What is the value of p?

The value of x in the equation a – bx = cx + d is = a - d / c + b

The value of x in the equation  5 – 6x = 8x + 17 is - 6 / 7

a - bx = cx + d

add bx to both sides of the equation

a - bx + bx = cx + bx + d

a = cx + bx + d

subtract d form both sides of the equation

a - d = cx + bx + d - d

a - d = cx + bx

Distributive law:

using distributive law on the right side of the equation

a - d = x (c + b)

divide both sides by (c + b)

Therefore,

x = a - d / c + b

Let's use the same method to solve 5 – 6x = 8x + 17

5 – 6x = 8x + 17

add 6x to both sides

5 – 6x  + 6x= 8x + 6x + 17

5 = 14x + 17

subtract 17 from both sides

5 - 17 = 14x + 17 - 17

-12 = 14x

divide both sides by 14

x = -12 / 14

x = - 6 / 7

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Answer:

13 , 24 , 14

Step-by-step explanation:

Note that technically there are two patterns. Each one adds 1.

The first pattern starts with 11. The third number is 12, which means that the fifth number will be 13, and the 7th number will be 14.

The second pattern starts with 22. The 4th number is 23, which means the sixth number will be 24.

~

Easy, it's going by adding 11's 11+11=22 than it subtracts by 10=12 and it keeps repeating until it's done.

Applying the relationship existing between angle pairs, the measure of each angle in the image are:

m<1 = 42°

m<3 = 75°

m<4 = 42°

m<5 = 63°

m<6 = 75°

m<7 = 105°

m<8 =  75°

m<10 = 75°

m<11 = 42°

m<12 = 138°

m<13 = 42°

m<14 = 138°

Given that a || b, where:

• m<2 = 63°
• m<9 = 105°, the missing angle measures will be determined as follows:

Find m<1:

m<1 + m<2 = m<9 (exterior interior angle theorem)

• Substitute

m<1 + 63° = 105°

m<1 = 105° - 63°

m<1 = 42°

Find m<3:

m<1 + m<2 + m<3 = 180° (angles on a straight line)

• Substitute

42° + 63°+ m<3 = 180°

105° + m<3 = 180°

m<3 = 180° - 105°

m<3 = 75°

Find m<4:

m<4 = m<1 (vertical angles theorem)

• Substitute

m<4 = 42°

Find m<5:

m<5 = m<2 (vertical angles theorem)

• Substitute

m<5 = 63°

Find m<6:

m<6 = m<3 (vertical angles theorem)

• Substitute

m<6 = 75°

Find m<7:

m<7 + m<6 = 180° (corresponding angles theorem)

• Substitute

m<7 + 75° = 180°

m<7 = 180° - 75°

m<7 = 105°

Find m<8:

m<8 = m<6 (alternate interior angles theorem)

• Substitute

m<8 =  75°

Find m<10:

m<10 = m<6 (corresponding angles theorem)

• Substitute

m<10 = 75°

Find m<11:

m<11 = m<4 (alternate interior angles theorem)

• Substitute

m<11 = 42°

Find m<12:

m<12 = m<6 + m<5 (alternate interior angles theorem)

• Substitute

m<12 = 75° + 63°

m<12 = 138°

Find m<13:

m<13 = m<11 (vertical angles theorem)

• Substitute

m<13 = 42°

Find m<13:

m<14 = m<12 (vertical angles theorem)

• Substitute

m<14 = 138°

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Answer:

a.    m<1 = 105° - 63°                  m<1 = 42°

b. m<3 + m<2 + m<1 = 180°      m<3 = 75°

c. m<4 = m<1                             m<4 = 42°

d. m<5 = m<2                            m<5 = 63°

e. m<6 = m<3                             m<6 = 75°

f. m<7 = m<9                             m<7 = 105°

g. m<8 = m<6                             m<8 = 75°

h. m<10 = m<8                            m<8 = 75°

i. m<11 = m<4                               m<11 = 42°

j. m<12 = 180° - m<11                   m<12 = 138°

k. m<13 = m<11                            m<13 = 42°

l. m<14 = m<12                            m<14 = 138°

Step-by-step explanation:  Sorry if not all are correct

Answer: option a. A customer earns 1 free night per 10 nights stayed.

Explanation:

Building a table can help you:

x: number of nigths stayed ---------- f(x) = 1/x: number of free nights

10 --------------------------------------------- 10/10 = 1

20 -------------------------------------------- 20/10 = 2

30 -------------------------------------------- 30/10 = 3

40 -------------------------------------------- 40/10 = 4

Then, the pattern permits you to conclude that a customer earns 1 free night per each 10 nights stayed, which is the option a.

Answer: a. A customer earns 1 free night per 10 nights stayed.

Step-by-step explanation:

A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.

When , we put x=1, we get

Here f(1)  represents the number of free nights earned by customer is 1 per 10 nights stayed.

Hence, the a customer earns 1 free night per 10 nights stayed.