A survey is taken of 50 people at a concert. 30

Consider the triangle A(4,0), B(-2,4), C(0,6) What will be the equation of the altitude BM?

katovenus [111]

Answer:

BM: y = (2/3) x + 16/3 with segment length of 2.77

Step-by-step explanation:

AC formula: m = (6-0)/(0-4) = -3/2

(y-0)/(x-4) = -3/2 y = (-3/2)x + 6 ... (1)

BM slope: BM⊥ AC m = 2/3

BM formula: (y-4) / (x- -2) = (y-4) / (x+2) = 2/3

y-4 = 2/3 x + 4/3

y = (2/3) x + 16/3 ... (2) -2≤x≤0.31

intercept of AC and BM (M) from (1) and (2): (-3/2)x + 6 = (2/3) x + 16/3

(13/6) x = 2/3 x = (2/3) / (13/6) = 4/13 ≈ 0.31

y = (2/3) (4/13) + (16/3) = (8/39) + (208/39) = 216/39 = 72/13 ≈ 5.54

M (4/13 , 72/13) or (0.31 , 5.54)

segment BM = √(4/13 - -2)² + (72/13 - 4)² = √1300/169 = 2.77

4 0

3 years ago

Earth is approximately 1.5x10^8 km from the sun. how many minutes does it take to travel from the sun to the earth? the speed of

Sonbull [250]

8.33 minutes .......

6 0

3 years ago

Evaluate the following function for (3, -1): f(x, y) = 2x – 3y + xy^2

satela [25.4K]

Answer:

f(3, -1) = 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x, y) = 2x - 3y + xy²

(3, -1) is x =3 and y = -1

Step 2: Evaluate

Substitute: f(3, -1) = 2(3) - 3(-1) + 3(-1)²
Exponents: f(3, -1) = 2(3) - 3(-1) + 3(1)
Multiply: f(3, -1) = 6 + 3 + 3
Add: f(3, -1) = 9 + 3
Add: f(3, -1) = 12

7 0

3 years ago

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Q 2 PLEASE HELP ME FIGURE THIS OUT

suter [353]

Answer: IV, positive, $\frac{\pi} {6}$ , - sec $\frac{\pi} {6}$ , $\frac{2\sqrt{3}}{3}$

Step-by-step explanation:

a) Look at the Unit Circle to see that $\frac{11\pi} {6}$ = 330°, which is located in Quadrant IV.

b) The coordinate (cos θ, sin θ) for $\frac{11\pi} {6}$ is: $(\frac{\sqrt{3}} {2},\frac{-1}{2})$

sec = $\frac{1}{cos}$ = $\frac{2}{\sqrt{3}}$ which is positive

c) Since the given angle is in Quadrant IV, which is closest to the x-axis at 360° = 2π, the reference angle can be found by subtracting the given angle $\frac{11\pi} {6}$ from 2π: $\frac{12\pi} {6}$ - $\frac{11\pi} {6}$ = $\frac{\pi} {6}$

d) the reference angle is below the x-axis so the given angle is equal to the negative of the reference angle: - sec $\frac{\pi} {6}$ .

e) sec $\frac{11\pi} {6}$ = $\frac{2}{\sqrt{3}}$ = $\frac{2}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}$ = $\frac{2\sqrt{3}}{3}$

***************************************************************************************

Answer: $\frac{18\pi}{11}$ , IV, $\frac{4\pi} {11}$

Step-by-step explanation:

2π is one rotation. 2π = $\frac{22\pi}{11}$

$\frac{-26\pi}{11}$ + $\frac{22\pi}{11}$ = $\frac{-4\pi}{11}$

$\frac{-4\pi}{11}$ + $\frac{22\pi}{11}$ = $\frac{18\pi}{11}$

Convert the radians into degrees to see which Quadrant it is in by setting up the proportion and cross multiplying:

$\frac{\pi}{180}$ = $\frac{18\pi}{11x}$

π(11x) = (180)18π

x = $\frac{180(18\pi}{11\pi}$

x = 295° which lies in Quadrant IV

Since the given angle is in Quadrant IV, which is closest to the x-axis at 360° = 2π, the reference angle can be found by subtracting the angle of least nonegative value $\frac{18\pi} {11}$ from 2π: $\frac{22\pi} {11}$ - $\frac{18\pi} {11}$ = $\frac{4\pi} {11}$

***************************************************************************************

Answer: $\frac{5\pi}{3}$ , IV, $\frac{4\pi} {11}$ , $\frac{\pi} {3}$

Step-by-step explanation:

2π is one rotation. 2π = $\frac{6\pi}{3}$

$\frac{-13\pi}{3}$ + $\frac{6\pi}{3}$ = $\frac{-7\pi}{3}$

$\frac{-7\pi}{3}$ + $\frac{6\pi}{3}$ = $\frac{-\pi}{3}$

$\frac{-\pi}{3}$ + $\frac{6\pi}{3}$ = $\frac{5\pi}{3}$

This is on the Unit Circle at 300°, which is located in Quadrant IV

Since the given angle is in Quadrant IV, which is closest to the x-axis at 360° = 2π, the reference angle can be found by subtracting the angle of least nonegative value $\frac{5\pi} {3}$ from 2π: $\frac{6\pi} {3}$ - $\frac{5\pi} {3}$ = $\frac{\pi} {3}$

7 0

4 years ago

Select the true statement. A. Neither function is even. B. Only function f is even. C. Only function g is even. D. Both function

astraxan [27]

Answer:

The answer is "Option C".

Step-by-step explanation:

The graph of the even function will have both ends pointed in the same direction, while the graph of the odd function will have both ends pointed inside the reverse way. Furthermore, as the y-axis approaches, and also regular expression graph becomes symmetric. The graph of an unusual function, on either hand, is symmetric around the origin and also has rotational symmetry around the origin. They could see that the graph of function g meets a function requirement by looking at it. That graph of function f, but on the other hand, is not symmetric about its y-axis, implying that function f is not even. As both a result, g is a function that is even.

5 0

3 years ago

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