7y = 21x + 14
In the equation shown, what is the value of x when y 4?
Give your answer as a fraction.

Answer: x=27

Step-by-step explanation:

Answer:

x = 1 , y = 1 , z = -3

Step-by-step explanation using elimination:

Solve the following system:

{3 x + 2 y - z = 8 | (equation 1)

2 z + 2 x = -4 | (equation 2)

3 y + x = 4 | (equation 3)

Subtract 2/3 × (equation 1) from equation 2:

{3 x + 2 y - z = 8 | (equation 1)

0 x - (4 y)/3 + (8 z)/3 = -28/3 | (equation 2)

x + 3 y+0 z = 4 | (equation 3)

Multiply equation 2 by 3/4:

{3 x + 2 y - z = 8 | (equation 1)

0 x - y + 2 z = -7 | (equation 2)

x + 3 y+0 z = 4 | (equation 3)

Subtract 1/3 × (equation 1) from equation 3:

{3 x + 2 y - z = 8 | (equation 1)

0 x - y + 2 z = -7 | (equation 2)

0 x+(7 y)/3 + z/3 = 4/3 | (equation 3)

Multiply equation 3 by 3:

{3 x + 2 y - z = 8 | (equation 1)

0 x - y + 2 z = -7 | (equation 2)

0 x+7 y + z = 4 | (equation 3)

Swap equation 2 with equation 3:

{3 x + 2 y - z = 8 | (equation 1)

0 x+7 y + z = 4 | (equation 2)

0 x - y + 2 z = -7 | (equation 3)

Add 1/7 × (equation 2) to equation 3:

{3 x + 2 y - z = 8 | (equation 1)

0 x+7 y + z = 4 | (equation 2)

0 x+0 y+(15 z)/7 = -45/7 | (equation 3)

Multiply equation 3 by 7/15:

{3 x + 2 y - z = 8 | (equation 1)

0 x+7 y + z = 4 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract equation 3 from equation 2:

{3 x + 2 y - z = 8 | (equation 1)

0 x+7 y+0 z = 7 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 2 by 7:

{3 x + 2 y - z = 8 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Subtract 2 × (equation 2) from equation 1:

{3 x + 0 y - z = 6 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Add equation 3 to equation 1:

{3 x+0 y+0 z = 3 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Divide equation 1 by 3:

{x+0 y+0 z = 1 | (equation 1)

0 x+y+0 z = 1 | (equation 2)

0 x+0 y+z = -3 | (equation 3)

Collect results:

Answer: {x = 1 , y = 1 , z = -3

Answer:

0.05 mile per minutes

Step-by-step explanation:

Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered

Miles covered = 1 mile

Time covered = 20 minutes

Jesse's rate of hiking (miles per minute) = Total miles covered / Time covered(minutes)

= 1 mile / 20 minutes

= 0.05 mile per minutes

20 minutes

= 20 × 60 seconds

= 1200 seconds

Jesse's rate of hiking (miles per seconds) = Total miles covered / Total time taken (seconds)

= 1 mile / 1200 seconds

= 0.0008333333333 miles per seconds

Approximately 0.000833 miles per seconds

Answer:

The bait is 14 feet below the water surface

Step-by-step explanation:

Here, we want to know the final position of the bait relative to the surface of the water.

Firstly, he starts with the bait at 2 feet below the water surface. The reels out the bait a further 19 feet, the new position of the bait relative to the water surface will be 2 + 19 = 21 feet

Now, he reels the bait back by 7 feet.

Thus, the new depth of the bait relative to the water surface will be 21-7 = 14 feet

Answer:

11

Step-by-step explanation:

The pattern here is to subtract by 4, so 15-4=11

Answer:3y^2+18y+7

:) happy to help

Answer:

the one on the right

Step-by-step explanation:

one input cannot have more than one output

Answer:

Step-by-step explanation:

Answer:

El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.

Step-by-step explanation:

En primer lugar, se determina la extensión de tiempo, medida en años, tanto de la época prehistórica como el período paleolítico: (Nótese que el signo negativo significa a.C.)

Época Prehistórica

[tex]\Delta T = -2500-(-2500000)[/tex]

[tex]\Delta T = 2497500\,years[/tex]

Período Paleolítico

[tex]\Delta t = -10000 - (-2500000)[/tex]

[tex]\Delta t = 2490000\,years[/tex]

La fracción de la época prehistórica que corresponde al período paleolítico es:

[tex]r = \frac{\Delta t}{\Delta T}[/tex]

[tex]r = \frac{2490000\,years}{2497500\,years}[/tex]

[tex]r = \frac{332}{333}[/tex]

El período paleolítico corresponde a [tex]\frac{332}{333}[/tex] de la época prehistórica.

Answer:

2√3=2√3, which is irrational

======================================================

Explanation:

Let's find the x intercept of f(x). Replace f(x) with 0 and solve for x

f(x) = -2x+2

0 = -2x+2

2x = 2

x = 2/2

x = 1

Plugging x = 1 into f(x) leads to f(x) = 0. The x intercept of f(x) is 1.

-----------------------

Now onto g(x). If we were given a row that had y = 0, then we'd immediately find the x intercept. However, that isn't given, so we'll have to do a bit of work to find the equation for g(x).

First we need the slope. Pick any two rows to find the slope. I'll pick the middle two rows.

m = (y2-y1)/(x2-x1)

m = (3-6)/(1-0)

m = -3/1

m = -3 is the slope

The y intercept is b = 6 as the table shows this pairs with x = 0. The y intercept always happens when x = 0.

So with m = -3 and b = 6, we see that g(x) = -3x+6.

-------------------------

Plug in g(x) = 0 and solve for x. We'll use similar ideas done in the first section at the very top

g(x) = -3x+6

0 = -3x+6

3x = 6

x = 6/3

x = 2 is the x intercept of g(x)

--------------------------

In summary, we found...

Subtract the x intercept values to get 2-1 = 1, which is the distance between the x intercepts. The distance is never negative.

Answer:  The distance is 15

Step-by-step explanation:

To find the distance between L and Y find the difference in the x and y coordinates then square them and add them to find their square root.

-7-5= -12

0-9 = -9

12^2 + 9^2 = d^2   where d is the distance

144 + 81 = d^2

225 = d^2

d= [tex]\sqrt{225}[/tex]  

d= 15

Answer:

6:13

Step-by-step explanation:

Answer:

x=4/3

Step-by-step explanation:

Answer:

length = (3*width) -2

length + 2 = 3*width

width = (length +2) / 3

2*length + 2*width = 68

OR: 2*length = 68 -2*width

If length = (3*width) -2 then

2*length = 6 * width -4

therefore,

6 width -4 = 68 -2 width

8 width = 72

width = 9

Since 2 length + 2 width = 68

then 2 length = 68 -2 width

2 length = 68 -18

length = 25

Step-by-step explanation:

Answer:

15 pints of paint 6 red 9 yellow

Step-by-step explanation:

3x3=9 so 9 yellow pints

and 2x3=6 so 6 red pints

6+9=15 so 15 pints of paint in total

Answer:

Step-by-step explanation:

Hello,

[tex](y-9)^2=(y-9)(y-9)=y^2-2*9*y+9^2=y^2-18y+81[/tex]

thanks

Answer:

yes

Step-by-step explanation:

Answer:

27 pages per hour

Step-by-step explanation:

81 pages divide by 3 hours. think of it as a fraction and divided 3 on both bottom and top then it gives you 27pages per hour as a fraction

Answer:

16 cents

Step-by-step explanation:

The answer is 16 cents because 207 cents divided by 12.5 oz equals 16 cents.

Answer:

Step-by-step explanation:

If the ratio is 2:4:5 there are 2+4+5=11 equal parts...

506/11=46

So each part is equal to 46 so 506 in a ratio of 2:4:5 is:

92:184:230

Answer:

The answer is c

Step-by-step explanation:

just did it on edg

Answer:

The answer is: C

Answer: I think the answer is "d = vt"

Step-by-step explanation:

Multiply both sides of the equation by;

t * d = v * (t)

Multiply, v by t

Answer; d = vt

Hope this helps :)

The value of d, is equivalent to d = v/t.

An expression in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). For example -

f(x) = 4x + 6

Given is the following equation -

dt = v

We have -

dt = v

d = v/t

Therefore, the value of d, is equivalent to d = v/t.

To solve more questions on functions, visit the link below -

brainly.com/question/26182329

#SPJ5

⅔ - ½ = 4/6 - 3/6 (make denomenator the same)

= 1/6

Thus, 1/6 = 40 litres

A full tank is 6/6 which equals to 1 whole

So,

1 unit (from 1/6) = 40 litres

6 units (from 6/6) = 40 × 6

= 240 litres

Therefore, the tank holds 240 litres when it is full.

( i hope my solution helps :3 )

The number of  liters does the tank hold when full is 240 liters.

Formulate

x=40÷⅔ - ½

Let find the common denominator

x=40÷4-3/6

Calculate the sum or the difference

x=40÷1/6

Divide the fraction

x=40×6

x=240 liters

Inconclusion the number of  liters does the tank hold when full is 240 liters.

Learn more about number of liters here:https://brainly.com/question/24928841

Answer:

543.6

Step-by-step explanation:

=> 6 x 90.6

=> 543.6

Total cost as the function of shirts is :

C(x) = mx + 500 .

It is given that , The total cost to produce 100 shirts is $800.

800 = 100m + 500

m = 3

So , cost is given by :

C(x) = 3x + 500 .

Now , putting x = 1000 .

We get :

C(x) = 3x + 500

C(x) = 3(1000) + 500

C(x) = $3500

Therefore , cost of producing 1000 shirts is $3500 .

Hence, this is the required solution .

   Total cost to produce 1000 shirts will be $3500.

            y = mx + b

            Here, m = constant

Given in the question,

Equation representing company's total cost C(x) and number of shirts 'x' as,

C(x) = mx + 500

Here, m = constant

And x > 0

          800 = m(100) + 500

             m = 3

        Equation for the total cost to produce the 'x' shirts will be,

        C(x) = 3x + 500

        C(x) = 3(1000) + 500

             x = $3500

     Therefore, total cost to produce 1000 shirts will be $3500.

Learn more about the linear equation here,

https://brainly.com/question/24391884?referrer=searchResults

Answer: 15

Step-by-step explanation: 5/9=15/27. 27-15=12

The number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.

A ratio is an ordered pair of numbers x and y which can be written as x / y where y does not equal 0.  A proportion is an equation in which two ratios are set equal to each other.

For given information,

The ratio of yellow to blue skittles in the bag is 5:9

The number of blue skittles in the bag = 12 + The number of yellow skittles in the bag= 12+Y

Fraction of the total skittles that are yellow = 5/(5 + 9) = 5/14

Fraction of the total skittles that are blue = 9/(5+9)= 9/14

The total number of skittles = Yellow + Blue

in this Y as yellow; Y+12 as blue.

Y + Y + 12 = 2·Y + 12

The fraction of the total skittles that are blue = 9/14

we have 9/14 × (2·Y + 12)  = Y + 12

-> 9 × (2·Y + 12) = 14 × (Y + 12)

-> 18·Y + 108 = 14·Y + 168

-> 18·Y - 14·Y = 168 - 108 = 60

-> 4·Y = 60

-> Y = 60/4 = 15

∴ The number of yellow skittles in the bag = 15

The number of blue skittles is given as = Y + 12 = 15 + 12 = 27.

Thus, the number of yellow skittles in the bag are 15 skittles while the number of blue skittles in the bag are 27 skittles.

Learn more about Ratio, here:

https://brainly.com/question/13419413

#SPJ5

Answer:

30/7

Step-by-step explanation:

So we have the equation:

[tex]2x-30+5x+2=2[/tex]

Combine like terms:

[tex](2x+5x)+(-30+2)=2[/tex]

Add:

[tex]7x-28=2[/tex]

Add 28 to both sides:

[tex]7x=30[/tex]

Divide both sides by 7:

[tex]x=30/7[/tex]

So, our answer is 30/7

Or approximately 4.2857 :)

Answer:

Step-by-step explanation:      

Step 1: Subtract 15 from both sides.

1.5r+15−15=2.25−15

1.5r=−12.75

Step 2: Divide both sides by 1.5.

1.5r

1.5

=

−12.75

1.5

r=−8.5

Answer: r=-8.5

Step-by-step explanation:

1.5r+15=2.25

1.5r+15-15=2.25-15

1.5r=-12.75

1.5r/1.5=-12.75/1.5

r=-8.5

Answer:

$500 per year.

Step-by-step explanation:

Car repairs and maintenance expense is based on the usage of car as well as its present condition. If the car is bought from showroom and is new then it will incur only small amount of expense as its maintenance but if the car is used by various owners then it is likely that maintenance expense can be huge. The average car repair expense is $500 to $800 per year depending on car condition. Since Jenna car is new she should keep the repair estimate to be minimum that is nearly $500 per year or $42 per month.