The equations of two functions are y =-28x + 8 and y=-29x + 7. Which function is changing more
quickly? Complete the explanation.
The (select) |function is changing more quickly because the (select) of ___
means that the line has a steeper slope.

Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0

Quadratic equation:

Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given,

Here we have the set of points (0.-8), (2, 0), and (-3, -5).

Now, we have to find the quadratic equation for this points.

We know that the standard form of the quadratic equation is,

y = ax² +  bx + c

Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,

First we have to take the point (0, -8) and apply it on the formula, then we get,

-8 = a(0)² +  b(0) + c

-8 = c

Now, use the point (2,0), then we get,

0 = a(2)² +  b(2) + c

0 = 4a + 2b + c --------------------(1)

Finally, take the point (-3, -5), then we get the equations,

-5 = a(-3)² +  b(-3) + c

-5 = 9a - 3b + c --------------------(2)

Now, apply the value of c as -8, then we get,

4a + 2b = 8 ----------------(3)

9a -3b = 3 -----------------(4)

Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,

2a + b = 4

3a - b = 1

When we subtract these equation then we get the value of

a = -3

Then the value of b is

2(-3) + b = 4

b = 4 + 6

b = 10

Therefore, the quadratic equation is -3x² + 10x -8 = 0

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Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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Answer:D

Step-by-step explanation:

please mark brainliest

The Greatest Common Factor of 15 and 21 is 3.

The greatest common factor is the largest number that is a factor of two or more numbers (GCF). The greatest number (factor) divides them, yielding a Natural number. Once all of the number's variables have been identified, there are a handful that are shared by both. The greatest common factor is the largest number found among the common factors. The GCF is often referred to as the Highest Common Factor (HCF)

Given:

We have to find the greatest common factor of 15 and 21 .

So factorizing each number

15 = 3 x 5

21 = 3 x 7

So, the Greatest Common Factor is 3.

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Answer:doubled

Step-by-step explanation:

Step-by-step explanation:

doubled is the right answer

Answer:

y = 11

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

Answer:

7.777777… is repeating

6.213 is repeating

5.152535 is non repeating

4.04 is repeating

Answer:6^21

Step-by-step explanation:

Answer:

0.001

Step-by-step explanation:

(0.0001)^-3/4=((0.1)⁴)^-3/4

(0.1)^4×-3/4

0.1^‐3

0.001

Answer:

16

Step-by-step explanation:

KEEP CHANGE FLIP

10/1 divided by 5/8 turns into

10/1 multiplied by 8/5, which is

80/5 = 16

Answer:

x-70

Step-by-step explanation:

Answer:

X-7

Step-by-step explanation:

Answer:

A. Obtuse B. Right C. Acute D. Acute Hope this helps :)

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer: B

Step-by-step explanation:

Edge 2023

Step-by-step explanation:

The given polynomial 81a² − 25z⁶ is not a difference of two squares because −25z⁶ is not a perfect square.

We can see that 81a² is a perfect square because it is equal to (9a)². However, 25z⁶ is not a perfect square because it can't be written as the square of a single term.

Therefore, we cannot factor 81a² − 25z⁶ into the difference of two squares.

\( \: \: \: \)

15 is the value of x that will make the linear equation true .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

x + 5= 20

X = 20 - 5

x = 15

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Answer:5.p/3=q

Step-by-step explanation: (The dot represents multiplication and the slash represents division.) You just have to write the equation down which would be that.

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

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Due to length restrictions, we kindly invite to see the explanation of this question to know how to simplify rational numbers to powers with least base.

In this question we have rational numbers to be simplified as powers of least base by means of factor decomposition and algebra properties for rational numbers and powers:

1) 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶

2) 625 = 5 × 5 × 5 × 5 = 5⁴

3) 1 / 9 = 1 / (3 × 3) = (3 × 3)⁻¹ = (3²)⁻¹ = 3⁻²

4) 1 / 16 = 1 / (2 × 2 × 2 × 2) = 1 / 2⁴ = (2⁴)⁻¹ = 2⁻⁴

5) 27 = 3 × 3 × 3 = 3³

6) 0.01 = 1 / 100 = 1 / (2 × 2 × 5 × 5) = 1 / (2² × 5²) = 1 / (2 × 5)² = [(2 × 5)²]⁻¹ = (2 × 5)⁻² = 10⁻²

7) 216 =2³ × 3³ = (2 × 3)³ = 6³

8) 1 / 81 = 1 / 3⁴ = (3⁴)⁻¹ = 3⁻⁴

9) 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸

10) 1 / 49 = 1 / 7² = (7²)⁻¹ = 7⁻²

11) 1 / 2 = 2⁻¹

12) 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 2³ × 5³ = (2 × 5)³ = 10³

13) 1 / 32 = 1 / (2 × 2 × 2 × 2 × 2) = 1 / 2⁵ = (2⁵)⁻¹ = 2⁻⁵

14) 1 / 25 = 1 / (5 × 5) = 1 / 5² = (5²)⁻¹ = 5⁻²

15) 0.1 = 1 / 10 = 1 / (2 × 5) = (2 × 5)⁻¹ = 10⁻¹

16) 243 = 3⁵

17) (1 / 4)ˣ = [1 / (2 × 2)]ˣ = [1 / 2²]ˣ = (2⁻²)ˣ = 2⁻²ˣ

18) (36)³ˣ = (2 × 2 × 3 × 3)³ˣ = (2² × 3²)³ˣ = [6²]³ˣ = 6⁶ˣ

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Answer: 23 ft (approximately)

==========================================================

Explanation:

Draw out a diagram as I've done so below. The unknown side x is opposite the reference angle 68. The hypotenuse (ladder length) is 25.

We'll use the sine rule

sin(angle) = opposite/hypotenuse

sin(68) = x/25

25*sin(68) = x

x = 25*sin(68)

x = 23.1795963641697

x = 23

The ladder reaches approximately 23 feet up on the wall.

I'm rounding to the nearest whole number because the other values given to you were also whole numbers. If your teacher says to round otherwise, then follow those instructions instead.

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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Answer:

I'm assuming that the range means the smallest number to largest number which will be 10 to 54

Step-by-step explanation:

Let x represent 1st number, y represent 2nd number and z represent 3rd number

rest of the working is in the picture attached. hope you understand it!

Answer:

y=in ×-3

it's the answer

Answer:

f(x) = -8

Step-by-step explanation:

f(x) = x² + 2x – 8

f(x) = (-2)² + 2(-2) – 8

f(x) = (-2)² + 2(-2) – 8

f(x) = 4 + (-4) – 8

f(x) = 4 – 4 – 8

f(x) = 0 – 8

f(x) = -8

I hope this helps

The equation of the line is y = 2/3x + 1

The graph represents the given parameter

From the graph, we have the following points that can be used in our computation:

(x, y) = (0, 1) and (3, 3)

The equation of the line is then calculated using the following equation

y = (y₂ - y₁)/(x₂ - x₁) * (x - x₁) + y₁

Where

(x, y) = (0, 1) and (3, 3)

Substitute the known values in the above equation, so, we have the following representation

y = (3 - 1)/(3 - 0) * (x - 0) + 1

Evaluate

y = 2/3 (x - 0) + 1

So, we have

y = 2/3x + 1

Hence, the line equation is y = 2/3x + 1

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