All categories

2 years ago

Find the value of r. Note: Write your answer as a decimal.

Mathematics

1 answer:

Solnce55 [7]2 years ago

8 0

Answer:

$\huge\boxed{\sf r = 10.5}$

Step-by-step explanation:

Since it is a right-angled triangle, it has base, perpendicular and hypotenuse.

Base = r

Perpendicular = 14

Hypotenuse = r + 7

Using Pythagoras theorem:

$(Hypotenuse)^2 = (Base)^2+(Perp)^2$

Put the values

(r + 7)² = (r)² + (14)²

Using formula a² + 2ab + b² = (a + b)²

r² + 14r + 49 = r² + 196

Subtract r² to both sides

14r + 49 = 196

Subtract 49 to both sides

14r = 196 - 49

14r = 147

Divide 14 to both sides

r = 147 / 14

r = 10.5

$\rule[225]{225}{2}$

You might be interested in

Need help with translation

sergij07 [2.7K]

Answer:

The translation rule will be: (x, y) → (x+3, y+9)

Step-by-step explanation:

As X'Y' is a translation of XY.

As the location of the vertix X is (-4, -9) and the coordinates of vertex Y is (-5, -5).

As X'Y' be the vertices of the translated figure.

So, if we translate the segment XY +3 units in the x-direction and +9 units in the y-direction, i.e.

(x, y) → (x+3, y+9) = (-4+3, -9+9) = (-1, 0) = X'

and

(x, y) → (x+3, y+9) = (-5+3, -5+9) = (-2, 4) = Y'

so, the image X'Y' will have the X' vertice at the location (-1, 0) and Y' vertice at the location (-2, 4).

Therefore, the translation rule will be: (x, y) → (x+3, y+9)

6 0

3 years ago

1. You are standing on top of a ridge using a clinometer trying to figure out how far your dog has wandered off in

olga_2 [115]

Given:

It is given that the ridge is 360 inches tall.

Assumptions:

Assume you are 170.1 cm tall which equals 67 inches tall, the height from your eye to the floor is $360+67 = 427$ inches.

The distance from your eye level to the bottom of the ridge is 427 inches.

Assume the angle A is 60°.

To find the distance from you to your dog.

Solution:

A right-angled triangle can be formed where the angle is 60°, the distance between you and the dog is the hypotenuse of the triangle and your height from the floor is the adjacent side of the triangle.

Assume the hypotenuse of the triangle measures x inches.

To determine the length of the hypotenuse, we determine the cos of the angle.

$cos \theta = \frac{adjacent side}{hypotenuse} .$

$cos A = \frac{427}{x} , x = \frac{427}{cos60} , cos60=0.5.$

$x=\frac{427}{0.5} = 854.$

So if the ridge is 360 inches tall and you are 67 inches tall and the angle A is 60°, the distance between your dog and you is 854 inches.

3 0

3 years ago

11 and 12 please explain on 12

Fiesta28 [93]

12. since the straws are 4 inches long and she wants to cut them into 1/2 in you would get eight 1/2 pieces on that one straw but since she has two straws she has sixteen 1/2 pieces so no she does not have enough to cut twenty 1/2 pieces

6 0

3 years ago

Read 2 more answers

Which equation represents the area of the triangle? A) A = 1 2 (AC)(AB)(sin A) B) A = 1 2 (AC)(BC)(sin A) C) A = 1 2 (BC)(BD)(si

Juliette [100K]

Answer:

The correct option is A.

Step-by-step explanation:

Let the vertices of the triangle be ABC.

Draw a perpendicular on AC from B. The height of triangle is represented by the altitude from B.

$\sin A=\frac{BD}{AB}$