40 points!! What is the area of the quadrilateral with vertices at (2, -4), (4, -4), (2, 1), and (4, 1)?

Mathematics

1 answer:

stiv31 [10]3 years ago

8 0

Answer:Expand areaofthequadrilateralwithverticesat(2, - 4),(4, - 4),(2,1),and(4,1)

Step 1: Multiply (areaofthequadrilateralwithverticesat) * (2, - 4,)

Step 1.1: Multiply areaofthequadrilateralwithverticesat by each term in 2, - 4,

Step 1.1.1: Multiply areaofthequadrilateralwithverticesat * 2,

Group constants and powers by variable

(1 * 1)(a1 + 1 + 1 + 1 + 1 + 1r1 + 1 + 1 + 1e1 + 1 + 1 + 1 + 1o1f1t1 + 1 + 1 + 1 + 1h1 + 1q1u1d1i1 + 1 + 1l1 + 1w1v1c1s1)

a6r4e5oft5h2qudi3l2wvcs

Step 1.1.2: Multiply areaofthequadrilateralwithverticesat * -4,

Group constants and powers by variable

(1 * 1)(a1 + 1 + 1 + 1 + 1 + 1r1 + 1 + 1 + 1e1 + 1 + 1 + 1 + 1o1f1t1 + 1 + 1 + 1 + 1h1 + 1q1u1d1i1 + 1 + 1l1 + 1w1v1c1s1)

a6r4e5oft5h2qudi3l2wvcs

Step 1 answer = a6r4e5oft5h2qudi3l2wvcs + 1a6r4e5oft5h2qudi3l2wvcs

Group all like terms

2a6r4e5oft5h2qudi3l2wvcs

Step-by-step explanation:

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A company makes concrete paving stones in different sizes. Each stone has a volume of 30 cubic inches and a height of 3 inches.

Zepler [3.9K]

Answer:

There are 5 different sized paving stones that can have a volume of 360 in³.

Step-by-step explanation:

Volume = Area x height.

We are given;

volume; V = 360 in³

Height; h = 3 in

Thus, 360 = A x 3

A = 360/3 = 120 in²

This is the area of the base, so we need to find the number of different stones which have a base area of 120 in².

Let's list all the factors of 120 which are;

1,2,3,4,5,6,10,12,20,24,30,40,60,120

The question says we shouldn't use 1 or 2 in inches as length and width.

Leaving us with the remaining listed factors.

So the pair of factors that give and area of 120 are;

Size;

3 x 40

4 x 30

5 x 24

6 x 20

10 x 12

Thus, there are 5 different sized paving stones that can have a volume of 360.

5 0

3 years ago

Please can you help me?

Gennadij [26K]

Answer:

$\large\boxed{C)\ \dfrac{3}{4}}$

Step-by-step explanation:

$\text{We know:}\ P(A')=1-P(A)\\\\\text{Therefore}\\\\P(A)-3\cdot P(A')=0\iff P(A)-3\cdot(1-P(A))=0\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\P(A)+(-3)(1)+(-3)(-P(A))=0\\\\P(A)-3+3P(A)=0\qquad\text{add 3 from both sides}\\\\P(A)+3P(A)=3\\\\4P(A)=3\qquad\text{divide both sides by 4}\\\\P(A)=\dfrac{3}{4}$