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77julia77 [94]
3 years ago
14

Find the value of x:

Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer:

x = 20

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Using ΔAHC , then

∠ACH = 180 - (2x + 100) = 180 - 2x - 100 = 80 - 2x

∠ECD = ∠ACB ( vertical angles are congruent ), thus

∠ECD = ∠ACH + ∠HCB, that is

3x = 80 - 2x + x

3x = 80 - x ( add x to both sides )

4x = 80 ( divide both sides by 4 )

x = 20

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Set up an equation and solve for x
k0ka [10]

Answer:

x = -10

Step-by-step explanation:

verticle angles are congruent

80 + x = 70

Subtract 80 from both sides

x = -10

7 0
3 years ago
A small auditorium has 10 rows of seats. There are 12 seats in the row and 16 seats in the second row the number of seats in a r
guapka [62]

This problem can be solved through simple arithmetic progression

Let

a1 = the first term of the sequence

a(n) = the nth term of the sequence

n = number of terms

d = common difference

Sn = sum of all terms

 

given

a1 = 12

a2 = 16

n = 10

 

d = 16 -12 = 4

@n = 10

a(n) = a1 + (n-1)d

a(10) = 12 + (9)4

a(10) = 48 seats

 

Sn = (n/2) * (a1 + a(10))

Sn = 5* (12 + 48)

Sn = 300 seats

 

Therefore the total number of seats is 300.

 

 

4 0
3 years ago
Identify the vertical shift, maximum and minimum values of each function
Delicious77 [7]

ANSWER

Vertical shift: 6 units up

Maximum value: 9

Minimum value: 3

EXPLANATION

The given since function is

y = 3(2 -  \sin(x))

Expand and rewrite to obtain,

y = 6 - 3 \sin(x)

Or

y =- 3 \sin(x) + 6

The vertical shift is 6 units up.

The maximum value is 6+3=9.

The minimum value is -3+6=3

5 0
3 years ago
Approximately 40% of the calls to an airline reservation phone line result in a reservation being made. (round to three decimal
IRISSAK [1]

Answer:

The probability that none of the 10 calls result in a reservation is 0.60%.  In turn, the probability that at least one call results in a reservation being made is 99.40%.

Step-by-step explanation:

Since approximately 40% of the calls to an airline reservation phone line result in a reservation being made, supposing an operator handles 10 calls, to determine what is the probability that none of the 10 calls result in a reservation, and what is the probability that at least one call results in a reservation being made, the following calculations must be performed:

0.6 ^ 10 = X

0.006 = X

0.006 x 100 = 0.60%

Therefore, the probability that none of the 10 calls result in a reservation is 0.60%.

100 - 0.60 = 99.40

In turn, the probability that at least one call results in a reservation being made is 99.40%.

3 0
2 years ago
Which of the following lists of network types appears in decreasing order of size?
Tju [1.3M]

WAN, LAN, PAN

Wide Area Network, Local Area Network, Personal Area Network

6 0
3 years ago
Read 2 more answers
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