How to find the perimeter and the area of a rectangle on a coordinate plane using the distance formula? : A(3,8) B(5,4) C(-4,-1) D(-6,3) Round to the nearest tenth if necessary.

Answers

Answer 1

Answer: I used some site to plot the points.

First, let's recall the formulas for Perimeter and Area of a Rectangle.
Perimeter = 2(l+w)
Area = l×w
Also, the distance formula is
D = $\sqrt{( x_(2)-x_(1))^2+{(y_(2)-y_(1))^2}$

Now, we need to determine l and w.
So, the length is the distance of AD or BC
and the width is the distance of DC or AB
(I'll just use the sides that I've labelled for ease)

So first to determine the length, we need to calculate the distance of AD
Points are A(3,8) and D(-6,3)
$x_(1) =3, x_(2) =8, y_(1) =6, y_(2) =-3$
$D_(AD)= \sqrt{( 6-3)^2+{(-3-8)^2}$
$D_(AD)= √((3)^2+(-11)^2)$
$D_(AD)= √(9+121)$
$D_(AD)= √(130) ≈ 11.40$
So the length of the rectangle is 11.40 units.

Now, the width!
So first to determine the width, we need to calculate the distance of DC
Points are D(-6,3) and C(-4,-1)
$x_(1) =6, x_(2) =-4, y_(1) =-3, y_(2) =-1$
$D_(DC)= \sqrt{(-4-6)^2+{(-1- -3)^2}$
$<span>D_(DC)= \sqrt{(-4-6)^2+{(-1+3)^2}$
$D_(DC)= √((-10)^2+(2)^2)$
$D_(AD)= √(100+4)$
$D_(AD)= √(104) ≈ 10.20$
So the width of the rectangle is ≈10.20 units.

Let's now solve for Perimeter and Area using
l = 11.40
w = 10.20

Perimeter = 2(l+w)
Perimter = 2(11.40+10.20)
Perimter = 2(21.60)
Perimter = 43.2 units

Area = l×w
Area = (11.40)(10.20)
Area = 116.28
Area = 116.3 units² (rounding)

In conclusion, given points A(3,8) B(5,4) C(-4,-1) D(-6,3), the Perimeter is 43.2 units and the Area is ≈116.3 units² using the distance formula.

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What is is 15% of 32.50 and how did u get your answer

Answers

15%=15/100=0.15
'of' means multiply
15% of 32.50=
0.15 times 32.50=4.875

or you can take 32.5 divide it by 100 and multiply it by 15. either way it is 4.875

What’s the slope? And can you please explain I don’t get it

Answers

As we can see, the line crosses the x-axis at (-2, 0). If we climb three units up from -2 and then go one unit to the right, we arrive at the next point on the line.

Since we climbed three points and went to the right one point, our slope = 3/1. But, we can reduce that.

Slope = 3/1 = 3

Answer:

The slope is 3.

Step-by-step explanation:

The way to find the slope is to find how many blocks/number it went up and to the side. The number of blocks it went up on the y-axis, in this case, is 3 and it went along the x-axis once. In order to actually find the slope, you need to put the y over the x. So, 3/1 is equal to three, so the slope of this line is 3

3 - 24 divided by 8 + 4 square

Answers

(3-24) / (8+4)^2
it's written like this right?

(-12) / (12)^2
do the work in the parenthesis first

(-12) / (144)
then square 12

(-1) / 12
simplify by dividing the numerator and the denominator by 12

The length of a rectangle is 5 5 centimeters less than six times six times its width. Its area is 14 14 square centimeters. Find the dimensions of the rectangle.

Answers

Answer:

Dimensions of rectangle are length = 7 cm and width = 2 cm

Step-by-step explanation:

Let l = length and w = width of the rectangle.

Given that, length is 5 cm less than 6 times width. Rewriting it in equation form,

L = 6 w - 5 cm

Also given that area of rectangle is 14 cm²

Now using formula for area of rectangle,

Area of rectangle = length × width

Area of rectangle = l × w

Substituting the values,

14 = (6 w - 5) × w

Simplifying by using distributive rule,

14 = 6 w² - 5 w

To find the value of b, use the quadratic formula. So rewriting the equation in quadratic form ax²+bx+c=0

Subtracting 14 on both sides,

0 = 6 w² - 5 w - 14

Rewriting,

6 w² - 5 w - 14 = 0

Now applying quadratic formula,

$x=(-b\pm √(b^2-4ac))/(2a)$

Rewriting the formula in terms of w,

$w=(-b\pm √(b^2-4ac))/(2a)$

From the 6 w² - 5 w - 14 = 0, value of a = 6 , b = - 5 and c = - 14.

Substituting the values,

$w=(-\left(-5\right)\pm √(\left(-5\right)^2-4\cdot \:6\left(-14\right)))/(2\cdot \:6)$

Simplifying,

$w=(-\left(-5\right)\pm √(25+336))/(12)$

$w=(-\left(-5\right)\pm √(361))/(12)$

Since √361 = 19,

$w=(-\left(-5\right)\pm 19)/(12)$

There will be two values of w,

$w=(-\left(-5\right)+19)/(12)$ and $w=(-\left(-5\right)-19)/(12)$

Simplifying,

$w=(5+19)/(12)$ and $w=(5-19)/(12)$

$w=(24)/(12)$ and $w=(-14)/(12)$

Reducing the fraction in lowest form, divide first expression by 12 and second expression by 2.

$w=2$ and $w=(-7)/(6)$

Since the length of width cannot be negative, so value of w = 2 cm

To find the value of length, Use equation L = 6 w - 5 cm

L = 6 (2) - 5 cm

L = 12 - 5 cm

L = 7 cm

Therefore l = 7 cm and w = 2 cm are the dimensions of the rectangle.

In a pair of similar polygons, corresponding angles are congruent.A.) cannot be determined
B.) sometimes
C.) always
D.) never

Answers

The correct answer would be option C. Similar polygons
Similar polygons are polygons wherein the corresponding angles are congruent and the corresponding sides are proportional with each other. Thus, having a pair of similar polygons would mean that its corresponding angles would always be congruent.

The correct answer would be C. Always

Paul filled pint containers with 440 cups of water. How many pint containers did Paul need?

Answers

220 because one pint equals 2 cups

what size do you know it can be 5 gal. or 1 gal.

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