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3 years ago

What is the area of rectangle ABCD in square units ?

Mathematics

2 answers:

zloy xaker [14]3 years ago

7 0

Answer:

34 square units

Explanation:

In any rectangle, each two opposite sides are equal

This means that, in the given rectangle:

AB = CD and AD = BC

Area of the rectangle is the product of its dimensions (length and width)

This means that:

Area of ABCD = AB × BC

1- getting the side length:

To get the side length, we will use the distance formula:

$D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

For AB, we have:

A = (-1,4) which means that x₁ = -1 and y₁ = 4

B = (3,3) which means that x₂ = 3 and y₂ = 3

Substitute in the equation:

$AB = \sqrt{(3-(-1))^2+(3-4)^2} = \sqrt{17}$ units

For BC, we have:

B = (3,3) which means that x₁ = 3 and y₁ = 3

C = (1,-5) which means that x₂ = 1 and y₂ = -5

Substitute in the equation:

$BC = \sqrt{(1-3)^2+(-5-3)^2} = 2\sqrt{17}$ units

2- getting the area:

Area of ABCD = AB × BC

Area of ABCD = $\sqrt{17} * 2\sqrt{17} = 34$ square units

Hope this helps :)

Licemer1 [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Square units = √( 4^2 + 1^2) * √( 8^2 + 2^2)

= √17 * √68

= √1156

= 34

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liubo4ka [24]

The answer is 10:00

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3 years ago

Solve the system 2x+2y+z=-2 -x-2y+2z=-5 2x+4y+z=0

drek231 [11]

The values of (x,y,z) are (3,-1,-2) , if the given are equations $2x+2y+z=- 2$ , $-x-2y+2z=-5$ and $2x+4y+z=0$ .

Step-by-step explanation:

The given is,

$2x+2y+z=- 2$ .......................................(1)

$-x-2y+2z=-5$ ......................................(2)

$2x+4y+z=0$ .........................................(3)

Step:1

Equation (2) is multiplied by -1 ( Eqn(2) × -1 )

$x+2y-2z=5$ .............................(4)

Subtract the equation (1) and (4)

$2x+2y+z=- 2$

$x+2y-2z=5$

( - )

$(2x-x)+(2y-2y)+(z+2z)=(-2-5)$

$x+3z=-7$ ......................(5)

Step:2

Equation (2) is multiplied by -2 ( Eqn(2) × -2)

$2x+4y-4z=10$ ........................(6)

Subtract equation (6) and (3),

$2x+4y-4z=10$

$2x+4y+z=0$

( - )

$(2x-2x)+(4y-4y)+(-4z-z)= (10-0)$

$-5z=10$

$z = - \frac{10}{5}$

z = -2

From the equation (5),

$x+3z=-7$

$x+(3)(-2)=-7$

$x = -7+6$

x = -1

From equation (1),

$2x+2y+z=- 2$

Substitute x and z values,

$(2)(-1)+2y+(-2)=-2$

$2y - 4=2$

$2y=4-2$

$2y=2$

$y=\frac{2}{2}$

y = 1

Step:3

Check for solution,

$-x-2y+2z=-5$

Substitute x,y and z values,

$-(-1)-(2)(1)+(2)(-2)=-5$

$1-2-4=-5$

-5 = -5

Result:

The values of (x,y,z) are (3,-1,-2) , if the given are equations $2x+2y+z=- 2$ , $-x-2y+2z=-5$ and $2x+4y+z=0$ .

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3 years ago

The scale of a map is 1 inch: 250 miles. City A is 378 miles from City B. To the nearest tenth, how far is its distance on the m

juin [17]

This is a proportion question. We can express this as an equation where the answer is x:

$\frac{1}{250}$ = $\frac{x}{378}$

From there, you can just cross-multiply and divide to get:

$\frac{1 * 378}{250}$

A tenth of 250 is 25, so this is roughly $\frac{375}{250}$ or $\frac{17}{10}$ , so it'll be approximately 1.7 inches on the map.

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4 years ago

Read 2 more answers

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Dmitrij [34]

Answer: Null hypothesis : $H_0:\ p=0.22$

Alternative hypothesis : $H_a:\ p$

Step-by-step explanation:

Given claim : The proportion of U.S. adults age 25 or older who smoke : $p=0.22$

A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree. i.e. $p$

Since the null hypothesis is a fact checked by the researcher or the experimenter that always contains a equals to sign.

∴ Null hypothesis : $H_0:\ p=0.22$

Alternative hypothesis : $H_a:\ p$

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3 years ago

Select all polynomials that have (x-3)(x−3)left parenthesis, x, minus, 3, right parenthesis as a factor. Choose all answers that

iVinArrow [24]

Answer:

A, C, D

Step-by-step explanation:

One way to answer this question is to use synthetic division to find the remainder from division of the polynomial by (x-3). If the polynomial is written in Horner form, evaluating the polynomial for x=3 is substantially similar.

A(x) = ((x -2)x -4)x +3

A(3) = ((3 -2)3 -4)3 +3 = -3 +3 = 0 . . . . . has a factor of (x -3)

B(x) = ((x +3)x -2)x -6

B(3) = ((3 +3)3 -2)3 -6 = (16)3 -6 = 42 . . . (x -3) is not a factor

C(x) = (x -2)x^3 -27

C(3) = (3 -2)3^3 -27 = 0 . . . . . . . . . . . . . has a factor of (x -3)

D(x) = (x^3 -20)x -21

D(3) = (3^3 -20)3 -21 = (7)3 -21 = 0 . . . . has a factor of (x -3)

___

The polynomials of choice are A(x), C(x), and D(x).

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3 years ago