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Fynjy0 [20]
3 years ago
9

Hellpp -4c - 9.6 +5c = 0

Mathematics
2 answers:
Komok [63]3 years ago
6 0

Answer:

c = 9.6

Step-by-step explanation:

Let's look at our equation; - 4c - 9.6 + 5c = 0. Now we need to collect the like terms which are -4c and 5c.

- 4c - 9.6 + 5c = 0

5c - 4c - 9.6 = 0

We get: c - 9.6 = 0

Now we will add 9.6 on each side to see what c is equal to.

c - 9.6 = 0

  +9.6    +9.6

c = 9.6

Yay! We got our answer! Nice job everyone!

Ray Of Light [21]3 years ago
4 0

Answer:

c =9.6

Step-by-step explanation:

-4c - 9.6 +5c = 0\\\\\mathrm{Group\:like\:terms}\\-4c+5c-9.6=0\\\\\mathrm{Add\:similar\:elements:}\:-4c+5c=c\\c-9.6=0\\\\\mathrm{Add\:}9.6\mathrm{\:to\:both\:sides}\\c-9.6+9.6=0+9.6\\\\Simplify\\c=9.6

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A train leaves at 1314 and arrives at 1508. It travelled at an average speed of 105 km/h.
Paraphin [41]

Answer: The train traveled 199.5 km

Step-by-step explanation:

We know the relationship:

Distance = Time*Speed

We know that the speed of the train was 105km/h

And we know that it leaves at 13:14, and arrives at 15:08.

Then the total amount of time that the train was traveling is:

T = (15 hours and 8 mins) - (13 hours and 14 mins)

= (15 - 13) hours and (8 - 14) mins

=  2 hours and (-6) mins.

We know that one hour has 60 minutes, then this is equal to:

T = 1 hour and 54 minutes.

But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.

This can be done as follows:

1 hour = 60 minutes.

Then: 54 minutes = (54/60) hours = 0.9 hours.

Then:

1 hour and 54 minutes = 1.9 hours.

Now we know the speed and the time, then the distance can be calculated as:

Distance = speed*time = 105km/h*(1.9 h) = 199.5 km

The train traveled 199.5 km

3 0
3 years ago
Read 2 more answers
How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used
MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the <em>n</em>-th term of the sequence, <em>a</em> (<em>n</em>), is given recursively by

• <em>a</em> (1) = 1

• <em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 21 … … … for <em>n</em> > 1

We can find the explicit rule for the sequence by iterative substitution:

<em>a</em> (2) = <em>a</em> (1) + 21

<em>a</em> (3) = <em>a</em> (2) + 21 = (<em>a</em> (1) + 21) + 21 = <em>a</em> (1) + 2×21

<em>a</em> (4) = <em>a</em> (3) + 21 = (<em>a</em> (1) + 2×21) + 21 = <em>a</em> (1) + 3×21

and so on, with the general pattern

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 21 (<em>n</em> - 1) = 21<em>n</em> - 20

Now, we're told that the sum of some number <em>N</em> of terms in this sequence is 2332. In other words, the <em>N</em>-th partial sum of the sequence is

<em>a</em> (1) + <em>a</em> (2) + <em>a</em> (3) + … + <em>a</em> (<em>N</em> - 1) + <em>a</em> (<em>N</em>) = 2332

or more compactly,

\displaystyle\sum_{n=1}^N a(n) = 2332

It's important to note that <em>N</em> must be some positive integer.

Replace <em>a</em> (<em>n</em>) by the explicit rule:

\displaystyle\sum_{n=1}^N (21n-20) = 2332

Expand the sum on the left as

\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332

and recall the formulas,

\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n

\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2

So the sum of the first <em>N</em> terms of <em>a</em> (<em>n</em>) is such that

21 × <em>N</em> (<em>N</em> + 1)/2 - 20<em>N</em> = 2332

Solve for <em>N</em> :

21 (<em>N</em> ² + <em>N</em>) - 40<em>N</em> = 4664

21 <em>N</em> ² - 19 <em>N</em> - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

<em>N</em> = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer <em>N</em> for which the first <em>N</em> terms of the sum add up to 2332.

4 0
2 years ago
Erin created a scale drawing for a garden that will be 10 ft by 5 ft. She plans to include a section in the garden for herbs, wh
Elanso [62]

Answer:

The dimensions of the herb garden in the scale drawing are 2.4 in. by 6 in

Step-by-step explanation:

we know that

The dimensions of the garden in the actual are 10 ft by 5 ft

The dimensions of the garden on the scale drawing are 12 in. by 6 in

step 1

Find the scale factor

To find the scale factor divide the corresponding side on the scale drawing by the corresponding side in the actual

so

\frac{12}{10}\ \frac{in}{ft}

simplify

1.2\ \frac{in}{ft}

That means

1.2 inches in the drawing represent 1 foot in the actual

step 2

Find out  the dimensions of the herb garden on the scale drawing

we know that

The dimensions of the herb garden in the actual are 2 ft by 5 ft

Multiply by the scale factor

so

2\ ft=2(1.2)=2.4\ in

5\ ft=5(1.2)=6\ in

therefore

The dimensions of the herb garden in the scale drawing are 2.4 in. by 6 in

5 0
3 years ago
Abe,a plumber, charges $50 per hour for making an in-home visit. The Plumbing Service $65 per hour but no set free for a visit.
ArbitrLikvidat [17]

Answer:

Plumber: 13 hours

Plumbing service: 10

Step-by-step explanation:

What you have to find is LCM(least common multiple in order to find the lcm all you have to do is list all the multiples and find their common multiple.

5 0
3 years ago
Read 2 more answers
Use technology to find the line of best fit for the following data.
likoan [24]

Given:

The data points are:

(1, 0), (2, 3), (3,1), (4,4), (5,5)

To find:

The equation of best fit line in the form of y=mx+b and then find the value of b.

Solution:

The general form of best fit line is:

y=mx+b              ...(i)

Where, m is the slope of best fit line and b is the y-intercept of the line.

Using the graphing calculator, we get the equation for the best fit line and the equation is

y=1.1x-0.7          ...(ii)

On comparing (i) and (ii), we get

b=-0.7

Therefore, the value of b is equal to -0.7.

3 0
3 years ago
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