What is the solution to the system of linear equations graphed below?

Given:

The vertices of the rectangle ABCD are A(0,1), B(2,4), C(6,0), D(4,-3).

To find:

The area of the rectangle.

Solution:

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the distance formula, we get

[tex]AB=\sqrt{(2-0)^2+(4-1)^2}[/tex]

[tex]AB=\sqrt{(2)^2+(3)^2}[/tex]

[tex]AB=\sqrt{4+9}[/tex]

[tex]AB=\sqrt{13}[/tex]

Similarly,

[tex]BC=\sqrt{(6-2)^2+(0-4)^2}[/tex]

[tex]BC=\sqrt{(4)^2+(-4)^2}[/tex]

[tex]BC=\sqrt{16+16}[/tex]

[tex]BC=\sqrt{32}[/tex]

[tex]BC=4\sqrt{2}[/tex]

Now, the length of the rectangle is [tex]AB=\sqrt{13}[/tex] and the width of the rectangle is [tex]BC=4\sqrt{2}[/tex]. So, the area of the rectangle is:

[tex]A=length \times width[/tex]

[tex]A=\sqrt{13}\times 4\sqrt{2}[/tex]

[tex]A=4\sqrt{26}[/tex]

[tex]A\approx 20[/tex]

Therefore, the area of the rectangle is 20 square units.

Answer: 240.6cm *squared*

Step-by-step explanation:

Surface Area= (2 x Area of 1st face) + (2 x Area of 2nd face) + (2 x Area of 3rd face)

= (2 x 10.5cm x 5.4 cm) + (2 x 10.5 cm x 4.0cm) + (2 x 5.4cm x 4.0cm)

= 113.4cm*squared* + 84.0cm *squared* + 43.2cm *squared*

= 240.6cm *squared*

OR

= 2 x (sum of the 3 faces)

= 2 x (56.7cm * squared* + 42.0cm *squared* + 21.6cm *squared*)

= 2 x 120.3cm *squared*

= 240.6cm *squared*

Answer:

b² =  13.2

Step-by-step explanation:

5.8²+b²=14.4²

33.64+b²=207.36

-33.64       -33.65

b²= √173.71

b² = 13.1799089526

b² =  13.2

Answer:

9

Step-by-step explanation:

No.of words in

- 8 minutes = 72

- 1 minute = 72/8

                = 9

Answer:

9 words per every minute

Step-by-step explanation:

Theres 72 words in 8 minutes, so to get her words to minute, ratio you do 72 divided by 8 to get 9, words per minute.

Answer:

y=x+12

Step-by-step explanation:

m (slope)=1

y-intercept=12

hope this helped have a great day :)

Answer:

near the coastline

Step-by-step explanation:

100%

Near the coastline. About 40% of Americans live on the coast.

Answer:

128

Step-by-step explanation:

If the area of a figure is 32 square centimeters then the length/breadth could be 8cm and 4cm or 16cm and 2cm.

Let’s assume that the the sides of the figure are doubled, if that’s the case then we would arrive at 8*2 * 4*2 or 16*2 * 2*2 in which 16*8 or 32*4 which will both result to 128 as the answer.

Answer:

15.48 yd squared

Step-by-step explanation:

This is because 6 yards can be used as the radius of your circle. square your radius, so 6x6 which is 36 then multiply by 3.14. You then get 113.04. Since it is a semicircle, divide it by 2. You now get 56.52. If you know your radius, you know your diameter which is 12. 12 is also the length of the rectangle so 6x12 is 72 which is the area of the rectangle. Now subtract 56.52 from 72 to get 15.48 which is the shaded region of the rectangle. So I believe that you are doing yards, so 15.48 yd squared. I hope this helps :)

Answer:

i think is c.

Answer:

3÷4 = 0. 75

1 ÷ 2 = 0 . 5

Step-by-step explanation:

3 ÷ 4 = 0 . 75

1 ÷ 2 = 0 . 5

Answer:

49

Step-by-step explanation:

1.21 x 49 = 59.29

Answer:

40

Step-by-step explanation:

100/10*2*4/2

10*2*4/2

20*4/2

20*2

40

If this helps please mark as brainliest

Answer:

40

Step-by-step explanation:

100/10=10

10*2=20

20*4=80

80/2=40

Answer:

30.8936

Step-by-step explanation:

Pressure guage reading is 8% lower than tbe actual pressure.

Therefore, for a tyre with guage pressure, 33.58 ;

The actual pressure of tyre would be :

Guage pressure - 8% of guage pressure

33.58 - (0.08 * 33.58)

33.58 - 2.6864

= 30.8936

Actual pressure = 30.8936

Answer:

A; infinitely many solutions

Step-by-step explanation:

first, let's simplify the first equation to make it simpler.

divide both sides by 5

y=3x-8

new system

y=3x-8

y=3x-8

as you can see, they are the same.

not mandatory but useful!⬇⬇⬇⬇

just to be more clear, let's substitute them. since they're both already in y=, we can make them both set to each other.

3x-8=3x-8

add 8 to both sides; subtract 3x from one side

0=0

the answer is A, Infinitely many solutions.

hope this helped <3333333

Step-by-step explanation:

you can use that same formula to answer that same question

The volume of the rectangular prism is [tex]6.75ft^{3}[/tex]

Diagram of a rectangular prism is shown in the attachment below.

Given that:

the height (h) = 1.5 ft

base area (B) = 4.5 sq ft

Volume of rectangular prism (V) [tex]= Bh[/tex]

Plug in the known values into the formula:

[tex]V = 4.5 \times 1.5\\V = 6.75 ft^{3}[/tex]

Volume of the rectangular prism is [tex]6.75ft^{3}[/tex]

Learn more about rectangular prism here:

https://brainly.com/question/11613210

Answer:

The answer is D or 36

Step-by-step explanation:

Divide the cups by servings

9/.25=36

Answer:

72 is equal to 2 yards.

Explanation:

There are 36 inches in one yard.

(another way to look at this is there are 3 feet in one yard, each feet is 12 inches. So, 12 multiplied by 3 is equal to 36 inches, or one yard)

Then, since in this question we are finding out in relation to 2 yards, add 36 inches + 36 inches, and that is equal to 72 inches.

72 and 72 are equal :)

Answer:

its b

Step-by-step explanation:

just did it on edge

Graph C represents a sequence that converges because the values approach 2.

Convergent definition in mathematics is a property (displayed by certain innumerable series and functions) of approaching a limit more and more explicitly as an argument (variable) of the function increases or decreases or as the number of terms of the series gets increased.

According to the given problem,

Graph 1, Graph 2 and Graph 4 are diverging graphs. We are assuming this because the a divergent sequence doesn't have a limit. Thus, this sequence converges to 0. In many cases, however, a sequence diverges that is, it fails to approach any real number.

Graph 3 has a limit and converges as it approaches 2.

Hence, we can conclude that Graph 3 converges because the values approach 2.

Learn more about converging graphs here: https://brainly.com/question/15415793

#SPJ2

Answer: x=4y+24

b=b

How to:  Solve in terms of the arbitrary variable  y  .

Have a great day and stay safe ! So sorry if im wrong .

Answer:

67

is it multiple choise

Answer:

9:10pm

Step-by-step explanation:

the game ended at 9:10pm

Answer:

21:10 (24-hour clock) or 9:10 ( 12-hour clock)

Step-by-step explanation:

Two ways it can be solved:

Starting time: 7:30

Game lasted- 1 hour and 40 minutes

Ending time-?

∴ hr  I min

   7   :  30 pm

+ 12  :  00

___________

=  19  :  30

Then, hr  I min

        19  :   30

    +   1    :   40

______________

=       20  :   70

    +    1   : - 60

______________

=       21   :  10

So it ended at 21:10 (24-hour clock) or 9:10 ( 12-hour clock).

  hr  I min

   7  : 30pm

+ 1   :  40

________

=  8 :  70

 + 1  : - 60

_________

=  9  : 10 pm

Answer:

14.04 ft^3

Step-by-step explanation:

2.4 ft x 4.5 ft x 1.3 = 14.04 ft^3

Answer:

Additive Property of Equality

Step-by-step explanation:

If we are discussing equations, then the property would be the Additive Property of Equality. It states that if we know something is added to both sides of an equation, the sides remain equal. If y+x=z+x, we know that y=z.

Answer:

(B)

They intersect at (8, 1)