7. Writing Write a paragraph proof showing that if
5(2x-3)= 25, then x = 4.

The expressions x and 15-x add back up to 15.

An example: Let x = 7 which means the remaining piece is 15-x = 15-7 = 8 feet long.

Answer: 5-x

Step-by-step explanation:

Answer:

27 more

Step-by-step explanation:

7/11 x 99 = 63

4/11 x 99 = 36

63-36 = 27

Answer:

27

Step-by-step explanation:

7/11 * 9/9 = 63/99

4/11 * 9/9 = 36/99

63-36 =27

Answer:

2200

Step-by-step explanation:

8+7=15 4125/15=275 275x8=2200

im positive the answer is x<3

The differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1To solve this differential equation, we need to integrate both sides with respect to x.

dy/dx = 3x² - 2

Integrating both sides:

∫dy = ∫(3x² - 2)dx

y = x³ - 2x + C

Here, C is the constant of integration that we need to find. To do that, we can use the initial condition f(-1) = 2.

Substituting x = -1 and y = 2 in the equation:

2 = (-1)³ - 2(-1) + C

2 = -1 + 2 + C

C = 1

Therefore, the solution to the differential equation is:

y = x³ - 2x + 1

To overlay this solution on a slope field for the differential equation, we need to first draw the slope field. We can do this by calculating the slopes at different points in the x-y plane.

Using the differential equation, we know that the slope at any point (x, y) is given by:

dy/dx = 3x² - 2

We can draw arrows with slopes equal to 3x² - 2 at various points in the plane to get the slope field.

Once we have the slope field, we can overlay the solution y = x³ - 2x + 1 on it by plotting the curve y = x³ - 2x + 1 and checking if the direction of the curve matches the arrows in the slope field.

Overall, the solution to the differential equation dy/dx = 3x² - 2 with f(-1) = 2 is y = x³ - 2x + 1, and we can overlay this solution on the slope field to visualize the behavior of the solution at different points in the plane.

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Answer:

$8000 / 2 = $4000 x 27 = $108000

Step-by-step explanation: i divided 8000 /2 then multiplied 27 to = 108000 I   hope this helps

First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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Answer:

Step-by-step explanation:

Find the volume of the sample container.

Given:

Volume formula:

Substitute to get:

Find the volume of the trace element, using the given proportion:

Answer: 22/25

Step-by-step explanation:

54x+6x-30=7(x+2)+3x

60x-30=7(x+2)+3x

60x-30=7x+14+3x

60x-30=10x+14

60x-10x-30=14

60x-10x=14+30

50x=14+30

50x=44

x=22/25

The relationship is that number sense can be used to solve area models or partial products.

Number sense refers to a set of important numerical skills. It includes the capacity to comprehend numbers and concepts such as more and less. Some people have a better sense of numbers than others.

Number sense is a set of abilities that enable humans to work with numbers. These abilities are essential for performing math as well as many other jobs.

In this case, partial products model of multiplication. This is a model which breaks numbers down into their factors. or place values in order to make multiplication easier. This depicts number sense.

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Answer:

192 cubes.

Step-by-step explanation:

The volume of each cube  = (side)³  = (1/4)³  = 1/64 units ³

Next is to find how many cubes are needed to fill the prism.

The number of cubes  that will fill the prism  :

Vol. of prism / Vol. of cube = 3 / \(\frac{1}{64}\)

                                            =192 cubes.

Therefore, it takes 192 cubes to fill the prism.

When x = π/2, the rate at which x is changing can be calculated by using the chain rule. The rate at which x is changing is equal to \(-5e^{(-sin(\pi /2))\), or -5.

We are given that \(y = 2e^{cos(x)\) and that y is increasing at a constant rate of 5 units per second. To find the rate at which x is changing when x = π/2, we need to differentiate y with respect to time using the chain rule.

Using the chain rule, we differentiate \(y = 2e^{cos(x)\) as follows: dy/dt = dy/dx * dx/dt. Since we know that dy/dt is 5 units per second, we can rewrite the equation as 5 = dy/dx * dx/dt.

To find dx/dt when x = π/2, we substitute x = π/2 into the equation. Now we need to find dy/dx. Taking the derivative of \(y = 2e^{cos(x)\) with respect to x, we get \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\)

Substituting x = π/2 into dy/dx, we have \(dy/dx = -2e^{cos(\pi /2)} sin(\pi /2)\). Since cos(π/2) = 0 and sin(π/2) = 1, we can simplify dy/dx to -2e⁰ * 1 = -2.

Finally, we can rearrange the equation 5 = dy/dx * dx/dt and substitute dy/dx = -2 to solve for dx/dt. We get -2 * dx/dt = 5, which implies dx/dt = -5/2 or -2.5.

Therefore, when x = π/2, the rate at which x is changing is -2.5.

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The derivative dy/dx is equal to -2 / (5x) in terms of x and y.

We are asked to find the derivative dy/dx of the implicitly defined function x² × \(y^5\) × \(e^y\) = 0. To find this, we'll use implicit differentiation.
Implicit differentiation means we differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx. So, let's differentiate both sides:
d/dx (x² × \(y^5\) × \(e^y\)) = d/dx (0)
First, we'll differentiate the left side using the product rule and chain rule:
(2x × y^5 × e^y) + (x² × 5y^4 × e^y × dy/dx) = 0
Now, we'll isolate dy/dx by subtracting the first term from both sides and then dividing by the second term:
dy/dx = - (2x × \(y^5\) × \(e^y\)) / (x² × \(5y^4\) ×\(e^y\))
We can simplify this expression by canceling out some common factors:
dy/dx = - (2x) / (5x²)
Further simplification gives:
dy/dx = -2 / (5x)
Thus, the derivative dy/dx is equal to -2 / (5x) in terms of x and y.

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80 coins

.15x=12

divide both sides by .15

x= 80

Answer:

The answer is C

Step-by-step explanation:

I may be wrong but you need to line the decimal

Pension plan assets were $120 million at the beginning of the year and $130 million at the end of the year. The return on plan assets was 5%. At the end of the year, cash invested in the pension fund was $8 million.The amount of retiree benefits paid by the trustee is $4 million.

To find the amount of retiree benefits paid by the trustee, we need to follow these steps:
1. Calculate the return on plan assets: Beginning assets * return = $120 million * 5% = $6 million
2. Calculate the total assets at the end of the year without the cash invested: Beginning assets + return on plan assets = $120 million + $6 million = $126 million
3. Calculate the assets at the end of the year including the cash invested: Total assets without cash invested + cash invested = $126 million + $8 million = $134 million
4. Find the difference between the ending assets and the assets including the cash invested: $134 million - $130 million = $4 million
The amount of retiree benefits paid by the trustee is $4 million.

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Answer:

Step-by-step explanation:

By using mid point formula ,

(X,Y) =( X1+X2/2) , Y1 +Y2/2

(-2+2/2) , (-4-10/2)

or, (0/2), (-7)

The equation we need to use to find the number of bills in Guy Granger's stack is 5b = 4, where b is the number of bills.

What is an Equation ?

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

This equation represents the fact that each of the 5 contestants received 4 one hundred-dollar bills, so the total number of bills is

= 4 x 5

= 20

To solve for b, we need to divide both sides of the equation by 5:

5b / 5 = 4 / 5

b = 4 / 5

So, the number of bills in Guy Granger's stack is 4 / 5 * 100 = 80.

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The paper clip costs $0.05 and the folder Costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

Let's solve this problem step by step:

Let's assume the cost of the paper clip is x dollars.

According to the information given, the folder costs $1.00 more than the paper clip, so the cost of the folder would be (x + $1.00).

The total cost of the folder and the paper clip is $1.10, so we can write the equation:

x + (x + $1.00) = $1.10

Combining like terms, we have:

2x + $1.00 = $1.10

Subtracting $1.00 from both sides of the equation, we get:

2x = $0.10

Dividing both sides by 2, we find the value of x:

x = $0.10 / 2

x = $0.05

Therefore, the paper clip costs $0.05.

In summary, the paper clip costs $0.05 and the folder costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

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Answer:

first one I think is 6 and then 3

Step-by-step explanation:

Using the discriminant the quadratic equation 4x² + 20x + 25 = 0 has a repeated real solution.

To determine the nature of the solutions of the quadratic equation 4x² + 20x + 25 = 0 using the discriminant, we need to calculate the discriminant value and analyze its relationship to the nature of the solutions.

The discriminant (D) is given by the formula: D = b² - 4ac

In the quadratic equation, 4x² + 20x + 25 = 0, we have:

a = 4

b = 20

c = 25

Calculating the discriminant:

D = (20)² - 4(4)(25)

D = 400 - 400

D = 0

Now, let's analyze the value of the discriminant (D):

If the discriminant (D) is greater than 0, the quadratic equation has two unequal real solutions.

If the discriminant (D) is equal to 0, the quadratic equation has a repeated real solution.

If the discriminant (D) is less than 0, the quadratic equation has no real solutions.

In this case, the discriminant (D) is equal to 0.

Therefore, the quadratic equation 4x² + 20x + 25 = 0 has a repeated real solution.

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Answer:

x=8 and y=23

Step-by-step explanation:

Rewrite equations:

y=2x+7;y=3x−1

Step: Solve y=2x+7 for y:

y=2x+7

Step: Substitute 2x+7 for y in y=3x−1:

y=3x−1

2x+7=3x−1

2x+7+−3x=3x−1+−3x(Add -3x to both sides)

−x+7=−1

−x+7+−7=−1+−7(Add -7 to both sides)

−x=−8−x−1=−8−1

(Divide both sides by -1)

x=8

Step: Substitute 8 for x in y=2x+7:

y=2x+7

y=(2)(8)+7

y=23(Simplify both sides of the equation)

Answer:

The answer will be 2a×3=6a

Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

To complete this activity using Excel, you can follow these: the probability of finding 198 correctly scanned packages for different sample sizes.

Open Excel and create a new spreadsheet. In the first column, enter the different sample sizes you want to analyze. For example, you can start with sample sizes of 10, 20, 30, and so on.

By following these steps, you will be able to use Excel to calculate the sample proportion, single-proportion sampling error, and the probability of finding 198 correctly scanned packages for different sample sizes.

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It's important to note that to calculate the probability accurately, you need to know the population proportion. If you don't have this information, you can use the sample proportion as an estimate, but keep in mind that it may not be as precise.

To complete this activity using Excel, you will need to perform the following steps:

1. Calculate the sample proportion for each sample size:
  - Determine the number of packages correctly scanned for each sample size.
  - Divide the number of packages correctly scanned by the sample size to calculate the sample proportion.
  - Repeat this calculation for each sample size.

2. Calculate the single-proportion sampling error for each sample size:
  - Determine the population proportion, which represents the proportion of correctly scanned packages in the entire population.
  - Subtract the sample proportion from the population proportion to obtain the sampling error.
  - Repeat this calculation for each sample size.

3. Calculate the probability of finding 198 correctly scanned packages for a sample of size n:
  - Determine the population proportion, which represents the proportion of correctly scanned packages in the entire population.
  - Use the binomial distribution formula to calculate the probability.
  - The binomial distribution formula is P(x) = \(nCx * p^{x} * q^{(n-x)}\), where n is the sample size, x is the number of packages correctly scanned (in this case, 198), p is the population proportion, and q is 1-p.
  - Substitute the values into the formula and calculate the probability.

Remember to use Excel's functions and formulas to perform these calculations easily.

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A) Given statement is true.

B)  Given statement is true.

C) Given statement is true.

D) Given statement is true.

E) Given statement is false.

F) Given statement is true.

A) True. If the system Ax=b is inconsistent, it means that there is no solution to the equation Ax=b. This implies that vector b is not in the column space of matrix A, since the column space of A consists of all possible linear combinations of its columns, which would include the solution to Ax=b if it existed.

B) True. If b is a linear combination of the columns of A, then there exists some vector x such that Ax=b. Conversely, if the equation Ax=b has at least one solution, then b is a linear combination of the columns of A, because any solution x to Ax=b can be expressed as a linear combination of the columns of A with coefficients given by the entries of x.

C) True. If the equation Ax=b is inconsistent for some b in R^n, then the augmented matrix [A | b] has no solution, and thus its RREF must have a row of the form [0 0 ... 0 | c], where c is nonzero. This row corresponds to an equation of the form 0x_1 + 0x_2 + ... + 0x_n = c, which has no solution. Therefore, the RREF of A cannot have a pivot position in every row.

D) True. If the columns of an m times n matrix A span R^m, then the equation Ax=b is consistent for each b in R^m. This is because any vector b in R^m can be written as a linear combination of the columns of A, and the coefficients of this linear combination can be found by solving the equation Ax=b.

E) False. If the augmented matrix [A | b] has a pivot position in every row, then the system Ax=b is consistent. This is because the RREF of [A | b] has a unique solution, which can be found by back substitution after reducing [A | b] to reduced row echelon form.

F) True. Any linear combination of vectors can be written in the form Ax, where A is a matrix whose columns are the given vectors, and x is a column vector of coefficients. Specifically, if \(v_1, v_2, ..., v_n\) are vectors, and\(c_1, c_2, ..., c_n\)are scalars, then the linear combination \(c_1v_1 + c_2v_2 + ... +\)\(c_nv_n\)can be written as the product Ax, where A = \([v_1 v_2 ... v_n]\) and x = \([c_1; c_2; ...; c_n].\)

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Answer:

254.3 inches squared

Step-by-step explanation:

r=9 inches

\(\pi = 3.14\)

Area of a circle=

\(\pi \: {r}^{2} \)

Therefore

\( area \: of \: circle = (3.14) \times ( {9}^{2} )\)

= 254.34

=254.3 to the nearest tenth

Answer: A

Step-by-step explanation: store B: 32 - 10% = 28.8  and Store A 36- 25% = 27  so the least number is 27 so the answer is A, store A because store B is more expensive after discount. Hoped i help have a nice day