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2 years ago

r E c B . . a 5 3 H a 3 5 C g G m m 8 a 5 m m . 9.. B gt 8 a r n 8 . Jim r . g W 7 i 9 m 9.8. g- a w o . 1. l I i

Mathematics

1 answer:

xeze [42]2 years ago

6 0

Im sorry but i dont understand your question. can you be more pacific.

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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

2 years ago

The zeros for f(x)=x^4-4x^3-9x^2+36x are

Mrrafil [7]

X^4 - 4x^3 - 9x^2 + 36x = 0
x(x^3 - 4x^2 - 9x + 36) = 0
x(x^2(x - 4) - 9(x - 4) = 0
x(x + 3)(x - 3)(x - 4) = 0

the zeroes are -3, 0, 3, 4 Answer

3 0

2 years ago

Millie has 15 counters. Sam has 8 counters. Write a sentence comparing how many counters each child has.

masya89 [10]

Answer:

Millie has 15 counters, and Sam has 8.

Step-by-step explanation:

7 0

2 years ago

If you apply these changes to the linear parent function, f(x) = x, what is the equation of the new function?

Maru [420]

Answer:

A, g(x) = 7x + 5

Step-by-step explanation:

applying these translations to the parent function f(x) = x, we would get the following equation:

g(x) = 7x + 5

a vertical compression is written before the parent function (in this case f(x)=x), and a shift up is written next to the function. both of these are without parentheses

the answer would be A, g(x) = 7x + 5

8 0

2 years ago

0 1 2 3. What is the least number that can be made

Black_prince [1.1K]

I think it would be .0123

7 0

3 years ago