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3 years ago

What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ?

2 answers:

7 0

I am finding the answer right now but there is a website that you can use for math that really helps. It's called Desmos.

lukranit [14]3 years ago

5 0

These have two sides with constant y values, i.e. two sides parallel to the x axis. We'll check they're the same length

AB=6 - -12 = 18

CD = -2 - -20 = 18 good

That's the base. The height is 2 - -3 = 5 so an area of 18(5)=90

Answer: 90

Even if we didn't know it was a nicely oriented parallelogram we can get the area with the shoelace formula, which says it's half the absolute value of the sum of the cross products of each side.

A(−12, 2) , B(6, 2) , C(−2, −3) , D(−20, −3)

B(6, 2) , C(−2, −3) , D(−20, −3) , A(−12, 2)

A = (1/2) | (-12)(2) - 2(6) + 6(-3) - 2(-2) + (-2)(-3) - (-3)(-20) + (-20)(2) - (-3)(-12) | = |-180|/2 = 90

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Kobotan [32]

Answer:

The dimension of the box is 18.66 in by 2.66 in by 1.17 in.

Step-by-step explanation:

Given that, The cardboard is 21 in. long and 5 in. wide.

Assume,x be the length of the each sides of the square .

Then the length of the box is = (21-2x) in.

The breadth of the box is =(5-2x) in.

The height of the box is = length of side of the square

= x in.

The volume of the box = length × wide × height

=(21-2x)(5-2x)x

=(105-52x+4x²)x

=( $105 x-52x^2+4x^3$ )

Let

V= $105 x-52x^2+4x^3$

Differentiating with respect to x

$V'=105-104x+12x^2$

Again differentiating with respect to x

$V''=-104+24x$

To find the dimension of the box, we set V'=0

$105-104x+12x^2=0$

Applying the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , here a=12, b= -104 and c =105

$\Rightarrow x=\frac{-(-104)\pm\sqrt{(-104)^2-4.12.105}}{2.12}$

$=\frac{104\pm 76}{24}$

=7.5, 1.17

For x= 7.5 , the wide of the box will be negative.

∴x=1.17 in.

$V''_{x=1.17}=-104+(24\times 1.17)$

Since at x= 1.17, V''<0 , therefore at x=1.17 in. the volume of the given box will be maximum.

The length of the box is = [21-(1.17×2)]=18.66 in.

The wide of the box is = [5-(1.17×2)]=2.66 in.

The height of the box is = 1.17 in.

The dimension of the box is 18.66 in by 2.66 in by 1.17 in.

5 0

4 years ago

Find the value of each variable. Write the<br> equation and solve showing ALL the work.

Anit [1.1K]

The angles must add up to 360 degrees, so we can set the sum of the interior angles equal to 360 and solve for x.

106 + 94 + 135 + x + (x + 5) = 360

Combine like terms:

340 + 2x = 360

2x = 20

x = 10

6 0

3 years ago

An isosceles triangle with equal sides of length 5 and base of length 6 is inscribed in a circle. Find the radius of this circle

Julli [10]

Answer:

So the answer is 30 of a length

Step-by-step explanation:

equal sides of the length 5 and length 6

6 0

3 years ago

Solve for x using logs- <br><br> 2*7^x=17*3^x

horsena [70]

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8 0

3 years ago

Whats 30% out of 720,000

Anarel [89]

Percent means parts out of 100
30%=30/100=3/10
3/10 out of 720000 means 3/10 times 720,000=2160000/10=216,000
the answer is 216,000

6 0

3 years ago