Find the values of a, b and c.

Mathematics

1 answer:

valina [46]3 years ago

7 0

Look at the picture.

Corresponding Angles are equal.

Alternate Angles are equal.

Consecutive Angles add up to 180°.

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3a and 45 are Consecutive Angles. Therefore

3a + 45 = 180 |subtract 45 from both sides

3a = 135 |divide both sides by 3

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(2c - 1) and 45 are Corresponding Angles. Therefore

2c - 1 = 45 |add 1 to both sides

2c = 46 |divide both sides by 2

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3a and (12b + 3) are Alternate Angles. Therefore

3(45) = 12b + 3

135 = 12b + 3 |subtract 3 from both sides

132 = 12b |divide both sides by 12

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1 year ago

The common ratio of a geometric series is \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction and the sum of the first

myrzilka [38]

Answer:

The common ratio of a geometric series is \dfrac14

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

$r = \frac{1}{4}$

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

$s_n=\frac{a_1(1-r^n)}{1-r}$

common ratio, n=4 and equate to 170.

$\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170$

$\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128$