73,404+27,865 what does it equal

Maggie graphed the image of a 90 counterclockwise rotation about vertex A of . Coordinates B and C of are (2, 6) and (4, 3) and

Lemur [1.5K]

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates $(x_A,y_A)$

Vectors AB and AB' are perpendicular, then

$\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0$

Vectors AC and AC' are perpendicular, then

$\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0$

Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$

Then

$y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2$

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

8 0

3 years ago

Construct a stem-and-leaf plot of the test scores 67 comma 72 comma 85 comma 75 comma 89 comma 89 comma 87 comma 90 comma 99 co

VMariaS [17]

Answer:

Option C. Stem Leaves 6 7 7 2 5 8 5 7 9 9 9 0 9 10 0

Option D.

Step-by-step explanation:

The data values are 67, 72, 85, 75, 89, 89, 87, 90, 99 and 100.

Arranging the data values in ascending order

67, 72, 75, 85, 87, 89, 89, 90, 99, 100

The stem and lead plot can be shown under and stem is denoted as "S" whereas leaves are denoted as "L".

S L

6 7

7 2 5

8 5 7 9 9

9 0 9

10 0

The longer row of stem indicates the higher frequencies and so the length of rows are similar to the heights of bars in histogram.

5 0

3 years ago

What fraction is equivalent to 3/9

Crazy boy [7]

Answer:

the simplified version of 3/9 would be 1/3 but other equivalent fractions of 3/9 would include but are not exclusive to: 2/6, 4/12, 5/15, and etc.

6 0

3 years ago

Read 2 more answers

Evaluate each logarithm. Do not use a calculator. Log (125)(1/25)

svetlana [45]

Answer:

-2/3

Step-by-step explanation:

Log125(1/25)=x

Raise each side to the base of 125

125^Log125(1/25)=125^x

1/25 = 125^x

Rewrite 25 as a power of 5 and 125 as a power of 5

1 / 5^2 = 5^3^x

The if power is in the denominator, we can bring it to the numerator by making it negative

5^-2 = 5^3^x

We know that a^b^c = a^(b*c)

5^-2 = 5^(3*x)

Since the bases are the same, the exponents are the same

-2 = 3x

Divide by 3

-2/3 = 3x/3

-2/3 =x

6 0

3 years ago

Jaime is 9 years old today. Assume that on every one of his birthdays since

Thepotemich [5.8K]

<u>Answer:</u>

The given statement is False statement

<u>Explanation:</u>

We are given that Jaime has blown out a number of candles equal to his age on each of his birthday till now and he is 9 years old now so the total number of candles blown by him all his life is given by the

arithmetic series

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 and

not the arithmetic series

0 + 1 + 2 + 3+ 4+ 5+ 6+ 7+ 9 as given

so the given statement is false.

6 0

3 years ago