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3 years ago

What is the sum of the first 7 terms of the geometric series: -8 + (-4) + (-2) + 1 + 1/2+...

1 answer:

s2008m [1.1K]3 years ago

4 0

$a_1=-8;\ a_2=-4;\ r=a_2:a_1\to r=-4:(-8)=\dfrac{1}{2};\ n=7\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\subtitute:\\\\S_7=\dfrac{-8\left[1-\left(\dfrac{1}{2}\right)^7\right]}{1-\dfrac{1}{2}}=\dfrac{-8\left(1-\dfrac{1}{128}\right)}{\dfrac{1}{2}}\\\\=\dfrac{-8\cdot\dfrac{127}{128}}{\dfrac{1}{2}}=-\dfrac{127}{16}\cdot\dfrac{2}{1}=-\dfrac{127}{8}=-15\dfrac{7}{8}$

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Ad libitum [116K]

In order for the triangle to be isosceles, we have to set two lengths of the triangle equal to each other.

Let's take the lengths 5x-12 and x+20 and set them equal to each other.

5x - 12 = x + 20

Combine like terms by moving them over to their respective sides.

Subtract x from both sides of the equation.

4x - 12 = 20

Add 12 to both sides of the equation.

4x = 32

Divide both sides by 4.

x = 8

Check your answer by substituting.

5x - 12 = x + 20

5(8) - 12 = 8 + 20

40 - 12 = 28

28 = 28

Solution: x = 8

5 0

3 years ago

WILL MARK BRAINLIEST FEELING LAZY WORTH 15 POINTS

Zinaida [17]

The irrational numbers are: √8, √10 and √15

Step-by-step explanation:

A rational number is a number that can be written in the form p/q where p&q are integers and q≠0.

"All the numbers whose square root is not a whole number and has an infinite number of digits after decimal, are irrational numbers"

So in the given options

$\sqrt{4} = 2$

Which can be written in the required form so √4 is a rational number

$\sqrt{8}=2.828427124746190097603.....$

√8 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

$\sqrt{10}=3.16227766016837933....$

√10 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

$\sqrt{15}=3.87298334620.....$

√15 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number

$\sqrt{36} = 6$

Which can be written in the required form so √36 is a rational number

Hence,

The irrational numbers are: √8, √10 and √15

Keywords: Rational numbers, Irrational numbers

Learn more about rational numbers at:

#LearnwithBrainly

4 0

3 years ago

By 2 2 1 S ut  at , where S is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time. Whi

slamgirl [31]

Answer:

Step-by-step explanation:

Given the equation of motion;

S = ut + 1/2 at² where;

u is the initial velocity,

a is the acceleration, and;

t is the time.

We are to express a in terms of u, t and S

Making a the subject of the formula;

S = ut + 1/2 at²

S-ut = 1/2at²

2(S-ut) = at²

a = 2(S-ut)/t²

Hence the acceleration a in terms of other variables is expressed as a = 2(S-ut)/t²

8 0

3 years ago

Which ordered pair is a solution of the equation? y-3=5(x-2) A.) (2,3) B.) (3,2) C.) Both D.) Neither

White raven [17]

Answer:

A is the only solution.

Step-by-step explanation:

A simple way to solve it is to plug in the x and y values

For A, we plug in 2 for x and 3 for y

3-3=5(2-2)

0=5(0)

0=0

Ordered pair A is a solution

For B, plug in 3 for x and 2 for y

2-3=5(3-2)

-1=5(1)

-1 does not equal 5

Therefore only A is a solution

5 0

3 years ago

Find an explicit formula for the arithmetic sequence 12, 5, -2, -9,...

Vadim26 [7]

Answer:

an = 12 -7(n-1)

an = 19-7n

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

an = a1 +d(n-1) where a1 is the first term and d is the common difference

a1 =12

We find d by taking the second term and subtracting the first term

d = 5-12

d = -7

an = 12 -7(n-1)

We can simplify this

an = 12 -7n+7

an = 19-7n

4 0

3 years ago