12x+12=13x−12 how many sultions

Yes.

8/7 (1 1/7) is rational.

Answer:

Step-by-step explanation:

Maybe you want to simplify each of these expressions.

  2a -1/2a = (2 -1/2)a = (3/2)a

__

  3a -1/3a = (3 -1/3)a = (8/3)a

Answer:

x(t) = 581.66 lb

Step-by-step explanation:

From the given information:

Consider the salt quantity in the tank at time t be x(t) lb.

∴ the rate of change of salt content in the tank is [tex]\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow[/tex]

where:

the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons

=21 lb/s

rate of outflow = salt conc. in the tank  × flow rate

= x/250 ×  9

= 9x/250  lb/s

∴

[tex]\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}[/tex]

[tex]\dfrac{dx}{dt} + \dfrac{9x}{250}= 21[/tex]

This is a 1st order linear differentiation,

The integrating factor if [tex]e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}[/tex]

∴

[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C[/tex]

[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C[/tex]

[tex]x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}[/tex]     at  t = (0) and x(0) = 100 lb

Hence;

[tex]100 = \dfrac{1750}{3}+C[/tex]

[tex]C = \dfrac{1750}{3} -100[/tex]

[tex]C = - \dfrac{1450}{3}[/tex]

∴[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}[/tex]

after time t = 1 minute i.e 60 s

[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}[/tex]

[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}[/tex]

x(t) = 581.66 lb

Answer:

is an=6n+3 your question?

Step-by-step explanation:

Answer:

Common Difference (d) =6

5th term = 33

Step-by-step explanation:

[tex]a_n= 6n +3.... (given) \\

Plug\: n = (n +1)\\

a_{(n+1)}= 6(n+1) +3 = 6n + 6 +3 = 6n + 9\\

Common \: Difference \: (d) = a_{(n+1)} - a_n\\

= 6n + 9 - (6n+ 3)\\

= 6n + 9 - 6n - 3\\

= 9-3\\

\red{\boxed{\bold {Common \: Difference \: (d) =6}}} \\

Plug \: n = 5 \: in\: a_n= 6n +3\: we \: find:\\

a_5= 6\times 5+3= 30 + 3 = 33\\

\huge\purple {\boxed {a_5= 33}} \\[/tex]

Answer:

5.1

Step-by-step explanation:

we have

5.1436

since 4 is less than five we cannot pass the 1 to 2

so it stays like

5.1

Answer:

8.71428571

do 61 divided by 7. Simple math.

Answer:

8.714

Step-by-step explanation:

Divide 61 centimeters by the 7 people getting the liquorice to get 8.7142857143.

From here you can round.

I rounded to the thousandths place but you can also round it up to 8.71 or 8.7 or any other digit if it suits your answer.

Hope this helps!

Answer:

The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]

Step-by-step explanation:

Given that,

The equation of cylinder is

[tex]x^2+y^2=9[/tex]

The part of the surface z = xy

The coordinates is,

[tex]z_{x}=y[/tex]

[tex]z_{y}=x[/tex]

We need to calculate the value of ds

Using formula of ds

[tex]ds=\sqrt{1+z_{x}^2+z_{y}^2}dA[/tex]

Put the value in to the formula

[tex]ds=\sqrt{1+y^2+x^2}dA[/tex]....(I)

We know that.

The polar coordinates,

[tex]x=r\cos\theta[/tex]

[tex]y=r\sin\theta[/tex]

The general equation of cylinder is

[tex]x^2+y^2=r^2[/tex]

compare from given equation

[tex]x^2+y^2=3^2[/tex]

0<=θ<=2π, 0<=r<=3

Area element in polar coordinates is,

[tex]dA=r dr d\theta[/tex]

Put the value of dA in equation (I)

[tex]ds=\sqrt{1+r^2}r dr d\theta[/tex]....(II)

We need to calculate the area of surface

Using equation (II)

[tex]s=\int_{0}^{2\pi}\int_{0}^{3}\sqrt{1+r^2}r dr d\theta[/tex]

[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+r^2)^{\frac{3}{2}})_{0}^{3}d\theta[/tex]

[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+3^2)^{\frac{3}{2}}-(1+0^2)^{\frac{3}{2}})d\theta[/tex]

[tex]s=(\dfrac{1}{3}((10)^{\frac{3}{2}}-1)\theta)_{0}^{2\pi}[/tex]

[tex]s=\dfrac{1}{3}(10^{\frac{3}{2}}-1)(2\pi-0)[/tex]

[tex]s=\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]

Hence, The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]

Answer:

16

Step-by-step explanation:

The mean of a group of values is calculated as

mean = [tex]\frac{sum}{count}[/tex]

Given 5 numbers with a mean of 12, then

[tex]\frac{sum}{5}[/tex] = 12 ( multiply both sides by 5 )

sum = 60

let the number removed be x , then

[tex]\frac{60-x}{4}[/tex] = 11 ( multiply both sides by 4 )

60 - x = 44 ( subtract 60 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

The number removed was 16

Answer:

4.2 rightttttrttr or no

Answer:

d. 674,800

Step-by-step explanation:

1 dekagram is equal to 1,000 centigrams so I multiplied 674.8 by 1000

Hope this helps, have a great day:)

Answer:

The answer is 674800 centigrams

Step-by-step explanation:

How many dekagram in 1 centigram? The answer is 0.001.

I assume you are converting between dekagram and centigram.

You can view more details on each measurement unit:

dekagram or centigram

The SI base unit for mass is the kilogram.

1 kilogram is equal to 100 dekagram, or 100000 centigram.

Note that rounding errors may occur, so always check the results.

Use this page to learn how to convert between dekagrams and centigrams.

Type in your own numbers in the form to convert the units! Hope this helps!

Answer:

Step-by-step explanation:

f(x) = 2x - 1

To find f(10) substitute the value of x that's 10 into f(x). That is for every x in f (x) replace it with 10

We have

f(10) = 2(10) - 1

= 20 - 1

We have the final answer as

Hope this helps you

J = 0 because it is the midpoint of K and P.

Since we know that K is at -5 and P is at 5, KP = 10

Both KP and JQ are equal to 10, therefore, they are equal.

Answer:

14. j=0

15. KP=10

16. yes

Step-by-step explanation:

(The two letters next to each other means that the question is asking for the distance between the points. For example, KP is the distance from K to P, or P to K.)

14.:

If P is the midpoint of J and Q, that means that there is an equal distance between Q and P and J and Q. So, you can see this because

Q-P=5 and 5*2= J

So the distance from J to Q is 10, but to find what J is, subtract the distance from Q, leaving you with 0. So, J=0.

15.:

Since each line represents 5 and the distance from -5 to 5 is 10, KP = 10.

16.:

Since KP = 10 and JQ = 10, then yes, they are the same.

Answer:

The answer is line EF, C is the correct answer!

Step-by-step explanation:

Just took the assignment. Maybe this will help you with your other problems with slopes and angles. If you have any more questions for me, I'll answer them! :D

The perpendicular line is line EF.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Slope = m = tan θ

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

Given:

slope = -1/3

then, the perpendicular line will have the slope = 3

Now, from the figure the line line represent the slope 3 is line EF

As, (0, -3) and (2, 3)

slope = 3+3 / 2-0

slope= 6/2

slope= 3

Hence, the perpendicular line is line EF.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

Answer:

4x-2

Step-by-step explanation:

First, distribute the minus sign.

-2x+3-(5-6x)

-2x+3+ -1(5)+ -1(-6x)

-2x+3+ (-5) + (6x)

-2x+3-5+6x

Next, combine like terms.

-2x+3-5+6x

(-2x+6x)+(3-5)

4x+(-2)

4x-2

Answer:

4x - 2

Step-by-step explanation:

-2x + 3 - -5 + 6x ( First distribute the parenthess and apply minus-plus rules making it -2x+3-5+6x )

-2x + 6x + 3 - 5 ( Group the equation like this putting like terms together)

4x + 3-5 ( From there add -2x and 6x- like terms to get 4x)

4x -2( After that subtract 3-5 ad the answer is -2)

THE FINAL ANSWER BECOMES 4x - 2

HOPE IT HELPED

Answer:

x > 1

Step-by-step explanation:

6x + 14 > 20

      -14    -14

6x > 6

/6    /6

x>1

Answer:

24 m

Step-by-step explanation:

The lenght of fencing needed is the sum of all sides the triangular garden represented on the coordinate grid.

The lenght of the triangular garden = 16 - 10 = 6 m

Lenght of the height = 8 - 0 = 8 m

Lenght of the hypotenuse can be calculated using coordinates of the two vertices of the ∆ that forms the hypotenuse lenght and also using the distance formula.

Coordinates of the two vertices = (10, 0) and (16, 8).

[tex] distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Let,

[tex] (10, 0) = (x_1, y_1) [/tex]

[tex] (16, 8) = (x_2, y_2) [/tex]

[tex] d = \sqrt{(16 - 10)^2 + (8 - 0)^2} [/tex]

[tex] d = \sqrt{(6)^2 + (8)^2} [/tex]

[tex] d = \sqrt{36 + 64} = \sqrt{100} [/tex]

[tex] d = 10 [/tex]

Length of fencing = 6 + 8 + 10 = 24 m

Answer:

10(x + 3) - (-9x - 4) = x - 5+ 3

10x+30+9x+4=x-2

19x+34=x-2

19x-x= -2-34

18x=-36

x= -2

Answer:

20s³ + 50s² + 32s + 6

Step-by-step explanation:

( 4s + 2 ) ( 5s² + 10s + 3)

use the distribution property:

20s³ + 40s² + 12s + 10s² + 20s + 6

combine like terms:

20s³ + 50s² + 32s + 6

therefore

the expand value = 20s³ + 50s² + 32s + 6

Answer: 1/10

Step-by-step explanation:

1/10 which means that 2/9 Was the wrong answer

Answer:

5 ounces

Step-by-step explanation:

Let the capacity of jug be j, bottle be b

[tex]2j + 4b = 40 \\ j + 3b = 25 \\ j = 25 - 3b \\ \\ therefore \: 50 - 6b + 4b = 40 \\ 2b = 10 \\ b = 5[/tex]

Answer: 7.808.

Take the 2 values and multiply them together using the digits

Answer:

-2

Step-by-step explanation:

because it is tilted so z+4 +2 so -2+4=2

Answer: rolling aa six sided die- fiona is deciding which forest

selecting a playing card- Athena has to select 1 student

spinning a spinner - Jenny isa picking a marble

Step-by-step explanation:

Answer:

Fiona- Rolling A Six-Sided Die.

Althea- Selecting A Playing Card From

The Hearts Suit.

Jenny-Spinning A Spinner Divided Into

Five Equal Sections  

To find explicit formulas, you need two things. The common difference and the first term.

For example, #18

The first term = -15

The common difference = -20 -(-15) = -20 + 15 = -5

y = A + B(n - 1)

A = our first term

B = our common difference

n = the term you want to find in the sequence.

Leta plug our numbers in from #18

y = -15 + -5(n - 1)

Let's find the 4th term in the sequence.

y = -15 + -5(4 - 1)

y = -15 + -5(3)

y = -15 + -15

y = -30

Answer: 8.9

Step-by-step explanation:

Let x = the number you are finding

SOLVE:

3.9+6x=57.3 ⇔ Given

6x=53.4 ⇔ subtract 3.9 on both sides

x=8.9 ⇔ Divide 6 on both sides

ANSWER:

The number is 8.9

Answer: YES

Step-by-step explanation:

THREE WAYS TO DETERMINE:

If the number given is in integer, it is rational.

If the number given is fraction, it is rational.

If the number given is decimal, as long as it is terminating or repetitive decimal, it is rational. (Because then you can write it as a fraction which leads to the second point)

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

-5 3/8

It is a fraction, which fits the second point.

Hope this helps!! :)

18.20 acres

28×65% =

= 28×65/100

= 1820/100

= 18.20 acres

Answer:

8-p=-12-3p

8+12-p = -3p

20 = -3p + p

20 = -2p

20/-2 = p

-10 = p

ans. p = -10

...