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3 years ago

14

What is the value of the geometric sequence for which a1=10 and r=0.5?

1 answer:

tiny-mole [99]3 years ago

3 0

The formula for an infinite geometric sequence is the following:

$S_{∞}= \frac{a_{1}}{1-r}$

Just substitute the values of $a_{1}$ and r into the formula.

$S_{∞}=\frac{10}{1-0.5}$
$S_{∞}=\frac{10}{0.5}$
$S_{∞}= 20$

Therefore, the answer is 20.

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(2A)<br> Find f(2x + 4) for f(x) = 1 - x2

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Answer:

f(2x + 4) = -4x² - 16x - 15

General Formulas and Concepts:

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Addition
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Step-by-step explanation:

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8 0

2 years ago

Choose the option that best answers the question.The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If Angl

Sunny_sXe [5.5K]

Answer:

The correct option is 1.

Step-by-step explanation:

Given information: The coordinates of a right angled triangle ABC are A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6). Angle ABC = 90°.

It means AB and BC are legs of the right angled triangle ABC.

Side AB lies on the y-axis because the x-coordinate of both A and B is 0.

Two legs are perpendicular to each other. So, BC must be parallel to x-axis and the y-coordinate of both B and C is must be same.

$4a-5=2a+6$

$4a-2a=5+6$

$2a=11$

Divide both sides by 2.

$a=\frac{11}{2}$

The value of a is 2. So the coordinates of triangle ABC are

$B(0,4a-5)=B(0,4(\frac{11}{2})-5)\Rightarrow B(0,17)$

$C(2a+1,2a+6)=C(2(\frac{11}{2})+1,2(\frac{11}{2})+6)\Rightarrow C(12,17)$

The area of a triangle is

$Area=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The area of triangle ABC is

$Area=\frac{1}{2}|0(17-17)+0(17-0)+12(0-17)|$

$Area=\frac{1}{2}|12(-17)|$

$Area=\frac{1}{2}|-204|$

$Area=\frac{1}{2}(204)$

$Area=102$

The area of triangle ABC is 102. Therefore the correct option is 1.

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3 years ago

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Charra [1.4K]

Step-by-step explanation:

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