When it was Tess' turn in the "Guess my number game, the gloves were off! She gave Davis the following 10 clues:
• A nine-digit whole number
• Even
. Each of the digits appears exactly three times
• Each digit is greater than 6
• All the digits in each period are the same
Greater than 800,000,000
Divisible by 3
Divisible by 4
• Its millions digit is 9
• Its thousands digit is 7
What is the number?

The number is 999777888.

Step-by-step explanation:

Reaching to the answer by solving the clues one by one.

The number is a 9 digit whole number. So it has to be 0 or greater than 0

The number is even .So its last digit will be even.

Each of the digit appears exactly thrice. So there will be three digits used three times each in the number.

Each digit is greater than 6. So there will be no digits less than 7 in the number.

All the digits in each period are same. So a period of three adjacent digits will have same the same digit.for ex.777 is  a period

The number is greater than 7. So the digit in the millions place and higher is 9.

The number is divisible by 3. So the sum of all the digits should be divisible by 3.

The number is divisible by 4. So the number formed by last two digits of the number should be divisible by 4.

Thousands digit is 7.

The number that satisfies all the given conditions is 999777888.

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°