Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?

Answer:

(- 3, 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , thus

(5, 3 ) → (- 3, 5 )

Answer:

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Step-by-step explanation:

Let suppose that A and B have one-dimensional coordinates. GIven that [tex]A = 8[/tex] and [tex]AB = 3[/tex], there are two possible locations for B:

[tex]B_{1} = A+AB[/tex]

[tex]B_{1} =8+3[/tex]

[tex]B_{1} = 11[/tex]

[tex]B_{2} = A-AB[/tex]

[tex]B_{2} = 8-3[/tex]

[tex]B_{2} = 5[/tex]

The midpoint equations for each case are, respectively:

[tex]m_{1} = \frac{A+B_{1}}{2}[/tex]

[tex]m_{1}=\frac{8+11}{2}[/tex]

[tex]m_{1} = \frac{19}{2}[/tex]

[tex]m_{2} = \frac{A+B_{2}}{2}[/tex]

[tex]m_{2} = \frac{5+8}{2}[/tex]

[tex]m_{2} = \frac{13}{2}[/tex]

The possible midpoints of AB are [tex]\frac{19}{2}[/tex] and [tex]\frac{13}{2}[/tex].

Answer:

a) 820

b)450

c)  -540

d) -294

e) 1440

f) 1425

Step-by-step explanation:

a) it is an arithmetic progression with ratio=4

   a1=3,

     a2=3+r=3+4=7.....

    a20=a1+19r

so a20=3+19*4=3+76=79

S=(a1+an)*n/2 where n=20

so S=(3+79)*20/2=820

b) a15=a1+14*r=2+14*4=2+56=58

S=(a1+a15)*15/2=(2+58)*15/2=60*15/2=30*15=450

It is the same formula for all  the exercises

S=(a1+an)*n/2 ,     where n is the number of terms

c) a40=30+39*(-3)=30-87=-57

So S=(30-57)*40/2=-540

d) a14=5+13*(-4)=5-52=-47

S=(5-47)*14/2=-42*14/2=-42*7=-294

e) it is 5+7+9+......+75

nr of  terms  = (an-a1) :r+1=(75-5):2+1=36

S=(5+75)*36/2=36*40=1440

f) ratio=7-4=3

the  same formula for n= (91-4):3+1=87:3+1=29+1=30

S=(4+91)*30/2=95*30/2=2850/2=1425

Answer:

Step-by-step explanation:

[tex]8 + 9x + 4(11 - 2x) \\ = 8 + 9x + 44 - 8x \\ = 8 + 44 + 9x - 8x \\ = 52 + x[/tex]

Answer:

0.06 cubic meters per year...

Step-by-step explanation:

The rate of water flows through a pipe is 0.06 cubic meters per year.

It is the volume of fluid flows out from the container per unit time.

Given that,

Water flows through a pipe at a rate of 6 fluid ounces per day. It can be written as:

Water flows per day ⇔ 6 fluid ounces

∴ Water flows per year ⇔  365 x (6 fluid ounces)

Volume of water in milliliter,

Water flows per year ⇔  365 x (6 x 29.574 ml )

Volume of water in cubic meter,

Water flows per year ⇔  365 x ([tex]\frac{6 x 29.574}{1000000}[/tex] [tex]m^{3}[/tex]) = 0.06477   [tex]m^{3}[/tex]

Hence Water flows per year round value to the nearest hundredth is 0.06  [tex]m^{3}[/tex].

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Answer:

a number squared plus twice a number minus one equals zero

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

82-12+10

82+10-12

92-12

80

The number of people in the restaurant will be 80

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 82 people in a restaurant. Four groups of 3 leave and then five groups of 2 enter.

The expression will be solved as below:-

E = 82-12+10

E = 82+10-12

E = 92-12

E = 80

Therefore, the number of people in the restaurant will be 80

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Answer:

length (x) = 15 or -11

Step-by-step explanation:

step-by-step in attached picture

Answer:

430 cm² is right answer ✔️

Step-by-step explanation:

A=2(wl+hl+hw)

=2(5×15+7×15+7×5)

=430cm²

hope it helped you:)

Answer:

$605

Step-by-step explanation:

The correct question is

Taho Earns His Regular Pay Of $11 Per Hour For Up To 40 Hours Of Work Per Week. For each hour over 40 hours of work per week. Taho earns 1½ times his regular pay. How much does Taho earn in a week in which he works 50 hours?

a. $550

b. $605

c. $625

d. $750

e. $825

For the first $40 that Taho works, he earns $11 x 40 = $440

For the extra $10 (since he worked 50 hrs that week)

1½ of $11 per hr = 1.5 x $11 = $16.5

for the 10 days extra = $16.5 x 10 = $165

total pay = $440 + $165 = $605

Answer:

Step-by-step explanation:

Hope it helps you..

Thanks..

Answer:

1/6

Step-by-step explanation:

The reciprocal of a fraction can be found by flipping the numerator (top number) and denominator (bottom number).

The number 6 is equivalent to the fraction 6/1.

Find the reciprocal of 6/1. Invert the numerator and denominator.

6/1 ⇒ 1/6

The reciprocal of 6 is 1/6

Answer:

Step-by-step explanation:

((b+2)(b+12)/(b+2)(b+3))*(b+3)

= (b+12)

Answer:

513.95

Step-by-step explanation:

First you have to divide 7776 by 343. Then you raise the answer to the second power

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{2}}}}[/tex]

Step-by-step explanation:

[tex] \sf{4x + 8 = 16}[/tex]

Move 8 to right hand side and change its sign

⇒[tex] \sf{4x = 16 - 8}[/tex]

Subtract 8 from 16

⇒[tex] \sf{4x = 8}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{8}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

3n + 2

Step-by-step explanation:

[tex]−n+(−4)−(−4n)+6[/tex]

Open the parentheses

[tex] - n - 4 + 4n + 6 \\ [/tex]

Add similar elements

[tex] - n + 4n - 4 + 6 \\ 3n + 2 \\ [/tex]

Answer:

[tex] - n + 6[/tex]

Step-by-step explanation:

[tex] - n + ( - 4) - ( - 4n) + 6 = - n - 4n + 4n + 6 = - 5n + 4n + 6 = - n + 6[/tex]

Answer:

(0, 6)

Step-by-step explanation:

Point T has a coordinate pair of (3, 4). That is, at point T, x = 3, while y = 4.

3 points to the left of T would be a movement on the x-axis. This movement is a run across the x-axis. At T, x = 3. Therefore, 3 points to the left would be a decrease by 3 = 3 - 3 = 0.

3 points to the left of T would leave us with an x coordinate of 0.

2 points above T suggest a rise, which is on the y-axis.

Therefore, at T, y = 4. 2 points above 4 = 4 + 2 = 6. y coordinate would now be 6.

In conclusion, the ordered pair representing 3 points to the left, and 2 points above point T is (0, 6).

Answer:

see explanation

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

- 27 = [tex]\frac{-27}{1}[/tex] ← in rational form

Thus - 27 is a rational number

Answer:

Line PQ. Not enough Info for the Plano tho.

Step-by-step explanation:

Look at the 2 points, and thats the name of the line.

Answer:

(- 1, 8 )

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(8, - 1 ) → (- 1, 8 )

The image of (8, -1) after a reflection over the line y = x is, (- 1, 8).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

A point (8, - 1) is reflected over the line y = x.

Now, We know that;

The image of point (x, y) after reflection over the line y = x is,

⇒ (x, y) → (y, x)

Thus, The image of (8, -1) after a reflection over the line y = x is,

⇒ (8, - 1) → (- 1, 8)

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The 2 unknown numbers are 4 and 5 .

Let the numbers be x and x + 1.

From the given information,

[tex]\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ [/tex]

[tex]\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ [/tex]

But, as we know -5 is not a natural number,

Hence, x = 4 .

So the 2 unknown numbers are :

★ Solution :

Let the number be x and x + 1.

[tex]\rule{130}1[/tex]

[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]

[tex]:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}[/tex]

⠀

We know that -5 is not a natural number. Hence, x = 4.

[tex]\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.[/tex]

Answer: m=6

Step-by-step explanation:

[tex]9+12m=6+15\left(m-1\right)[/tex]

[tex]6+15\left(m-1\right)=15m-9[/tex]

[tex]9+12m=15m-9[/tex]

subtract 9 on both sides

[tex]9+12m-9=15m-9-9[/tex]

[tex]12m=15m-18[/tex]

subtract 15m on both sides

[tex]12m-15m=15m-18-15m[/tex]

[tex]-3m=-18[/tex]

divide by -3 on both sides

[tex]\frac{-3m}{-3}=\frac{-18}{-3}[/tex]

since [tex]\frac{-a}{-b}=\frac{a}{b}[/tex]

[tex]\frac{-18}{-3}=6[/tex]

[tex]m=6[/tex]

Answer: 40%

Step-by-step explanation:

Answer: 2/5 or 40%

Step-by-step explanation: 15 + 10 = 25 and 10/25 simplifies to 2/5.

Answer:

57

Step-by-step explanation:

all you have to do is take the 10,602 and divide it by 186

and you end up with 57. to check this just do 10,602 divided by 57 or 57 times 186.

Answer:

Step-by-step explanation:

taking A(3, 3), B(6, 6), C(9,3) and D(6,0)

we have:  [tex]y_A=y_C\quad and\quad x_B=x_D[/tex] so the AC and BD are diagonals, that means:

AB = BC = CD = DA = s

[tex]s=\sqrt{(6-3)^2+(6-3)^2}=\sqrt{3^2+3^2}=\sqrt{18}\\\\\\A=s^2=(\sqrt{18})^2=18[/tex]

Answer:

que????? no entiendo??????

Answer:

length= 5 + x

breadth = 6 + 2x

area = 30 + 16x + 2x^2

Answer:

12.34

Step-by-step explanation:

Answer:

(x-10)(5x+2)

Step-by-step explanation:

this is the answer of the question.you can clearly see in the pic of the solution

Answer:A)Gives hints to reader about a future event.

Step-by-step explanation:

Answer:

A) Gives hints to reader about a future event.

Step-by-step explanation:

Foreshadowing is one of the storytelling device that gives hints to readers about the future events.

Hope this helps ;) ❤❤❤