10. A student solves the following problem:
Problem:
2 (x-3) + 3x = 19
2x - 6 + 3x = 19
(2x + 3x) - 6 = 19
5x - 6 - 19
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
5x - 6+ 6 = 19+ 6
5x = 25
X = 5
What property justifies step 4?
a. Commutative Property of Addition
c. Multiplication Property of Equality
b. Addition Property of Equality
d. Substitution

Potential energy can be defined as energy that is stored inside an object due to its position or configuration.The potential energy function for f⃗ is given by:-U = α (x^2 / 2)

Given a force vector f⃗ and its corresponding potential energy function u(x,y,z), the force is defined as the negative gradient of the potential energy function. In order to get the potential energy function for f⃗ , we need to integrate force with respect to distance. We know that force is equivalent to the derivative of potential energy with respect to distance, so we can use the fundamental theorem of calculus to solve for u(x).We are given that u=0 when x=0, so we can define our initial condition. Using the above equation, we get:-du/dx = f(x)⇒ du = -f(x)dx Integrating both sides, we get: u(x) = -∫f(x)dx + Cwhere C is a constant of integration. We can solve for C using our initial condition: u(x=0) = 0 = CSo, the potential energy function for f⃗ is:u(x) = -∫f(x)dx + 0Now, we can express f⃗ in terms of α and x, which yields :f⃗ = -αxî where î is the unit vector in the x-direction. Substituting this value for f⃗ into our equation for potential energy function, we get:u(x) = -∫(-αx)dx = 1/2αx² + C.

Therefore, the potential-energy function for f⃗ when u=0 at x=0, and expressed in terms of α and x, is given by u(x) = 1/2αx².

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Answer:

6x-y+7x-7y

6x+7x-y-7y

13x-8y.

Answer:

y=3x-13

Step-by-step explanation:

Since the parallel equations have equal slope.

The equation of line parallel to y=3x+7 will be y=3x+k.

(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13

Answer:

B. One whole number one over two. 1½

Expression is a combination of numbers, operators and variables. the value of the expression −51 − 17 − (−37) is -31.

Expression is a combination of numbers, operators and variables.

The given expression is minus fifty one minus seventeen minus of minus thirty seven.

−51 − 17 − (−37)

We have to use BODMAS rule to solve this expression

-51-17+37

Now add  minus fifty one and minus seventeen

We get minus 68

-68+37

Now subtract 37 from 68 and put minus sign in the answer.

We get answer as minus thirty one.

-31

Hence option C is correct. the value of the expression −51 − 17 − (−37) is -31.

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Here is the ans of this ques. Hope it helps

Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

Answer:

5.25

Step-by-step explanation:

butterfly method

x   3

--   --

7    4

7(3)=4x

21=4x

/4   /4

x=5.25

If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.

Let's start by using the formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

In this case, we have:

(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)

(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)

We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:

(x + 1)^2 = (x - 3)^2 + 120

Substituting the expressions we found above, we get:

x^2 + 2x + 1 = x^2 - 6x + 9 + 120

Simplifying, we get:

8x = 110

Therefore, the solution is:

x = 13.75

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Complete question is:

The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?

The best findings that support the hypothesis that NPY is necessary for the generation of the preovulatory LH surge include studies that show NPY acting on neurons in the hypothalamus, which is a critical brain region involved in regulating reproductive functions.

Additionally, experiments in animals have shown that disrupting NPY signaling can prevent the preovulatory LH surge and ovulation. Finally, clinical studies in women have found that alterations in NPY levels or activity can lead to menstrual irregularities and infertility, further supporting the role of NPY in ovulation.
To best support the hypothesis that NPY (neuropeptide Y) is necessary for the generation of the preovulatory LH (luteinizing hormone) surge, which triggers ovulation, scientists would need to find evidence such as:

1. A positive correlation between NPY levels and LH surge timing, indicating that higher NPY levels are associated with the initiation of the LH surge.
2. Experimental manipulation of NPY levels leading to changes in LH surge and ovulation, showing a cause-and-effect relationship between NPY and the hormonal event.
3. Identification of NPY receptors on the gonadotropin-releasing hormone (GnRH) neurons, which are responsible for releasing LH, suggesting a direct mechanism of action.

These findings would provide strong evidence for the proposed role of NPY in the generation of the preovulatory LH surge and ovulation.

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Answer:

Step-by-step explanation:

Slope =

\( \frac{change \: in \: y}{change \: in \: x} \)

X1=2 X2=7

Y1=-1 Y2=-1

hence

\( \frac{ - 1 - ( - 1)}{7 - 2} \)

\( \frac{ - 1 + 1}{7 - 2} \)

\( \frac{0}{5} \)

\(slope = 0\)

Answer:

A is 805i tink and B is for sure 17

Step-by-step explanation:

Answer:

51, 53, 55, 58, 60

Step-by-step explanation:

The minimum is the lowest value in the data set, that is 51

The maximum is the largest value in the data set, that is 60

The median is the middle value of the data, arranged in ascending order. If there is no exact middle then it is the average of the 2 values either side of the middle.

51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60

                                     ↑ middle

median = 55

The lower quartile is the middle value to the left of the median

51, 51, 53, 53, 54, 55

               ↑

Q₁ = \(\frac{53+53}{2}\) = \(\frac{106}{2}\) = 53

The upper quartile is the middle value of the data to the right of the median

56, 58, 58, 58, 59, 60

                 ↑

Q₃ = \(\frac{58+58}{2}\) = \(\frac{116}{2}\) = 58

Answer:1) 32.  2).  3) 21.  4) 4

Step-by-step explanation: 1) 4*8=32m, 2) I don't know, 3) 6*7=42 for the area of a square but since a triangle half it so its 21, An the last is by 4 for example 4*10=40 but if doubled its 20*8 and that equals 160. and 160/40=4

the value of ∠C is 20°

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The answer is ∠C= 20 degree

We have given:

AB= 5

AC = 14

and we have to find ∠c to the nearest degree.

So,

We know that:

tan(C)= AB/AC

tan(C)= 5/14

tan(C)= 0.3571

C=20 degree

Thus the value of ∠C is 20°

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Answer:

E

Step-by-step explanation:

A function that is linear is a straight line. A linear function can be found using [ y = mx + b ]

F shows an example of a quadratic function. A quadratic function can be found using [ f(x) = ax² + bx + c ]

Best of Luck!

\( \LARGE{ \underline{ \blue{ \bf{Required \: answer:}}}}\)

The answer is E because the graph of linear equation is a straight line whereas the graph of a quadratic equation is a parabola opening upwards or downwards depends upon the coefficient of a in standard form : ax² + bx + c.

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Answer:

tranform the 1st one to: 3m-n=11

add the 1st and 2ns equations: 5m+2n=11

Answer:

9:15 and 18:30

Explanation:

To determine which ratios are equivalent, we reduce each one to its lowest form and see if they are the same.

Next:

Next we have:

Finally:

Therefore, the ratios which are equivalent are Options A and D.

the area of section A, which has side lengths of 7 inches each.

To determine the area, we will use the following terms:

Area = Side length × Side length

Area = 7 inches × 7 inches

7 inches × 7 inches = 49 square inches

So, the area of section A is 49 square inches (OA).

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Answer:

300

Step-by-step explanation:

25×8= 200 spent

500-200=300 left

Answer:

=> $300

Step-by-step explanation:

here's your solution

=> Amount of money Trent has = $500

=> Amount spent by him in one week = $25

=> Amount left with him after 8 weeks =

= $500 - ($25*8)

=> $500 - $200

=> Amount left = $300

hope it helps

The range, mean, and median of the given data set are equal to 38, 20, and 5 respectively.

Data set = {2, 7, 15, 3, 29, 40, 6, 28, 3}

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 40 - 2

Range = 38.

Data set = {12, 34, 31, 8, 15, 20}

F(x) = 12 + 34 + 31 + 8 + 15 + 20 = 120

Mathematically, the mean of a data set can be calculated by using this formula:

Mean = F(x)/n

Mean = 120/6

Mean = 20.

Data set = {2, 4, 5, 7, 10}

Median = 5.

The total number of shots = 18 × 3 = 54 shots.

P(11) = 100 - P(T)

P(11) = 100 - 54

P(11) = 56%.

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Answer:

9300 maybe

Step-by-step explanation:

Julia understands that the initial addition of 4 coins to 5 coins results in 9 coins.

Julia's understanding of the situation demonstrates her ability to grasp the concept of addition and subtraction in relation to coins. Let's break down the scenario step by step:

1. Julia begins with 5 coins.
2. She adds 4 coins to the existing 5 coins, resulting in a total of 9 coins.
3. Julia recognizes that by adding 4 coins to 5 coins, she obtains 9 coins.

Now, let's move on to the subtraction part:

1. Julia starts with 9 coins (the sum of 5 coins and the additional 4 coins).
2. She subtracts 4 coins from the existing 9 coins.
3. Julia realizes that by subtracting 4 coins from 9 coins, she obtains 5 coins.

In summary, Julia understands that the initial addition of 4 coins to 5 coins results in 9 coins. Additionally, she comprehends that subtracting 4 coins from the sum of 9 coins gives her 5 coins. Her understanding reflects a grasp of the inverse relationship between addition and subtraction.

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To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.

1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways

2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways

3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways

So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.

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Answer:

Its still a rectangle, just move the triangles, you get 450

Step-by-step explanation:

If you think of it like a triangle, you can use the base, the 90 degree angle, and the hypotenuse to get the area, do it twice since there are two, and your result is 225 for one triangle, 450 for both.

Answer:

19

Step-by-step explanation:

2d + 3      d = 8

2(8) + 3

16 + 3

19

The correct solutions to the equation Ut = -3ux are U = 0 and U = x + 3t.

We have,

The equation Ut = -3ux is a linear first-order partial differential equation, where U represents a function of two variables (x and t).

To find the solutions to this equation, we can use the method of characteristics.

In the method of characteristics, we introduce parameter s and consider curves in the (x, t, U) space.

Along these curves, the derivatives of U with respect to x and t are related to the parameter s.

For the given equation Ut = -3ux, we have the following characteristic equations:

dx/ds = -3

dt/ds = 1

dU/ds = 0

From the first two equations, we can solve for x and t in terms of s:

x = -3s + C1

t = s + C2

Here, C1 and C2 are constants determined by the initial conditions.

Now, we substitute these expressions for x and t into the equation for U:

dU/ds = 0

Integrating this equation with respect to s, we get:

U = C3

Here, C3 is another constant determined by the initial conditions.

Therefore,

The general solution to the equation Ut = -3ux is U = C3, where C3 is a constant.

Now, let's consider the given options:

A. U = 3x + t: This is not a solution to the equation Ut = -3ux, as the coefficient of x and t does not match the given equation.

B. U = 3x - t: This is not a solution to the equation Ut = -3ux, as the coefficient of x and t does not match the given equation.

C. U = 0: This is a valid solution to the equation Ut = -3ux, as it satisfies the equation for all values of x and t.

D. U = x + 3t: This is a valid solution to the equation Ut = -3ux, as it satisfies the equation for all values of x and t.

H. None of the above: This option is correct, as only options C and D are valid solutions to the equation Ut = -3ux.

Therefore,

The correct solutions to the equation Ut = -3ux are U = 0 and U = x + 3t.

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Answer:

Great

Step-by-step explanation:

However, you're missing a factor of 9.

Answer:

1x81 =81

3x27=81

9 x 9 =81

1,3,27,81 These are factors too, but you missed of the number 9.