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3 years ago

When it was Tess' turn in the "Guess my number game, the gloves were off! She gave Davis the following 10 clues:

Mathematics

1 answer:

astra-53 [7]3 years ago

5 0

The number is 999777888.

S<u>tep-by-step explanation:</u>

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.

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What is one of the solutions to the following system of equations? y2 + x2 = 53 and y − x = 5

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Y2 + x2 = 53
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Answer: $7\frac{5}{7}$ unit and 18 unit

Step-by-step explanation:

Let ABCD is a trapezoid where AB and CD are the bases. ( In which AB is greatest base which shown in below figure)

AD and BC are the legs of the trapezoid ABCD.

Now, we have ( According to the question ),

AB = 18 unit, BC = 7 unit, AD = 3 unit and DC = 11 unit.

Here the leg AD extends from point D.

Similarly leg BC extends from point C.

Let they meet at point P ( shown in below diagram)

Since In triangles PAB and PDC,

∠PDC ≅ ∠PAB ( because DC ║ AB )

And, ∠ PAB ≅ ∠ PBA

∠DPC ≅ ∠ APB ( reflexive)

Therefore, By AAA similarity postulate,

$\triangle PDC \sim \triangle PAB$

Thus, By the definition of similarity,

$\frac{PD}{PA} = \frac{DC}{AB}$

$\frac{PD}{PD+3} = \frac{11}{18}$ ( because PA = PD+DA)

⇒ 18 PD = 11 PD +33

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⇒ PD = 33/7

Again by the definition of similarity,

$\frac{PC}{PB} = \frac{DC}{AB}$

$\frac{PC}{PC+7} = \frac{11}{18}$ ( because PB = PC + CB)

⇒ 18 PC = 11 PD +77

⇒7PC = 77

⇒ PC = 11

Thus, PA = PD+DA = 33/7 + 3 = $7\frac{5}{7}$

And, PB = PC + CB = 11 + 7 = 18

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