1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
babunello [35]
4 years ago
5

What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-

half) Superscript n minus 1
Mathematics
2 answers:
11Alexandr11 [23.1K]4 years ago
8 0

Step-by-step explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = -144, and r = ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288

VLD [36.1K]4 years ago
4 0

Answer:

The answer is C (40)

Step-by-step explanation:

You might be interested in
Which equation represents a proportional relationship that has a constant of proportionality equal to StartFraction 4 over 5 End
e-lub [12.9K]

Answer:

  y=\dfrac{4}{5}x

Step-by-step explanation:

A proportional relationship is modeled by the equation ...

  y = kx

When the constant of proportionality (k) is 4/5, this equation becomes ...

  y = (4/5)x

5 0
4 years ago
Read 2 more answers
Q14
posledela

Answer:

42.6cm

Step-by-step explanation:

The sum total of all the sides of the shape is the perimeter of the shape. Hence;

Perimeter = x+3 + 4 + x+9 + 2x+5

Perimeter = 4x + 21

Given

Area of the figure = 75cm^2

Area = (x+3)(2x+5) + (2x+1)(6)

75 = 2x²+5x+6x+15+12x+6

75 =  2x²+23x+21

2x²+23x+21-75 = 0

2x²+23x-54 = 0

x = -23±√23²-4(2)(-75)/4

x = -23±√529+600/4

x = -12±√1129/4

x = -12+33.6/4

x = 21.6/4

x = 5.4

Recall that;

Perimeter = 4x+21

Perimeter = 4(5.4) + 21

Perimeter = 21.6+21

Perimeter = 42.6cm

Hence the perimeter is 42.6cm

8 0
3 years ago
What is the property of 6+9+x(4×5)
UNO [17]
Addition, distributive, and multiplication property
6 0
3 years ago
What value(s) of x will make each equation below true
Dahasolnce [82]

We need to solve for x. Let's try problem b:

2x-6=3x+1-x-7

Let us first combine line terms. 3x and -x as well as 1 and -7 can be combined. Let's do that:

2x-6=2x-6

Since this is true, your answer would be:

All real numbers

------------------------------------------------------------------

Let's solve for problem c:

3x+1=43

Let's isolate x, so subtract 1 from both sides:

3x=42

Since x can't have a coefficient, divide both sides by 3:

\frac{3x}{3}=\frac{42}{3}

x=14

So, only the value of 14 would make this equation true.

------------------------------------------------------------------

Let's try problem d:

4x-1=4x+7

Let's get our whole numbers on the right side. Add 1 to both sides:

4x=4x+8

Subtract 4x from the right side on both sides:

0=8

Since this is not true, your answer would be:

No solution

7 0
4 years ago
The proof for the product property of logarithms requires simplifying the expression logb(bx y) to x y. Which property is used t
masya89 [10]

You can use the properties of logarithm to derive the simplified form of the given expression.

The simplification of the given expression requires the given below properties of logarithm

  • log_a(b^c) = c \times log_a(b)\\\\
  • log_b(b) = 1

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

  • b = log_a(c)

Some properties of logarithm are:

log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1

<h3>Using the above properties, to get to the simplified form of the given expression</h3>

The given expression is

log_b(b^{x+y})

Using the property log_a(b^c) = c \times log_a(b)\\\\, we get

log_b(b^{x+y}) = (x+y)\times log_b(b)

Using the property log_b(b) = 1, we get

log_b(b^{x+y}) = (x+y)\times log_b(b) = (x+y) \times 1 = x + y

Thus,

The simplification of the given expression requires the given below properties of logarithm

  • log_a(b^c) = c \times log_a(b)\\\\
  • log_b(b) = 1

Learn more about logarithms here:

brainly.com/question/20835449

3 0
2 years ago
Read 2 more answers
Other questions:
  • Peter has 18 oranges, 27 pears, and 12 bananas. He wants t o make fruit baskets with the same number of each fruit in each baske
    14·2 answers
  • What is the following product?
    13·2 answers
  • 91284 the nearest ten thousand
    7·2 answers
  • Find the radius of a circle with a circumfrence of 64pi inches
    11·1 answer
  • Simplify Expression-
    15·1 answer
  • A machine can produce 27 inches of ribbon every 3 minutes. How many feet of ribbon can the machine make in one hour? Explain.
    6·1 answer
  • 7th grade math help me pleaseeee
    12·1 answer
  • Find the next three terms in the sequence. 24,20,16,12…. (If you could explain it that would be great too. It’s a bit confusing)
    13·2 answers
  • Point q is located on the coordinate grid at (-9.73,-3.32) in which quadrant is point q called
    14·1 answer
  • Referring to question 1, what is the predicted strength of a weld with a diameter of 51?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!