \frac{m^{5} }{162n}[/tex]

Answer:

m^5/ 162 n

Step-by-step explanation:

( 3 m^-2 n) ^-3 / (6mn^-2)

We know a^ -b = 1/ a^b

1 / ( 3 m^-2 n) ^3 *(6mn^-2)

Distribute the power of 3

1 / ( 3^3 m^ -2 ^ 3 n^3) * ( 6m n^-2)

We know a^ b^ c = a^ ( b*c)

1 / ( 27 m^( -2 * 3) n^3) * ( 6m n^-2)

1 / ( 27 m^( -6) n^3) * ( 6m n^-2)

We know a^b * a^c = a^ ( b+c)

1 / ( 27*6 m^( -6+1) n^(3-2))

1/ (162 m^ -5 n^1)

We know a^ -b = 1/ a^b

m^5/ 162 n

Answer:

D. ( 2w+6). (w)

i tried my best

hope this is the answer

stay at home stay safe

Answer:

m(m-3)=108

Step-by-step explanation:

Complete question below:

Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

m(m – 3) = 108

m(m + 3) = 108

(m + 3)(m – 3) = 108

(m – 12)(m – 9) = 108

Solution

On the number line,

Let

m= larger integer

The integers are 3 numbers apart on the number line, so

m-3=smaller integer

The product (×) of the larger and smaller integers=108

(m)*(m-3)=108

m(m-3)=108

Therefore, the equation that can be used to solve for m, the larger integer is:

 m(m – 3) = 108 

Answer:

its a

Step-by-step explanation:

XD

Answer:

20

Step-by-step explanation:

use the cos or sin function to solve

Step-by-step explanation:

using 30°

we use cos

using 60

we use Sin

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Two numbers that only have 1 as a common factor are called co-prime numbers.

Example:

Factors of 3 ⇒ 1, 3

Factors of 4 ⇒ 1, 2, 4

These numbers only have 1 as a common factor. So 3 and 4 are co-prime numbers.

Answer:

5/18

Step-by-step explanation:

There are 36 possible outcomes

There are 6 with a 2 as the first roll

There are 4 with a sum of 9

P( sum is 9 or that the first number is a 2)

                        =  sum is 9 or that the first number is a 2/total

                           ( 6+4) / 36

                          =10/36

                           =5/18

Answer:

B and D

Step-by-step explanation:

B: 14x and 14x cancel out, so there would be no x left.

D: 14 x and 14x cancel out, as well as -23 and -23, therefore leading to no solution.

Hope this is helpful! :)

Answer:

The answer is B

Step-by-step explanation:

I got this answer on Khan Academy.

Hope this helps! :)

Answer:

2x-11

Step-by-step explanation:

2 x X = 2x + 11

Answer:

[tex]\boxed{D = 15/8}[/tex]

Step-by-step explanation:

=> [tex]x^2-\frac{1}{2} x +\frac{1}{2} = 0[/tex]

Comparing it with the standard form of quadratic equation [tex]ax^2+bx+c = 0,[/tex] we get

a = 1, b = -1/2 and c = 1/2

Discriminant = [tex]b^2-4ac[/tex]

[tex]D = (-1/2)^3+4(1)(1/2)\\D = -1/8 + 2\\D = \frac{-1+16}{8} \\D = \frac{15}{8}[/tex]

Answer:

1.  20 tins of milk

2.  Weight of the Carton = 8,4kg ot 8400g

Step-by-step explanation:

Given

Volume of a Tin = 77cm³

Weight of a tin = 5000g

Volume of Empty Carton = 1540cm³

Weight of Empty Carton = 5000g

Calculating the number of tins of milk

To do this, we have to make use of the given volumes;

And this is done as follows;

[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]

Substitute  77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton

[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]

[tex]Number = 20[/tex]

Hence, 20 tins of milk will filled the empty carton

Calculating the weight of the Carton after filled with tins of milk

This is calculated as thus;

Total Weight = Weight of Empty Carton + Weight of Tins of Milk

Substitute 5000g for Weight of Empty Carton

Total Weight = 5000g + Weight of Tins of Milk

_________________________________________

Calculating Weight of Tins of Milk

Since 20 tins of milk will fill the empty carton, the

Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk

Weight of Tins of Milk = 20 * 170g

Weight of Tins of Milk = 3400g

_________________________________________

Substitute 3400g for Weight of Tins of Milk

[tex]Total\ Weight = 5000g + 3400g[/tex]

[tex]Total\ Weight = 8400g[/tex]

In Kilograms:

[tex]Total\ Weight = 8.4kg[/tex]

Answer:

Step-by-step explanation:

To find the hypotenuse we use Pythagoras theorem which is given by

a² = b² + c²

where a is the hypotenuse

So we have

a² = 10² + 3²

a² = 100 + 9

a² = 109

Hope this helps you

Answer:

10.4

Step-by-step explanation:

Answer:

Option (A)

Step-by-step explanation:

Every cube has 8 vertices and 6 faces.

Cube shown in the picture attached,

Diagonal through interior of the given cube will be the segments joining the vertices A-H, G-B, C-F and D-E.

Therefore, from the given options diagonal of the interior of the cube will be Side AH.

Option A will be the answer.

Answer:

the awnser is A

Step-by-step explanation:

i took a quiz

Answer:

[tex]\boxed{\sf 30 \ bean \ cans}[/tex]

Step-by-step explanation:

The ratio of bean cans to corn cans is 6 : 7

Given that Corn cans = 35

Let the bean can be x

So,

The proportion for it will be:

6 : 7 = x : 35

Product of Means = Product of Extremes

7 * x = 6 * 35

7x = 210

Dividing both sides by 7

x = 30

So, 30 bean cans have to be put on the table to hold the needed ratio

Answer:

Step-by-step explanation:

[tex]100x^2-20x+1=0\\\\(10x)^2-2\cdot10x\cdot1+1^2=0\\\\(10x-1)^2=0\\\\10x-1=0\\\\10x=1\\\\x=0.1[/tex]

Answer:

[tex]Angle = 54[/tex]

Step-by-step explanation:

Given

Kano = 45;

Kwara  = 410;

Ogun = 105;

Ondo = 126;

Oyo = 154

Total Distribution = 840

Required

Determine the angle subtended by Ondo (in a pie chart)

The general formula to calculate subtended angle in a Pie chart is;

[tex]Angle = 360 * \frac{Frequency}{Total\ Frequency}[/tex]

In this case of Ondo

Frequency = 126

Total Frequency = Total Distribution = 840

Substitute these values in the given formula;

[tex]Angle = 360 * \frac{126}{840}[/tex]

[tex]Angle = \frac{360 *126}{840}[/tex]

[tex]Angle = \frac{45360}{840}[/tex]

[tex]Angle = 54[/tex]

Hence, the angle subtended by Ondo is 54

Answer:

Hey there!

We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)

7x-10=0.5(120)

7x-10=60

7x=70

x=10

Hope this helps :)

Answer:

x = 10

Step-by-step explanation:

Tangent Chord Angle = 1/2 Intercepted Arc

7x-10 = 1/2 ( 120)

7x -10 = 60

Add 10 to each side

7x -10+10 = 60+10

7x = 70

Divide by 7

7x/7 = 70/7

x = 10

Answer:

Chocolate bars: $0.95 each

Sour keys: $0.05 each

Total cost for 8 chocolate bars and 24 sour keys: $8.80

Step-by-step explanation:

sour keys=x

chocolate bars=y

15x+2y=2.65

10x+3y=3.35

multiply the second equation by 1.5

15x+4.5y=5.025

2.5y=2.375

y=0.95

Chocolate bars are $0.95 each.

Now substitute the y value in one of the equations

15x+2(0.95)=2.65

15x+1.9=2.65

15x=0.75

x=0.05

Sour keys are $0.05 each.

For the second part of the question, just multiply the number of chocolate bars by the cost and same thing with the sour keys and add them.

Final answer: $8.80

Answer:

Step-by-step explanation:

i^{11}+i^{16}+i^{21}+i^{26}+i^{31}

[tex]=(i^{2} )^5i+(i^{2} )^8 +(i^{2} )^{10} i+(i^{2} )^{13}+(i^{2} )^{15} i\\=(-1)^5 i+(-1)^8+(-1)^{10} i+(-1)^{13} +(-1)^{15} i\\=- i+1+i-1-i\\=0- i[/tex]

Answer:

Option : Statistic because the value is a numerical measurement describing a characteristic of a sample.

Step-by-step explanation:

A sample of professors is selected and it is found that Modifying 35 % with underline own a television.

The 35% is the value that summarizes the characteristic of the sample taken from the population. Thus, the value 35% is a statistic.

While a parameter gives a value describing the characteristic of the population itself

Given: Sample proportion is (P)=[tex]35%[/tex]%.

Statistics are the constants that are computed from sample observations alone. This is a simple definition of statistics.

Answer: The correct statement is  Statistic because the value is a numerical measurement describing a characteristic of a population.

Explanation: That is, statistic because the value is a numerical measurement describing the characteristic of a sample.

The remaining statements are incorrect.

As parameters are the constants of the population. They describe only the population not the sample.

Learn more: https://brainly.com/question/10211620

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer:

Rs. 924000.

Step-by-step explanation:

Cost of  house = 765000

Additional money spent on it = 115000

Total cost incurred by Ravi = 765000 + 115000 = 880000

Gain  = 5% of total cost

gain in Rs = 5/100 * 880000 = Rs. 44000

Total selling price of house = total cost incurred + profit = 880000+ 44000

Total selling price of house = Rs. 924000

Thus, Ravi got  Rs. 924000.

Answer:

x = 2

Step-by-step explanation:

5x = 10

x = 2

Answer:

x = 2

Step-by-step explanation:

5x-10=0

Add 10 to each side

5x-10+10=0+10

5x = 10

Divide by 5

5x/5 = 10/5

x = 2

Answer:

-2

Step-by-step explanation:

your equation is

f(x) = -2x+8

-2x

-2 is the slope

Answer:

The slope is -2

Step-by-step explanation:

Rewriting f(s) as y

y = -2x+8

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -2x+8

The slope is -2

Answer:

see explanation

Step-by-step explanation:

Any point that lies on the line is a solution to the equation.

Thus

(0, 1 ), (2, 0 ), (- 2, 2), (4, - 1 ) are all solutions

Answer:

[tex]\boxed{(6, -2)}[/tex]

Step-by-step explanation:

Any of the points that lies on the line is the solution to the equation of the line.

(-2, 2), (0, 1), (2, 0), (4, -1), (6, -2) are all solutions.

Answer:

33

Step-by-step explanation:

15019 / 53 = 283 R20

53 − 20 = 33

He needs 33 more trees so that every row can have the same number of trees.

Answer:

           [tex]\bold{a=5\,,\quad b=-4\frac27}[/tex]

Step-by-step explanation:

[tex]5+\frac{2\sqrt3}7+4\sqrt3=5+\frac27\sqrt3+4\sqrt3=5+4\frac27\sqrt3=5-(-4\frac27)\sqrt3[/tex]

Answer:

77

Step-by-step explanation:

slope equation

Answer:

where's the graph??? .......

Answer: 120

Step-by-step explanation:

Given: A bag contains two red marbles, two green ones, one lavender one, five yellows, and six orange marbles.

The total number of marbles in the bag : 2+2+1+5+6=16

Now, the number of ways of selecting sets of four marbles include one of each color other than lavender is

[tex]\( C(2,1) \times C(2,1) \times C(5,1) \times C(6,1)=2 \times 2 \times 5 \times 6\)=120[/tex]  [[tex]\because\ C(n,1)=n[/tex]]

Hence, the number of sets of four marbles include one of each color other than lavender = 120