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Kobotan [32]
3 years ago
13

How many numbers are reciprocal of themselves?

Mathematics
1 answer:
const2013 [10]3 years ago
6 0

Answer:

  two: +1 and -1

Step-by-step explanation:

If a number is equal to its own reciprocal, it will satisfy the equation ...

  x = 1/x

Multiplying by x and subtracting 1 gives ...

  x^2 -1 = 0

This factors as ...

  (x -1)(x +1) = 0

By the zero product rule, the solutions are those values of x that make one or more factors zero:

  x = 1

  x = -1

There are two self-reciprocals.

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I feel 12 less than 4 times a number is 8, the number is 5. Write a different sentence where the unknown number is also 5.
Lyrx [107]

9 less than 3 times a number is 6

8 0
3 years ago
two trains leave stations 210 miles apart at the same time and travel tword each other. one train at 85 miles per hour while the
hodyreva [135]

recall your d = rt, distance = rate * time.


let's say we have two trains, A and B, A is going at 85 mph and B at 65 mph.


they are 210 miles apart and moving toward each other, at some point they will meet, when that happens, the faster train A has covered say d miles, and the slower B has covered then the slack from 210 and d, namely 210 - d.


When both trains meet, A has covered more miles than B because A is faster, however the time both have been moving, is the same, say t hours.


\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Train A}&d&85&t\\ \textit{Train B}&210-d&65&t \end{array}\\\\ \dotfill\\\\ \begin{cases} \boxed{d}=85t\\ 210-d=65t\\[-0.5em] \hrulefill\\ 210-\boxed{85t}=65t \end{cases} \\\\\\ 210=150t\implies \cfrac{210}{150}=t\implies \cfrac{7}{5}=t\implies \stackrel{\textit{one hour and 24 minutes}}{1\frac{2}{5}=t}

3 0
3 years ago
O points
astraxan [27]

7.5 %

Step-by-step explanation:

We by finding how far from the mean the 999 volume caps are, using z score;

Z = (x – μ) / σ

Z = (999 – 998) / 7

Z = 0.143    

We use the z-table to find the confidence levels;

= 85%

= 0.85

Since we are finding proportion of bottles have volumes greater than 999

mL;

1 – .85 = .15

0.15/2 = 0.075

= 7.5%

5 0
2 years ago
A ) Rotate Trapezoid ABCD 90° counterclockwise around the origin .
FinnZ [79.3K]

Answer:

A" (3,3)

B" (3,5)

C" (5,7)

D" (5,1)

Yes they are congruent as they are similar and have the same shape and size.

Step-by-step explanation:

-y,x is the formula for a 90° counter clockwise rotation, And since the shape nor size doesnt change it is congruent.

8 0
1 year ago
20.35 - 08.57 - 09.99 ​
rewona [7]
Your answer will be 1.49
7 0
2 years ago
Read 2 more answers
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