Mateo has 60 wooden tiles in the shape of diamonds as shown below. He plans to glue these tiles side by side onto a tabletop. What will the area of the tabletop be?

Given:

[tex]ST=4y,TU=2y+6[/tex]

To find:

The value of  y, ST and TU.

Solution:

In triangle STV and UTV,

[tex]m\angle TSV\cong n\angle TUV[/tex]            (Given right angles)

[tex]m\angle SVT\cong n\angle UVT[/tex]            (Given)

[tex]TV\cong TV[/tex]            (Common side)

The corresponding two angles and a non included sides in both triangles are congruent. So, the triangles are congruent by using AAS congruence postulate.

[tex]\Delta STV\cong \Delta UTV[/tex]           (AAS congruence postulate)

Corresponding parts of congruent triangles are congruent. So,

[tex]ST\cong UT[/tex]              (CPCTC)

[tex]4y=2y+6[/tex]

[tex]4y-2y=6[/tex]

[tex]2y=6[/tex]

[tex]y=3[/tex]

Now,

[tex]ST=4y[/tex]

[tex]ST=4(3)[/tex]

[tex]ST=12[/tex]

And,

[tex]TU=2y+6[/tex]

[tex]TU=2(3)+6[/tex]

[tex]TU=6+6[/tex]

[tex]TU=12[/tex]

Therefore, [tex]y=3,\ ST=12\ units,\ TU=12\ units[/tex].

Answer:

596.34m approx

Step-by-step explanation:

Given data

Let the Starting point be x

A helicopter flew north 325 meters from x

Then flew east 500 meters

Let us apply the Pythagoras theorem to solve for the resultant which is the distance from the starting position

x^2= 325^2+500^2

x^2=105625+250000

x^2= 355625

x= √355625

x=596.34m

Hence the distance from the starting point is 596.34m approx

Answer:15 ft

Step-by-step explanation:

Given

The total perimeter needed is [tex]40\ ft[/tex]

The available width of the room is [tex]w=5\ ft[/tex]

Suppose l is the length of the room

So, the perimeter of a rectangle-shaped room is [tex]2(l+w)[/tex]

Putting values

[tex]\Rightarrow 40=2(l+5)\\\Rightarrow l+5=20\\\Rightarrow l=15\ ft[/tex]

[tex]{ \sf{ \red{using \: pythagoras \: theorem}}} \\ \\ { \sf {(20)}^{2} - {(16)}^{2} = {x}^{2} } \\ \\ { \sf{400 - 256 = {x}^{2} }} \\ \\ { \sf{144 = {x}^{2} }}[/tex]

[tex]{ \sf{x = \sqrt{144} }} \\ \\ { \boxed{ \boxed{ \green{x = 12}}}}[/tex]

option (C)

2

Step-by-step explanation:

I think it 4/2 because I multiplied it

Answer:

5 to 3

Step-by-step explanation:

The desired outcomes are 4 or red.

Here are all the possible outcomes:

1 red

1 red

1 red

2 green

3 blue

3 blue

4 yellow

4 yellow

The desired outcomes are in boldface. There are 5 desired outcomes.

There are 3 outcomes that are not desired.

odds of 4 or red = 5 to 3

Answer:

5/8

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1x1

thinking you braindead mf

Answer:

1800

Step-by-step explanation:

Answer:

the fist one is A and the second one is D

Step-by-step explanation:

Answer:

c=10

Step-by-step explanation:

Hope it helps. Doing all your questions that you send XD

Answer:

10

Step-by-step explanation:

using the pythagorean theory the missing side would be [tex]c^{2}[/tex] bs its the hypotenuse so

[tex]a^{2} + b^{2} = c^{2}[/tex]

[tex]8^{2} + 6^{2} = c^{2}[/tex]

[tex]64 + 36 = c^{2}[/tex]

[tex]100 = c^{2}[/tex]

and the square root of 100 is 10, which makes your equation

[tex]c = 10[/tex]

Answer: I think 72 sorry if this didnt help

Step-by-step explanat

Answer:

It's symmetrical to the origin

Step-by-step explanation:

Use desmos for further graphing

Answer:

13.9

Step-by-step explanation:

7² x 12² = 49 + 144 = 193

√193= 13.89

Answer:

D

Step-by-step explanation:

12.50 x 5 = 62.5

62.5 + 20 = 82.5

Answer:

jhhfhgk

Step-by-step explanation:

Answer:

Hey, the correct nswer is option A

Step-by-step explanation:

A. V = [tex]\pi[/tex]r3

Complete question :

Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below. Obtain the area of the front face of the model.

Answer:

12500 mm²

Step-by-step explanation:

The front face of the mode consista of both triangle and rectangle

Area of rectangle :

Height * Base

Height = 200 m ; Base = 50

Area = 200 m * 50 m = 10,000 mm²

Area of triangle :

1/2 * base * height

1/2 * 50 * (300 - 200)

1/2 * 50 * 100

= 2500 mm²

Area of front face = Area of rectangle + Area of triangle

Area of front face = (10,000 + 2500) m²

Area of front face = 12500 mm²

1500+5%= 1505 that is the answer I got I hope this was helpful

Answer:

729

Step-by-step explanation:

9x9x9 = 729 in^3

Answer:

b

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Answer:

14.4222051019 or 14.42

Step-by-step explanation:

a^2 + b^2 = c^2

x^2 + 9^2 = 17^2

x^2 + 81 = 289

x^2 = 289 - 81

x^2 = 208

x = 14.4222051019 or 14.42

Answer:

Step-by-step explanation:

a computer company features a new model with the larger 20-in flat panel display. the flat panel sizes it diagonal length of its screen. the new computer joins earlier computer models with 15 and 17 inch screens.​

Answer:

1

Step-by-step explanation:

you need to multiplau with is 12x+9-42

Answer:

Step-by-step explanation:

Notice that the difference is in the y-intercept.  The first equation has a y-intercept of 0 since y = 4x + 0, the second has a y-intercept of 1 since

y = 4x + 1.  In other words, the graph is translated up 1 unit to cross at (0,1) instead of (0,0)

Answer: -21x + 32z + 15

Step-by-step explanation:

Answer:

40.8 minutes

Step-by-step explanation:

Element X decays radioactively with a half life of 8 minutes. If there are 480 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 14 grams?

The formula to find how long it would take which is the time elapsed is given as:

t = t½ × In(Nt/No)/-In2

t = ?

t½ = 8 minutes

Nt = Amount after the time of decay = 14 grams

No = Original Amount of substances = 480 grams

t = 8 × In(14/480)/-In2

t = 40.796285388407 minutes

Approximately to the nearest tenth = 40.8 minutes

Therefore, it would take the element X, 40.8 minutes to decay to 14 grams

Answer:

X + 4 = 48

Step-by-step explanation:

Before hat purchase :

Michael has $68

Craig has $24 less than Michael;

Hence, Craig = $68 - $24 = $44

Michael purchased hat worth, $20

x = amount Craig has after Michael purchase hat:

x = Amount Michael has - $24

Amount Michael has after hat purchase = $68 - $20 = $48

x + 4 = 44 + 4

X + 4 = 48

Answer: pretty sure 25 feet

Step-by-step explanation: