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3 years ago

Answer the following.

Mathematics

1 answer:

Sindrei [870]3 years ago

4 0

Answer:

78.33°
71°

Step-by-step explanation:

1) The sum of angles in a triangle is 180°, so ...

(x +3)° +(x +24)° +(x -10)° = 180°

3x +17 = 180 . . . . . . . . divide by °, collect terms

3x = 163 . . . . . . . . . . . .subtract 17

x = 54 1/3 . . . . . . . . . . .divide by 3

m∠B = (x +24)° = (54 1/3 + 24)°

m∠B ≈ 78.33°

2) An exterior angle is equal to the sum of the opposite interior angles.

m∠ACD = m∠A + m∠B

(3x -10)° = (x +9)° + 105°

2x = 124 . . . . . . . . . . . . . . divide by °, add 10-x to both sides

x = 62 . . . . . . . . . . . . . . . . divide by 2

m∠A = (x +9)° = (62 +9)°

m∠A = 71°

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Write the following sum using summation notation -2/5+3/6-4/7........11/14

horrorfan [7]

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$\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )$

Step-by-step explanation:

Given: $\frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}$

To write: the given expression using summation notation

Solution:

Summation notation helps to write a long sum as a single expression.

In the summation notation, the variable $\sum$ is called the index of summation.

Let $x_1,x_2,x_3,...,x_n$ denote a set of n numbers.

Then in summation notation,

$x_1+x_2+x_3+...+x_n=\sum_{i=1}^{n}x_i$

$\frac{-2}{5}=(-1)^1\left ( \frac{1+1}{1+4} \right )\\\frac{3}{6}=(-1)^2\left ( \frac{2+1}{2+4} \right )\\\frac{-4}{7}=(-1)^3\left ( \frac{3+1}{3+4} \right )\\.\\.\\.\\\frac{11}{14}=(-1)^10\left ( \frac{10+1}{10+4} \right )\\\therefore \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}=\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )$

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