3. A certain 50 cm spring will stretch (in
cm) the weight (in kg) attached to
it. How long will the spring be if a 35
kg weight is attached to it?

Answer:Example 1:

Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.

S8=1(1−28)1−2=255

Example 2:

Find S10 of the geometric sequence 24,12,6,⋯.

First, find r.  

r=r2r1=1224=12

Now, find the sum:

S10=24(1−(12)10)1−12=306964

Example 3:

Evaluate.

∑n=1103(−2)n−1

(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)

Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023  

In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1.  Then as n increases, rn gets closer and closer to 0.  To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

Example 4:

Find the sum of the infinite geometric sequence

27,18,12,8,⋯.

First find r:  

r=a2a1=1827=23

Then find the sum:

S=a11−r

S=271−23=81

Example 5:

Find the sum of the infinite geometric sequence

8,12,18,27,⋯ if it exists.

First find r:  

r=a2a1=128=32

Since r=32 is not less than one the series has no sum.

Step-by-step explanation:

Answer:

6 jellybean

Step-by-step explanation:

Given that:

Esmeralda received a bag of jellybean the contains regular flavored jelly beans and surprise jelly bean.

Consider the regular flavored jellybean to be = r;  &

The surprise jelly bean.= s

From the bag, there are 40 jellybeans of which 15% is surprise jellybean.

Therefore the number of expected surprise jellybeans is:

= total number of jellybeans × percentage of surprise jellybean

= 40 × (15 /100)

= 6 jellybean

If  6 surprise jellybean is presented in the bag; then the number of regular flavored jellybean = 40 - 6 = 34 regular flavored jellybean

Answer:

3 cups per batch

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

What is 9 divided by 3.... 3 ok so that is your answer. Hope this helped you!! Give brainliest..

Answer:

y=-1/8x +4

Step-by-step explanation:

1. First, write the equation in point-slope form: y-y1=m(x-x1)

y-1=-1/8(x-24)

2. Distribute -1/8 to x and -24

-1/8 times x = -1/8x

-1/8 times -24 = 3

y-1=-1/8x+3

3. Add 1 to both sides

y=-1/8x +4

Step-by-step explanation:

1/8+1/4+1/8=1/8+2/8+1/8=4/8=1/2

Answer:

1,2,1, 4, 1

These numbers correspond with the boxes in order from left to right.

Answer:

D. 3,158

Step-by-step explanation:

h(-67) means to plug the x in h(x)=-49x-125 into the function as -67

The function will then be:

h(-67)=-49(-67)-125

Multiply -49 and -67

h(-67)=3283-125

subtract

h(-67)=3158

so the answer is D

Hope this helps!  

Answer:

2 is the slope

Step-by-step explanation:

the equation is y=mx+b so if it is

y= 2x+7 that means the slope is 2

Answer:

2

Step-by-step explanation:

This equation is in y=mx+b form.

Slope = m

Y-intercept = b

This will give you the slope of 2 :)

Answer:

Do you need all 6 of them?

Answer and Step-by-step explanation:

w = -1

x = 6

y = 3

z = -2

32. Plug -2 for z and 6 for x.

(9(-2)) / 6

-18 / 6

3

33.

[tex]6^{2} - 3^{2}[/tex]

36 - 9

27

34.

[tex]3^{2} - (-2)^{2}[/tex]

9 - 4

5

35.

[tex]\frac{2(6)+3}{-2 + -1} \\\\\frac{12+3}{-3}\\\\\frac{15}{3} \\\\5[/tex]

36.

[tex]\frac{3(6)-(-2)}{-(-1)} \\\\\frac{18 + 2)}{1)} \\\\\frac{20}{1} \\\\20[/tex]

37.

[tex]\frac{6 + -1}{3 - (-2)} \\\\\frac{5}{5}\\\\1[/tex]

#teamtrees #WAP (Water And Plant) #SPEW (Society for the Promotion of Elfish Welfare)

Answer:

8/3

Step-by-step explanation:

Use rise over run. Find two points that are at perfect points. For example (3,2). Don't use something like (2.45, 7.34), That will make it difficult. I used (0, 4) and (-3, 4). To get from (-3,4) to (0,4), you have to go up 8 and to the right 3. Always count up or down first and then side to side.  

9514 1404 393

Answer:

  19.5 hours

Step-by-step explanation:

The number in the dish at time t (in hours) can be described by ...

  n(t) = 100·2^(t/26)

We want to find t such that ...

  n(t) = 168

  100·2^(t/26) = 168

  2^(t/26) = 1.68 . . . . . . divide by 100

  (t/26)log(2) = log(1.68) . . . . . take logarithms

  t = 26·log(1.68)/log(2) ≈ 19.459992 . . . . divide by the coefficient of t

  t ≈ 19.5 . . . hours

It would be about 19.5 hours until there are 168 bacteria.

Answer:

The vertical asymptotes occur at x = 4 and x = -4

The zero of the function is (0, 0)

Step-by-step explanation:

The given function is [tex]f(x) = \dfrac{4\cdot x}{x^2 - 16}[/tex]

Therefore, we have;

[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = \dfrac{4\cdot x}{(x - 4) \cdot (x + 4)}[/tex]

The asymptote is given at the value of x for which the denominator = 0, therefore, the asymptote are the values of x that make the denominator of the equation equal to zero, which are given as follows

For the asymptote, the denominator = x² - 16 = (x - 4)·(x + 4) = 0

Therefore, the vertical asymptotes are the lines x = 4 and x = -4.

The zero of the function is given as follows;

[tex]f(x) = \dfrac{4\cdot x}{x^2 - 16} = 0[/tex]

Therefore, 4·x = (x - 4)·(x + 4) × 0 = 0

x = 0/4 = 0

Therefore, when f(x) = 0, x = 0 and the zero of the function = (0, 0).

Answer:

-6

Step-by-step explanation:

The formula of slope Y2-Y1/X2-X1

so you actually use this formula equal to -2

10-6/X-(-4) = -2

Step-by-step explanation:

2002 can be rounded to a compatible number such as 2000.

2000 / 2 = 1000.

They each received around 1000 marbles.

Answer (3 different forms):

1st Form:

[tex]2+-\frac{1}{3} \sqrt{6} <x<2+\frac{1}{3} \sqrt{6}[/tex]

2nd Form:

[tex]-\sqrt\frac{2}{3}+2<x<\sqrt\frac{2}{3}+2[/tex]

3rd Form:

[tex]\frac{6-\sqrt{6}}{3}<x< \frac{6+\sqrt{6}}{3}[/tex]

Or

[tex](\frac{6-\sqrt{6}}{3}),(\frac{6+\sqrt{6}}{3})[/tex]

Step-by-step explanation:

You can see that I put three different forms of answers, but they are all still equivalent answers. The reason why I got three different answers is because I put the inequality in three different calculators and they all got me different answers, but all three are still equivalent. The following three attachments are images of the three calculators that I used to solve.

Hope this helps and answers your question! :)

Answer:

y=−2/5x+4/5y

Step-by-step explanation:

Hope's this helps

Answer: 22 Marbles

Step-by-step explanation:

1,518 - 1,320 = 198

198 ÷ 9 = 22

Answer:

22 marbles

Step-by-step explanation:

1518 - 1320 = 198

198/9 = 22

Answer:

4

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

4.572 meters

Step-by-step explanation:

hope it helps, mark brainliest please

Answer:

4.572 meters; 4.6 rounded.

Step-by-step explanation:

Multiply the foot value by 0.3048 or divide by 3.280839895

15x0.3048

=4.572

Answer:

y= -5x/4 + 3

Step-by-step explanation:

To find slope, use the equation [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], so m(the slope) = (-7+2)/(8-4) = -5/4.

Now let us use (4,-2) in the equation [tex]y-y_1=m(x-x_1)[/tex].

So y - (-2) = (-5/4)(x - 4) (equation of the line)

y + 2 = -5/4(x - 4)

y + 2 = -5x/4 + 5

y= -5x/4 + 3 (slope-intercept form, also known as fully reduced form)

You could also use (8,-7) instead of (4,-2).

Answer:

(1 /a+ 1/b) (a+b-c)+(1/b+1/c) (b+c-a) + (1/c+1/a)(c+a-b)

plz solve this question

Step-by-step explanation:

3 is the ans

Answer:

1/2 of her book

Step-by-step explanation:

1/6 + 2/6 = 3/6 = 1/2

Answer:

I think that it is 1/2 of her books

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

It is 52

Step-by-step explanation:

Hope this helped have an amazing day!

9514 1404 393

Answer:

  1) W = 10

  2) x = 33/2

Step-by-step explanation:

These are 2-step linear equations. Step 1: Add the opposite of the constant on the right. Step 2: Divide by the coefficient of the variable.

__

1) 15 = 2W -5

  20 = 2W . . . . . add +5

  10 = W . . . . . . . divide by 2

__

2) 24 = 2x -9

  33 = 2x . . . . . add +9

  33/2 = x . . . . divide by 2

_____

As always, whatever you do to one side of the equation must also be done to the other side. That is, the same number is added to both sides; both sides are divided by the same number.

Answer:

5%

Step-by-step explanation:

Given that:

Principal = $3000

Simple Interest paid = $600

Period = 4 years

Simple interest = principal * rate * time

$600 = $3000 * rate * 4

$600 = $12000 * rate

Rate = $600 /$12000

Rate = 0.05

Hence, simple interest rate paid = (0.05 * 100%) = 5%

Answer:

$600

Step-by-step explanation:

because 40 hours at a rate of $15/hours adds up to $600.

(40*15= 600)

Answer:

Alternate Interior Angles

Step-by-step explanation:

Angle 3 and angle 6 are inside the parallel lines and are opposite sides of the transversal line so, it'd be alternale interior angles.

Answer:

The distance between the two points is [tex]\sqrt{26}[/tex]

Step-by-step explanation:

The formula of the distance between two points (x1, y1) and (x2, y2) is

d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

∵ The points are (-1, 3) and (4, 2)

∴ x1 = -1 and x2 = 4

∴ y1 = 3 and y2 = 2

→ Substitute them in the formula of the distance above

∵ d = [tex]\sqrt{(4--1)^{2}+(2-3)^{2}}[/tex]

∴ d = [tex]\sqrt{(4+1)^{2}+(-1)^{2}}[/tex]

∴ d = [tex]\sqrt{(5)^{2}+1}[/tex]

∴ d = [tex]\sqrt{25+1}[/tex]

∴ d = [tex]\sqrt{26}[/tex]

∴ The distance between the two points is [tex]\sqrt{26}[/tex]

Answer:

he will be 17 in

Step-by-step explanation:

Answer:

it will be 1.75$

Step-by-step explanation:

56-18

38x2.25

117$ - 85.5$

31.5 / 18