PYTHAGORAS THEROM AND TRIGONOMETRY RATIO

Mathematics

1 answer:

marysya [2.9K]3 years ago

7 0

Answer:

1) ΔACD is a right triangle at C

=> sin 32° = AC/15

⇔ AC = sin 32°.15 ≈ 7.9 (cm)

2) ΔABC is a right triangle at C, using Pythagoras theorem, we have:

AB² = AC² + BC²

⇔ AB² = 7.9² + 9.7² = 156.5

⇒ AB = 12.5 (cm)

3) ΔABC is a right triangle at C

=> sin ∠BAC = BC/AB

⇔ sin ∠BAC = 9.7/12.5 = 0.776

⇒ ∠BAC ≈ 50.9°

4) ΔACD is a right triangle at C

=> cos 32° = CD/15

⇔ CD = cos32°.15

⇒ CD ≈ 12.72 (cm)

Step-by-step explanation:

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Which of the following is correct equation for the trend line in the scatter plot? A. Y= 2/5 x -2 B. Y= 5x-1 C. Y= 5x +5 D. Y= -

Dafna11 [192]

Answer: C. Y = 5x + 5

Step-by-step explanation:

We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. See attached for a visual.

First, we will find our slope. We will use $\frac{rise}{run}$ for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.

-> Slope = 5

Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.

-> Y-intercept = 5

Lastly, we will write our equation and decide on an answer.

y = mx + b

y = (5)x + (5)

Y = 5x + 5

C. Y = 5x + 5