MATHEMATICS HIGH SCHOOL

Translate a point (x, y) 3 units left and 5 units up. Then translate the image 5 units right and 2 units up. What are the coordinatesof the point after the translations?
The coordinates are

Answers

Answer 1
Answer:

Answer:

Please check the explanation.

Step-by-step explanation:

Given the point

P(x, y)

Please note that when we translate a point 'c' units left, the 'c' units are subtracted from the x-values, and when translating a point 'c' units right, we add the 'c' units to the x-values.

Also, note that when we translate a point 'c' units down, the 'c' units are subtracted from the y-values, and when translating a point 'c' units up, we add the 'c' units to the y-values.

After First Translation:

3 units left and 5 units up

P(x, y) → P'(x-3, y+5)

After Second Translation:

Translate the image 5 units right and 2 units up.

P'(x-3, y+5)  → P''(x-3+5, y+5+2) = P''(x+2, y+7)

Thus, the coordinates  of the point(x, y) after the translations are:  P''(x+2, y+7)

TAKING AN EXAMPLE

Let us consider that point

P(0, 0)

After First Translation:

3 units left and 5 units up

P(0, 0) → P'(0-3, 0+5) = P'(-3, 5)

After Second Translation:

Translate the image 5 units right and 2 units up.

P'(-3, 5) → P''(-3+5, 5+2) = P''(2, 7)

Thus, the coordinates  of the point P(0, 0) after the translations are:

  • P''(2, 7)
Answer 2
Answer:

The final coordinates of the point after the translations are (x + 2, y + 7). Let's start with a point (x, y) and apply the translations step by step: 1. Translate the point 3 units left and 5 units up:

New coordinates after the first translation: (x - 3, y + 5)

2. Translate the new point 5 units right and 2 units up:

New coordinates after the second translation: (x - 3 + 5, y + 5 + 2)

Now, simplify the expressions inside the parentheses:

New x-coordinate: x - 3 + 5 = x + 2

New y-coordinate: y + 5 + 2 = y + 7

So, the final coordinates of the point after the translations are (x + 2, y + 7).

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Answers

log_927=log_93^3=3log_93=3log_9\sqrt9=3log_99^(1)/(2)\n\n=(1)/(2)\cdot3log_99=(3)/(2)
You would use some properties of the logarithm. First, log_927=log_(3^2)27=(1)/(2)log_327. So, now you have log_327 to calculate. It's log_33^3=3, so the final result is (1)/(2)*3=(3)/(2)
Hope it helps.

Solve for x.

-ax + 3 b > 5

Answers

- a x + 3 b < 5
- a x < - 3 b + 5  / *( - 1 )
a x > 3 b - 5
x > ( 3 b - 5 ) / a
Thank you.

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)?

Answers

f_(2) = 100 - 8 = 92
f_(3) = 92 - 8 = 84
f_(4) = 84 - 8 = 76
f_(5) = 76 - 8 = 68
f_(6) = 68 - 8 = 60

f_(6) = 60

Answer:

60

Step-by-step explanation:

Thelma thrifty went to her bank. she had a balance of $1,209.76 in her savings account. she withdrew $131.44 and the teller credited her account with $6.67. what is her new balance?

Answers

Based on the given information above, Thelma had a balance of $1,209.76 and withdrew $131.44, so the remaining would be $1,708.32. But the teller credited her account with $6.67. Credited this means that the money is into your account. So, her new balance would be therefore, $1,084.99. Hope this answers your question.

Answer:

her new balance is $1,084.99

What fraction of all the 10-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?

Answers

The fraction of all the 10-digit numbers with distinct digits that have the property that the sum of every pair of neighboring digits is odd is 1/126.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

For a 10-digit number to have the property that the sum of every pair of neighboring digits is odd, the digits must alternate between odd and even numbers.

Specifically, if the firstdigit is odd, then the second digit must be even, the third digit must be odd, the fourth digit must be even, and so on.

If the firstdigit is even, then the second digit must be odd, the third digit must be even, the fourth digit must be odd, and so on.

There are 5 odd digits and 5 even digits, so there are 5 choices for the first digit. After selecting the first digit, there are 5 choices for the second digit (it must be one of the other type), 4 choices for the third digit (it must be the opposite type of the second digit), 4 choices for the fourth digit (it must be the opposite type of the third digit), and so on.

Therefore, the number of 10-digit numbers with distinct digits that have the given property is:

5 x 5 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 5! x 4!

where the factorials arise from the number of choices for each digit.

The totalnumber of 10-digit numbers with distinct digits is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

Therefore, the fraction of all the 10-digit numbers with distinct digits that have the given property is:

(5! x 4!) / 10! = (5! x 4!) / (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 1/126

Thus,

The fraction of all the 10-digit numbers with distinct digits that have the property that the sum of every pair of neighboring digits is odd is 1/126.

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Answer:

1/126

Step-by-step explanation:

Answer attached, I hope this is the answer.

the sum of every pair of neighboring digits is odd must be odd number and even number in the neighbor. (different parity)

How to find exact value of tan 75°

Answers

tan \alpha = (sin \alpha )/(cos \alpha ) \n--------\n\ntan75^0= \frac{\big{sin75^0}}{\big{cos75^0}} \n\nsin75^0=sin(45^0+30^0)=sin45^0\cdot cos30^0+sin30^0\cdot cos45^0=\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = ( √(2) )/(2) \cdot ( √(3) )/(2) + (1)/(2) \cdot( √(2) )/(2) = ( √(6)+ √(2) )/(4)
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