with the assumption this is a geometric sequence and thus it as an "r" common ratio, so we know that the 3rd term must be 12 * r and the 4th term must be 12 * r * r, so let's make a quick table
![\begin{array}{rll} term&value\\ \cline{1-2} a_2&12\\ a_3&12\cdot r\\\cline{1-2} a_4&(12\cdot r)r\\ &12r^2\\ &\frac{16}{3}\\\cline{1-2} a_5&12r^3\\ a_6&12r^4\\ a_7&12r^5\\ a_8&12r^6\\ a_9&12r^7 \end{array}\qquad \implies \begin{array}{llll} 12r^2=\cfrac{16}{3}\implies r^2=\cfrac{16}{12\cdot 3}\implies r^2=\cfrac{4}{9}\\\\\\ r=\sqrt{\cfrac{4}{9}}\implies r=\cfrac{\sqrt{4}}{\sqrt{9}}\implies r=\cfrac{2}{3} \end{array} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brll%7D%20term%26value%5C%5C%20%5Ccline%7B1-2%7D%20a_2%2612%5C%5C%20a_3%2612%5Ccdot%20r%5C%5C%5Ccline%7B1-2%7D%20a_4%26%2812%5Ccdot%20r%29r%5C%5C%20%2612r%5E2%5C%5C%20%26%5Cfrac%7B16%7D%7B3%7D%5C%5C%5Ccline%7B1-2%7D%20a_5%2612r%5E3%5C%5C%20a_6%2612r%5E4%5C%5C%20a_7%2612r%5E5%5C%5C%20a_8%2612r%5E6%5C%5C%20a_9%2612r%5E7%20%5Cend%7Barray%7D%5Cqquad%20%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%2012r%5E2%3D%5Ccfrac%7B16%7D%7B3%7D%5Cimplies%20r%5E2%3D%5Ccfrac%7B16%7D%7B12%5Ccdot%203%7D%5Cimplies%20r%5E2%3D%5Ccfrac%7B4%7D%7B9%7D%5C%5C%5C%5C%5C%5C%20r%3D%5Csqrt%7B%5Ccfrac%7B4%7D%7B9%7D%7D%5Cimplies%20r%3D%5Ccfrac%7B%5Csqrt%7B4%7D%7D%7B%5Csqrt%7B9%7D%7D%5Cimplies%20r%3D%5Ccfrac%7B2%7D%7B3%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
The type and number of solutions is (b) two imaginary solutions.
<h3>How to determine the type and number of solutions?</h3>
The equation is given as:
3x² + 5x + 5 = 0
A quadratic equation can be represented as:
ax^2 + bx + c = 0
Where, the discriminant (d) is
d = b^2 - 4ac
So, we have
d = 5^2 - 4 * 3 * 5
Evaluate
d = -35
The value of d is negative
This means that the equation has only imaginary solutions
Hence, the type and number of solutions is (b) two imaginary solutions.
Read more about number of solutions at
brainly.com/question/25275758
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Answer:
5 = 1/4c
Step-by-step explanation:
Answer:
the answer is seven
Step-by-step explanation:
We have a base 2 with an exponent power raised to -3
so in order to have a positive exponent factor, we take reciprocal of the number1/2^3.
now that the base has a positive exponent number, we simply multiply it the times on the exponent number, so: 1/2*2*2 = 1/8
hope this help
