Carl buys seven 5-gallon jugs of water for the water cooler. How many liters of water did Carl buy? Show your work.

Answer:

[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]

Or, by approximating:

[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]

Step-by-step explanation:

Let’s convert this to standard form. We have:

[tex]-6x-1+5x^2=8x^2[/tex]

Subtract 5x² from both sides:

[tex]-6x-1=3x^2[/tex]

And add 6x and 1 to both sides:

[tex]0=3x^2+6x+1[/tex]

This is not factorable. So, we will need to use the quadratic formula.

The quadratic formula for a quadratic in standard form is given by:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]

In this case, a=3; b=6, and c=1.

Substitute appropriately:

[tex]\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}[/tex]

Simplify:

[tex]\displaystyle x=\frac{-6\pm\sqrt{24}}{6}[/tex]

We can simplify the square root:

[tex]\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}[/tex]

Hence:

[tex]\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}[/tex]

Simplify:

[tex]\displaystyle x=\frac{-3\pm\sqrt{6}}{3}[/tex]

Hence, we will have two solutions:

[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]

Approximating them, we can see that our solutions are approximately:

[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]

Answer:

quadrilateral

Step-by-step explanation:

Answer:

Johan spends $70.50.

Step-by-step explanation:

3 * 2 * 11.75 = 70.50

Answer:

Im a little confused on what your asking but for 0.4 as a decimal is 0.4,for a fraction 0.4 is 2/5 and for a percent 0.4 is 40%

Step-by-step explanation:

I hope this helps!!

Answer:

See Attached

Step-by-step explanation:

See Attached for proof of RHS = LHS

Answer:

Chase and his brother will both have a score of 31 points by making 4 successful shots.

Step-by-step explanation:

Given that initially Chase has 19 points and his brother has 27 points.

In one successful flip, Chase get 3 points and in one successful flip, his little brother get 3 points

Assuming that both have the same score after n number successful flip of the coin.

So, points earned by Chase in n successful flip [tex]= 3\times n =3n[/tex]

and points earned by his little brother in n successful flip [tex]= 1\times n=n[/tex].

Total points of Chase [tex]= 19+3n\cdots(i)[/tex]

Total points of his little brother [tex]= 27 + n\cdots(ii)[/tex]

As the brothers have tied scores in the game, that means both have the same score, so from equations (i) and (ii), we have

[tex]19+3n = 27 + n \\\\\Rightarrow 3n-n = 27-19 \\\\\Rightarrow 2n=8 \\\\\Rightarrow n=8/2=4[/tex]

So, after n successful throw, both have the same score.

Hence, each brother made 4 additional successful shots.

Now, put n=4 inequation (i) or (ii) to get the total points, i.e

Total points of each brother [tex]= 19+ 3\times 4 = 31.[/tex]

Hence, each brother has 31 points.

Answer:

X=2.5

Step-by-step explanation:

On Edge

Answer: 40320 ways

Step-by-step explanation:

From the question, we are informed that we should the number of arrangements that are in the letters in the word: CHAPTERS.

First, we should note that there are 8 letters in the word CHAPTERS, therefore the number of ways that the word can be arranged is 8! which simply means:

8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320 ways

Answer:

Step-by-step explanation:

1/3(12x+6x-21)

Take 1/3 of everything in the ()

4x+2x-7 combine like terms

6x-7

The equivalent expression is 6x - 7

Given the function 1/3(12x+6x-21), to get the equivalent expression, we will open the parenthesis using the distributive law;

= 1/3(12x+6x-21)

=  1/3(12x) + 1/3(6x) - 1/3(21)

= 4x + 2x - 7

On simplification, the resulting expression will be:

= 6x - 7

Hence the equivalent expression is 6x - 7

Learn more on functions here: https://brainly.com/question/19999031

Answer:

-11

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

13 ÷ 4 = 3.25

but you wont by .25 of a shirt so he can only buy 3 shirts

Answer:

(15, 12)

Step-by-step explanation:

Let's generate two systems of equations that fit this scenario.

Number of trips to the airport = x

Number of trips from the airport = y

Total number of trips to and from the airport = 27

Thus:

[tex] x + y = 27 [/tex] => equation 1.

Total price for trips to the Airport = 14*x = 14x

Total price of trips from the airport = 7*y = 7y

Total collected for the day = $294

Thus:

[tex] 14x + 7y = 294 [/tex] => equation 2.

Multiply equation 1 by 7, and multiply equation 2 by 1 to make both equations equivalent.

7 × [tex] x + y = 27 [/tex]

1 × [tex] 14x + 7y = 294 [/tex]

Thus:

[tex] 7x + 7y = 189 [/tex] => equation 3

[tex] 14x + 7y = 294 [/tex] => equation 4

Subtract equation 4 from equation 3

-7x = -105

Divide both sides by -7

x = 15

Substitute x = 15 in equation 1

[tex] x + y = 27 [/tex]

[tex] 15 + y = 27 [/tex]

Subtract both sides by 15

[tex] y = 27 - 15 [/tex]

[tex] y = 12 [/tex]

The ordered pair would be (15, 12)

Answer: 13,12,5

Step-by-step explanation:

According to the triangles inequality : The sum of any two sides of a triangle must be greater than the third.

since [tex]6+5 =11 \ngtr 15[/tex]

[tex]20+10=30\ngtr40\\\\ 16+2=18\ngtr19[/tex]

Only pipe lengths with measure 13,12,5 can form triangle as

13+12 >5

12+5>13

13+5>12

Hence, the correct option is 13,12,5.

Answer:

D

Step-by-step explanation:

Answer: 2.5-1.4=1.1 your welcome

Answer:

1.1

Explanation:

If you subtract 2.5 by 1.4, you get 1.1

I'VE SAVED THE DAY MARK ME THE BRAINLIEST

Answer:

3.05 ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) (x+2)(x+2)=-x-2

[tex]x^{2}[/tex] +2x +2x +4+=-x-2

[tex]x^{2}[/tex]+4x+4+x+2

[tex]x^{2}[/tex]+5x+6

2) [tex]x^{2}[/tex] +4x +12 -16x +24=0

[tex]x^{2}[/tex] -12x+36=0

3) (x-4)(x+1)

x=4 and/or x=-1

4) (x-5)(x-6)

x=5 and/or x=6

5) (x-7)(x+2)

x=7 and/or x=-2

6) [tex]x^{2}[/tex]+3x-10=0

(x-5)(x+2)

x=5 and/or x=2

7) [tex]x^{2}[/tex]+x-20

(x-5)(x+4)

x=5 and/or x=-4

Answer:

It is not

Step-by-step explanation:

It is not because this is an exponential function

y=x^2

1^2=1

2^2=4

3^2=9

4^2=16

Answer:

r = 5y/8

Step-by-step explanation:

isolate the variable by dividing each side by factors that contain the variable.

Answer:

((7

Step-by-step explanation:

Answer:

its 6 because the lines show they are parellel so it has to be equal to 18 and 12 plus 6 is 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

So first I divided 240 by 2 to get the hourly rate, which is 120. Then i multiplied 120 times 36 and got 4,320 quarts in 36 hours. The daily rate is 2,880, I got that by multiplying 120 by 24 because there are 24 hours in a day.

Answer:

≈ 5 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle.

let the height of the board be h , then

tan22.5° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{12}[/tex] ( multiply both sides by 12 )

12 × tan22.5° = h , then

h ≈ 5 ft ( to the nearest whole number )

Answer:

Step-by-step explanation:

9x-5 is a factor of [tex]81x^{2} -25[/tex]

5/8 ÷ 1/4

5/8 • 4/1

5/2

Answer:

2.5 If I am right

Step-by-step explanation:

5/8 divided by 1/4= 2.5

I think  

Answer:

Option 3

Step-by-step explanation:

The two triangles are proved congruent to each other so CPCTC proves that the angles are also congruent.