The sum of two consecutive even integers is 26. Find the number

The upper-left coordinates on a rectangle are (-5, 6), and the upper-right coordinates are (-2, 6). The rectangle has a perimete

In-s [12.5K]

Answer:

Step-by-step explanation:

Given the upper-left coordinates on a rectangle as (-5, 6), and the upper-right coordinates as (-2, 6), the distance between the two coordinates will be equal to the length of one side of the rectangle. Using the formula for calculating the distance between two points as shown;

D = √(x2-x1)²+(y2-y1)²

The the upper left coordinates be A (-5, 6) and the upper right coordinates be B(-2, 6).

AB = √(-2-(-5))²+(6-6)²

AB = √(-2+5)²

AB = √3²

AB = 3 units = Breadth of the rectangle

Give the perimeter of the rectangle to be 16 units, we can get the length of the rectangle using the formula;

Perimeter of a rectangle = 2(L+B)

16 = 2(3+L)

16 = 6+2L

10 = 2L

L = 5units

The length of the triangle is 5units

Find the diagram of the rectangle on the coordinate plane in the attachment below.

7 0

4 years ago

find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.

Aleks04 [339]

Answer:

$(0, 8\sqrt{3})$ and $(0, -8\sqrt{3})$ are both 14 units from points (-2, 0) and (2, 0).

Step-by-step explanation:

distance formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

We want the distance, d, from points (-2, 0) and (2, 0) to be 14.

Point (-2, 0):

$14 = \sqrt{(x - (-2))^2 + (y - 0)^2}$

$\sqrt{(x + 2)^2 + y^2} = 14$

Point (2, 0):

$14 = \sqrt{(x - 2)^2 + (y - 0)^2}$

$\sqrt{(x - 2)^2 + y^2} = 14$

We have a system of equations:

$\sqrt{(x + 2)^2 + y^2} = 14$

$\sqrt{(x - 2)^2 + y^2} = 14$

Since the right sides of both equations are equal, we set the left sides equal.

$\sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2}$

Square both sides:

$(x + 2)^2 + y^2 = (x - 2)^2 + y^2$

Square the binomials and combine like terms.

$x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2$

$4x = -4x$

$8x = 0$

$x = 0$

Now we substitute x = 0 in the first equation of the system of equations:

$\sqrt{(x + 2)^2 + y^2} = 14$

$\sqrt{(0 + 2)^2 + y^2} = 14$

$\sqrt{4 + y^2} = 14$

Square both sides.

$y^2 + 4 = 196$

$y^2 = 192$

$y = \pm \sqrt{192}$

$y = \pm \sqrt{64 \times 3}$

$y = \pm 8\sqrt{3}$

The points are:

$(0, 8\sqrt{3})$ and $(0, -8\sqrt{3})$

6 0

3 years ago

There are 4 roads leading from Bluffton to Hardeeville, 6 roads leading from Hardeeville to Savannah, and 5 roads leading from

Dmitrij [34]

Answer:

120 ways.

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to Hardeeville = 4

Total number of roads leading from Hardeeville to Savannah = 6

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to Macon.

Total number of ways to get from Bluffton to Macon = $4\times 6\times 5= 120$

Therefore, there are 120 required number of ways to get from Bluffton to Macon.

7 0

3 years ago

Write 720,080 in expanded form with exponents

disa [49]

Why are you having us do your homework

7 0

3 years ago

Read 2 more answers

Cecilia is making cookies for her friends. The recipe, which makes 48 cookies, calls for 4 cups of flour and 1 1/3 cups of sugar

Vsevolod [243]

Answer:

2. Cecilia uses 3 cups of flour for 36 cookies

4. Cecilia is making 3/4 of the original recipe

Step-by-step explanation:

Recipe for 48 cookies

Flour = 4 cups

Sugar = 1 1/3 cups

Recipe for 36 cookies

48 cookies : 36 cookies

= 4 : 3

Flour used in 36 cookies = x cups

Flour used in 48 cookies = 4 cups

4 cups : x cups

4 : 3 = 4 : x

4/3 = 4/x

4*x = 3*4

4x = 12

x = 12/4

x = 3 cups

Sugar = 1 1/3 cups

Sugar used in 36 cookies = y cups

Sugar used in 48 cookies = 1 1/3 cups

4 : 3 = 1 1/3 : y

4/3 = 4/3 ÷ y

4/3 = 4/3 × 1/y

4/3 = 4/3y

4*3y = 3*3

12y = 9

y = 9/12

= 3/4

y = 3/4

The true statement are:

2. Cecilia uses 3 cups of flour for 36 cookies

4. Cecilia is making 3/4 of the original recipe

8 0

3 years ago