Which three side lengths best describe the triangle in the diagram?
O NG
1
2
3
0 1 2
3 4
5 6 7 8 9 10 11 12 13
LLLLLLL
12 13
5
8 9 10 11
4
O NCS 2 3
2
O NOS
O A. 5 cm, 12 cm, and 13 cm
OB. 5 cm, 10 cm, and 13 cm
O C. 4 cm, 8 cm, and 12 cm
OD. 7 cm, 12 cm, and 13 cm

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

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

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)

Answer:

U

Step-by-step explanation:

Answer:

V

Step-by-step explanation:

Sum of angles in a triangle = 180°

66c + 40c +74c = 180°

106c + 74c =180

180c = 180

c=1

Side v is the largest

Answer:

[tex]x = 18[/tex]

Step-by-step explanation:

Given

[tex]\frac{x}{6} - 7 = -4[/tex]

Required

Solve for x

[tex]\frac{x}{6} - 7 = -4[/tex]

Add 7 to both sides

[tex]\frac{x}{6} - 7+7 = -4+7[/tex]

[tex]\frac{x}{6} = -4+7[/tex]

[tex]\frac{x}{6} = 3[/tex]

Multiply through by 6

[tex]6 * \frac{x}{6} = 3 * 6[/tex]

[tex]x = 3 * 6[/tex]

[tex]x = 18[/tex]

Answer:

I would just search online what are corresponding angles and then base it off of angles like angle number 4 is corresponding because corresponding angles are just angles with the same size and same line

Answer:

The answer is 1/6

Step-by-step explanation:

This is the answer because it is.

Answer:

(half * base 1 * base 2)/height

base 1 is 6 and base 2 is 9

get the height from similarity

6/9 = 8/CE

therefore CE = 72/6

Answer:

30cm²

Step-by-step explanation:

AE/BD = CE/CD

9/6 = CE/8

CE = 9/6 x 8

CE = 12cm

DE = CE - CD

DE = 12 - 8 = 4 cm

½(6 + 9)4 = 30cm²

Answer:

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

Ok so

2 cm is 5 feet and there are 24

2 = 5

4 = 10

6 = 15

8 = 20

10 = 25

11 = 30

So for this one there are about . 10 feet at the top and 8 feet for the other

Answer:

The scale of the drawing is

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale drawing

x-----> the area of the playground in the scale drawing

y----> the area of the actual playground

we have

substitute

simplify

or

Divide by 4 both numerator and denominator

Answer:

3

Step-by-step explanation:

Answer:

x-3*2

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x4x4x4x4=4^5=1024

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

Answer:

The total of all the boxes would be $5.00.

Answer:

i think 1/4

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

We name the coins coin 1 and coin 2 for the sake of simplicity.

There are four possible situations:

coin 1 head, coin 2 head

coin 1 head, coin 2 tails

coin 1 tails, coin 2 head

coin 1 tails, coin 2 tails

Only case 1 results in both 'heads'. So the probability is 1/4.

Answer:

12 small, 18 large

Step-by-step explanation:

x - small

y - large

z- medium

4z=2x=3y then she orders 24

24/4=6 times more than usually, so we should *6 for every x and z

24z=6*2x=6*3y

12 - x - small tshirt

18 - y - large

Answer:

The team building event will cost $24 for 4 attendees.

Step-by-step explanation:

Given,

Cost charged corporate team building = $6 for every attendee

Number of attendees = 4

We will multiply the amount of one ticket with number of attendees in order to find the total cost.

Cost charged for 4 attendees = 6*4

Cost charged for 4 attendees = $24

Answer:

y = 7   x = 9

Step-by-step explanation:

2y-x=8

2(2y-x=8)

4y-2x=16

-(y-2x= -5)

3y +0x= 21

3y=21

y=7

2(7)-x=8

14-x=8

9=x

Answer:

y=x+4

Step-by-step explanation:

Slope intercept is y= mx+b

The slope is rise/run or change in y/change in x. Here the slope is 1 since when y goes up1, x goes to the right 1 (1/1=1).

The y intercept is 4 since it hits the y axis at 4.

so it would be y= 1x+4 which is y=x+4

A Cause I'm big brain and we learned that

Answer:

T is correct (the fourth answer)

Step-by-step explanation:

Step-by-step explanation:

I believe it's graph T..

Answer:

x = 65.4

Step-by-step explanation:

I solved this question already. My explanation is here: https://brainly.com/question/20456072

Hope this helped! <3

Answer:

76.09 pounds

Step-by-step explanation:

From the information given:

[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]

[tex]R_{in} =3 \ lb/min[/tex]

At a slower of 4 gal/min, the solution gets pumped out;

So,

[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]

[tex]R_{out} = \dfrac{2A}{50+t }[/tex]

The differential of the equation is:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]

For the linear differential equation, the integrating factor is determined as:

[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]

[tex]= (50+t)^2[/tex]

Multiplying [tex](50+t)^2[/tex] with the above integration factor;

[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]

[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]

[tex](50+t)^2 A = (50 +t)^3 + c[/tex]

[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]

By using the given condition:

A(0) = 40

40 = 50 + c (50)⁻²

10 = c(50)⁻²

OR

c = -10 × 2500

c = -25000

A = (50 + t) - 25000(50 + t)⁻²

The number of pounds of salt in the tank after 30 min is:

A(30) = (50+30) - 25000(50 + 30)⁻²

[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]

[tex]A(30) = 76.09 \ pounds[/tex]

Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.

Answer:

i thinking a or d

Step-by-step explanation:

The absolute value equation is |x+15|=25. Therefore, option B is the correct answer.

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

Given that, on average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.

Let x represent the maximum and minimum time.

So, the absolute value equation is |x+15|=25

Therefore, option B is the correct answer.

To learn more about a absolute value equation visit:

https://brainly.com/question/2166748.

#SPJ2

Answer:

10(10)-3(10)-2/4+5=149/2 (decimal 74.5)

Answer:

more context please:)

Step-by-step explanation:

Answer:

3 + x + 3

Step-by-step explanation:

Hope it helps!

Answer: 8

Step-by-step explanation:

I think the answer is 8

Answer:

x=3 in equation ;5x=15 and in equation C.

Answer:

B. -8+10

Step-by-step explanation: keep the -8 change - sign to +sign then change -10 to 10 .

Hope it helps :)

Answer:

Graph A <==

Step-by-step explanation:

$ 50 for 5 hours......50/5 = 10...thats $ 10 per hr

so the equation would be : y = 10x...with x being the number of hrs and y being the total cost.

So ur x axis will be the hours and your y axis will be the total cost.

so ur answer is :the title of the graph is cycle renting. the x axis (the horizontal axis)...since it is the hours, will be labeled 0,1,2,3,4,5,6

the y axis (the vertical axis)...since it is the total cost, will be labeled  

0,10,20,30,40,50,60. points are plotted on (1,10),(2,20), and (3,30)