A. Use this diagram of a right triangle to derive and prove the Pythagorean Identity, based on sin θ and cos θ. Start with what you know about the relationship among a (adjacent side), o (opposite side), and h (hypotenuse). Using the diagram and the labeled components, define sine and cosine. Incorporate these definitions in your equation. In your response, include all steps and calculations.



B. With respect to , the adjacent side of the triangle has a length of 6 cm and the opposite side has a length of 3 cm. Find the value of the hypotenuse . Then, use these values to confirm the Pythagorean Identity for this triangle.

Answer:

The speed of the car is 75 mph.

The speed of the truck is 56 mph.

Step-by-step explanation:

Call the speed of the truck (x) miles per hour. As per the given information, the car is (19) miles per hour faster. Thus, one can form expressions to represent the speeds of the vehicles.

car = ( x + 19 ) mph

truck = ( x ) mph

Using the formula, ( (speed) * (time) = (distance) ), one can say that the speed of the car, times the time it took plus the speed of the truck times the time will equal the distance between the two vehicles:

(( car speed )( time )) + (( truck speed )( time )) = ( distance between vehicles )

Substitute,

( ( x + 19 ) ( 8 ) ) + ( ( x ) ( 8 ) ) = 1048

Simplify,

8x + 152 + 8x = 1048

16x + 152 = 1048

       -152     -152

16x = 896

/16     /16

x = 56

Add (19) to find the speed of the car:

truck speed + 19

= 56 + 19

= 75

The speed of the car is 75 mph.

The speed of the truck is 56 mph.

Answer:

The truck traveled at 81

mph. The car traveled at 100

mph.

Step-by-step explanation:

Answer :

Hey there! I'm happy to help!

To find the area of a triangle you multiply the base by the height.

We see that our base is 5 units long because it stretches from -6 to -1 on the coordinate plane. Our height is 8 because the y value goes from 3 to -5.

To find the area of a triangle, you just multiply the base by the height then divide by 2.

5(8)=40

40/2=20

The area is 20 square units.

Have a wonderful day! :D

Is This What You Triangle Looks Like?

Answer:

4

Step-by-step explanation:

Let the numbers be 2x,5x and 7x respectively.

2x+5x+7x=28

14x=28

x=28/14=2

Therefore the numbers are 2(2)=4,5(2)=10 and 7(2)=14

The smallest number is 4

Answer:

14.6

Step-by-step explanation:

For this case we have the following trigonometric relationship:

sine (x) = C.O / h

Where,

x: angle

C.O: opposite leg

h: hypotenuse

Substituting values we have:

sine (20) = 5 / c

Clearing c:

c = 5 / sine (20)

c = 14.619022

Rounding:

c = 14.6 in

Answer:

c = 14.6 in

option 4

Answer: y>(1/3)x-3

Step-by-step explanation: The slope is 1/3. The dotted line means it is not inclusive, and the value of k means it is going down three units.

Answer:

Me ha quedado una cuarta parte de la cantidad inicial, es decir, me he gastado tres cuartas partes de la cantidad inicial comprando crustácea importada en la pescadería y marisquería.

Step-by-step explanation:

Asumamos que hacemos la compra en una pescadería y marisquería. Si la razón inicial equivale a 1, gasta inicialmente la mitad de la razón inicial, luego gasta la mitad de la razón resultante. El gasto se entiende como una forma de sustracción mientras que la sucesión como una multiplicación. Por consiguiente, tenemos el siguiente producto:

[tex]c = \left(1-\frac{1}{2} \right)\cdot \left(1-\frac{1}{2} \right)\cdot c_{o}[/tex]

[tex]c = \frac{1}{4}\cdot c_{o}[/tex]

Donde [tex]c_{o}[/tex] es la cantidad inicial.

Me ha quedado una cuarta parte de la cantidad inicial, es decir, me he gastado tres cuartas partes de la cantidad inicial comprando crustácea importada en la pescadería y marisquería.

Answer:

A.

Step-by-step explanation:

vertical translation UP 1 unit

Answer:

41

Step-by-step explanation:

Hey There!

So to solve this problem the first thing that we want to do is solve for x

angle P and angle S are supplementary angles meaning that they will add up to equal 180

so 180=8x+3+2x+7

step 1 combine like terms

8x+2x=10x

3+7=10

now we have

180=10x+10

step 2 subtract each side by 10

180-10=170

10-10 cancels out

now we have

170=10x

step 3 divide each side by 10

10/10 cancels out

170/10=17

so x=17

So remember in parallelograms opposite angles are congruent so angle Q is congruent with angle S

so we just plug in 17 into 2x+7 and we will get the value of angle Q

17x2=34

34+7=41

so angle Q = 41

Answer:

m=1/4

Step-by-step explanation:

5m+2-m=12m

4m+2=12m

2=12m-4m

2=8m

2/8=m

1/4=m

m=1/4

Answer:

Rs 720.

Step-by-step explanation:

4 dozen = 48 pencils.

By proportion 48 pencils cost

(48/40) * 600

= 6/5 * 600

= Rs 720.

Answer:

(1/3) * (3/8) = 1/8

Step-by-step explanation:

Multiple: 1/3* 3/8

= 1 · 3/3 ·8

= 3/24

= 1  3/8·3

= 1/8

Answer:

Step-by-step explanation:

Answer:

the x is 5

Step-by-step explanation:

x=5y+20:

x=5y+20

x=(5)(-3)+20

x=5 (simplify boy sides of the equation)

Answer:

344 m^2

Step-by-step explanation:

Area of the 2 triangles: (2)(1/2)(10)(5)=50

Area of three sides:3(7)(14)=294

294+50=344

Answer:

246

Step-by-step explanation:

Answer:

25+22

Step-by-step explanation:

When you subtract 27 to 22

Answer:

31 and 26

Step-by-step explanation:

31 + 26 = 57

31 - 26 = 5

Therefore, your answer is 31 and 26

Answer:

x = -3

y = -2

Step-by-step explanation:

Answer:

( x,y ) = ( 72/163,-3294/163

Answer:

Step-by-step explanation:

A road

Answer:

3⅗

Step-by-step explanation:

5×3 =15

18 - 15 = 3

therefore

18÷5

is

3⅗

Convert in to mixed fractions 18 and 5

Multiply the newest quotient digit (3) by the divisor 5 . Subtract 15 from 18 . The result of division of 185 is 3 with a remainder of 3 .

Hopefully help:)

Answer:

You can't.

Step-by-step explanation:

You have nothing to substitute for the x.

Answer:

One serving of orange juice has 30 mg more vitamin C per serving than one serving of cranberry juice

Step-by-step explanation:

Answer: x = -33

Step-by-step explanation:

27 + 3 = 30

-3 - 30 = -33

Answer:

-33

Step-by-step explanation:

I already took it TwT

Answer:

Step-by-step explanation:

It’s a right triangle, so use the Pythagorean Theorem.

x^2 = 30^2 + 16^2 = 1156

x = 34

9514 1404 393

Answer:

  A)  16

Step-by-step explanation:

The ratio of long-side to short-side is the same for all of these similar triangles, so we have ...

  e/8 = 8/4

  e = 8(8/4) = 8(2) = 16

The value of e is 16.

Answer:

From left to right:

x=-9

x=-23

x=24

x=8

x=-9

x=-28

Step-by-step explanation:

63/-7=-9

-15-8=-23

12*2=24

-4*-2=8

-20+11=-9

-7*4=-28

-7x=63 answer is -9

x + 8=-15 answer is -7

1/2x=12 answer is 24

x/-2= -4 answer is 8

x-11=-20 answer is -9

1/4x=-7 answer is -28

Answer:

245/5 = 49 tickets per day

Answer:

245 / 5 = 49 so

49 tickets per day

Answer:

2/7

Step-by-step explanation:

The total number of possibilities is 7 * 6 * 5

The number of possibilities for all girls is 5 * 4 * 3

so the probability is:

[tex]\frac{5*4*3}{7*6*5} \\\frac{4*3}{7*6} \\\frac{12}{42} = \frac{2}{7}[/tex]