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3 years ago

Show your work on the 2 questions shown in the picture.

Mathematics

1 answer:

Montano1993 [528]3 years ago

4 0

Answer:

1. The answer is b ≥ 4

2. m = -11; m> -11

Step-by-step explanation:

1. solve your inequality step-by-step.

-4b + 9 ≤ -7

subtract nine from both sides.

-4b + 9-9 ≤ -7-9

-4b ≤ -16

then divide both sides by 4,

-4b/4 and -16/4,

you get: b ≥ 4

2. to solve:

2m+18>-4

subtract 18 from both sides.

2m + 18 -18 >-4 -18

= 2m>-22,

divide both sides by 2,

2m/2, -22/2

you end up with: m > -11

Hope this helps. Graph attached

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<u>Step-by-step explanation:</u>

(1) (12, 18, 27, ...)

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$a_n=a_o(r)^{n-1}\\\\Given:a_o=12,\ r=\dfrac{3}{2}\\\\\\Equation:\\a_n =12\bigg(\dfrac{3}{2}\bigg)^{n-1}\\\\\\\\9th\ term:\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{9-1}\\\\\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{8}\\\\\\.\quad =\large\boxed{\dfrac{19643}{64}}$

$(2)\qquad \bigg(\dfrac{1}{16},\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2}\bigg)\\\\\\\text{The common ratio is}:\\\\r=\dfrac{a_{n+1}}{a_n}\quad r=\dfrac{\frac{1}{8}}{\frac{1}{16}}=\boxed{2}\quad \rightarrow \quad r=\dfrac{\frac{1}{4}}{\frac{1}{8}}=\boxed{2}$

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$a_n=a_o(r)^{n-1}\\\\Given:a_o=\dfrac{1}{16},\ r=2\\\\\\Equation:\\a_n =\dfrac{1}{16}(2)^{n-1}\\\\\\\\9th\ term:\\a_9=\dfrac{1}{16}(2)^{9-1}\\\\\\a_9=\dfrac{1}{16}(2)^{8}\\\\\\.\quad =\large\boxed{16}$

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