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iris [78.8K]
3 years ago
14

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

Mathematics
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
Aleksandr-060686 [28]

Answer:

f(2x + 4) = -4x² - 16x - 15

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Distributive Property

<u>Algebra I</u>

  • Terms/Coefficients
  • Expanding (FOIL)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

f(x) = 1 - x²

<u>Step 2: Evaluate</u>

  1. Substitute in <em>x</em> [Function f(x)]:                                                                          f(2x + 4) = 1 - (2x + 4)²
  2. Expand [FOIL]:                                                                                                  f(2x + 4) = 1 - (4x² + 16x + 16)
  3. (Parenthesis) Distribute negative:                                                                   f(2x + 4) = 1 - 4x² - 16x - 16
  4. Combine like terms:                                                                                          f(2x + 4) = -4x² -16x - 15
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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Step-by-step explanation:

2πr

2x 3.14 x 8.1 = 50.22in

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