Select the correct answer.
What is the justification for step 2 in the solution process?

12y − 40 − 4y = 6y − 18
Step 1: 8y − 40 = 6y − 18
Step 2: 2y − 40 = -18
A.
the subtraction property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the multiplication property of equality

As x approaches positive infinity, m(x) approaches positive infinity.

As x approaches negative infinity, m(x) approaches negative infinity.

An expression, rule, or law in mathematics that establishes a connection between one variable (the independent variable) and another variable (the dependent variable).

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.

A function is a rule that is applied to a number, known as an input, in order to produce a result, known as an output.

when \($x^n$\) ( n is odd number and n > 0), a > 0 and c is any constant,

\($$x \rightarrow \infty, a x^n+c \rightarrow+\infty\)

\($x \rightarrow-\infty, a x^n+c \rightarrow-\infty$\)

The complete question is;

The function f(x) = x^3 has been transformed, resulting in function m.

m(x) = 1\3x^3 + 6

As x approaches positive infinity, m(x) approaches___

As x approaches negative infinity, m(x) approaches___

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Mother spent (4r - 8) dollars more on cherries than did the father.

An expression using numbers and related operations is called a numerical expression.

According to the question, a pound of cherries costs $4.

Mom purchased r pounds.

The price of the cherry is calculated as follows: 4r = weight x $/lb.

Father purchased 2 pounds, thus the price of the cherries is 4 (2), or $8.

We remove the smaller value from the higher value, which is 4r - 8, where r must be more than two. Given that the mother spent more money on cherries than the father, the mother's cost of cherries is a greater value.

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Check the picture below.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4\)

When a simple pendulum with a length of 1.53 m and a mass of 6.84 kg is given an initial speed of 1.06 m/s at its equilibrium position, the length and mass of the pendulum will affect its subsequent motion.

The period of a simple pendulum is proportional to the square root of its length, which means that the longer the pendulum, the slower it will swing. The mass of the pendulum also affects its period, but to a lesser extent. Therefore, the pendulum will continue to swing back and forth at a constant frequency, determined by its length and the acceleration due to gravity..

In terms of the amplitude and energy of the pendulum's motion, its initial speed will determine the maximum height it reaches on each swing, which will decrease over time due to frictional losses. The mass of the pendulum will also affect its energy, as a heavier pendulum will require more energy to set in motion and will lose energy more slowly over time.

In conclusion, the length and mass of a simple pendulum will influence its period, amplitude, and energy when given an initial speed. Understanding these relationships can help predict and explain the behavior of simple pendulums in various contexts.

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Answer:

x = -5

Step-by-step explanation:

− 6 x − 15 = 4 x + 35

Add 6x to each side

− 6 x+6x  − 15 = 4 x+6x + 35

-15 = 10x+35

Subtract 35 from each side

-15-35 = 10x+35-35

-50 = 10x

Divide each side by 10

-50/10 = 10x/10

-5 =x

Answer: x = -5

Step-by-step explanation:

In order to solve this problem, you need to isolate the variable.

In this problem, you need to isolate the x.

-6x -15 = 4x +35

10x = -50

x = -5

In Cynthia's physics class, she is required to submit four lab reports. To earn extra credit, her percent error for each report should be less than 5%. Percent error is calculated by taking the absolute value of the difference between the experimental value and the accepted value, dividing it by the accepted value, and multiplying by 100.

To calculate percent error for each lab report, Cynthia needs to follow these steps:

1. Obtain the accepted value for the measurement or quantity mentioned in the lab report.
2. Measure or calculate the experimental value for the same measurement or quantity.
3. Subtract the accepted value from the experimental value.
4. Take the absolute value of the difference.
5. Divide the absolute difference by the accepted value.
6. Multiply the result by 100 to get the percent error.

If the percent error for any of Cynthia's lab reports is less than 5%, she will earn extra credit for that report. However, if the percent error is equal to or greater than 5%, she will not receive the extra credit for that particular report.

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To earn extra credit for each lab report, Cynthia must ensure that the absolute value of the difference between her measured value and the accepted value is less than 5% of the accepted value. This will help her minimize the percent error and demonstrate accurate measurements in her lab reports.

In Cynthia's physics class, she needs to submit four lab reports. To earn extra credit for each report, her percent error should be less than 5%.

Percent error is a measure of how inaccurate a measurement is compared to the accepted value. It is calculated using the formula:

    Percent error = (|Measured value - Accepted value| / Accepted value) * 100

To ensure that her percent error is less than 5%, Cynthia needs to make sure that the absolute value of the difference between her measured value and the accepted value is less than 5% of the accepted value.

For example, if the accepted value for a measurement is 10 cm, Cynthia's measured value should be within 0.5 cm of the accepted value to satisfy the 5% requirement.

In conclusion, to earn extra credit for each lab report, Cynthia must ensure that the absolute value of the difference between her measured value and the accepted value is less than 5% of the accepted value. This will help her minimize the percent error and demonstrate accurate measurements in her lab reports.

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The correct answer is C. To increase the strength of a solenoid, you need to increase the number of loops or the amount of electric current. A solenoid is a type of electromagnet that consists of a coil of wire with an electric current running through it, creating a magnetic field.

A solenoid is a type of electromagnet that consists of a coil of wire with an electric current running through it, creating a magnetic field. The strength of the magnetic field is directly proportional to the number of loops of wire and the amount of current flowing through the coil. Therefore, to increase the strength of a solenoid, you can either increase the number of loops in the coil or increase the amount of current flowing through the coil.

Option A (plugging up multiple items in the circuit) and option D (arranging the resistors of the circuit in a series circuit) do not increase the strength of a solenoid. These options relate to the circuit's resistance, which can affect the amount of current flowing through the solenoid but does not directly impact its strength.

Option B (arranging the resistors of the circuit in a parallel circuit) could potentially increase the current flowing through the solenoid, but it would not increase the number of loops in the coil, which is necessary to increase the strength of the solenoid. Therefore, option C is the correct answer.

In summary, to increase the strength of a solenoid, you need to increase the number of loops or the amount of electric current flowing through the coil.

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The number of ways that the teacher can arrange the row is  185328000

Given,

Number of male students = 12

Number of female students = 13

Number of students teacher needs to select = 8

The row arrangement is like; 4 men in the middle and  2 women on each end;

Here,

Order of the arrangement is considered.

So, permutation can be used.

Female students selected = ¹³P₂

Male students selected = ¹²P₄

Then,

Number of ways for the arrangement =  ¹³P₂ × ¹²P₄

= 15600 × 11880

= 185328000

That is,

The teacher can arrange a row with 4 men in the middle and 2 women on each end in 185328000 ways.

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Answer:

Step-by-step explanation:

The ground level is zero, then we have the following equations.

2 levels below ground level:

5 levels up:

Answer:

\(here \: elevator \: is \: at \: below \: ground \: \\ level \: by \: two \: floors \\ so \: take \: it \: as \: 1 \: so \: then \: ground \: level = 3 \\ \\ then \: the \:upper \: floor \: is \: 5 \\ \\ then \: upper \: - ground = 5 - 2 = 23\ so \: answer \: is3 \\ thank \: you\)

Answer: A. 241 feet

Step-by-step explanation:

The figure shows two rectangular triangles.

These triangles are similar since they have two identical angles:

the first angle is 90 degrees;

the second angle is equal because the law of reflection states that the angle of incidence is equal to the angle of reflection.

The law of reflection states that the angle of incidence is equal to the angle of REFLECTION.

Let's make the proportion:

\(\dfrac{4}{273} =\dfrac{5}{x} \\\\x=\dfrac{273 \cdot 5}{4} =341.25 \: (feet)\\\)

It takes a minimum of 100 feet for a parachute to open and safely land without injury, so:

341.25 - 100 = 241.25 (feet)

241.25 ≈ 241 (feet)

Answer:

The first option (angle 2 and 5)

Step-by-step explanation:

Vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent, meaning that they have the same angle measure.

In this case, angle 2 and angle 5 are vertical angles. So, the measure of angle 2 is equal to the measure of angle 5. Angle 6 and angle 3 are also vertical angles. So, the measure of angle 6 is equal to the measure of angle 3.

Answer:

90 degrees

Step-by-step explanation:

Given the trig expression cos x ( cos x - 2) = 0, we are to find the value of x;

The expression can also be expressed as;

cos x = 0 and cos x - 2 = 0

If cos x = 0

x = cos^-1 0

x = 90

Hence the value of x is 90 degrees

Note that if cos x = 2, then x does not exist in this case

Answer:

The answer is "\(\frac{26}{7}\)"

Step-by-step explanation:

The whole question can be found in the file attached.

\(\to x + \frac{5}{7} = \frac{31}{7}\\\\\)

Subtracting the \(\frac{5}{7}\) from both sides of the equations:

\(\to x +\frac{5}{7} - \frac{5}{7} = \frac{31}{7} - \frac{5}{7} \\\\\)

                    \(= \frac{31-5}{7} \\\\= \frac{26}{7} \\\\\)

Answer:

5.387 \times 10^{10}

Step-by-step explanation:

Answer:

A... 12

Step-by-step explanation:

Answer: There are 30 cubes in each layer and 3 layers. (Up to down.)

Explanation: You can multiply the x and y axis for one layer, and then count how many layers there are. There are 90 cubes in all.

I hope this helps, have a good day!

Answer:

12 months

Explanation:

Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;

T is the total charges,

m is the number of months of storage

Given

T = $260.00

we are to find the value of m

Substitute

260 = 35 + 18.75m

18.75m = 260 - 35

18.75m = 225

m = 225/18.75

m = 12

Hence it will take 12 months to cost a new custimer $260.00

Answer:

A

Step-by-step explanation:

The denominator does not change....just add the numerators

(x-2)  - ( x^2-2x+6)

x -2 - x^2 + 2x - 6   = -x^2 + 3x -8  

Answer:

Step 1: Box A

Step 2: Box C

Step 3: Box A

Step 4: Box B

Step-by-step explanation:

Answer:

Step-by-step explanation:

( 3m + 2) (4m-3)

The if  they will have exactly the same length to donate. The long will their hair be is 8.5

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given ,

Two friends, Jeanette and Zoe, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer.

Jeanette's hair is already 29 centimeters long and grows at a constant rate of 1 centimeter per month.

29+n = 12+2n

2n-n = 29-12

n = 17/2

n = 8.5

Hence, The if  they will have exactly the same length to donate. The long will their hair be is 8.5

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Answer:

To find the scale factor, you need to divide the width of the large figure by the width of the smaller figure (4/1). You also need to divide the length of the large figure by the length of the smaller figure (8/2). After you divide these numbers, you'll get 4 as an answer. Therefore, the scale factor from the small to larger figure is 4.

4/1 = 4

8/2 = 4

Answer:

He should have said that his small brother had 100 small building bricks, but lost 5 in total now.

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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Answer:

16 key chains

Step-by-step explanation:

Given

\(f(x) = 0.85x + 3.99\) ---company A

\(g(x) = 1.10x\) --- company B

Required

Value of x when \(f(x) = g(x)\)

We have:

\(f(x) = g(x)\)

\(0.85x + 3.99 = 1.10x\)

Collect like terms

\(0.85x - 1.10x = -3.99\)

\(-0.25x = -3.99\)

Solve for x

\(x = \frac{-3.99}{-0.25}\)

\(x = 15.96\)

\(x= 16\) --- approximated

Answer: inscribed angle

Answer:

the above answer is correct

Step-by-step explanation:

I got it right on the test

Answer:

3.7 miles per day

Step-by-step explanation:

a) The time for the battery to be 40% charged is given as follows: 48 minutes.

b) The charge in 1 hour and 48 minutes is given as follows: 90%.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The constant for this problem is given as follows:

k = 10/12 = 30/36 = 5/6.

Hence the equation is given as follows:

y = 5x/6.

The battery will be 40% charged when y = 40, hence:

5x/6 = 40

5x = 40 x 6

5x = 240

x = 240/5

x = 48 minutes.

1 hours and 48 minutes is equivalent to 108 minutes, hence the charge is given as follows:

y = 5 x 108/6

y = 90%.

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For the function "f(x) = -(x+1)²(2x-3)(x+2)²" , the degree is 5 and the y-intercept is (0,12) .

The function is : f(x) = -(x+1)²(2x-3)(x+2)² ,

To find the degree of the function, we need to find the highest power of x in the function.

On expanding the function,

We get ,

⇒ f(x) = -(x+1)²(2x-3)(x+2)²

⇒ -(x²+2x+1)(2x-3)(x²+4x+4)

⇒ -2x⁵ + 7x⁴ - 19x³ - 24x² + 52x + 48

The highest power of x in this function is x⁵, so the degree of the function is 5.

To find the y-intercept of the function, we evaluate function when x=0.

Substituting x = 0 into the function,

We get ,

⇒ f(0) = -(0+1)²(2(0)-3)(0+2)²

⇒ -1²(-3)(2)²

⇒ -1(-3)(4)

⇒ 12

Therefore , the degree of function is 5 and the y-intercept is 12.

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The given question is incomplete , the complete question is

Find the degree and y-intercept of the function , f(x) = -(x+1)²(2x-3)(x+2)² .