Every time Martina orders Chinese food, she gets egg drop soup. So, she decides to learn how to make it herself. Her recipe calls for 8 cups of broth, but she can only find 32-fluid-ounce cartons at the store. How many cartons should she buy?
cartons

Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is given by:

[tex]\frac{dy}{dx} = 2x[/tex]

Then, applying separation of variables:

[tex]dy = 2x dx[/tex]

[tex]\int dy = \int 2x dx[/tex]

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

Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:

y(x) = x² + 2.

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The differential equation is y(x) = x² + 2.

Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.

The given equation is;

[tex]\rm \dfrac{dy}{dx}=2x[/tex]

Applying the variable separation method;

[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]

The value of c when y( 0 ) = 2 is c =2.

Hence, the required differential equation is y(x) = x² + 2.

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Answer:

Step-by-step explanation:(206-3x)+x

2(3x)+x+12

ok as i think one no is statsfy this equation .

The two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.

A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.

The standard form of the quadratic equation is,

[tex]ax^2+bx+c=0[/tex]

Here, (a,b,c) are the real numbers and x is the variable.

To find the value of x, the following formula is used,

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

The given equation is,

[tex]2(x+ 3)^2 - 4 = 0[/tex]

To solve this equation, we need to apply some mathematical operations over it. Let's start with opening the brackets.

[tex]2(x+ 3)^2 - 4 = 0\\2(x^2+6x+9)-4=0\\2x^2+12x+14-4\\2x^2+12x+12=0\\x^2+6x+7=0[/tex]

On comparing with standard equation we get,

[tex]a=1, b=6, c=7[/tex]

Put this values in the above formula,

[tex]x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(7)}}{2(1)}\\x=-4.41,-1.59[/tex]

Hence, the two values when the provided quadratic equation is solved for the x are -4.41 and -1.59 to the nearest hundredth.

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The equation of the line in slope-intercept form and standard form that passes through the line are  y = -5 / 6x - 43 / 6 and  5x + 6y = -43 respectively.

The Slope intercept equation is use to represent a linear table or graph. Therefore, the formula is represented as follows

y = mx + b

where

m = slope

b = y-intercept

Hence,

(-5, -3)(1, -8)

m = -8 + 3 / 1 + 5 = - 5 / 6

Using (1, -8) let's find b

-8 = -5 / 6 (1) + b

-8 + 5 / 6 = b

-48 + 5/6 = b

b = -43 / 6

Therefore, the slope intercept equation is y = -5 / 6x - 43 / 6

The equation in standard form is represented as Ax + By = C. Therefore,

y + 5 / 6 x = - 43/6

5x + 6y = -43

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Answer:

A parallelogram by definition has 2 pairs of parallel sides.

A parallelogram could be:

____________

|                        |

|___________|

A rectangle in euclidean geometry has 4 right angles.

For example:

________________

|                                 |

|_______________|

However, a parallelogram may have 2 pairs parallel sides but not 4 right angles.

For example:

______________

\                              \        

 \______________\

Therefore, A parallelogram is not always a rectangle.

Hope this helps!!!

Please mark me as brainliest!!!

Step-by-step explanation:

x^2 + (4+3)X + 12

x^2 + 4x + 3X + 12

X (X + 4) + 3 ( X + 4)

( X + 3) (X +4)

Solving steps:

[tex]\sf \rightarrow x^2\:+\:7x\:+\:12[/tex]

breakdown the following

[tex]\sf \rightarrow x^2\:+\:3x + 4x\:+\:12[/tex]

break the expressions into groups

[tex]\sf \rightarrow \left(x^2+3x\right)+\left(4x+12\right)[/tex]

factor the following

[tex]\rightarrow \sf x\left(x+3\right)+4\left(x+3\right)[/tex]

factor the common term: (x+3)

[tex]\rightarrow \sf \left(x+3\right)\left(x+4\right)[/tex]

Answer:

139

Step-by-step explanation:

A = Pe^rt

A = 600$

P = 300$

R = 0.005

T = ?

600 = 300e^(0.005)(t)

t = 138.63

Answer:

12cm²

Step-by-step explanation:

Area of triangle =1/2×h×b

1/2×4×6

2×6

12cm²

hope dis helps!!!!!

Answer:

[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]

Step-by-step explanation:

[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]

Answer:

4

3

Step-by-step explanation:

Answer:

1200 packets of tea

Step-by-step explanation:

Its because theres 1000 grams in 1kg so it would be 600000 grams and you would divided 600000 over 500 and get 1200

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Answer:

1,200 packets of tea

Step-by-step explanation:

1. First, convert 600 kilograms into grams.

1 kilogram = 1,000 grams

So,

600 kilograms = 600,000 grams.

Now divide the previous value by 500.

[tex]\frac{600,000 g}{500 g} = 1,200[/tex]

Therefore, there are 1,200 packets of tea.

Answer:

See below.

Step-by-step explanation:

Let x = amount of money you have in your account.

The money in your account plus the $125 extra that you need equals the total cost of the computer.

The equation is:

x + 125 = 2250

Now we solve the equation by subtracting 125 from both sides.

x = 2125

Answer: You have now $2125 in your account

Answer:

Step-by-step explanation:

The molar solubility of Ba₃(PO₄)₂ is its concentration of pure substance

The correct equation for the ksp is Ksp = 6x⁵

Start by writing the reaction for the solution of Barium phosphate

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Next, we make an ICE chart

Let "x" be the molar solubility of Barium phosphate

          Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp)

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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The molar solubility of Ba₃(PO₄)₂ is its concentration of a pure substance.

The correct equation for the ksp is Ksp = 6x⁵.

The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is denoted by the symbol Ksp.

Start by writing the reaction for the solution of Barium phosphate.

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Let "x" be the molar solubility of Barium phosphate

         Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp),

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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Answer:

4

Step-by-step explanation:

[tex]gradient = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]y2 = - 3 \\ y1 = 3 \\ x2 = 2 \\ x1 = 3[/tex]

[tex] \frac{ - 3 - 1}{2 - 3} = \frac{ - 4}{ - 1} = 4[/tex]

Answer:

C, Almost fifty percent

Step-by-step explanation: I just got it right.

By using a right triangle as a model, we will see that height of the roof is 9.38 ft.

The slant height is equivalent to the hypotenuse of a right triangle, so we know the length of the base and the hypotenuse of a right triangle. The cathetus will be half of 18ft

We need to find the other cathetus, so we can use the Pythagorean theorem, if X is the other cathetus we will get:

X^2 + (9ft)^2 = (13 ft)^2

X = √( (13 ft)^2 - (9 ft)^2) = 9.38ft

So the height of the roof is 9.38 ft.

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Step-by-step explanation:

what is the question ?

to find Craig's score ?

if that is the case :

Craig's score = 62 - 16 = 46

The rigid transformation of figure JKLM would not change the side length and angle measure

The features of the figure JKLM that would remain the same are its side lengths and angles

A rigid transformation is any of the following

All of the above transformation do not change the side length and the angle measure of the shape they transform

Hence, the features of the figure JKLM that would remain the same are its side lengths and angles

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Answer:

Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes.

So he does 1/20 of the job per minute.

.

Rob can do the job in 30 min. His rate is 1/30 of the job per minute.

.

Working together how does it take?

.

1/20*x + 1/30*x = 1 job done

, where x = minutes.

.

Step-by-step explanation:

The x-intercept of the function h(x) is when the function h(x) = 0

The x-intercept of the function is -2

From the question, the function is given as:

[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]

Set the function h(x) to 0, to calculate the x-intercept

[tex]8 * \sqrt[3]{x - 6} + 16= 0[/tex]

Subtract 16 from both sides of the equation

[tex]8 * \sqrt[3]{x - 6} +=-16[/tex]

Divide through by 8

[tex]\sqrt[3]{x - 6} =-2[/tex]

Take the cube of both sides

[tex]x - 6 =-8[/tex]

Add 6 to both sides

[tex]x =-2[/tex]

Hence, the x-intercept of the function is -2

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Answer:

-2

Step-by-step explanation:

The person above me explained it perfectly! Also, I got this answer correct on my test.

Answer:

  (a)  156 cm²

Step-by-step explanation:

The total surface area of the 12 blocks can be computed by first finding the surface area of one block. That result can then be multiplied by 12. The area of one rectangular prism is given by the formula ...

  A = 2(LW +H(L +W))

  A = 2(4·1 +1/2(4+1)) = 2(4 +5/2) = 13 . . . cm²

The area of 12 such prisms will be ...

  12 × (13 cm²) = 156 cm²

Victor needs 156 cm² of fabric to cover 12 blocks.

_____

Additional comment

This problem offers an opportunity to exercise your number sense. The area of the largest surface of one block is (4 cm)×(1 cm) = 4 cm². 12 of these surfaces will have an area of 48 cm². This is only part of the total area, so the only reasonable choice among those offered is 156 cm².

Answer:

156 cm² for K12

Answer:

[tex] \frac{1}{ \sqrt{2} } [/tex]

Step-by-step explanation:

Given

[tex]theta = 22 \frac{1}{2} = \frac{45}{2} [/tex]

[tex]2 \times theta = \frac{45}{2} \times 2 = 45[/tex]

Sin2theta=sin45⁰=1/√2

[tex] \frac{1}{ \sqrt{2} } [/tex]

is your answer

Answer:

[tex]\sf \dfrac{\sqrt{2}}{2}[/tex]

Step-by-step explanation:

[tex]\sf If\:\theta=\left(22\dfrac12\right)^{\circ}[/tex]

[tex]\sf \implies2\theta=2\cdot\left(22\dfrac12\right)^{\circ}=45^{\circ}[/tex]

[tex]\sf Therefore\:\sin2\theta=\sin(45)^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]

Proof

If a right triangle has an interior angle of 45°, then the third interior angle will also be 45° (since the sum of the interior angles of a triangle is 180°).

This means that the two legs of the right triangle are equal in length.

Using Pythagoras' Theorem, we can state that the hypotenuse of a right triangle with two legs of equal length will be √2 times the length of a leg.

Let a = b = 1

⇒ 1² + 1² = c²

⇒ c = √2

The sine trig ratio is:

[tex]\mathsf{\sin(\theta)=\dfrac{O}{H}}[/tex]

where:

[tex]\implies \sf \sin(45^{\circ})=\dfrac{1}{\sqrt{2} }[/tex]

[tex]\implies \sf \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}}{2}[/tex]

[tex]\implies \sf \sin(45^{\circ})=\dfrac{\sqrt{2}}{2}[/tex]

Una ecuación cuadratica que solo tiene el termino cuadratico se escribe como:

y = a*x^2

La ecuación cuadratica general se escribe como:

y = a*x^2 + b*x + c

Donde el termino cuadratico es el primero, el segundo es el lineal y el tercero es el constante.

Entonces, si queremos una ecuación cuadratica que solo tenga el termino cuadratico, la ecuación sera:

y = a*x^2

Sí quieres aprender más sobre cuadraticas, puedes leer:

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Answer:

side length = 4

Step-by-step explanation:

Let x = the side length

Area is x•x, which is x^2.

Perimeter is x+x+x+x, which is 4x.

x^2 = 4x

x^2 - 4x = 0

Factor.

x(x-4) = 0

x = 0 or x = 4

Discard 0 as an answer as it is not useful.

x = 4.

Area = 4^2 = 16

Perimeter = 4(4)= 16

The side length is 4.

The formula of the farm agency illustrates a geometric progression

The formula the farm agency could use is y = 3^n

The number of characters is given as:

n(A,B,C) = 3

Represent the number of tags to create with y.

So, we have:

y = 3×3×3×3×..........×3( in n places)

Express as exponent

y = 3^n

Hence, the formula the farm agency could use is y = 3^n

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Answer: y=4^n

Step-by-step explanation: I got the question right and this was the answer, I believe its because the company uses A,B,C and blank spaces so that adds one.

Answer:

(2,0) is not a point on the graph of the function y=x+2

Step-by-step explanation:

Go to the TI-84 plus calculator and go to the y= button and then type in x+2 and then press the 2nd button and then the graph button and then you should get your answer.

Answer:

11: x=60   12:x=27

Step-by-step explanation:

For the first one, we know that all triangle angles add up to 180, so we take 180 and divide by 3 to get each of the angles and we get 60. For the second one, like I said earlier, all triangles add up to 180 so you add all the angles together and make them equal 180. You simplify and you get x=27

(also i changed my answer because I double checked it and it was wrong

Answer:

  1

Step-by-step explanation:

The square of the value in the empty space is the constant in the expanded expression. That is ...

  [ ]² = 1

The value in the space is ...

  [ ] = √1 = 1

The filled-in equation is ...

  (3x -1)² = 9x² -6x +1

_____

The expansion of the square of a binomial is ...

  (ax -b)² = a²x² -2abx +b²

Above, we used the constant term to find 'b', but we could also have used the linear term:

  -6x = -2(3)bx . . . . . a=3 in this problem

  1 = b . . . . . . . divide by -6x