Solve Multi-Step Equations, Part 2 - Instruction
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Solve the equation - 10(g - 6) = 65.
») What is the value of g?
g=
?

It looks like the differential equation is

[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]

Factorize the right side by grouping.

[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]

[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]

Now we can separate variables as

[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]

[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]

[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]

You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

Answer:

120 meters

Step-by-step explanation:

1.2  x 10 000 = 12000 cm   = 120 meters  

Answer:

-ax² + bx + c and satisfies the condition b² = 4ac

Step-by-step explanation:

that's my answer

{Correct me if I'm not correct}

Keep safe|

Step-by-step explanation:

please can you divide it will give you the answer

Answer:

-10

Step-by-step explanation:

if we put f(n)=3 , Then

f(3)=f(3-2) + f(3-1)

= f(1) + f(2)

= -6+(-4). [since f(1)= -6 and f(2) = -4)

= -6-4

= -10

Answer:

8x

Step-by-step explanation:

We can add all of the side lengths of the triangle to figure out the perimeter. 3x-1+3x+1=6x+2x=8x

Answer:

3/10

Step-by-step explanation:

So you have 2/5 left in your cupboard. Say the amount of chips originally in your cupboard would be 30. 2/5 of 30 would be 12.

Then multiply 12 by 3/4 so it would be 3/4 of 12.

The result would be 9

9/30 = 3/10

this is complicated explanation

there are much easier explanations tho

Answer:

in terms of pi: A = 14,400pi

A = 14,400(3.14) is 45,216

Step-by-step explanation:

Area of a circle is pir^2

Radius = diameter / 2

Radius = 240 / 2 which is 120

A = pi(120)^2

A = 14,400pi

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the area of a circle with a diameter of 240.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

We can find the radius by dividing the diameter by 2:

[tex]\star~\large\pmb{240\div2=120}[/tex]

The radius is 120. Now it's time to compute the area!

///\\\///\\\///\\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\

                                    Computing The Area

The formula for the area is:

[tex]\star~\large\pmb{Area_{(circle)}=\pi r^2}}[/tex]

See, there's the radius, r; we found a minute ago, and it equals 120 cm.

Now, substitute the value of r into the formula:

[tex]\begin{gathered} \sf{\longmapsto{A=\pi (120)^2} \\ \sf{\longmapsto{A=\pi\times14,400} \\ \sf{\longmapsto{A=45,238.9\;cm^2 \end[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

4

Step-by-step explanation:

8/2 is 4

Answer:

  318

Step-by-step explanation:

The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.

__

The amount of the penalty is 5.3% of 6000:

  0.053 × 6000 = 318

Wendy paid a penalty of 318 for her early withdrawal.

Answer: 121.375

Step-by-step explanation:

[tex]2^4=16[/tex]

[tex]\frac{1942}{2^4}[/tex]

[tex]\frac{1942}{16}=121.375[/tex]

Answer:

6 m²

Step-by-step explanation:

Original area :

12 × 14 = 168 m²

New area :

(12-3) × (14+4) =  

9 × 18 = 162 m²

168 - 162 = 6

Area would change by 6 m²

Answer:

x = 3

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve for x.

The value of x is 3.

We can plug it back in to check if it works.

Correct!

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

9 - 2(x - 5) = x + 10

Distribute

9 - 2x + 10 = x + 10

Subtract 10 to both sides

9 - 2x = x

Add 2x to both sides

9 = x + 2x

9 = 3x

Divide 3 to both sides

9/3 = 3x/3

3 = x

OR

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex] ln(x) + ln(y) + ln(3) [/tex]

[tex] ln(3xy) [/tex]

Any line with a slope different than 3 will intercept the given line only once.

The answer will be any line that is not parallel (nor the same) to the given line.

Remember two lines are parallel if the lines have the same slope and different y-intercept

In this case, the given linear equation is:

6x - 2y = 10

y = 3x - 5

So the slope is 3 and the y-intercept is -5.

Then, any line with a slope different than 3 will intercept this line only once.

An example can be:

y = 314*x

If you want to learn more about linear equations:

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Answer:

x = 3.4

Step-by-step explanation:

Use the sin formula, due to the fact of the hypotenuse being known, and the variable being across 70.

Sin(70) = x / 3.6

Sin(70) * 3.6 = x

3.3828934 = x

Round to nearest tenth, as question asked

3.4 = x

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,

∠A = 2(∠B) = 2[3(∠C)] = 6x

∠B = 3x

∠C = x

Now, since the sum of all the angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180°

6x + 3x + x = 180°

10x = 180°

x = 18°

Hence, the measure of ∠C is 18°.

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Answer:

Coordinate pair for Friday (3, 55). This means the length of the eruption was 3 minutes, and the wait time between the eruptions was 55 minutes.

Paulo and Jason wear smaller shoe sizes than Carmen.

Jason and Carmen scored more runs than Paulo.

Step-by-step explanation:

Paulo wears size 5 and Jason wears size 4. Carmen wears size 10, therefore the players wear smaller shoe sizes than he does

Jason scored 10 runs, and Carmen scored 11. Since Paulo only scored 5 runs, the other players scored more than him

The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

let

x = cost of the meal

Both = 2x - 3

3/4x + 1/2x = 2x - 3

(3+2)x / 4 = 2x - 3

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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x=4

Step-by-step explanation:

4x=16y

x=16divide4

x=4

Answer:

y = 4x

Step-by-step explanation:

Take a pair of coordinates, like

(8,32) ; (4,16)

m = (Δy):(Δx)

   = (32-16) : (8 - 4) = 4

y = mx + c

  = 4x +c

Now substitute the values from one of the 2 coordinates' pair.

16 = 16 + c

c = 0

Therefore,

y = 4x

Answer:

d.  ΔMNO

Step-by-step explanation:

In geometry, two figures are congruent if they are the same shape and size (they can also be a mirror image of each other).  If they are the same shape but a different size (e,g, one is an enlargement or reduction of the other), then they are similar.

All the given triangles have the same interior angles, so we need to find a triangle with the same side lengths as ΔABC.  

The only triangle that has the same side length as ΔABC is ΔMNO:
they both have bases of 8cm.

Therefore, ΔMNO is congruent to ΔABC.

Answer:

[tex]a. {( \sqrt{36} )}^{2} = 36[/tex]

[tex]b. ({ \sqrt{ \frac{25}{81} } })^{2} = \frac{25}{81} = 0.3086[/tex]

[tex]c. {( \sqrt{1.99} )}^{2} = 1.99[/tex]

[tex]d. {( \sqrt{x} })^{2} = x[/tex]

The square exponent is removed with the root .

Answer:

w = (12p - 7) / 2

Step-by-step explanation:

p = (2w + 7) / 12

12p = 2w + 7

2w = 12p - 7

w = (12p - 7) / 2

The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x  for finding the values of y.

Thus,

       16*(-2)+4y=12

      -32+4y=12

      4y=12+32

     4y=44

      y=11

         16*(-1)+4y=12

         16*(0)+4y=12

         16*(1)+4y=12

         16*(2)+4y=12

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How to solve your problem

x^{2}-21=100

Quadratic formula

Factor

1

Move terms to the left side

x^{2}-21=100

x^{2}-21-100=0

2

Subtract the numbers

x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0

x^{2}\textcolor{#C58AF9}{-121}=0

3

Use the quadratic formula

x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x^{2}-121=0

a=\textcolor{#C58AF9}{1}

b=\textcolor{#F28B82}{0}

c=\textcolor{#8AB4F8}{-121}

x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}

4

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Add zero

Multiply the numbers

x=\frac{\pm 22}{2}

5

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{22}{2}

x=\frac{-22}{2}

6

Solve

Rearrange and isolate the variable to find each solution

x=11

x=-11