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3 years ago

Help me solve the problem! Please help

Mathematics

1 answer:

Sav [38]3 years ago

6 0

Answer:

m+n=140

Step-by-step explanation:

So the angles in a triangle always add up to 180. We already know that the first angle in the triangle is 40 degrees because it's shown in the angle below the triangle. So we have 140 degrees left since 40 is taken up. That eans m+n=140

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Identify the following series as arithmetic, geometric, both, or neither.

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2 years ago

A (0, 2) and B (6,6) are points on the straight line ABCD.

elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance is denoted by: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Let's find the distance between A and B:

d = $\sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}$

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = $\sqrt{(6-a)^2+(6-b)^2}$

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0

3 years ago

Read 2 more answers

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