3. A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute?
(b) What is the change in volume of the solution after 15 seconds? Show necessary work.
(c) What does the change in volume after 15 seconds mean in the real world? Answer in complete sentences.

Answer:

free energy, in thermodynamics, energy-like property or state function of a system in thermodynamic equilibrium. Free energy has the dimensions of energy, and its value is determined by the state of the system and not by its history.

Answer:

Answer:

Part A

The two variables are the amount of pounds that we dont know yet for the nuts and the almonds so we would have to put x for the amount of pounds for pecans and y for the amount of pound for nuts

Part B

2x + 4.50y = 15.25

Step-by-step explanation:

Step-by-step explanation:

x = pounds of pecans bought

y = pounds of almonds bought

x + y = 6

x×2 + y×4.5 = 15.25

x = -y + 6

(-y+6)×2 + y×4.5 = 15.25

-2y + 12 + 4.5y = 15.25

2.5y = 3.25

y = 3.25 / 2.5 = 3 1/4 / 2 1/2 = 13/4 / 5/2 = 13×2 / 4×5 =

= 26/20 = 13/10 = 1.3 pounds

x = -y + 6 = -1.3 + 6 = 4.7 pounds

Cody could buy 4.7 pounds of pecans and 1.3 pounds of almonds.

Answer:

6x-6

Step-by-step explanation:

(2x+6)+(4x-12)=2x+6+4x-12

                      =6x-6

Similar figures are two or more given figures that have some common properties. The answers to the questions are;

14. m<WYZ = [tex]157^{o}[/tex]

15. m<ACB = [tex]87^{o}[/tex]

Two or more figures are said to be similar if they have some common properties. Note that similar figures may not be congruent.

Thus, the solutions to the questions can be determined as follows:

14. Comparing WYZ and VXYZ, we can deduce that:

<WYZ + <YVX = [tex]180^{o}[/tex] (sum of angles on a straight line))

So that;

(16x - 3) + (3x - 7) = [tex]180^{o}[/tex]

19x - 10 = [tex]180^{o}[/tex]

19x = [tex]190^{o}[/tex]

x = [tex]\frac{190}{19}[/tex]

  = [tex]10^{o}[/tex]

Then,

m<WYZ = (16x - 3) = (16(10) -3)

             = [tex]157^{o}[/tex]

The measure of angle WYZ is [tex]157^{o}[/tex].

15. (11x - 2) = (6x + 13)     (similarity property)

11x - 6x = 13 + 2

5x = 15

x = 3

So that;

m<ABC = (6x + 13) = (6(3) + 13)

             = [tex]31^{o}[/tex]

m<ABC = [tex]31^{o}[/tex]

But,

m<BAC + m<ABC + m<ACB = [tex]180^{o}[/tex]  (sum of angles in a triangle)

[tex]62^{o}[/tex] + [tex]31^{o}[/tex] + m<ACB = [tex]180^{o}[/tex]

m<ACB = [tex]180^{o}[/tex] - 93

             = [tex]87^{o}[/tex]

m<ACB = [tex]87^{o}[/tex]

The measure of angle ACB is [tex]87^{o}[/tex].

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Answer:7 deadly sins cursed by light

Step-by-step explanation:

Answer:

The answer is 11 your welcome

Answer:

11

Step-by-step explanation:

The lines that are parallel continuously have equal distances from each

other and perpendicular lines form 90° angle at their intersection.

The correct responses are;

Reasons:

Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel where; Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex]

[tex]\displaystyle \overline{AB} \ and \ \overline{CD} \ are \ perpendicular\ where; \ Slope \ of \ \overline{AB} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex]

[tex]1. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{13 - 3}{-2 - 0}} = \frac{10}{-2} = -5[/tex]

[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{3 - 0}{10 - (-5)} = \frac{1}{5}[/tex]

[tex]\displaystyle \mathbf{Slope \ of \ \overline{AB}} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]2. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{7- 1}{3 - (-6)}} = \frac{6}{9} =\frac{2}{3}[/tex]

[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{-5 - (-1)}{-6 - 0} = \frac{-4}{-6}=\frac{2}{3}[/tex]

Slope of [tex]\mathbf{\overline{AB}}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel

[tex]3. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{ \frac{2- 4}{-6 - (-2)} = \frac{-2}{-4}} =\frac{1}{2}[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{11 - (-7)}{-1 - 5} = \frac{18}{-6}=-3[/tex]

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

[tex]4. \ \displaystyle Slope \ of \ \overline{AB} = \frac{8- 3}{-3 - 2} = \frac{5}{-5} =-1[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{6 - 2}{-4 - (-8)} = \frac{4}{4}=1[/tex]

[tex]\displaystyle Slope \ of \ \overline{AB} = \mathbf{-\frac{1}{Slope \ of \ \overline{CD}}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular

[tex]5. \ \displaystyle Slope \ of \ \overline{AB} = \frac{-1 - 2}{-8 - (-4)} = \frac{-3}{-4} =\frac{3}{4}[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-3 - 6}{0 - 12}} = \frac{-9}{-12}=\frac{3}{4}[/tex]

Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel

[tex]6. \ \displaystyle Slope \ of \ \overline{AB} = \frac{5 - (-1)}{6 - 3} = \frac{6}{3} =2[/tex]

[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-5 - 7}{2 - (-4)}} = \frac{-12}{6}=-2[/tex]

[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular

Directions: To determine if the equations are parallel or perpendicular

Solution:

The equations are parallel if when expressed in the form, y = m·x  + c, the value of m are equal

The equations are perpendicular, when we have;

[tex]\displaystyle The \ value \ of \ \mathbf{m} \ in \ one \ equation = -\frac{1}{The \ value \ of \ \mathbf{m} \ in \ the \ other\ equation }[/tex]

7. First equation

3·x + 2·y = 6

Therefore; [tex]\displaystyle y = -\frac{3}{2} \cdot x + 3[/tex]

Second equation; [tex]\displaystyle y = \mathbf{-\frac{3}{2} \cdot x + 5}[/tex]

The value of m which is the coefficient of x are both equal to [tex]\displaystyle -\frac{3}{2}[/tex]

Therefore, the equations are parallel

8.  Equation 1; 3·y = 4·x + 15

Therefore;

[tex]\displaystyle y = \frac{4}{3} \cdot x + 5[/tex]

Equation 2; 9·x + 12·y = 12

[tex]\displaystyle y = -\frac{9}{12} \cdot x + 1 = 1 - \frac{3}{4} \cdot x[/tex]

The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular

9. Equation 1: 8·x - 2·y = 4

Therefore;

y = 4·x - 2

Equation 2: x + 4·y = -12

Therefore;

[tex]\displaystyle y = -\frac{1}{4} \cdot x - 3[/tex]

The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular.

10. Equation 1: 3·x + 2·y = 10

Therefore;

[tex]\displaystyle y = -\frac{3}{2} \cdot x - 5[/tex]

Equation 2: 2·x + 3·y = -3

[tex]\displaystyle y = -\frac{2}{3} \cdot x -1[/tex]

The slopes of the equation 1 and 2 are not equal, and are not  the negative inverse of each other, therefore, the equations are neither parallel nor perpendicular.

Learn more about parallel and perpendicular lines here:

https://brainly.com/question/7197064

Answer: 11 hours and 29 min

Step-by-step explanation:

Answer:

4.79 or 4.789

Step-by-step explanation:

the first answer is if you need to round to the nearest hundredth, the second if you need to round to the nearest thousandth. you didn't tell us which was correct so I put both

Answer:

1 2/3, and -1 2/3

Step-by-step explanation:

Im wondering how old you are, and since you seem young just based off the math you're asked to do, please listen to the explanation and teach yourself this. This skill in particular is SOOO important to the rest of the math world. So since your number line is already divided into thirds, there are two ways you could find your answer. One, you can count 5 thirds away from zero, or two, you could simplify 5/3 from an improper fraction to a mixed number (1 2/3) and find your spot from there. "and the opposite" means not only the point 5/3 Away from zero on the Right, but also 5/3 away from zero on the Left. start from zero again and count the same amount away but in the opposite direction. With negatives it can help to think of how all numbers are just descriptions of how far left or right a number is from zero. i hope this helped lol, negatives are a confusing batch, but they're so so important to math as a whole.

Answer:

absolute value

coefficient

constant

counterexample

equation

expression

evaluate

inequality

I hope that helps maybe give brainliest if it does!

Love,

-Banana

Answer:

Approximately 11.1666666667 rows

Step-by-step explanation:

134/12= 11.1666666667

Answer:

  12 rows

Step-by-step explanation:

  (134 students) / (12 students/row) = 11 2/12 rows

The 6th-graders will need 12 rows of seats. The last row will not be filled.

Answer:

600 boys

800 girls

Step-by-step explanation:

Ratio is 3:4

let total number of boys be x

3/4=x/1400-x

4x=3(1400-x)

4x=4200-3x

7x=4200

x=600

600 boys

1400-600 = 800 girls

Answer: The radius increases by 0.032 cm/minute.

Step-by-step explanation:

The volume, V, of a sphere is V = (4/3)πr^3.

For the volume to increase at a rate of 10cc (cubic centimeters) per minute, the radius must increase such that the additional radius (r)^3 = 10

V = (4/3)πr^3

V = (4/3)π5^3

V = 524 cc

We add 10 cc to have the balloon hold 544 cc.  We calculate the increase in radius:

534=(4/3)*pi*x^3

We can now calculate the new radius, x.

x = 5.032 cm

The radius increased by 0.032 cm/minute.

Answer:

6250

Step-by-step explanation:

62 hundreds is the same as 62 X 100 which equals 6200.

5 tens is the same as 5 X 10 which equals 50.

And if we add these together, we get a total of 6250

Answer:

y= 8

Step-by-step explanation:

y= -x +5

To find the value of y when x= -3, substitute -3 into x and solve the equation.

When x= -3,

y= -(-3) +5

y= 3 +5

y= 8

Answer:

Both triangles are congruent.

so 30/36 = 5/6 = 0.83333333333...

35/x  should also be 0.83333333333.. so 35/0.83333333333.. is x

x = 42

Answer:

the answer is 5×9+2=47

Step-by-step explanation:

the answer is 47

Answer:

there

Step-by-step explanation:

1

Answer:

y=m+p

Step-by-step explanation:

take the p to the other side.

p crosses = sighn and becomes +

hence ans = y=m+ p

Answer:

look at the picture ..........

Answer:

A woman got on the elevator on the fourth floor. The elevator went down 2 11 floors. Then, the woman got off the elevator. On which floor did the woman exit the elevator

Answer:

angel b is 70 because all the degrees in a triangle must add up to 180

Answer:

Isabella paid more.

Step-by-step explanation:

$72/6 = $12.67

She paid twelve dollars for 1 lb of steak while Mason paid 6 dollars for 1 lb.

Answer:

Isabella has a greater ratio of dollars/lbs

Step-by-step explanation:

Mason paid $6/1 lb

Isabella paid $12/1 lb

Hope this helps!

Answer:

Replace the value of r in the formula :

A = π • r²

A = π • 6²

A = 113,097

Since you need to round off your answer to one decimal, your final answer is :

A = 113.1 square ft

Step-by-step explanation:

Answer:

everything but the 4th are true

Step-by-step explanation:

fax

Answer:

B,C,E

Step-by-step explanation:

Answer:

Line 1 & 2 is Perpendicular

Line 1 & 3 is Neither

and Line 2 & 3 is Neither