the temperature 0 F ,3 F ,6 F ,5 F,and -1 F have also been recorded in florida .graph these temperature on the number line .

17. Farimah and Helio are standing 15 ft. apart from each other and looking up at a kite that is with the flying between them. F

miss Akunina [59]

Answer:

Helio is 53.2 feet from the kite ⇒ the last answer

Step-by-step explanation:

* Lets change this story problem to a trigonometry problem

- Assume that there is a triangle joining between the

kite, Farimah and Helio

- The name of the triangle is KFH, where K position of the kite,

F position of Farimah and H is the position of Helio

∵ Farimah and Helio are standing 15 feet apart from each other

∴ FH = 15 feet

∵ Farimah is flying the kite on a 57 feet string at an angle

of 68 with the ground

∴ FK = 57 feet

∴ m∠KFH = 68°

∵ We need to know that Helio is how far from the kite

∴ We need to calculate the length of KH

* Now lets find the best way to find the length of KH

using the trigonometry

- We have the length of two sides and the measure of the included

angle between them , then the best way is the cosine Rule

* Lets explain the cosine rule:

- In ΔABC:

∵ a is the length of the side opposite to ∠A ⇒ a is BC

∵ b is the length of the side opposite to ∠B ⇒ b is AC

∵ c is the length of the side opposite to ∠C ⇒ c = AB

∴ a² = b² + c² -2bc × cos(A)

∴ b² = a² + c² -2ac × cos(B)

∴ c² = a² + b² -2ab × cos(C)

* We will use the rule in our problem to find HK

∵ FH is k , HK is f , KF is h

∴ f² = h² + k² - 2hk × cos(F)

∵ h = 57 feet , k = 15 feet , m∠F = 68°

∴ f² = (57)² + (15)² - 2(57)(15) × cos(68) = 2833.4227

∴ f = √2833.4227 = 53.2 feet

* Helio is 53.2 feet from the kite

7 0

3 years ago

1. The backdrop of the altar in a church is triangular in shape. It has a base of 10.5 meters

FrozenT [24]

Answer:

#1

Area of triangle backdrop:

A = 1/2bh = 1/2(10.5)(8.5) = 44.63 m²

Area of the cloth:

A = 4.5*4 = 18 m²

Uncovered area:

44.63 - 18 = 26.63 m²

Choice A

#2

Area of the cut piece:

A = πr² = 3.14*7.6² = 181.37 cm²

Area of the square piece:

A= a² = 34² = 1156 cm²

Remaining piece is:

1156 - 181.37 = 974.63 cm²

Choice B

8 0

2 years ago

P= A. i B. -1 C. -i D. 1

Molodets [167]

Answer:

la respuesta es capó la B

Step-by-step explanation:

xeos para rellenar ti dirección para saber cómo está buenardo que la mujer de mi celular no puedo consultar con ningún compañero

7 0

3 years ago

Hello If You Have Please Help Thank You Solve for x. −7x−15<6

bonufazy [111]

Answer:

x > -22/7

Step-by-step explanation:

Given inequality:

- 7x - 15 < 6

adding 15 to both sides:

==> -7x - 15 + 15 < 6 + 16

==> -7x < 22

dividing both sides by 7:

==> -x < 22/ 7

multiplying both sides by -1

(anytime you multiply the inequality by -1 you must flip the inequality sign– replace the "<" with ">")

==> x > -22/7

3 0

2 years ago

Find the point of intersection (if any) of the following pairs of lines: a) x – 2y +1=0 2x + 3y – 7 = 0 b) x-2y+11=0 -x+2y-13 =

pychu [463]

Answer:

a) (11/7, 9/7)

b) There's no point of intersection

Step-by-step explanation:

a) x - 2y + 1 = 0

2x + 3y - 7 = 0

To find the point of intersection, we need to solve the system of equations and the result will be the point of intersection (x,y)

$x-2y+1=0\\x= 2y-1$

Now we substitute x in the second equation:

$2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7$

Now we substitute y in our first equation.

$x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7$ .

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

-x + 2y - 13 =0

We are going to follow the same procedure:

$x-2y+11=0\\x=2y-11$

$-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2$

Since this system of equations doesn't have a solution, the system has no point of intersection.

5 0

3 years ago