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Nuetrik [128]
2 years ago
7

Solve using long division SHOW WORK

Mathematics
2 answers:
SSSSS [86.1K]2 years ago
7 0

Answer:

there is no work shown

Step-by-step explanation:

sineoko [7]2 years ago
4 0

Answer:

where is the work

Step-by-step explanation:

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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
2 years ago
A certain drink is made by adding 4 parts water to 2.5 part drink mix. What percent of the mixture is water? Omit % sign in your
Maru [420]

The mixture contains 61.5% of water.

<u>Step-by-step explanation:</u>

Total parts = 4+ 2.5 = 6.5

Parts of water =4

parts of drink = 2.5

Percent of water in the mixture = 4 × 100/ 6.5

                                                     = 400/6.5

                                                      = 61.53%

It is rounded to the nearest tenth as 61.5%.

8 0
3 years ago
Please help this is due tomorrow morning
Minchanka [31]

Answer:

I can try to help you..uhh alright 1ll it's definitely multiplying by 4 on the bottom but adding 1 one the top. I'm not sure if i'll be correct but try 1 and 4 i'm so sorry if it doesn't help!

7 0
3 years ago
Hiiiooo! Can someone please help ❤️
V125BC [204]

Answer:

B. √21

Step-by-step explanation:

x^2 = √5 x √5 + 4 x 4

x^2 = 5 + 16

x^2 = 21

x = √21

<em>Hope that helps! :)</em>

<em></em>

<em>-Aphrodite</em>

4 0
3 years ago
Read 2 more answers
The ice-cream truck had 112 ice-cream bars when it went out on its afternoon route. The driver sold 76 ice cream bars at the fir
Yuri [45]
I believe it would be 54 dollars.

Hope it helps,
3 0
3 years ago
Read 2 more answers
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