3(x - 2) + 6 = 3x - 6 please show all steps im trying to finish so i can go to bed

Answer:

Using Descartes' Rule of Signs, we observe whether each consecutive term has a + or - sign:

f(x) = 3x4 − 5x3 − x2 − 8x + 4

Signs are: + - - - +

There are 2 sign changes (from +3 to -5, then from -8 to +4). This means that there are either 2 or 0 positive roots. (We take the number of sign changes, which is 2, and subtract by 2s to get all possible numbers of positive roots.)

For negative roots, we first invert all the odd-powered terms in f(x):

3x4 + 5x3 − x2 + 8x + 4

Signs are: + + - + +

There are 2 sign changes, from +5 to -1, and from -1 to +8. Therefore, there are either 2 or 0 negative roots.

Since the overall degree of f(x) is 4, the total number of roots must sum up to 4. There are either 2 or 0 positive roots, and 2 or 0 negative roots, and everything that remains will be a complex root. The possibilities are:

2 positive, 2 negative, 0 complex

2 positive, 0 negative, 2 complex

0 positive, 2 negative, 2 complex

0 positive, 0 negative, 4 complex.

Therefore we can have either 0, 2, or 4 complex roots.

The correct answer is the last choice.

The simple reason why it is very important for a given measurement always be reported to the correct number of significant figures is because solved answers usually, frequently and most of the time depend on the number of significant figures in the values used during the calculation

There are accurate figures which is used in solving mathematical problems

So therefore, the simple reason why it is very important for a given measurement always be reported to the correct number of significant figures is because solved answers usually, frequently and most of the time depend on the number of significant figures in the values used during the calculation

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Answer:

Hello,

\(\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\\)

Step-by-step explanation:

\(\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\\)

Quotient rule of differentiation.

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

d/dx(csc x) = -csc x cot x.

To show that d/dx(csc x) = -csc x cot x, we will use the quotient rule of differentiation.

Recall that csc x is defined as 1/sin x.

Therefore, we can rewrite the function as:

csc x = (sin \(x)^{-1}\)

Taking the derivative of csc x with respect to x using the quotient rule, we get:

d/dx(csc x) = (-1)(sin x) (cos x)

Now we need to simplify this expression using trigonometric identities. Recall that

cot x = cos x/sin x.

Therefore, we can rewrite the above expression as:

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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To show that d/dx(csc x) = -csc x cot x, we need to differentiate csc x with respect to x using the chain rule and trigonometric identities.

Recall that csc x is the reciprocal of sin x, so we can write:

csc x = 1/sin x

Then, using the chain rule, we can differentiate csc x as follows:

d/dx(csc x) = d/dx(1/sin x) = -1/sin^2 x * d/dx(sin x)

Now, we can use the derivative of sin x with respect to x, which is cos x:

d/dx(csc x) = -1/sin^2 x * cos x

Next, we can use the identity cot x = cos x/sin x to simplify the expression:

d/dx(csc x) = -cos x/(sin x)^2 = -csc x * cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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we can use a number line

the distance between two numbers on number line is calculated subtracting the greater number from the other

then to calculate each distance from 0

-7 to 0

0 to 7

it's the same distance

Proposals for research studies include a methodology section.

This section is an important component of a research proposal as it outlines the procedures and techniques that will be used to conduct the study. It provides the reader with a detailed description of the research design, the data collection methods, and the data analysis methods that will be employed. The methodology section of a research proposal should be well-structured and clearly written to demonstrate the feasibility and validity of the proposed study.

Here are some key components of a methodology section in a research proposal:

Research design: This section describes the overall approach that will be taken to conduct the research, including the type of study (e.g. experimental, qualitative, quantitative), the sample size and selection method, and the data collection methods that will be used.

Data collection methods: This section outlines the methods that will be used to collect data, including the type of data that will be collected (e.g. surveys, interviews, observations), the instruments or tools that will be used, and the procedures for collecting and storing the data.

Sampling method: This section describes the method that will be used to select the participants for the study, including the criteria for inclusion and exclusion, and the process for obtaining informed consent from participants.

Data analysis methods: This section outlines the methods that will be used to analyze the data, including the statistical methods and software that will be used, and any assumptions or limitations associated with the analysis methods.

Ethics and safeguards: This section discusses any ethical considerations associated with the study, including informed consent, confidentiality, and protection of participants' rights. It should also describe any safeguards that will be put in place to ensure that the data is collected and analyzed in a valid and reliable manner.

By including a well-structured methodology section in a research proposal, researchers can demonstrate their understanding of the research process, and provide a clear and detailed plan for conducting the study. This helps to increase the credibility and feasibility of the proposed study, and can increase the chances of the proposal being approved and funded.

Therefore, Proposals for research studies include a methodology section.

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The value of the variables in figure x and y are 14 and 28.5 respectively.

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

We have been given the following parameters;

The two lines a and b are parallel to each other.

Therefore, Angle (5x - 7) and Angle (3x + 17) are the same because of alternate interior angles.

Thus, (5x - 7) =  (3x + 17)

Solving;

(5x - 7) =  (3x + 17)

5x - 3x = 17 + 7

2x = 28

x = 14

Now, we can see that Angle (5x - 7) and Angle (4y + 3) makes linear pairs on line A.

Thus,  (5x - 7) + (4y + 3) = 180

Substitute x = 14

(5(14) - 7) + (4y + 3) = 180

70 - 7 + 4y + 3 = 180

4y + 66 = 180

4y = 114

y = 28.5

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Answer:

18 u multiply 2 and 7 first equal 14 plus 4 equals 18 hope this helps

Step-by-step explanation:

In  Arithmetic Progression , 56 inches of snowfall will cause the snowplow to be immobile.

What is Arithmetic Progression in math?

Let x inches of snowfall will cause the showplow to be immobile .

By a.p. formula ,

                aₙ = a + ( n - 1) d

                 aₙ= 0 ( show plow's speed is 0 ,miles/hour )

              a = 39

              n = x inches

             d = - 2.5 mile/hour

         0 = 39 + ( n - 1 ) ( -2.5)

            ( n - 1 ) ( -2.5) = -39

              n- 1 = -39/2.5 = 15.6

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Answer:

The third one, 2c - 6

Step-by-step explanation:

Answer:

2304pi inches³

Step-by-step explanation:

volume of ball = 4/3pi r³

=4/3 x pi x 12³=2304 pi inches³

Answer:

v = lhw

Step-by-step explanation:

\(\frac{v}{lh} = w\)

v = lhw

Pythagoras theorem is a formula that helps us determine the missing side of a triangle, with the measure of two sides, given.

The Pythagoras theorem formula is expressed as:

\((\small\text{Hypotenuse})^{2} = (\small\text{side}_{1} )^{2} + (\small\text{side}_{2} )^{2}\)

Now, let us take an example to understand the concept better.

A triangle with longest side given as 15 centimeters. The base of the triangle has a length of 9 centimeters. What is the measure of the height?

We are given the following:

When we plug the hypotenuse and the base, in the formula, we get;

Subtract 9² on both sides of the equation to isolate (side₂)².

We can use the rule [a² - b² = (a - b)(a + b)] to simplify the L.H.S

Now, take square root on both sides of the equation to determine the measure of the missing side (height of triangle).

Therefore, the measure of the height is 12 centimeters.

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The indefinite integral is: (t^2)i + (t)j + (3t)k + C

To find the indefinite integral of the given vector function (2ti + j + 3k) with respect to t, we need to integrate each component separately.

Step 1: Integrate the i-component with respect to t:
∫(2t) dt = t^2 + C1

Step 2: Integrate the j-component with respect to t:
∫(1) dt = t + C2

Step 3: Integrate the k-component with respect to t:
∫(3) dt = 3t + C3

Now, combine the integrated components and the constants of integration (C1, C2, C3) to form the final result:

Your answer: (t^2)i + (t)j + (3t)k + C

Here, C = (C1)i + (C2)j + (C3)k is the constant of integration in vector form.

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To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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New Mean of the marks is 76 and standard deviation of the marks is 14.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

Given,

Out of 50, for a history test have a mean of 38 and standard deviation of 7.

Marks are doubled to get a percentage mark

μ = 38

When marks are doubled, sum of marks will also get doubled

Mean = 2×38 = 76

Standard deviation = √∑(2xₙ - 2μ)²/N

Standard deviation = 2×7 = 14

Hence, new mean of the marks = 76

new standard deviation of the marks = 14

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Answer:

A

Step-by-step explanation:

f(2 – 3i) = (2 – 3i)^2

f(2 – 3i) = (2)^2 + (-3i)^2

f(2 – 3i) = 4 + (9)(-1)

f(2 – 3i) = 4 - 9

f(2 – 3i) = -5

These are functions in another function. The result of the function f(2-3i) is -5-12i

These are functions in another function. Given the function shown below;

f(x) =  x²

In order to determine  f(2 – 3i), you will replace as 2 - 3i to have:

f(2 - 3i) = (2 - 3i)²

Expand
f(2 - 3i) = 2² - 12i + 9i²
f(2 - 3i) =4 - 12i - 9
f(2 - 3i) = -5-12i

Hence the result of the function f(2-3i) is -5-12i

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Answer:

g(x) = -4g(x) = -x+4

= g(5) = -4(5) = -(5)+4

= g(5) = -20 = -1

Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

If a is a non-zero, real number and equation a(x − 3)² − b = c then x = 3 ± √b+c/a and  the condition on c that restricts the solutions for x to real numbers is c ≥ -5.

To prove that x = 3 ± √(b+c)/a, let's start with the given equation: a(x - 3)² - b = c.

Add b to both sides of the equation to isolate the quadratic term:

a(x - 3)² = c + b.

Divide both sides by 'a' to obtain the quadratic term by itself:

(x - 3)² = (c + b)/a.

Take the square root of both sides to solve for x:

x - 3 = ±√(c + b)/a.

Add 3 to both sides to isolate x:

x = 3 ± √(c + b)/a.

Therefore, we have proven that x = 3 ± √(b+c)/a.

Now, let's consider the case where a = 2 and b = 5.

Substituting these values into the equation x = 3 ± √(b+c)/a, we have:

x = 3 ± √(5 + c)/2.

For the solutions to be real numbers, the expression under the square root (√(5 + c)) must not be negative. In other words, (5 + c) ≥ 0.

Therefore, the condition on c that restricts the solutions for x to real numbers is c ≥ -5.

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Photic zone: seaweeds and corals live here

aphotic zone: mid-ocean level where no light reaches

deep ocean floor: animals that glow are found here

Hope this helped!

Answer:

deep ocean floor - animals that glow are found here

photic zone - seaweeds and coral live here

aphotic zone mid-ocean level where no light reaches

Step-by-step explanation:

I rly hope this helps!! :D

Answer:

Yes, you have enought money

Step-by-step explanation:

45 times 107% (100 for the total cost and and 7 for the tax) is equal to 48.15. You have 50 dollars, therefore you can buy your shoes.

Answer:

I think the answer is 0.

Step-by-step explanation:

To evaluate an expression, you need to substitute the number(18) into the equation:

2/3(18)-12

=12-12

=0

I hope this helps!

Answer: 0

Step-by-step explanation:

2/3(18) is the same as (2*18)/3

This means it would be 36/2 which is 36.

Then you have to divide it by 2 which would give you 12. They you still have the -12 in the original problem, so you get 12-12 which is 0.

The diameter of the circle is twice its radius and the area of the circle is given by the equation A = πr²

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the area of the circle be represented as A

Let the radius of the circle be represented as r

Let the diameter of the circle be represented as d

Now , the diameter of the circle = 2 x radius of the circle

Substituting the values in the equation , we get

d = 2r

And , The area of the circle = πr²

Therefore , the value of A is πr²

Hence , the area of the circle is πr²

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The probability that this person choosen only visited one of the two places is 9/20

What is Probability?

Probability is a measure of the possibility that an event to occur.

 The probability for an event to occur= Possible outcome /Total outcome

to get the possible out come we must Know the number of people that visited ET and NDC only.

using set theory;

if x is the no of people that visited both places then,

8-x =ET only

13-x= NDC only

5= none visited ET and NDC

x+13-x+8-x+5=20

collect like terms

26-x= 20

x =6

therefore ET only= 2

NDC only= 7

probability of ET = 2/20

probability of NDC= 7/20

therefore probability that the person chosen only visited one place = p(ET)+P(NDC)= 7/20+2/20

= 9/20

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Answer:

9000

Step-by-step explanation:

(x/2)-(x/3) = 1500

(x/6)=1500

x= 9000

The student needs a minimum score of 956 to stay in the top 15% of the normal distribution.

Normal distributions are fundamental to statistics because they are widely used in the social and natural sciences to represent real-valued regressors with uncertain distributions.

Now top 15%

Therefore P=0.15

P(X<x) = 1 -0.15 = 0.85

Z-score = 1.04

Now we know that

z=(x-μ)/σ

Solving we get :

1.04 = (x - 800)/150

or, x = 956

hence the minimum score is 956.

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Answer:

First, find the answer for 36 ÷ 4. Which is 9.

Now calculate each expression until you get the answer of 9.

4 ÷ 36 = 4 * 1/36 = 4/36 = 1/9

36 ÷ 1/4 = 36 * 4 = 144

1/36 * 1/4 = 1/144

36 * 1/4 = 36/4 = 9

So, the last option is the answer. D. 36 * 1/4.

Answer:

35 1/3 I believe

Step-by-step explanation:

36 divided by 4/6 and you 35 1/3

Based on the unique situation, the compound interest is obtained from 300(1 + 0.15/12)^12t.

The term compound interest refers to the type of interest that is charged on both the principal and interest. The total money to be paid back is referred to as the amount.

A compound interest is calculated form the formula;

P(1 + r/n)^nt

Where;

P = principal

r = rate

n = number of times interest is compounded in a year

t = time in years.

Based on his situation, we have; 300(1 + 0.15/12)^12t.

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