Gomez has 30 cans of regular soda and 18 cans of diet soda. He wants to create some identical refreshment tables that will operate during the football game. He also doesn’t want to have any sodas left over. What is the greatest number of refreshment tables that Gomez can stock?

Answer:

x = 5, y = -2

Step-by-step explanation:

Given equations:

From the first equation we get:

Substitute x in the second equation, find y:

Find x:

Answer: I am pretty sure it is a rational number!

Step-by-step explanation:

Answer:

a) 18.5832 m^2

b) length 5.34 ≈ to one decimal point 5.3m

width 3.48 ≈ to one decimal point 3.5m

Step-by-step explanation:

Answer:

[tex]6\sqrt{7}[/tex]

Step-by-step explanation:

If you bring 252 to its prime numbers, its 2, 2, 3, 3, and 7. Just multiply 2 and 3 and you get 6 root 7.

The expression equivalent to the square root of 252 is 6[tex]\sqrt{7}[/tex].

That number which can be divided by itself or 1 only. eg. 2, 3, 5, 7, 11, 13 etc.

Given value,

252

Expressed in prime numbers as:

252 = 2x2x3x3x7 or [tex]2^{2}[/tex] x [tex]3^{2}[/tex] x 7

∴ [tex]\sqrt{252}[/tex] = 2x3 [tex]\sqrt{7}[/tex] = 6 [tex]\sqrt{7}[/tex]

Hence [tex]\sqrt{252}[/tex] can be expressed as 6 [tex]\sqrt{7}[/tex]. Similarly any real number can be represented as the product of prime numbers.  

To learn more about prime numbers, refer to the link:

https://brainly.com/question/9315685

#SPJ2

Answer:

(2,5) and (5,8)

Step-by-step explanation:

you can just plug in the numbers to get your answer and if two numbers aren't the same then its not a solution

example: (2,5)

5 = 2 + 3

5 = 5

5 does equal 5 making it a solution because it makes sense right?

example: (4,6)

6 = 4 + 3

6 = 7

this isn't a solution because six doesn't equal 7

Answer:

[see below]

Step-by-step explanation:

[tex]y=x+3[/tex]

The ordered pair is a solution.

The ordered pair is not a solution.

The ordered pair is a solution.

[tex]7=3+3\\\\\boxed{7\neq 6}[/tex]

The ordered pair is not a solution.

Hope this helps.

Answer:

x≤-4

Step-by-step explanation:

There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

8x≤-32

1. Divide both sides by 8

Answer:

The number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.

Step-by-step explanation:

We are given that Old Mc Donald raises ducks and cows. The animals have a total of 100 heads and 354 feet.

Let the number of ducks Old Mc Donald raises be 'x' and the number of cows Old Mc Donald raises be 'y'.

So, according to the question;

                                   [tex]x+y=100[/tex]

                                    [tex]x=100-y[/tex]  -------------------- [equation 1]

{because one head of a duck and one head of cow}

                                   [tex]2x+4y=354[/tex]

                                   [tex]x+2y=177[/tex]   --------------- [equation 2]

{because there are two feet of a duck and four feet of cow}

Now, putting the value of x in equation 2 we get;

                                  [tex]100-y+2y=177[/tex]

                                  [tex]y=177-100[/tex]

                                    y = 77 cows

Putting this value of y in equation 1 we get;

                                 x = 100 - y

                                 x = 100 - 77 = 23 ducks

Hence, the number of ducks Old Mc Donald raises are 23 and the number of cows Old Mc Donald raises are 77.

Answer:

The answer is -7

5k=-30-5.

5k=-35.

k= -7.

Hi there! Hopefully this helps!

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

[tex]-30=5k+5[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]5k+5=-30[/tex]

Subtract 5 from both sides.

[tex]5k=-30-5[/tex]

Subtract 5 from −30 to get −35.

[tex]5k=-35[/tex]

Divide both sides by 5.

[tex]k=\frac{-35}{5}[/tex]

You can also do "5(-7) + 5 = ??" For proof.

Nope

Step-by-step explanation:

Pi is an irrational number because it can not be expressed by a simple fraction.

Answer: No it's a rational number

Step-by-step explanation:

Answer:

k=6

Step-by-step explanation:

25=19+k

Subtract 19 from each side

25-19=19-19+k

6 = k

Answer:

k = 6

Explanation:

to find the value of k in the equation provided, you must subtract nineteen from both sides. this will isolate the variable.

25 = 19 + k

25 - 19 = 19 - 19 + k

6 = k

k = 6

therefore, the value of the variable k in 25 = 19 + k is 6.

Answer:

5 is a solution

Answer:

The speed of the stream is 5 km/hr.

Step-by-step explanation:

- Let's assume that the speed of stream is = x km/h

- Speed of boat in still water v = 15 km/h

- Total time taken = 4 hour and 30 mins or 9/5 hrs

- Distance covered (one way) = 30 km/s

Then,

Speed of boat downstream =( 15 + x ) km/h

Time taken downstream = (30/15 + x ) hrs

As time = distance / speed

Speed of boat upstream = ( 15 - x ) km/h

Time taken upstream =( 30/15 - x ) hrs

Now,

     Total time taken = Time taken downstream + Time taken upstream

or, 9/2 = (30/15 + x ) + (30/15 - x )

or, x = 5 km/h

The speed of the stream is 5 km/h

I hope my answer helps

Answer:

11

Step-by-step explanation:

AB = 3x + 4 and AC which is twice of AB is equal to 11x - 17

2 (3x + 4) = 11x - 17

6x + 8 = 11x - 17

8 + 17 = 11x - 6x

25 = 5x

5 = x

AC = CD = 11x - 17 ➡ 11×5 - 17 = 38

CD = 38 and DE = 49 - 38 = 11

we'll divide 10 by 5..the answer is 2 then we'll add it to the other 5 making it to be 7

Answer: 7

How to: To add fractions, find the LCD and then combine.

Answer:

$7

Step-by-step explanation:

t = ticket price

We know the total cost of the ticket and snacks was $15, and just the snacks were $8 so:

t + $8 = $15

To find the amount of the ticket, subtract $8 from each side

t + $8 - $8 = $15 - $8

The $8 cancels and you're left with

t = $7

So the ticket costs $7

The remaining cost after the snack cost is the cost of the movie ticket and it is $7.

To subtract in mathematics is to take something away from a group or a number of objects.

In a different sense, subtraction refers to a mathematical procedure where two values will be subtracted to produce a new value.

Total spent = cost of snacks + cost of a movie ticket

Given that,

Total spent = $15

Cost of snacks = $8

So,

15 = 8 + cost of movie ticket

Cost of movie ticket = 15 - 8 = $7

Hence "The remaining cost after the snack cost is the cost of the movie ticket and it is $7".

For more about subtraction,

https://brainly.com/question/1927340

#SPJ2

Answer:

10^(-1)

Step-by-step explanation:

Recall that a value that is multiplied by a number that is between 0 and 1 will result in a number that is smaller than the original number.

the first 3 are all greater than 1, hence will result in a greater value if when multiplied with another number.

The last one is 10^(-1) = 0.1

Anything multiplied by 0.1 will result in a value that is 1/10th of the original value.

Hence this is the answer.

Answer:

10/\-1 is correct

Step-by-step explanation:

Answer:

(D) ab + bc =ad

    ab-ad = -bc

    a(b-d) =bc

     a = bc / b-d

(e) The Pythagoras Theorem states that in a Right angled triangle the {hypotenuse}^2 = {opposite}^2 + {adjacent}^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the incomplete quadratic equation [tex]\[x^2 + \dfrac{4}{5}x + \underline{~~~~}\][/tex], we are to complete it so that the result will be the square of a binomial. To do that, we will use the completing the square method.

Completing the square method is a way of completing a quadratic equation by solving for a constant to add that will make the quadratic equation a perfect square of a binomial.

To get the constant term using the method, we will take the square of the alf of the coefficient of x in the equation given.  

Coefficient of x = 4/5

half of the coefficient of x = 1/2(4/5)

half of the coefficient of x = 4/10 = 2/5

Square of the half of the coefficient of x = (2/5)²

Square of the half of the coefficient of x = 4/25

Hence the constant that we will use to complete the equation to make if a square of a binomial is 4/25

The equation will become:

[tex]= \[x^2 + \dfrac{4}{5}x +\dfrac{4}{25} \\\\= \[x^2 + \dfrac{4}{5}x +(\dfrac{2}{5})^2\\\\= (x +\dfrac{2}{5})^2[/tex]

Hence the constant value that will make the resulting quadratic the square of a binomial is 4/25

Answer:

4/25

Step-by-step explanation:

Suppose the quadratic is the square of the binomial $x+c.$ We have $(x+c)^2 = x^2+2cx + c^2.$ Comparing the linear term of $x^2 + 2cx+c^2$ to the linear term of $x^2 + \frac{4}{5}x + \underline{~~~~},$ we have $2c = \dfrac{4}{5},$ so $c = \dfrac{2}{5}.$ Therefore, the constant term is

\[c^2  = \left(\dfrac{2}{5}\right)^2 = \boxed{\frac{4}{25}}.\]

Answer:

y=5x+2

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-4,-18), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-4 and y1=-18.

Also, let's call the second point you gave, (0,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=0 and y2=2.

Now, just plug the numbers into the formula for m above, like this:

m= (2 - -18)

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

(0 - -4)

or...

m= 20

-------

4

or...

m=5

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=5x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-4,-18). When x of the line is -4, y of the line must be -18.

(0,2). When x of the line is 0, y of the line must be 2.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=5x+b. b is what we want, the 5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-4,-18) and (0,2).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(-4,-18). y=mx+b or -18=5 × -4+b, or solving for b: b=-18-(5)(-4). b=2.

(0,2). y=mx+b or 2=5 × 0+b, or solving for b: b=2-(5)(0). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(-4,-18) and (0,2)

is

y=5x+2

Answer:

A rational number is a number able to be put into a fraction, an irrational number is not able to be. Therefore, when adding the two, the rational and the irrational will be irrational. For example, 2 is a rational number, and 1.8903 is irrational. If you add the two, you will get 3.18903, which is unable to be put into a fraction.

Answer:

vertical

Step-by-step explanation:

Answer:

19.84 Miles

give or take

Step-by-step explanation:

1 km is .62 miles

.62 x 32 = 19.84

Answer:

19.88 miles

Step-by-step explanation:

Answer: (-0.5, 4)

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

(x1, x2)=(2, -3)

(y1, y2)=(2, 6)

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

 [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

=[tex](\frac{2-3}{2} ,\frac{2+6}{2} )[/tex]

=[tex](\frac{-1}{2} ,\frac{8}{2} )[/tex]

=[tex](-0.5, 4)[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

[tex]M=(-\frac{1}{2},4)[/tex]

Step-by-step explanation:

The midpoint formula is given by:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Let (2,2) be x₁ and y₁ and let (-3,6) be x₂ and y₂. Therefore:

[tex]M=(\frac{2+-3}{2},\frac{2+6}{2})[/tex]

Simplify:

[tex]M=(-\frac{1}{2},\frac{8}{2})\\M=(-\frac{1}{2},4)[/tex]

Answer: (2 1/2, 0) (the last option)

Step-by-step explanation:

I guess the function is:

f(x) = (2  1/2) - (3  1/2)*x

now, the rule for f-1(x) that we know is:

f-1( f(x) ) = x.

So if we want to find the x-intercept of f-1(x), we must evaluate it in f(0)

f-1(f(0)) = 0.

And we have that f(0) = (2  1/2) - (3  1/3)*x = 2  1/2

This means that the x-intercept of f-1(x) will be when x= 2  1/2, so the intercept is:

(2 1/2, 0)

Answer:

If 30 unicorns out of 300 walk away then it will be 300-30=270 unicorns left.

If 50 dragons fly away out of 200 then it will be 200-50=150.

Therefore there are 270 unicorns and 150 dragons left.

I hope this helps you...Thank you...

Answer:

s= number of shirts

3/2= constant of proportionality

Step-by-step explanation:

Josh takes a load of dress shirts to the dry cleaners. The amount he pays for dry cleaning (

f. is given by the equation f=3/2s, where s is the number of shirts. What is the constant of proportionality in terms of the cost per shirt?

Given:

f= 3 / 2s

Where,

f= amount Josh paid for dry cleaning

s= number of shirts

3= constant of proportionality

2= amount paid per shirt

For example, if Josh took 3 shirts to the dry cleaner, the amount Josh will pay is

f= 3 / 2s

= 3 / 2(3)

= 3 / 6

= 1 / 2

f= 1 /2

Answer:

45, 46, 33, 0, 6

Step-by-step explanation:

Answer:

The dimensions of the field is 185 yards by 48 yards

Step-by-step explanation:

Here, we are interested in calculating the dimensions of the field.

Let the width of the field be x yards

From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width

So mathematically, the length of the field will be ;

(4x -7) yards

The perimeter of the field mathematically is:

2(l + b)

Thus;

2(x + 4x- 7) = 466

2(5x -7) = 466

divide both side by 2

5x - 7 = 466/2

5x - 7 = 233

5x = 233 + 7

5x = 240

x = 240/5

x = 48 yards

Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards