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Naya [18.7K]
3 years ago
11

12.) Write y = 1/6 x + 7 in standard form using integers.

Mathematics
1 answer:
Trava [24]3 years ago
3 0

Option A

-x + 6y = 42 is the standard form

<u>Solution:</u>

Given that we have to write y = \frac{1}{6}x+7 in standard form

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

Given equation is:

y = \frac{1}{6}x+7

Let us convert the above equation into standard form

y = \frac{x}{6} + 7

y = \frac{x}{6} + \frac{7}{1}

Make the denominator same in R.H.S

y = \frac{x}{6} + \frac{7 \times 6}{1 \times 7}

Solve the above equation

y = \frac{x}{6} + \frac{42}{6}

y = \frac{x+42}{6}

Move 6 from R.H.S to L.H.S

6y = x + 42

Bring all the terms to one side, leaving only constant on R.H.S

-x + 6y = 42

The above equation is of form Ax + By = C

Thus option A is correct

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Each day, a factory produces a total of 280 containers of ice cream. The flavors are vanilla, chocolate, and strawberry. Each da
GalinKa [24]

Answer:

The correct equation in terms of s is: 4s=260

  • The number of strawberry ice cream produced per day, s=65.
  • The number of chocolate ice cream produced per day ,c=130.
  • The number of vanilla ice cream produced per day ,v=85.

Step-by-step explanation:

Let the number of containers of strawberry ice cream produced per day=s

Let the number of containers of vanilla ice cream produced per day=v

Let the number of containers of chocolate ice cream produced per day=c

Total Number of Ice Cream Containers=280

  • s+v+c=280

Given:

The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:

  • c=2s

The factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:

  • v=s+20

Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280

s+s+20+2s=280

4s=280-20

4s=260

Divide both sides by 4

s=65

The number of strawberry ice cream produced per day is 65.

The number of chocolate ice cream produced per day =2s=2(65)=130.

The number of vanilla ice cream produced per day =s+20=65+20=85.

3 0
3 years ago
What is the unit rate for 180 miles in 3 hours
Ugo [173]

Hello

Answer:

60 miles per hour

I have given a detailed explanation of the logic behind this.

Explanation:

Consider the structure of the wording: "miles per hour"

The word "per" means for each. There is you clue.

Each is, one of and one of is unit measurement

So the controlling element in this question is that you need to convert the 3 hours into 1 hour.

Using ratio properties

180

3

=

x

miles

1

hour

We need to 'force' the left hand side into the same form as the right. That is: we need to convert the denominator into 1 and see what happens to the numerator.

⇒

180

÷

3

3

÷

3

=

x

1

⇒

60

1

=

x

1

So the unit rate of speed is  

60

miles

per

−−−

hour

Hope this helps

Plz mark me as Brainliest

3 0
3 years ago
A number x increased by 4 is less than -18
Bond [772]

x + 4 < -18

x < -18 - 4

x < -22

x is less than -22

5 0
3 years ago
Write the following as an inequality.
Ilia_Sergeevich [38]

Answer:

  -2 < w ≤ 6

Step-by-step explanation:

The inequalities you're asked to combine are ...

  -2 < w

  6 ≥ w

Turn one of these around so the "arrows" point in the same direction. (My preference is that they point to the left.) Now you have ...

  -2 < w

  w ≤ 6

You combine these by putting w in the middle:

  -2 < w ≤ 6

_____

<em>Alternate solution</em>

I like the above solution because it puts the components of the expression in the same (left-right) order as they appear on a number line. However, both inequalities can be turned around to get ...

  6 ≥ w > -2

6 0
3 years ago
a science quiz has eight multiple choice questions with five choices for each. Find the total number of ways to answer the quest
almond37 [142]

Answer:

390625

Step-by-step explanation:

The questions are all independent -- the answer on one question does not limit the number of possible answers on another question.

The quiz has 5 choices for each question, so there are

5\times5\times5\times5\times5\times5\times5\times5 ways to answer the quiz questions.

Notice that this could be written 5^8.  You could say that the number of ways to answer the questions is

number \, of \, choices^{number \, of \, questions}

Use a calculator to find 5^8

8 0
3 years ago
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