Given the labeled diagram at the left. Find X.

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

6 0

Answer:

x = 55°

Step-by-step explanation:

Measure of central angle is equal to the measure of the corresponding minor arc

Therefore, m(central angle) = 70°

Since, radii of same circle are equal

Therefore, measure of the angles opposite to them are also equal.

So, by interior angle sum postulate of a triangle:

x + x + 70° = 180°

2x = 180° - 70°

2x = 110°

x = 110°/2

x = 55°

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Sid starts with savings of £13

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Answer:

The savings of Sid and Tim will be in 17:9 in 6 weeks.

Step-by-step explanation:

Initial savings of Sid = £ 13

Initial savings of Tim = £ 0

For each successive week Sid saved = £ 3.5

For each successive week Tim saved = £ 3

Let us assume that after "x weeks" the amounts of Sid and Tim are in ratio 17:9.

If Sid saves £ 3.5 in one week, in x weeks he will £ 3.5x. Since he had £ 13 initially, total amount he would have in x weeks will be £ (13 + 3.5x)

If Time saves £ 3 one week, in x weeks he will save £ 3x. Since, he didn't have any money initially, in x weeks he would have saved £ 3x

The ratio of their savings in x weeks would be 17:9

So,

Sid's saving : Tim's saving = 17 : 9

Using the values of expressions, we get:

$13+3.5x:3x=17:9\\\\\frac{13+3.5x}{3x}=\frac{17}{9}\\\\ 9(13+3.5x)=17(3x)\\\\ 117+31.5x=51x\\\\ 117=51x-31.5x\\\\ 117=19.5x\\\\ x=\frac{117}{19.5}\\\\ x=6$