Match each quadratic function to its graph.

What is the sum of the infinite geometric series 9−6+4−83+...9-6+4-83+...??

vivado [14]

Successive terms have a common factor of $-\dfrac23$ , which means the $n$ th partial sum of the series can be written as

$S_n=9-6+4-\dfrac83+\cdots+9\left(-\dfrac23\right)^{n-1}$
$S_n=9\left(1+\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\cdots+\left(-\dfrac23\right)^{n-1}$

$\implies-\dfrac23S_n=9\left(\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\left(-\dfrac23\right)^4+\cdots+\left(-\dfrac23\right)^n\right)$

$\implies S_n-\left(-\dfrac23\right)S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$\dfrac53S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$S_n=\dfrac{27}5\left(1-\left(-\dfrac23\right)^n\right)$

As $n\to\infty$ , the geometric term vanishes, leaving you with

$S=\displaystyle\lim_{n\to\infty}S_n=\dfrac{27}5$

7 0

3 years ago

Are the two triangles similar? how do you know

Zinaida [17]

I forgot what they’re called but the angles opposite to each other are the same degree. It’s a theorem, just search up the name

7 0

3 years ago

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa

12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

Samuel traveled 3 km/h faster than Heather
After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

#LearnwithBrainly

3 0

3 years ago

The fence along the length of a ranch measures 4,450.5 meters and the fence along the width of a ranch measures 2,890 meters.

lawyer [7]

Given:Length = 4,450.5 metersWidth = 2,890 meters
1 kilometer = 1,000 meters
Length: 4,450.5 meters * 1km/1,000 meters = 4,450.5 km/1,000 = 4.4505km
Width: 2,890 meters * 1km/1,000 meters = 2,890 km/1,000 = 2.89 km
4.4505 km - 2.89 km = 1.5605 km
The length of the fence is 1.5605 km longer than the width of the fence.

3 0

3 years ago

How to add fractions? with unlike denominators

stellarik [79]

Answer:

The recipe calls for 19/12 or 1 7/9 cups.

Step-by-step:

In order to get this answer, we have to add all three fractions together. First, we have to find the LCM (Least Common Multiple) between the three denominators:

2: 2, 4, 6, 8, 10, 12

3: 3,6,9,12

4: 4,8,12

The LCM between these three denominators is 12.

4x3=12

2x6=12

3x4=12

You now multiply the numerator by the same number you multiplied by for the denominator in order to get 12:

3/4 becomes 9/12

1/2 becomes 6/12

1/3 becomes 4/12

We now add all the fractions together:

9/12+6/12+4/12= 19/12

We got 19/12 but the answer is an improper fraction so we turn it into a mixed number:

12x1=12 (7 remaining)

This is written as 1 7/12.

Hope this helps! :)

<h3>CloutAnswers</h3>

3 0

3 years ago