13. Solve and graph -21 < 3x - 12<6. Show your work.

According to the distributive property:

[tex] \alpha ( \beta + \gamma ) = \alpha \beta + \alpha \gamma [/tex]

So, applying this to our equation:

[tex]7(x + 3y) = 7 \times x + 7 \times 3y \\ 7(x + 3y) = 7x + 21y[/tex]

The result of simplifying the number (4¹)⁵ using the exponent rules is 1024

To solve this exercise we have to resolve algebraic operations following the exponent rules.

Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

(4¹)⁵ =

4 ⁽¹*⁵⁾ =

4⁵ =

4*4*4*4*4 =

1024

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Using the relation between velocity, distance and time, it is found that the average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

"The record for the Boston Marathon’s wheelchair division is 1 hour,

18 minutes, and 27 seconds.

The Boston Marathon is 26.2 miles long. What was the average speed of the record winner of the wheelchair division?"

Velocity is distance divided by time, that is:

v = d/t.

For this problem, we have that:

Hence the velocity is given by:

v = 26.2/1.3075 = 20.04 miles per hour.

The average speed of the record winner of the wheelchair division was of 20.04 miles per hour.

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The value of x using the properties of logarithm is 1.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: 3/2 log₂4 - ½ log₂x = 3

Using properties of the logarithm, we have

3/2 log₂4 - ½ log₂x = 3

3/2 (2 log 2 / log 2) - ½ (log x / log 2) = 3

3 - ½ (log x / log 2) = 3

½ (log x / log 2) = 0

log x = 0

log x = log 1

On applying exponent both sides, we get,

x = 1

Hence, the value of x is 1.

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Answer:

25.49

Step-by-step explanation:

[tex]5^2 + 0.7^2 \\ \\ =25+0.49 \\ \\ =25.49[/tex]

Answer:

2 hours 45 minutes.

Step-by-step explanation:

12.00 - 11.20 = 40 minutes

2. 05 = 14.05

14.05 - 12.00 = 2.05 = 2 hours 5 minutes

Answer = 2 hours 45 minutes.

Answer: y=3(x+3)^3-1

Step-by-step explanation:

The values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2

[tex] {(x + 1) }^{3/2} [/tex] - 2 = 25

Adding 2 on both the sides of the equation we get

[tex] {(x + 1) }^{3/2} [/tex] - 2 + 2 = 25 + 2

[tex] {(x + 1) }^{3/2} [/tex] = 27

On squaring both the sides of the equation we get

[tex] {x + 1}^{3/2 \times 2} [/tex] = 27²

(x + 1)³ = 729

Now, using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we get

x³ + 1 + 3x² + 3x = 729

x³ + 3x² + 3x - 728 = 0 : Equation 1

By hit and trial method x = 8 is the solution of the equation 1.

Now, by remainder theorem we can write the equation 1 as

x³ + 3x² + 3x - 728 = (x - 8)(x² + 11x + 91) + 0

On solving quadratic equation x² + 11x + 91, we get

x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a

x = -11+✓(11² - 4×1×91)/2×1 and -11-✓(11² - 4×1×91)/2×1

x = -11+✓(121 - 364)/2 and -11-✓(121 - 364)/2

x = -11+✓(-243)/2 and -11-✓(-243)/2

x = -11/2 + ✓243i/2, -11/2 - ✓243i/2

Thus, the values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2

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Answer:

b = 15

Step-by-step explanation:

[tex]\frac{5\left(\frac{b-1}{2}-1\right)+2b}{3}\\5\left(\frac{b-1}{2}-1\right)+2b\\5\left(\frac{b-1}{2}-1\right)\\5\cdot \frac{b-1}{2}-5\cdot \:1\\5\cdot \frac{b-1}{2}\\\frac{\left(b-1\right)\cdot \:5}{2}\\\frac{5b-5}{2}\\\frac{5b-5}{2}-5\\\frac{5b-5}{2}-5+2b\\=\frac{5b-5}{2}+\frac{2b\cdot \:2}{2}\\=\frac{5b-5+2b\cdot \:2}{2}\\5b-5+4b\\5b+4b-5\\9b-5\\\frac{9b-5}{2}\\=\frac{9b-5}{2}-5\\=\frac{\frac{9b-5}{2}-5}{3}\\\frac{9b-5}{2}-5\\\frac{9b-5}{2}-\frac{5\cdot \:2}{2}\\[/tex]

[tex]=\frac{9b-5-5\cdot \:2}{2}\\9b-5-5\cdot \:2\\9b-5-10\\9b-15\\=\frac{9b-15}{2}\\=\frac{\frac{9b-15}{2}}{3}\\=\frac{9b-15}{2\cdot \:3}\\=\frac{9b-15}{6}\\\frac{3\left(3b-5\right)}{6}\\\frac{3b-5}{2}\\=\frac{3b}{2}-\frac{5}{2}\\\frac{3b}{2}-\frac{5}{2}=5+b\\=\frac{3b}{2}\cdot \:2-\frac{5}{2}\cdot \:2=5\cdot \:2+b\cdot \:2\\\frac{3b}{2}\cdot \:2\\\frac{3b\cdot \:2}{2}\\=3b\\-\frac{5}{2}\cdot \:2\\=\frac{5}{2}\cdot \frac{2}{1}\\=-\frac{5}{1}\\=-5\\5\cdot \:2\\=10\\=3b-5=10+b\cdot \:2[/tex]

[tex]\mathrm{Add\:5--both\:\:sides\:of\:the\:expression}\\3b-5+5=10+b\cdot \:2+5\\3b=2b+15\\\mathrm{Subtract}\\3b-2b=2b+15-2b\\\mathrm{Thus,}\\b=15[/tex]

Hope it helps. :-)

The translations for each sentence are listed below:

Herein we find nine sentences that must be translated in terms of algebraic expressions, that is, combinations of constants, variables and operators. Now we proceed to present the result of each case:

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The scatterplot is the correct answer.

A scatter plot uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

The dots in a scatter plot not only report the values of individual data points but also patterns when the data are taken as a whole.

Identification of correlational relationships is common with scatter plots. In these cases, we want to know, if we were given a particular horizontal value, what a good prediction would be for the vertical value.

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The magnitude of the sum of these two vectors is approximately 11.791 units.

In this question we have the representations of two vectors on a Cartesian plane, of which we must find the magnitude of the two vectors. There are different methods to find it, we decide to use a vectorial method. First, sum the two vectors:

R(x, y) = A(x, y) + B(x, y)

R(x, y) = 7.70 · (cos 27.8°, sin 27.8°) + 16.3 · (- sin 20°, - cos 20°)

R(x, y) = (6.811, 3.591) + (- 5.574, - 15.317)

R(x, y) = (1.237, - 11.726)

Second, use the Pythagorean theorem:

R = √[1.237² + (- 11.726)²]

R ≈ 11.791

The magnitude of the sum of these two vectors is approximately 11.791 meters.

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Alan drive if he uses 4 gallons of gas is 75 miles distance

The following function calculates the distance (in miles) he travels on gallons of gas. D(g)=25g

Where D(g) is the distance traveled in gallons.

and g denoted the quantity of gasoline used

We are asked to calculate the distance traveled in three gallons of gasoline. To do this, we will set the value of g to 3 in our function.

D(3)=25 x 3 = 75

As a result, Chris's automobile traveled 75 miles on three gallons of petrol.

The length of the line segment connecting two places, for example, is the distance between them. a two-dimensional plane, which may also be  in a three-dimensional plane. In coordinate geometry, there are several forms of distance formulae.

Distance between two locations in a two-dimensional plane

Distance between two locations in a three-dimensional plane

Distance in 2D from a point to a line

2D distance between two parallel lines

3D distance from a point to a line

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Answer:

I think the answer is 234 miles and 78 gallons.

Step-by-step explanation:

Hope this helped :)

Answer:

You didn't show the problem so ill just make it to where you can answer yourself

Step-by-step explanation:

so if he uses 3 gallons per 21 miles just divide 3 by 21(yes 3 by 21)

So 0.142 is used per mile

So because you don't show how many miles he traveled just take the number of miles he traveled and times it by 0.142

Example: 42 x 0.142 = 5.964 which when rounded is 6

Answer:

That is a quadratic equation and must be factorized using two brackets. It is just a little confusing to recognize it as a quadratic as the middle x value is not there so we treat it as 0 - which means the two numbers must cancel each other out:

(2x + 1) (2x - 1)

Step-by-step explanation:

help

Answer:

(2x - 1)(2x + 1)

Step-by-step explanation:

4x² - 1

is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4x² - 1

= (2x)² - 1²

= (2x - 1)(2x + 1)

The rate of increase in the water pressure will be

0.000993 atmosphere per kilometers.

From the information given,it should be noted that the water pressure on Mustafa was illustrated by 0.993 atmosphere per meter.

Therefore, it should be noted that the rate of increase per kilometers will be illustrated as:

1000 meters = 1 kilometer

This will be

= 0.993 / 1000

= 0.000993

This will be illustrated as 0.000993 atmosphere per kilometers.

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Answer: The value of p(x) = (-2,6) or p(x) = (-2,0)

Step-by-step explanation:

Given that,

p(x) = x^3-4x^2-8x

p(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] - 8x

and replace with '0'.

x^3-4x^2-8x = 0

Now, factorizing equation is,

(x+2) ([tex]x^{2}[/tex] - 6x) = 0

(x+2) = 0

x= -2

Therefore, x = -2

and,

([tex]x^{2}[/tex] -6x) = 0

([tex]x^{2}[/tex] -6x+0) = 0

using quadratic formula = - [b ± √[tex]b^{2}[/tex]-4ac] / 2a

substitute the values,

a = 1, b = -6 , c = 0

                          p(x) = - [-6 ± √[tex]-6^{2}[/tex]-4.1.0] / 2.1

                           p(x) = - [-6 ± √36-4.1.0] / 2.1

                            p(x) = - [-6 ± √36-(0)] / 2.1

                             p(x) = - [-6 ± √36] / 2.1

                             p(x) = - [-6 ± 6] / 2

                              p(x) = [6 ± 6] / 2

                             p(x) = 3 ± 3

Therefore, p(x) = 3+3 = 6

                  p(x) = 3-3 = 0

So, that we can say the value of p(x) = (-2,6) or p(x) = (-2,0).

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Answer:

0.75

Step-by-step explanation:

[tex]\frac{6}{8}[/tex] = 6 ÷ 8 = 0.75

The type of fallacy which is being used in the statement is: Dicto Simpliciter.

A fallacy can be defined as a mistaken or false belief that are based on illogical arguments or reasoning.

In English literature, there are different types of fallacy and these include the following:

Dicto Simpliciter can be defined as a type of fallacy in which a general observation or rule is taken and assumed as generally (universally) true, regardless of the circumstances involved.

In this context, we can reasonably infer and logically deduce that the type of fallacy which is being used in the statement is Dicto Simpliciter.

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Complete Question:

Identify the type of fallacy being used in the statement. Gone with the Wind is the top grossing movie of all time, so it must be the greatest movie of all time.

Post Hoc, Ergo Propter Hoc

Non Sequitur

Dicto Simpliciter

Straw Man

Ad Hominem

False Dilemma

Petitio Principii

Argumentum ad populum

Answer:

168.75 km.

Step-by-step explanation:

Distance = speed * time

               = 75 * 2.25

               = 168.75 km.

The probability that only one of the counter is white is 6/11.

So we know that there are 11 counters, 5 of them are white, 6 are not white.

Let's assume that first we take the white one, the probability is equal to the quotient between the number of white counters and the total number of counters, so we have:

p = 5/11

Now for the second one, we don't want to take a white one, so here the probability is equal to the quotient between the number of non-white counters (6) and the total number of counters (now there are 10, because we took one)

q = 6/10

The joint probability is the product of the individual probabilities, this is:

P = p*q

And, also notice that there are 2 permutations:

So we need to add a factor 2.

P = 2*p*q = 2*(5/11)*(6/10) = 6/11

The probability is 6/11

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The equity capital the firm raise from this sale is $15 million.

Equity capital refers to the funds paid into a business by investors in exchange for common or preferred stock. It can be solved by subtracting the total liabilities from the total assets.

Equity Capital = Total Assets – Total Liabilities

If a company sold 1 million shares of common stock at $10 book value, then its total liabilities is $10 million.

If the stock price then rose to $25 per share on the New York stock exchange, then the total assets is $25 million.

Equity Capital = Total Assets – Total Liabilities

Equity Capital = $25 million – $10 million

Equity Capital = $15 million

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Answer: 36 degrees

Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees

Answer:

A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45

The inequalities and their graphs are;

1)  -x - 5 ≤ -2 is represented by the third graph

2) 6 + x ≤ 3 is represented by the fourth graph

3) x - 4 < -7 is represented by the second graph

4) 2x > -6 is represented by the first graph

1) We are given the inequality;

-x - 5 ≤ -2

Rearranging gives us;

-x ≤ -2 + 5

- x ≤ 3

Divide both sides by -1 to get;

x ≥ -3

The graph must be a closed circle starting at -3 and pointing to the right.

It is the third graph in the link at the end of this answers.

2) We are given the inequality; 6 + x ≤ 3

Rearranging gives;

x ≤ -6 + 3

x ≤ -3

The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.

3) We are given the inequality; x - 4 < -7

Rearranging gives us;

x < -7 + 4

x < -3

The graph must be an open circle starting at -3 and pointing to the left.

Thus, it is the second graph.

4) We are given the Inequality; 2x > -6

Divide both sides by 2 to get;

x > -6/2

x > -3

It must be a graph with an open circle starting at -3 and then to the right.

Thus, it is the first graph as seen in the attached link

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Answer:

24 gallons

Step-by-step explanation:

The total fuel capacity is 2/(1/24) = 24 gallons.

Using proportions and the percentage concept, it is found that:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for percentage problems.

This is because a percentage of an amount a divided by a total amount b is given by the following proportion:

P = a/b x 100%.

From the image, we have that 3 out of 12 apples are of the Jonagold variety, hence:

3/12 x 100% = 0.25 x 100% = 25%.

Each apple in the image is equivalent to 7 apples, hence:

9 x 7 = 63.

63 apples are not of the Jonagold variety.

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Answer:

x=-5nakalimutan ......................

......