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ANEK [815]
3 years ago
6

A segment with endpoints X (6, 2) and Y (- 1, - 3) is rotated 90º about the origin. What are the coordinates of X Prime and Y Pr

ime?

Mathematics
1 answer:
Minchanka [31]3 years ago
8 0
The line XY is shown in the diagram below
Coordinate X (-6, 2) rotated 90° through the origin, then coordinate X' is (2, 6)
Coordinate Y (-1, -3) rotated 90° through the origin, then coordinate Y' is (-3, -1)

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What is the true solution to 3 in 2 + in 8 = 2 in (4x)
11Alexandr11 [23.1K]
The first step for solving this equation is to determine the defined range.
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑(a^{x}) = x × ㏑(a),, transform the expression.
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑(a^{x}),, transform the expression on the left side of the equation.
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑(a^{x}),, transform the expression on the right side of the equation.
㏑((4x)²) = ㏑(2^{6})
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² = 2^{6}
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
         , x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)
5 0
2 years ago
Read 2 more answers
P(t) = t^2- t; Find p(6)
Mars2501 [29]

Answer:

P(t)=30

Step-by-step explanation:

Plug in t=6 into the equation: P(t)=t^2-t

So P(t)= (6)^2-6

P(t)=36-6

P(t)=30

4 0
2 years ago
Read 2 more answers
The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width
andre [41]

Answer:

60 yards

Step-by-step explanation:

300 = 2(30 + w) + 2(w)

300 = 60 +2w + 2w

300 = 60 + 4w

240 = 4w

60 = w

5 0
2 years ago
PLEASE HELP !!!!!!!
N76 [4]

Answer:

(B) Time (min) 2 , 3 , 7 , 9

Temperature (°C) 60.6 , 64.3 , 79.1 , 86.5

Step-by-step explanation:

The rate of change is found by using the formula for slope:

m=\frac{y_2-y_1}{x_2-x_1}

For option A, this gives us

m =(64.4-61.0)/(3-2) = 3.4/1 = 3.4

This is not more than relationship A.

For option B, we have

(64.3-60.6)/(3-2) = 3.7/1 = 3.7

This is more than relationship A.

For option C, we have

(65.3-61.8)/(3-2) = 3.5/1 = 3.5

This is not more than relationship A.

For option D, we have

(64.6-61.0)/(3-2) = 3.6/1 = 3.6

This is not more than relationship A.

7 0
3 years ago
Read 2 more answers
Reduce 36/45 to lowest terms and write the denominator in the blank.
Firlakuza [10]

Answer:

4/5

Step-by-step explanation:

Step 1:

36/45 = 12/15

Step 2:

12/15 = 4/5

Answer:

4/5

Hope This Helps :)

5 0
3 years ago
Read 2 more answers
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