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What is the area of the rectangle?

Colt1911 [192]

Answer:

$A=50\ units^2$

Step-by-step explanation:

we know that

The area of rectangle is equal to

$A=LW$

The coordinates of vertices are

$A(-5,5),B(-1,7),C(4,-3),D(0,-5)$

using a graphing tool

Plot the coordinates of rectangle to better understand the problem

see the attached figure

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have that

$L=AD,W=AB$

<em>Find out the distance AD</em>

we have

$A(-5,5),D(0,-5)$

substitute in the formula

$L=\sqrt{(-5-5)^{2}+(0+5)^{2}}$

$L=\sqrt{(-10)^{2}+(5)^{2}}$

$L=\sqrt{125}\ units$

<em>Find out the distance AB</em>

we have

$A(-5,5),B(-1,7)$

substitute in the formula

$W=\sqrt{(7-5)^{2}+(-1+5)^{2}}$

$W=\sqrt{(2)^{2}+(4)^{2}}$

$W=\sqrt{20}\ units$

The area of rectangle is equal to

$A=(\sqrt{125})(\sqrt{20})$

$A=50\ units^2$

6 0

3 years ago

Eduardo has purchased a home with an assessed value of $179,000. The property tax rate in his area is 2.3%. What is his monthly

ad-work [718]

Answer:

C. 343.08

Step-by-step explanation:

Convert the tax rate into a decimal and multiply by the house price:

.023(179,000) = 4,117

Divide by 12 (to get monthly rate):

4,117/12 ≈ 343.08

Option C should be the correct answer.

7 0

3 years ago

5.3.21<br>Solve the equation P= r+t+s for r<br>(Simplify your answer.)

Sever21 [200]

Answer:

r = P -t -s

Step-by-step explanation:

This is a one-step linear equation in r. Subtract the terms that don't contain r:

P = r + t + s . . . . . . . . . . given

The terms on the right that don't include r are (t+s). We want to subtract that to get r by itself.

P -(t+s) = r +(t+s) -(t+s) . . . subtract (t+s)

P -t -s = r . . . . . . . . . . . . . . simplify

r = P - t - s

8 0

4 years ago

Let x = a bi and y = c di and z = f gi which statements are true? check all of the boxes that apply. x y = y x (x × y) × z = x ×

Alex73 [517]

A complex number is a part of a number system that includes a real unit and an imaginary unit. All the statements are true except C and E.

<h3>What is a Complex Number?</h3>

A complex number is a part of a number system that includes the real numbers as well as a particular element labelled i, sometimes known as the imaginary unit, and which obeys the equation i² = 1.

As it is given that x=(a+bi), y=(c+di), and z=(f+gi), therefore, we need to plug in the values to check which all are true.

A.) x+y=y+x

$x+y=y+x\\a+bi+c+di=c+di+a+bi$

As the two sides of the equation are equal, the equation is true.

B.) (x × y) × z = x × (y × z)

$(x \times y) \times z = x \times (y \times z)\\\\\ [ (a+bi) \times (c+di) ]\times (f+gi) = (a+bi) \times [(c+di) \times (f+gi)]\\\\(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)$

$(ac+adi+bci-bd) \times (f+gi)= (a+bi) \times (cf+cgi+fdi-dg)\\\\\\acf+adfi+bcfi-bdf+acgi-adg-bcg-bdgi = acf+acgi+afdi-adg + bcfi-bcg-bfd-bdgi$

As the two sides of the equation are equal, the equation is true.

C.) x−y=y−x

$x-y=y-x\\\\(a+bi)-(c+di)=(c+di)-(a+bi)\\\\a+bi-c-di=c+di-a-bi$

As the two sides of the equation are not equal, the equation is not true.

D.) (x+y)+z=x+(y+z)

$(x+y)+z=x+(y+z)\\\\(a+bi+c+di)+f+gi = a+bi+(c+di+f+gi)\\\\a+bi+c+di+f+gi = a+bi+c+di+f+gi$

As the two sides of the equation are equal, the equation is true.

E.) (x−y)−z=x−(y−z)

$(x-y)-z=x-(y-z)\\\\(a+bi-c-di)-f-gi = a+bi-(c+di-f-gi)\\\\a+bi-c-di-f-gi =a+bi-c-di+f+gi)$

As the two sides of the equation are not equal, the equation is not true.

Hence, all the statements are true except C and E.

Learn more about Complex Number:

brainly.com/question/12464608

6 0

2 years ago

What is 7/22 of a minute into seconds

Shtirlitz [24]

18.6 seconds ...................

8 0

3 years ago

Read 2 more answers