fractorise the following (a-b)²+(a-b)​

Answer: The correct option is 5.7/20 = x/200

Step-by-step explanation: Please refer to the diagram attached for more details.

From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;

Mean = Summation of observed data / Number of observations

Mean  = (3 + 5 + 7 + 5 + 6 + 8)/6

Mean = 34/6

Mean = 5.6667

Mean ≈ 5.7

Also the mean number of all fish is derived as follows;

Mean = Summation of observed data / Number of observations

Mean = (20 + 20 + 20 + 20 + 20 + 20)/6

Mean = 120/6

Mean = 20

Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.

Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;

StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.

OR better expressed as;

5.7/20 = x/200

Answer:

5.7/20 = x/200

Step-by-step explanation:

Answer:

The equation above represents the total time the play director spent preparing for a play.

Step-by-step explanation:

The time spent by the play director for preparing for a play is, 190 hours.

Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.

Let the varying amounts of time be denoted by, x.

The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.

The equation provided is:

[tex]35x+\frac{3}{4}=190[/tex]

The equation above represents the total time the play director spent preparing for a play.

Answer:

A

Step-by-step explanation:

vol of a cylinder = pie* r^2×h

r= 5

h= 9

......vol= 9×5^2 pie= 225pie units ^3

Answer:

[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]

Step-by-step explanation:

Given that there are 2 points

[tex]A(-8,8)[/tex] and

[tex]B(1,-10)[/tex]

So, the coordinates are:

[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]

Equation of a line is given as:

[tex]y =mx+c[/tex]

where 'm' is the slope of the line, formula for 'm' is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex](x,y)[/tex] are the points that satisfy the equation of the line.

[tex]c[/tex] is the [tex]y -[/tex] intercept.

Calculating the value of m using the given coordinates:

[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]

So, the equation of line becomes:

[tex]y =-2x+c[/tex]

Now, putting the coordinates of point [tex]A(-8,8)[/tex]

[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]

Please refer to the graph of given equation of line.

The equation of line is:

[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]

Answer:

g=number of girls in the class b=number of boy in the class

g+b=28

g=11+b

Answer:

21u-16v+18w

Step-by-step explanation:

(7u-4v+4w) 14u-12v+14w

21u-16v+18w

Answer:

= 21u−16v+18w

Step-by-step explanation:

Let's simplify step-by-step.

7u−4v+4w−2(−7u+6v−7w)

Distribute:

=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)

=7u+−4v+4w+14u+−12v+14w

Combine Like Terms:

=7u+−4v+4w+14u+−12v+14w

=(7u+14u)+(−4v+−12v)+(4w+14w)

=21u+−16v+18w

Answer:

=21u−16v+18w

Answer: No solution

Step-by-step explanation:

This system of equation has no solution because...

-3x+4y=12

1/4x-1/3y=1

[tex]-3x+4y-4y=12-4y[/tex]

[tex]-3x=12-4y[/tex]

[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]

[tex]x=-\frac{12-4y}{3}[/tex]

substitute

[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]

[tex]-1=1[/tex]

-1=1 is false so therefore this system has no solution

Answer:

The answers are options A and E

x² + 4x-9 = 5x + 3

Group like terms

x² + 4x - 5x - 9 - 3 = 0

x² - x - 12 = 0

Using factorization method

(x + 3)( x - 4) = 0

x = - 3 x = 4

Hope this helps

Answer:

  [tex]S_8=\dfrac{1640}{27}=60\frac{20}{27}[/tex]

Step-by-step explanation:

The formula for the sum of a geometric series with first term a1, common ratio r, and n terms is ...

  [tex]S_n=a_1\dfrac{1-r^n}{1-r}[/tex]

This series has 8 terms, a common ratio of -1/3, and a first term of 81. Its sum is ...

  [tex]S_8=81\dfrac{1-(-\frac{1}{3})^8}{1-(-\frac{1}{3})}=81\dfrac{6560/6561}{4/3}=\dfrac{6560(3^4)(3)}{(4)(3^8)}\\\\\boxed{S_8=\dfrac{1640}{27}=60\frac{20}{27}}[/tex]

Answer:

4m X 6m

Step-by-step explanation:

This is because if there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.

Because the 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.

Becuase 4m is the width, there is 10 - 4 = 6m along each rectangle's length.

The 4m is the width, there is 10 - 4 = 6m along each rectangle's length. the area he will use is 4m x 6m.

The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.

Given information; A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch we need to find which he cannot use.

He divides his usable space into four congruent rectangular patches.

If there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.

The 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.

The 4m is the width, there is 10 - 4 = 6m along each rectangle's length.

Learn more about congruent triangles here:

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Answer:

x=(π+√π)/1-π

or x=(π-√π)/1-π

Step-by-step explanation:

since it is a square all sides are equal

Area of square=x*x=x^2

Area of a circle=πr^2

A=π(x-1)^2

two areas are equal

x^2=π(x^2-2x_1)

x^2=πx^2-2πx-π  

x^2-πx^2-2πx-π=0

x^2(1-π)-2πx-π=0  

using quadratic formula with a=1-π , b=-2π and c=-π

equation of the form ax^2+bx+c=0 by using the quadratic formula:

x=(−b±√b2−4ac)/2a

x=(π+√π)/1-π

or x=(π-√π)/1-π

Answer:

[tex] \sqrt{ {2}^{5} } [/tex]

Step-by-step explanation:

[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]

Answer:

11 1/2

Step-by-step explanation:

Convert improper fraction to mixed number

23 over 2

= 11 and 1/2

23 ÷ 2 = 11 remainder 1

Answer:

11whole,1 and a half

Step-by-step explanation:

divide 23 by 2

Answer:

a I believe sorry if I'm wrong

Answer:

I think its B: $56.26

Answer:

[tex]\frac{1}{9}[/tex]

Step-by-step explanation:

Data provided in the question

There is a total group of 45 students

Art + biology = 5

8 study biology but not Art

Neither subject studied = 9

Based on the above information, the probability of student that studies

art and biology is

Since there is a group of 45 students out of which 5 study both art and biology

So, the ratio is

4: 5

Now divide both sides by 5

So, now the ratio is

9:1

Therefore it means the probability is [tex]\frac{1}{9}[/tex]

Answer:

1800 (packages )muffins

Step-by-step explanation:

360  muffins         x muffins

--------                 =    --------

12 min                       60 min

Answer:

1800 maybe

Step-by-step explanation:

in 12 minutes can wrap 360

in 1 hr have 60 minutes

60/12=5

than 360*5 = 1800

Answer:

y=2 is the correct ans.

here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.

we have, equn of st line parallel to y xaus is y= b

so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).

Answer:

Step-by-step explanation:

To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as

Volume = 1/3 × base area × height

Since the base is rectangular, base area = length × width = 3 × 5 = 15 m

Given that height = 3.6m, therefore, the amount of ice needed for this sculpture is

1/3 × 15 × 3.6 = 18 m³

Answer: To calculate the amount of ice needed for this sculpture, we would apply the formula for determining the volume of a rectangular base pyramid which is expressed as Volume = 1/3 × base area × heightSince the base is rectangular, base area = length × width = 3 × 5 = 15 mGiven that height = 3.6m, therefore, the amount of ice needed for this sculpture is 1/3 × 15 × 3.6 = 18 m³

Step-by-step explanation:

Answer:  No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

Answer:

The correct answer is C

Step-by-step explanation:

As you can see Town A is on top of Town B this means that Town B has symetric points to town A. This also shows how Town A is Positively skewed.

Answer:

B. [tex]y = 3x^2 -6x -3[/tex]

Step-by-step explanation:

Well, we can use the following formula to find the x coordianate of the vertex  -b / 2a.

So let’s start with a)

-6 / 6

-1

A. is wrong because its vertex starts with -1.

b)

6 / 6

1

now that we have our x coordinate we can plug it into the equation to get our y.

3 - 6 - 3

So the y coordinate is -6.

Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]

look at the image below.

hello,

the first term is 250 so this is the initial invested amount

[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

Answer:

B

Step-by-step explanation:

The measure of the tangent- chord angle XYZ is half the measure of its intercepted arc, thus

arc YZ = 2 × 84° = 168° → B

Answer:

n=65th term

Step-by-step explanation:

AP:3,15,27,39......

From the AP

a=3

a+d=15

a+2d=27

3+d=15 (1)

3+2d=27 (2)

Subtract (1) from (2)

We have,

2d-d=27-15

d=12

54th term=a+(n-1)d

=3+(54-1)12

=3+(53)12

=3+636

=639

The term is 132 more than the 54th term

132+54th term

=132+639

=771

Find the term

771=a+(n-1)d

771=3+(n-1)12

771-3=12n-12

768=12n-12

768+12=12n

780=12n

n=780/12

=65

n=12

The term which is 132 more than the 54th term is the 65th term

Answer:

£14.29

Step-by-step explanation:

0.98x=14

x=14.29

Answer:

14.28

Step-by-step explanation:

Answer: Find a common denominator on the right side of the equation

Step-by-step explanation:

You can see that they found the common denominator of 4 therefore that is the correct answer

Answer:

Step-by-step explanation:

5x+y-7=0 isolate y

y=-5x+7 (m=-5,b=7)

9x+7y-14=0

7y=14-9x ( divide both sides by 7)

y=-9x/7 +14/7

y=-9/7 + 2  (m=-9/7, b=2)

x+y=1000

4x+3y=3600 ( multiply the first equation by 3 to eliminate y)

3x+3y=3000

4x+3y=3600 ( subtract the two equations)

3x+3y-(4x+3y)=3000-3600

3x+3y-4x-3y=-600

-x=-600

x=600 ( substitute x in the equation)

x+y=1000

600+y=1000

y=1000-600=400

check : x+y=1000 , (600+400)=1000

check : 4x+3y=3600 = (4(600)+3(400))=2400+1200=3600

how many tickets are sold :

adults x=600/4=150

kids (y)=400/3=133 tickets+1 dollars left

unless( x represent kids then x=200, y represent adult = 100)

Answer:

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

Step-by-step explanation:

Question 1:

[tex]5x+y-7=0[/tex]

Write in slope intercept form.

[tex]y=-5x+7 \\m=-5,b=7\\9x+7y-14=0[/tex]

Write in slope intercept form.

[tex]7y=14-9x\\y=-9x/7 +14/7\\y=-9/7 + 2\\m=-9/7, b=2[/tex]

Question 2:

[tex]x+y=1000\\4x+3y=3600[/tex]

[tex]3x+3y=3000\\4x+3y=3600\\3x+3y-(4x+3y) = 3000-3600\\3x+3y-4x-3y=-600\\-x=-600\\x=600[/tex]

[tex]x+y=1000\\600+y=1000\\y=1000-600=400[/tex]

Tickets sold:

Adults:

[tex]x=600[/tex]

Kids:

[tex]y=400[/tex]

Answer:

0.03 feet

Step-by-step explanation:

d = 0.03r² + r

When d = 0: 0.03r² + r = 0

r(0.03r + 1) = 0

∴ r = 0

When r = 0: d = 0.03 feet

Answer:

-3

Step-by-step explanation:

x-6=3x

2x=-6

x=-3

The required number is -3 decreased by 6 equals 3 times.

A number to be determine when decreased by 6 equals 3 times the number.

it explores the numbers of operations according to the statements.

Let the number be x,
Now,
x-6=3x
x= -3

Thus, the required number is -3 decreased by 6 equals 3 times.

Learn more about arithmetic here:

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solution,

X=5

[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]

hope this helps...

Good luck on your assignment..

Answer:

When x=5

Y=(5+9)÷(5-3)

= 14 ÷2

= 7