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Answer:

The construct a line through P that is  perpendicular to the line.

Step-by-step explanation:

Given that,

Construct a line through P that is  perpendicular to the line.

We need to construct a perpendicular line P

Using given data

We draw an arc across the line on each side of the point P.

Now, from each arc on the line, draw another arc on the opposite side of the line from the point P.

The  point P to the point where the arcs intersect Q.

Hence, The construct a line through P that is  perpendicular to the line.

The equation of the perpendicular line through point 'P' is [tex](y-y_1)=-\dfrac{1}{m'}(x-x_1)[/tex] and this can be determined by using the point-slope form of the line.

The following steps can be used in order to construct a line through P that is perpendicular to the line:

Step 1 - The equation of a line that passes through point 'P' is given below:

[tex](x-x_1)=m(y-y_1)[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] is the point 'P' on the line.

Step 2 - So, the slope of the perpendicular line through point 'P' is:

[tex]mm' = -1[/tex]

[tex]m'=-\dfrac{1}{m}[/tex]

Step 3 - So, the equation of the perpendicular line through point 'P' is:

[tex](y-y_1)=-\dfrac{1}{m'}(x-x_1)[/tex]

For more information, refer to the link given below:

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Answer:

Step-by-step explanation:

2/3 x -1/4 + 9/6)

-2/12 + 9/6

-1/6 + 8/6 = 7/6 = 1 1/6

Answer:

lt is rational number .

Answer:

480

Step-by-step explanation:

Take 96 and divide it by 2 to get what ten percent would be: 48

Then just multiply 48 by ten for 100% (The number): 480.

To check, take a calculator and do 480-20% and it equals 96.

Answer: 2 meters.

Step-by-step explanation:

Let w = width of the cement path.

Dimensions of pool : Length = 15 meters , width = 9 meters

Area of pool = length x width = 15 x 9 = 135 square meters

Along width cement path, the length of region = [tex]2w+15[/tex]

width = [tex]2w+9[/tex]

Area of road with pool =  [tex](2w+15) (2w+9)[/tex]

[tex]= 4w^2+30w+18w+135\\\\=4w^2+48w+135[/tex]

Area of road = (Area of road with pool ) -(area of pool)

[tex]\Rightarrow\ 112 =4w^2+48w+135- 135\\\\\Rightarrow\ 112= 4w^2+48w\\\\\Rightarrow\ 4 w^2+48w-112=0\\\\\Rightarrow\ w^2+12w-28=0\ \ \ [\text{Divide both sides by 4}]\\\\\Rightarrow\ w^2+14w-2w-28=0\\\\\Rightarrow\ w(w+14)-2(w+14)=0\\\\\Rightarrow\ (w+14)(w-2)=0\\\\\Rightarrow\ w=-14\ or \ w=2[/tex]

width cannot be negative, so w=2 meters

Hence, the width of the road = 2 meters.

Answer:

The perimeter of the shape below is 44.48cm

Step-by-step explanation:

To calculate the perimeter of this figure we have to add

7cm + 12cm + 7cm + ( perimeter of semicircle)

To calculate the perimeter of the semicircle we have to use the following equation

d = 12cm

r = d/2 = 12cm/2 = 6cm

c = perimeter of semicircle

r = radius = 6cm

π = 3.14

c = π * r

we replace with the known values

c = * 3.14 * 6cm

c = 18.84cm

The perimeter of the semicircle is 18.84cm

Now that we have this value we can calculate the perimeter of the figure

7cm + 12cm + 7cm + ( 18.84cm ) = 44.48cm

The perimeter of the figure is 56.84 cm

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: A semicircle on top of the rectangle with dimensions 12, 7 cm respectively .

Thus perimeter of the figure = perimeter of semi circle+ perimeter of rectangle

∴ 3.14×6+2(12+7)=56.84 cm

Hence, The perimeter of the figure is 56.84 cm

Learn more about area here:

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Answer: C. 4 1/4 > 2 3/4

Step-by-step explanation: Option C is correct because when comparing mixed numbers, we first compare the whole numbers. In this case, 4 is greater than 2. Then, if the whole numbers are the same, we compare the fractions. In this case, 1/4 is greater than 3/4. Therefore, 4 1/4 is greater than 2 3/4.

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Answer:

7/10

Step-by-step explanation:

1/10 + 3/5

1/10 + 6/10

7/10

Answer:

A-3:1

Step-by-step explanation:

Simplify 6:2 by dividing by 2

Answer: Tenemos que usar 750L de la salsa con 25% de azúcar, y 250% con la salsa de 45% de azúcar.

Step-by-step explanation:

Lo que tiene la planta es:

Una salsa con 25% de azúcar

Una salsa con 45% de azúcar.

Vamos a definir dos cantidades, A y B.

A es la cantidad de salsa con 25% de azúcar usada, y B es la cantidad de salsa con 45% de azúcar usada.

Como queremos producir 1000 litros de salsa, tenemos la ecuación:

A + B = 1000 L

Ahora, queremos que el producto final tenga 30% de azúcar.

El porcentaje de azúcar se define como:

(Cantidad de azúcar/Cantidad total de salsa)*100%.

Ahora, si la cantidad A tiene 25% de azúcar, entonces la cantidad total de azúcar es:

0.25*A

Y la cantidad B tiene 45% de azúcar, entonces acá la cantidad es:

0.45*B

Entonces cuando los mezclamos, la cantidad total de azúcar es:

(0.25*A + 0.45*B)

Y usando la formula de arriba, tenemos que:

100%*(0.25*A + 0.45*B)/(A + B) = 30%

Ahora divido ambos lados por 100%.

(0.25*A + 0.45*B)/(A + B) = 0.30

Entonces tenemos un sistema de dos ecuaciones:

A + B = 1000 L

(0.25*A + 0.45*B)/(A + B) = 0.30

El primer paso es aislar una de las variables en una de las ecuaciones, en este caso voy a aislar A en la primer ecuación:

A = 1000L - B

Ahora puedo reemplazar esto en la segunda ecuación:

(0.25(1000L - B) + 0.45*B)/(1000L - B + B) = 0.30

Y ahora lo resolvemos para B.

(250 L - 0.25*B + 0.45*B)/1000L = 0.30

250L + 0.20*B = 0.35*1000L = 300L

0.20*B = 300L - 250L = 50L

B = 50L/0.2 = 250L

Entonces:

A = 1000L - 250L = 750L.

Tenemos que usar 750L de la salsa con 25% de azúcar, y 250% con la salsa de 45% de azúcar.

Answer:

75

Step-by-step explanation:

Your target number of calories is 2,400 per day inorder to lose some amount of weight.

Instead 3,200 calories is consumed

Therefore the percentage of target that is consumed can be calculated as follows

= 2,400/3,200 × 100

= 0.75 × 100

= 75

Hence the percentage of calories that is consumed is 75

Please find attachment for full question Answer:

1. Stays same

2. Decrease

3. Stays same

4. Decrease

Explanation:

Please find attachment

Step-by-step explanation:

hope This helps for you

Answer:

Step-by-step explanation:

Common factors are the number's , variables found in each of the terms

1) 21x²y = 3 * 7 * x * x * y

  35xy² = 5 * 7 * x    *  y * y

Common factor = 7 * x * y

                          = 7xy

Answer :(iii) 7xy

2)a² - b² = (a + b)(a - b)

1 - x² = (1 - x) (1 +x)

(ii)

3) x³ - x = x(x² - 1)

            = x(x + 1)(x - 1)

Answer: (iv)

4) 225 =  15 * 15 = 15²

x³ - 225x = x(x² - 225)

                = x(x² - 15²)            {a² - b² =(a + b)(a - b)}

                = x(x + 15)(x - 15)

Answer: (ii)

5) 12a²b = 3 * 4 * a * a * b

   15ab² = 3 * 5 * a *     b * b

Common factor = 3 * a * b = 3ab

12a²b + 15ab² = 3*4*a²*b +  3*5*a*b²

                      = 3ab (4a + 5b)

Answer:(ii)

3x - y = 5

2x + y = 10  | ×2

x - 2y = -5

4x + 2y = 20

x - 2y = -5

add

4x + x + 2y - 2y = 20 - 5

5x = 15

x = 15 : 5

x = 3

replace x

4(3) + 2y = 20

12 + 2y = 20

2y = 8

y = 8 : 2

y = 4

3x - y =

= 3(3) - 4

= 9 - 4

= 5

Answer:Yes

Step-by-step explanation:

Kind of like the Declaration of Independence if you’re in the US people gathered to create the declaration of our freedom from British control, way back in 1776

Step-by-step explanation:

g(x) = 3x² + 2x - 1

g(-1) = 3(-1)² + 2(-1) - 1

= 3(1) -2 -1

= 3 - 3

= 0

Answer:

A. True

Step-by-step explanation:

congruent- in agreement or harmony

both triangles are the same

Answer: B. 473.176

Step-by-step explanation: 3.78541 Liters are in one gallon, so if you multiply 3.78541 Liters by 125 gallons then you will end up with 473.176 liters. If you have to add tax then it would be A. 475.250

Answer:

5n/2 - b =a

Step-by-step explanation:

5n/2 = (a + b)

subtract b from both sides

5n/2 - b = a

Answer:

The answer would be South x

Step-by-step explanation:

Answer:

50 cent

Step-by-step explanation:

Answer:

.50¢

Step-by-step explanation:

50 cents = 1 pound

$1.00 = 2 pound

$1.50 = 3 pounds

$2.00 = 4 pounds

basically adding 50 cents equals to $2

Answer:

t= -0.18

Step-by-step explanation:

Isolate t to get the unknown number:

(-4.5t)(49.5t) = 40

      Multiply (-4.5t)(49.5t):

                     (-4.5t)(49.5t) = -222.75t

      Now, write full equation:

          -222.75t = 40

      Isolate t by dividing -222.75 on both sides:

           [tex]\frac{-222.75}{-222.75}t=\frac{40}{-222.75}[/tex]

      Cancel out left hand side:

            [tex]t=\frac{40}{-222.75}[/tex]

      Simplify your answer:

              [tex]t=-0.17957351[/tex]

      Approximate to 2 decimals:

           [tex]t=-0.18[/tex]

Answer:

x=-4,-3,-2or-1

Step-by-step explanation :0

Answer:

Step-by-step explanation:

y - 4 = -(x - 2)

y - 4 =-x + 2

y = -x + 6

Answer:

8× (8 times)

Explanation:

For this question, divide.

72 ÷ 9 = 8.

Your answer will be 8.

Answer:

8 times as many

Step-by-step explanation:

8x9=72

Answer:

f(-3) = 10

Step-by-step explanation:

Simply plug in x as -3 to find f(-3):

f(-3) = -6(-3) - 8

f(-3) = 18 - 8

f(-3) = 10