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Olegator [25]
3 years ago
10

Your mother saw a sale at the music store on tax-free weekend that advertised two CD’s for $15.95. Your mother said that you hav

e been very well behaved lately and your grades are quite good so she will give you $60 to help increase your CD collection. How many CD’s will you have after you purchase the new CD’s if you already have 14?
Mathematics
1 answer:
Neko [114]3 years ago
3 0

Answer:

20 CDs

Step-by-step explanation:

Assuming you can't buy 1 CD, you have to buy 2 CD's for 15.95, let's see how many 2CD-Batches we can buy with 60:

60/15.95 = 3.76 CD batches

We can't buy the fractional amount, so we have to buy "3" 2-CD-Batches.

Thus, we will have 3 * 2 = 6 CD's  now

Since we had 14 and now we buy 6, we will have

14 + 6 = 20 CDs now.

20 CDs

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Solve the given linear Diophantine equation. Show all necessary work. A) 4x + 5y=17 B)6x+9y=12 C) 4x+10y=9
aliina [53]

Answer:

A) (-17+5k,17-4k)

B)  (-4+3k,4-2k)

C) No integer pairs.

Step-by-step explanation:

To do this, I'm going to use Euclidean's Algorithm.

4x+5y=17

5=4(1)+1

4=1(4)

So going backwards through those equations:

5-4(1)=1

-4(1)+5(1)=1

Multiply both sides by 17:

4(-17)+5(17)=17

So one integer pair satisfying 4x+5y=17 is (-17,17).

What is the slope for this equation?

Let's put it in slope-intercept form:

4x+5y=17

Subtract 4x on both sides:

     5y=-4x+17

Divide both sides by 5:

      y=(-4/5)x+(17/5)

The slope is down 4 and right 5.

So let's show more solutions other than (-17,17) by using the slope.

All integer pairs satisfying this equation is (-17+5k,17-4k).

Let's check:

4(-17+5k)+5(17-4k)

-68+20k+85-20k

-68+85

17

That was exactly what we wanted since we were looking for integer pairs that satisfy 4x+5y=17.

Onward to the next problem.

6x+9y=12

9=6(1)+3

6=3(2)

Now backwards through the equations:

9-6(1)=3

9(1)-6(1)=3

Multiply both sides by 4:

9(4)-6(4)=12

-6(4)+9(4)=12

6(-4)+9(4)=12

So one integer pair satisfying 6x+9y=12 is (-4,4).

Let's find the slope of 6x+9y=12.

6x+9y=12

Subtract 6x on both sides:

      9y=-6x+12

Divide both sides by 9:

       y=(-6/9)x+(12/9)

Reduce:

       y=(-2/3)x+(4/3)

The slope is down 2 right 3.

So all the integer pairs are (-4+3k,4-2k).

Let's check:

6(-4+3k)+9(4-2k)

-24+18k+36-18k

-24+36

12

That checks out since we wanted integer pairs that made 6x+9y=12.

Onward to the last problem.

4x+10y=9

10=4(2)+2

4=2(2)

So the gcd(4,10)=2 which means this one doesn't have any solutions because there is no integer k such that 2k=9.

6 0
3 years ago
What is 0.1 as a fration and simple form if can be
Kisachek [45]

Answer:

1/10 is the simplest form

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3 years ago
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Great Granola makes a trail mix consisting of peanuts, cashews, raisins, and dried cranberries. The trail mix sells for $3.50, a
Leno4ka [110]

Answer:

the answer is the average amount of cashews per bag to determine average cost

the amount of variation in ounces of cashews in the bags of trail mix

which factory produces the most consistent ounces of cashews in each bags of trail mix

Step-by-step explanation:

5 0
3 years ago
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4. What is the value of the underlined digit?
Arisa [49]

Answer:

hundreth, because it is the second digit after the decimal point.

3 0
3 years ago
..........................
Rainbow [258]
Option A

x+8=-3
x+8-8=-3-8
x=-11


Hope I didn't mess up for your sake!
7 0
3 years ago
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