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2 years ago

Find the value of x. A.75 B.25 C.35 D.105

Mathematics

1 answer:

Tcecarenko [31]2 years ago

8 0

Answer:

B. 25

Step-by-step explanation:

$3x \degree = 75 \degree \\ (alternate \: \angle \: s) \\ \\ 3x = 75 \\ \\ x = \frac{75}{3} \\ \\ x = 25$

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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

Studies show that a typical giant hummingbird can flap its wings once in 0.08 of a second.

Licemer1 [7]

Answer:

a. 90

b. 360

Step-by-step explanation:

The time taken by humming bird to flap its wings= 0.08 sec

by flying 7.2 seconds a typical giant hummingbird flap its wings $\frac{7.2}{0.08}$ times

= 90 times

Since, A ruby-throated hummingbird can flap its wings 4 times faster than a giant hummingbird, it will flap its wings in every 0.02 sec

so in 7.2 seconds it will flap $\frac{7.2}{0.02}$ times = 360 times

4 0

3 years ago

Given that x = 5.4 m and 0 = 26°, work out BC rounded to 3 SF.

bagirrra123 [75]

Answer:

BC ≈ 4.85 m

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos26° = $\frac{adjacent}{hypotenuse}$ = $\frac{BC}{AC}$ = $\frac{BC}{5.4}$ ( cross- multiply )

5.4 × cos26° = BC , then

BC ≈ 4.85 m ( to 3 s f )

4 0

2 years ago

I cannot figure this problem out

sveta [45]

Answer:

31 customers

Step-by-step explanation:

First, find the percentage of customers who wore a large. This is 26/(26 + 52), or 1/3 of the customers. Take 1/3 of the new customers, and 1/3 of 93 is 31. 31 customers will wear a size large.

Hopefully this helps! Let me know if you have any questions

7 0

3 years ago

Identify the cross section that results from slicing the three-dimensional figure.

dangina [55]

Answer:

Step-by-step explanation:

7 0

2 years ago

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