Simplify each expression.
10 ln e

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:

7

Step-by-step explanation:

-4d+3

-4(-1) + 3   Insert -1 for d

4+3=7

Answer:

25.49

Step-by-step explanation:

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

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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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:

7.25, 0​, -9.8

Step-by-step explanation:

Answer:

24 gallons

Step-by-step explanation:

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

A = $ 1100.76 the amount in a continuously compounded account for the given conditions.

What does compound interest entail?

principal: $ 1000 annual

interest rate: 4.8%

time: 2 years

We know that continuously compound interest

A = [tex]P_{0} e^{rt}[/tex]

   = [tex]1000 e_{(0.048)(2)}[/tex]

   = [tex]1000 (e)^{0.096}[/tex]

   = [tex]1000 ( 1.10075906 )[/tex]

  = 1100 . 75906

A = $ 1100.76

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Answer:

184

Step-by-step explanation:

92 x 4.6 is 423.2 then you divide it by 2.3 which gets you 184.

Answer:

184

92 times 4.6 = 423.2

423.2 divided by 2.3 = 184

Step-by-step explanation:

Hope it helps! =D

Step-by-step explanation:

the total charge is £195.

we have 36 students. each paying £4.25.

we have 3 parents. each paying 2×£4.25 = £8.50

we have 3 teachers. each paying £0.

a.

the payments are

36×4.25 + 3×8.50 = 153 + 25.5 = £178.50

that is clearly below the total charge of £195.

there is a deficit of 195 - 178.5 = £16.50

b.

3 teachers.

so, each should pay

16.5 / 3 = £5.50

c.

8 students drop out.

that means

8× 4.25 = £34.00 are not paid.

we have now

28 students

3 parents

3 teachers

on the bus.

these are 34 persons.

34 / 34 = £1.00

they each would have to pay £1.00 as extra payment.

The relationship must hold for the point to be equidistant from the origin and the x z-plane is a^2+b^2+c^2 > b^2.

What is equidistant point:

A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.

Now,

distance from P(a, b, c) and the Origin (0,0,0)

[tex]\sqrt{(a-0)^2+(b-0)^2+(c-0)^2} =\sqrt{a^2+b^2+c^2}[/tex]

distance from p(a ,b, c) and the x-z plane

[tex]\sqrt{(0-0)^2+(b-0)^2+(0-0)^2} = |b|[/tex]

Here,

P is equidistant from the Origin and the x - z plane

[tex]\sqrt{a^2+b^2+c^2} = |b|[/tex]

[tex]a^{2} +b^2+c^3 = b^2[/tex]

[tex]a^{2} +c^2 = 0[/tex]

Hence a=c=0 ,thus the point P must be of the form (0,b,0) for any b ∈R

Again,

point P far the from the origin than from the x z plane

[tex]\sqrt{a^2+b^2+c^2} > |b|[/tex]

[tex]a^{2} +b^2+c^2 > b^2[/tex]

[tex]a^{2} +c^2 > 0[/tex]

Hence a, c ∈R such that atleast one of the a ,b ,c is non-zero.

Therefore,

(a ,b ,c) for any b∈ R and for a, c ∈ R with atleast one of the a and c is non-zero.

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The angle number that represents the linear pair of angle FHC is: angle 5.

The linear pair consists of two adjacent angles that are on a straight line, whose sum will be equal to 180 degrees when added together.

Thus, the two adjacent angles share a common side and a common vertex, and they are supplements of each other. That is, they have a sum of 180 degrees.

Angle 4 represents angle FHC. Angle 5 is adjacent to angle 4, and both lie on a straight line.

Therefore, angle FHC + angle 5 = 180 degrees.

In conclusion, we can state that, the angle number that represents the linear pair of angle FHC is: angle 5.

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The number 8 is a natural number, whole number, integer, rational number, real number.

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well. In this post, let's study all there is to know about whole numbers.

The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.

Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers.

Real number is a value of a continuous quantity that can represent a distance along a line. Real numbers can be defined as the union of both rational and irrational numbers.

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The length of the golden gate bridge is -163.250975.

What is trigonometry?

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

What is length?

Length is a measure of distance. According to the International System of Quantities, length has the dimension of distance. Most measurement systems select a length base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.

Given that,

The height of the bridge is 300m,

The angle of depression in the middle of the river are 25⁰ and 32⁰ respectively.

[tex]\frac{300}{tan(32)}[/tex] -[tex]\frac{300}{tan(25)}[/tex],

[tex]\frac{300}{0.624869}[/tex]-[tex]\frac{300}{0.466308}[/tex],

= -163.250975.

The length of the golden gate bridge is -163.250975.

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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:

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 solution is 10

Firstly rewriting the equation to frame the steps of solution -

√(5x-1) + 3 = x

Shifting 3 to the Right Hand Side of the equation -

√(5x-1) = x - 3

Now taking square of both sides of the equation

(√(5x-1))² = (x - 3)²

On solving the square we get the equation -

(5x - 1) = x² + 9 - 6x

Further solving the equation -

5x - 1 - 9 = x² - 6x

5x - 10 + 6x = x²

x² - 11x + 10 = 0

Solving the equation by factorizing -

x² - 1x - 10x + 10 = 0

x (x - 1) - 10(x - 1) = 0

(x - 1)  (x - 10) = 0

x = 1, 10

Keeping the value of x in equation to find the solution and check the results-

x = 1

√(5×1-1) +3 = 1

√(5 - 1) + 3 = 1

√4 + 3 = 1

2 + 3 = 1

5 = 1

x = 10

√(5×10-1) +3 = 10

√(50 - 1) + 3 = 10

√49 + 3 = 10

7 + 3 = 10

10 = 10

Since, 10 = 10, the result is correct.

Hence, the solution is 10

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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 intersection point of two lines are (-4 , -19)

The intersection point are those point where two line met of cut each other are called intersection point.

the given line of equation are

y = 5x + 1

y = 2x - 11

On solving these two equation we get the values as follow,

value of x = -4

value of y = -19

hence by this we can say the the intersection point of the above lines are

( -4 , -19 )

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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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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

Answer:

hope it helped!

Step-by-step explanation:

With the SmartScore, the learning process is rewarded and your students are constantly reassessed. When a student starts practicing a skill, the SmartScore ...

Missing: s ‎h, ‎r, ‎p. ‎Quest ‎12th ‎Leap: ‎MI

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

The extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.

We are given an equation:

5(3 x + 1)^ ( 1 / 4) = 10

Divide each side by 5, we get that:

⁴√3 x + 1 = 2

Raise both sides to the power 4, we get that:

3 x + 1 = 2⁴

3 x + 1 = 16

3 x = 16 - 1

3 x = 15

x = 15 / 3

x = 5

Therefore, we get that, the extraneous solution for the equation 5(3 x + 1)^ ( 1 / 4) = 10 is x = 5.

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Answer:

12,000

Step-by-step explanation:

Since we're just estimating, we can just round the two numbers.

180 rounded to the nearest hundred is 200.

586 rounded to the nearest hundred is 600.

200 * 600 = 12,000

Therefore, 180 * 586 is roughly 12,000.

Raj is incorrect as the negative signs are put in different place.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

given:

-(5^4) = (-5^4).

Raj is incorrect because the in LHS part the negative sign is out of the exponent term and in RHS part the negative sign is within exponent.

-(5^4) gives - 625

and,  (-5^4) gives 625

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The number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35  = 154.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jackson has a points card for a movie theater. He receives 35 reward points just for signing up. He earns 8.5 points for each visit to the movie theater.

Let x be the number of visits Jackson must make to earn a free movie ticket.​

8.5x + 35  = 154

8.5x = 154 - 35

8.5x = 119

x = 119/8.5

x = 14

Thus, the number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35  = 154.

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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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