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3 years ago

What is the value of x?

Mathematics

1 answer:

Yuliya22 [10]3 years ago

4 0

Answer:

Step-by-step explanation:

∠QRT and ∠SRT are supplementary angles,

therefore m∠QRT + m∠SRT = 180°.

(45x)° + m∠SRT = 180° <em>subtract (45x)° from both sides</em>

m∠SRT = 180° - (45x)°

We know: the sum of the measures of the angles of the triangle is equal to 180 °. Therefore we have the equation:

(180 - 45x) + (57 + x) + 25x = 180 <em>combine like terms</em>

(-45x + x + 25x) + (180 + 57) = 180

-19x + 237 = 180 <em>subtract 237 from both sides</em>

-19x = -57 <em>divide both sides by (-19)</em>

x = 3

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<u>Checkmark:</u>

✓ The sequence is geometric

✓ The recursive formula for the sequence is $An = A_{n-1}(-3)$ ; $A_{1} =-2$

✓ The explicit formula for the sequence is $t_{n} = (-2) (-3)^{n-1}$

Step-by-step explanation:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by -3 gives the next term.

r = -3

$t_{n} = t_{1} r^{n-1}$

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Substitute the values in the equation:

$t_{n} = (-2) (-3)^{n-1}$

This is a explicit formula since the next value depends on the position of n (1, 2, 3 .etc)

The recursive formula would be:

$An = A_{n-1}(-3)$

Checkmark:

✓ The sequence is geometric

✓ The recursive formula for the sequence is $An = A_{n-1}(-3)$ ; $A_{1} =-2$

✓ The explicit formula for the sequence is $t_{n} = (-2) (-3)^{n-1}$

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