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3 years ago

A chain 5 links long is joined to a chain 7 links long. How many links long is the resulting chain

Mathematics

2 answers:

Anna [14]3 years ago

3 0

12 links long because 5 + 7 = 12

lapo4ka [179]3 years ago

3 0

The chain is 12 link long

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A certain ball is dropped from a height of x feet. It always bounces up to 2/3 x feet. Suppose the ball is dropped from 10 feet

galina1969 [7]

Given that if a ball is dropped from x feet, it bounces up to 2/3 x feet.

And the ball is dropped from 10 feet, that is x=10 feet,

So,before the first bounce it travels 10 feet distance.

Between first and second bounce it travels $\frac{2}{3}* 10 + \frac{2}{3} * 10 = 20*(\frac{2}{3})$

Between second and third bounce, it travels $20*(\frac{2}{3})^{2}$

Between third and fourth bounce, it travels $20*(\frac{2}{3}) ^{3}$

Like that between 29th and 30th bounce, it travels $20*(\frac{2}{3} )^{29}$

Hence total distance traveled is

$10+20*(\frac{2}{3} )+20*(\frac{2}{3})^{2} + 20*(\frac{2}{3}) ^{3}+......+20*(\frac{2}{3})^{29}$

= $10+20[(\frac{2}{3}) +(\frac{2}{3}) ^{2} +(\frac{2}{3}) ^{3} +.....+(\frac{2}{3} )^{29} ]$

= $10+20[\frac{\frac{2}{3}*(1-(\frac{2}{3})^{29}) }{1-\frac{2}{3} }]$

= 10+20*2*(1- $(\frac{2}{3}) ^{29}$ )

= 49.9997 feet ≈ 50 feet approximately.

7 0

3 years ago

Read 2 more answers

Can a triangle have sides with the given lengths?<br><br> (a) 4, 7, 10<br><br> (b) 8, 9, 17

soldier1979 [14.2K]

Answer:

yes it can be scaline triangle

8 0

2 years ago

Solve the inequality. Graph the solution set, and write it using interval notation. |5x+4|less than or equal to 10

aniked [119]

we have the inequality

$\lvert5x+4\rvert\leq10$

step 1

Find out the first solution (positive case)

$\begin{gathered} +(5x+4)\leq10 \\ 5x\leq10-4 \\ 5x\leq6 \\ x\leq\frac{6}{5} \\ x\leq1.20 \end{gathered}$

The first solution is all real numbers less than or equal to 1.20

Interval (-infinite,1.20]

step 2

Find out the second solution (negative case)

$-(5x+4)\leq10$

Multiply by -1 both sides

$\begin{gathered} (5x+4)\ge-10 \\ 5x\ge-10-4 \\ 5x\ge-14 \\ x\ge-\frac{14}{5} \\ x\ge-2.8 \end{gathered}$

The second solution is all real numbers greater than or equal to -2.8

the interval [-2.8, infinite)

step 3

Find out the solution to the given inequality

The solution is

[-2.8, infinite) ∩ (-infinite,1.20]=[-2.8,1.20]

the solution is the interval [-2.8,1.20]

see the attached figure to better understand the problem

8 0

1 year ago

What is the solution of the system? Use elimination.

Anit [1.1K]

Note that if we add each side of the 2 equations, y will cancel out:

-12x-y+(17x+y)=6+4

5x=10

x=2

Substituting x=2 in either of the equations, we find the value of y.

Let's use the first equation:

-12x-y=6

-24-y=6

-y=24+6

-y=30, so y=-30.

Thus, the solution is (2, -30)

Answer: C

6 0

3 years ago

Which expression is a factor of this polynomial x^3+2x^2-9x-18

REY [17]

Answer: (x+2)

Step-by-step explanation:

4 0

3 years ago