Two lines are perpendicular. If one line has a slope of 1/2, what is the slope the other line?​

It looks like the equation is

cos(2x) + cos(x) = 0

Use the double angle identity for cosine to write this as

(2 cos²(x) - 1) + cos(x) = 0

2 cos²(x) + cos(x) - 1 = 0

Factorize the left side:

(2 cos(x) - 1) (cos(x) + 1) = 0

Then either

2 cos(x) - 1 = 0   or   cos(x) + 1 = 0

2 cos(x) = 1   or   cos(x) = -1

cos(x) = 1/2   or   cos(x) = -1

[x = cos⁻¹(1/2) + 2nπ   or   x = -cos⁻¹(1/2) + 2nπ]

…   or   [x = cos⁻¹(-1) + 2nπ]

(where n is any integer)

x = π/3 + 2nπ   or   x = -π/3 + 2nπ   or   x = π + 2nπ

We get the following solutions in the interval [0, 2π):

x = π/3   and   x = π   and   x = 5π/3

Answer:

z=60º, x=10º

Step-by-step explanation:

Question 1: 180º - 120º = 60º

Question 2:

(9x+30) = 120º

-30          -30

9x=90º

/9    /9

x=10º

Answer:

First one

SA = 2lw + 2lh + 2wh

Step-by-step explanation:

The area is this, it is a fact..

A=2(wl+hl+hw)

Answer:

first one

Step-by-step explanation:

SA = 2wl + 2lh + 2hw

Answer:

Step-by-step explanation:

The domain is the allowed 'x' values that the function can take on without it being undefined. The natural log function is undefined for negative numbers and zero. It can only take on positive inputs. Therefore, we can set up an inequality:

[tex]3-4x > 0[/tex]

Subtrauct 3 on both sides:

[tex]-4x > -3[/tex]

Divide both sides by -4. When you divide an inequality by a negative number, you must switch the sign of the inequality:

[tex]x < 3/4[/tex]

Therefore, our allowed 'x' values is anything less than 3/4:

-∞ < x < 3/4

Answer:

See below ↓↓↓↓

Step-by-step explanation:

⇒ 3

⇒ 2

⇒ 6

⇒ 4

Answer:

Step-by-step explanation:

Reflections of a line or a figure across an axis does not change its lengths.

Therefore, the corresponding parts are equal.

Solving for x

Solving for y

Solving for z

Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Based on the inventory on hand, the lead time, and the standard deviation, the in-stock probability will be 96.56%

To find the in-stock probability, you first need to find the Z score as:

= On-hand inventory / Standard deviation x √(lead time + 1)

Solving gives:

= 5,050 / 800 x √(11 + 1)

= 5,050 / 2,771.28

= 1.82

With a Z score of 1.82, the probability according to the Z tables will be 96.56%

Find out more on Z scores at https://brainly.com/question/25638875.

The domain for the rational expression as given in the task content is; All real numbers except -5.

The domain of a rational function such as that given in the task content includes all possible values of the variable except that which renders the expression undefined.

On this note, the expression is undefined when, 3x + 15 = 0.

Hence, the domain is All real numbers except -5.

Read more on rational functions;

https://brainly.com/question/13763081

Answer:

B) V= 4/3πr^3

Step-by-step explanation:

The volume of the cone according to the given condition is V = 4πr³/3

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.

Given that the height of a cone is two times its base diameter. we need to find the formula for the volume of cone in terms of base radius,

So, the volume of a cone in general is = π × radius² × height/3

According to the question,

The height is 2x the base diameter, that mean =

h = 2d

Since, d = 2r

So, h = 2(2r)

h = 4r

So the volume according to this condition is =

π × r² × 4r/3

V = π × 4r³/3

V = 4πr³/3

Hence the volume of the cone according to the given condition is V = 4πr³/3

Learn more about cones, click;

https://brainly.com/question/16394302

#SPJ7

Answer:

  (a)  90°

Step-by-step explanation:

A graph can help you answer the question about where the graphs of the two functions intersect. It shows the one angle of intersection to be 90°.

__

You can also determine this analytically.

  f(x) = g(x)

  cos(x/2) = √2 -cos(x/2)

  2cos(x/2) = √2 . . . . . . . . . . add cos(x/2)

  cos(x/2) = √2/2 . . . . . . . . divide by 2

  x/2 = ±45° +360°×n . . . . . for an integer n

  x = ±90 +720°×n . . . . multiply by 2

  x = 90° is the only solution in the desired range.

Answer:

Wow that's a lot of questions. The answers are 2, 3/4, 4, 6, 10, 5, 48500, 48000, and 50000

Step-by-step explanation:

Hope this helped

Answer:

30,000

Remember the hundreds place rounding rule...

Answer:

30,000

Step-by-step explanation:

the answer is 30,000 because, the three is getting rounded up or down based on the zero behind it. Since there is no way the three can round up because the zero is under five, all the numbers after it shall become a zero. But if it were a decimal, the answer would just be thirty. But the actual answer is 30,000

Answer: There is not enough evidence to support a relationship between lunch preference and role at the school.

Answer:

The answer is 5550

Step-by-step explanation:

Just do

6154- 604=5550

Answer:

Number of 7th Graders= 360 - X

Step-by-step explanation:

As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from &th grade. As we know: Total number of students on the A honor roll = 360 We are asked to calculate, number of students from 7th grade on the A honor roll. So, let's assume that "X" represents the all the students who are on the A honor roll except 7th grade. Mathematical Expression: Number of 7th Graders = Total number of students on the A honor roll - X Number of 7th Graders = 360 - X So, if you know the value of X, you can easily calculate the number of students which are from 7th grade on the A honor roll.

Answer:

2,500 square feet is the answer

Some General Information:

  ⇒ both triangles are isosceles triangle

    ⇒because two of the angles are equal to each other

       ⇒ which means there are two equal sides that always join at the

           same angle to the base (the third side), and meet directly above    

           the midpoint of the base (I attached a diagram for a better

           explanation)

Question 11:

 ⇒ x and 10 are equal

   ⇒ because their sides join the third side at the base with the same

       angle

       ⇒ so x = 10

Question 12:

 ⇒ '2x + 23' and 7 are equal

   ⇒ because their sides join the third side at the base with the same

       angle

      ⇒ so:

           [tex]2x+23=7\\2x=-16\\x = -8[/tex]

         ⇒ thus x = -8

Hope that helps!

Answer:

29.7 cm

Step-by-step explanation:

Since A and B are related by a scale of 3:1 then :

3 × (hypotenuse of A) = (hypotenuse of B)

then

(hypotenuse of A) = (hypotenuse of B)/3

                              = 89/3

                              = 29.7

Answer:

x = 146

Step-by-step explanation:

x and 34° are adjacent angles and sum to 180°, then

x + 34 = 180 ( subtract 34 from both sides )

x = 146

Answer:

gang

Step-by-step explanation:

ion

Answer:

2inches=5.08cm

TSA of cylinder=2πr(r+h)

2×22/7×5.08(5.08+5.08)

6×5.08×10.16

324.42cm^3

Answer:

1/105

Step-by-step explanation:

Total Marbles= 2+6+7=15

2/15 * 1/14 = 2/210 = 1/105

(It becomes 1/14 since you take out own red marble)

Answer:

5 and 6 are vertical

1 and 2 are linear pair

Step-by-step explanation:

1 and 2 are linear pair because they add up to 180 degrees

5 and 6 are across from each other so they are vertical angles

Answer:

2/8

Step-by-step explanation:

denominator is 8 as it's the total of the entire dice.

your numerator is 2 as you only have 1 #8 and 1 #7 so 1+1=2

answer is 2/8

4000 pieces of stones needed

Explanation:

All measurements should be taken in cm unit wise

For wall:

For each stone:

Volume of the wall:

Volume of each stone:

Pieces of stone needed:

Answer:

=> 4000 pieces

Step-by-step explanation:

First change m into cm

20m -> 2000cm

2m -> 200cm

volume of wall = 2000×200×60

=> 24000000 cm³

volume of each stone = 20×30×10

=> 6000 cm³

stone needed = 24000000/6000

=> 4000 pieces