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3 years ago

What are the solutions of x ^ 2 + 6x - 6 = 10 ? x = - 11 x = 1 x = - 11 x = - 1 x = - 8x = - 2 x = - 8x = 2

Mathematics

1 answer:

zmey [24]3 years ago

8 0

Answer:

x=-8 ,2

Step-by-step explanation:

x ^ 2 + 6x - 6 = 10

Add 6 to each side

x ^ 2 + 6x - 6+6 = 10+6

x ^ 2 + 6x = 16

Complete the square take the coefficient of the x terms, divide by 2 and square it. Then add it to each side

6/2 =3 , 3^2 =9

x ^ 2 + 6x +9 = 16+9

(x+3)^2 = 25

Take the square root of each side

sqrt((x+3)^2) = ±sqrt(25)

x+3= ±5

Make 2 equations

x+3 = 5 x+3 = -5

Subtract 3 from each side

x+3-3 =5-3 x+3-3 = -5-3

x =2 x=-8

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A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it

makvit [3.9K]

Answer:

The length of the hallway is 10 m.

Step-by-step explanation:

Given:

Time taken to cover 1 km = 2.5 hours

Distance covered in 2.5 hours = 1 km

Therefore, speed of robot = $\frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h$

Now, speed is constant.

Now, time taken to cover the length of hallway = 90 s

Speed of the robot = 0.4 km/h

Converting 0.4 km/h to m/s, we multiply by the factor $\frac{5}{18}$ . This gives,

$0.4\times \frac{5}{18}=\frac{1}{9}\ m/s$

Now, distance of the hallway is equal to the product of speed and time. So,

Distance of hallway = Speed $\times$ Time

Distance of hallway = $\frac{1}{9}\times 90=\frac{90}{9}=10\ m$

Therefore, the length of the hallway is 10 m.

5 0

3 years ago

From a point p on level ground, the angle of elevation of the top of a tree is 60°. If the tree is 39m high, how far is its base

zzz [600]

Hello,

tan 60°=√3
d/39=tan 60°==>d=39/√3=39√3/3=13√3=22,516660498... (m)

5 0

3 years ago

Use the given figure to solve the remaining parts of the triangle AIR.

PIT_PIT [208]

Answer:

1. 15.49 cm

2. 14.39 cm

3. 17.32 cm

4. 11.53 cm

5. 5 cm

Step-by-step explanation:

In the given problem, you can solve the unknown side of the triangle using either Pythagorean Theorem or SOA CAH TOA method. In Trigo, you can use the Pythagorean Theorem if the triangle has 90 degrees, or it is a right triangle.

In the given problem, the angle of the triangles are unknown, therefore to solve the unknown side of triangles, we will you use the SOA CAH TOA.

In this case, since the given side are b and c, we can use CAH (Cos Teta equals Adjacent over Hypotenuse), and TOA ( Tan Teta equals Opposite over Adjacent)

Lets provide the solution for the number, and the rest have the same solutions and process.

b= 17, c= 3, let u is the angle

Cosu= 17/23, to get the angle, use inverse cosine.

The result will be 42.34°, and to get the unknown side, use TOA

Tanu=a/17, a=17Tanu

It will give you 15.49 cm

In the number 2 and 5, it will be the same when you rotate the triangle.

Read more about the concept of SOA CAH TOA at

brainly.com/question/22767551

#BrainlyFast

3 0

2 years ago