H) find the solution of the equation

In ( x + 2 ) = 4

how?

so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

we can start by squaring the equation x²+(1/x)=3

so we have x⁴ + 2x² + (1/x)² = 9

x⁴ + 2x² + 1 = 9x²

x⁴ - 7x² + 1 = 0

Now we can factor it

(x²-1)(x²-1) = 0

so x² = 1

now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1

x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1

= x⁴-2x³-2x-1

= (x⁴-2x³) - (2x+1)

= x⁴-2x³-2x-1

= (x²-x)² - (2x+1)

= (x-1)² - (2x+1)

so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

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The domain of the equation is (A) All real numbers and the range of the equation is (A) y≥-4.

The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

The domain of the equation is (A) All real numbers because the value of x is all real numbers.

and the range of the equation is (A) y≥-4, because the value of variable y is greater than and equal to -4 for all values of x.

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Answer: 7

Step-by-step explanation:

Distance (d) = √(4 - -3)2 + (5 - 5)2

= √(7)2 + (0)2

= √49

= 7

ΔX = 4 – -3 = 7

ΔY = 5 – 5 = 0

y = 0x + 5

When x=0, y = 5

Answer:

Step-by-step explanation:

D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2

X2 Y2

(-3,5)

X1 Y1

(4,5)

D= SQRT (-3-4)^2 + (5-5)^2

D= SQRT 49

D=7

a. The exponential function that is good model for the country population is:

Pₙ = 8100000(1.02)ⁿ ,

b. It will take 5.27 years to reach 9 million.

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Function Formula

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent.

a. Given,  initial population P₀ = 8100000, Rate of increase R = 2%.

If a constant rate of growth be R% per annum,

then function for population after n years

Pₙ = P₀ x (1+R/100)ⁿ

Population Pₙ = 8100000 × (1+2/100)ⁿ

Pₙ = 8100000(1.02)ⁿ

b. Let after x years population will be 9 million.

then,

9000000 = 8100000 (1 + 2/100)ˣ

(1 + 2/100)ˣ = 9000000/8100000

(1.02)ˣ = 90/81

(1.02)ˣ = 1.11

Taking log on both sides

ln (1.02)ˣ = ln (1.11)

ln(a)ⁿ = n ln(a)

x ln(1.02) = ln (1.11)

x = ln(1.11)/ln(1.02)

x = 5.27 years

Hence, the population will reach 9 million in 5.27 years.

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1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.

Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.

To find the winning combination we use the following formula

n !/ r!( n – r ) !

Where n = total number of to be drawn

r = the number which are drawn

In this question, n = 13, and r = 5

from the formula

13 !/5!( 13 – 5 ) !

= 13! / 5! 8!

= 13*12*11*10*9*8! / 5*4*3*2*1*8!

= 154,440 / 120

= 1287

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Answer:

median= 1/3

Step-by-step explanation:

It is recommended that when an ambulance arrives at an accident scene, it should park a safe distance away from the scene, at least 500 feet away.

This is to ensure the safety of the paramedics and other emergency responders, as well as to ensure that the ambulance does not impede the movement of other emergency vehicles. Additionally, it is also to protect the privacy of the individuals involved in the accident and ensure that the scene is not tampered with.

It is also important to follow any additional instructions given by the police or fire department at the scene, as they may have specific parking instructions based on the situation.

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The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .

The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.

The side lengths of the triangle are given as 4 units , 5 units and 6 units ,

According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]36 = 16 + 25[/tex] ;

[tex]36 \neq 41[/tex]

that means the given side do not form a right triangle .

Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .

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Answer:

70

Step-by-step explanation:

nk

The 40 50 90 triangle can be solved using Pythagoras theorem.

A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given:

We have 40 50 90 triangles.

A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.

Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.

So, Such type of Triangles can be solved using Pythagoras theorem.

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Distributive Property

Factoring

Functions

Let's organize what is given to us in the problem.

We are given a function f, defined as f(x) = x² + 3x - 10.

We are asked to find the values of b and c in f(x - 2) = x² + bx + c.

In order to solve the question, we first must find the full function of f(x - 2):

[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]

∴  [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]

Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:

[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]

∴ we have found the values of b and c.

∴ the value of b is equal to -1 and the value of c is equal to -12.

___

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Topic: Algebra I

Unit: Factoring

There are total 30 positive 3-digit palindromes are multiples of 3.

The numbers are as follows,

111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999.

Palindrome numbers

A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis.

A palindrome number is a number that is same after reverse.

For example - 121, 34543, 343, 131, 48984 are the palindrome numbers.

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The fifth term of the given arithmetic sequence is 36.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d

Given that, in a sequence the first term of 4 and the common difference is 8.

Here, a=4 and d=8

Now, the fifth term is

a₅=4+(5-1)×8

= 4+32

= 36

Therefore, the fifth term of the given arithmetic sequence is 36.

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Answer: 4 1/4

Step-by-step explanation: Decimal= 4.25

Answer:

Exact form: 17/4

Decimal Form: 4.25

Mixed number form: 4 1/4

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a specific unit, then dividing that value to figure out the needed value. Simply put, the unit method is employed to derive a single system value from a multiple that is supplied. For example, 40 pens might cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, computational equations, or algebra of matrices or operators.

given

time separation of gold medalists by silver medalists is equal to 0.14 minus 0.2, or 0.11.

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

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The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.

The given inequality is 3(2m - 1) ≤ 4m + 7

Remove the brackets by multiplying 3 with each term inside it:

6m - 3 ≤ 4m + 7

Subtract 4m from both sides of the equation.

6m - 3 - 4m ≤ 4m + 7 - 4m

2m -3 ≤ 7

Add 3 to both sides of the equation.

2m - 3 + 3 ≤ 7 + 3

2m ≤ 10

Divide both sides of the equation with 2.

2m/2 ≤ 10/2

m ≤ 5

Hence the solution of the equation is m ≤ 5, that is option A.

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Answer:

Submarine must descend by 12 feet in the fifth minute.Average of the data:Average of a data set is calculated by dividing the sum of terms by the number of the terms of the set.From the table given in picture,Let the distance descended by submarine in 5th minute = x feetAverage distance descended by the submarine =                                                                                 =                                                                                 =  feet per minuteStatement given in the question → "Submarine must descend at an average rate of at least 10 feet per minute"So the inequality for the statement will be,38 + x ≥ 50x ≥ 50 - 38x ≥ 12    Therefore, submarine must descend 12 feet in the 5th minute.

Step-by-step explanation:

A triangle that is equilateral has three equal sides and three equal angles.

The angles are all 60 degrees each. Two 90-degree angles are formed when the height of an equilateral triangle is drawn to the base of the triangle, and the top angle is divided into two 30-degree angles. A triangle with sides of 30-60-90 always has sides that are 1:3:2.

The 30-60-90 triangle formula for sides y is also known as y3: 2y. The angles of the triangle are always 30, 60, and 90 degrees. Given that one of the angles is 90 degrees, this triangle is always a right triangle. These angles come together to form a right-angled triangle. Furthermore, the right angle is equivalent to the sum of two sharp angles, which will have the ratios of 1: 2 or 2: 1.

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Exact length of border required by Kristin is calculated to be 9.42 ft.

This question can be solved using the concept of circumference of a circle.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve/arc length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles.

Circumference of a circle is given by 2πr.(r is the radius of the circle)

In the given question,

diameter= 3ft

radius= half times of diameter

radius= 1.5 ft.

Circumference= 2πr

= 2×3.14×1.5

=9.42 ft

Kristin will require 9.42 ft of border around the edge of the table.

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Answer:

m∠A=126°

Step-by-step explanation:

Supplementary means that they add up to 180°.

Therefore we can do 180-54 to get 126° for the m∠A.

Hope this helped! :)

The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.

Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.

The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.

First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.

We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.

[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]

To calculate 'c', we can first calculate 'a' by using the formula:

a = c * sin(A)

Then we plug 'a' into the equation for 'c':

c = sqrt(2*(c * sin(A))^2)

c = sqrt(2)*c*sin(A)

Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.

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The percentage of cars traveling east is 28% of the total number of cars.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The commission counted 486 cars traveling east and 189 cars traveling west.

We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.

From this concept, the percentage of the cars were traveling east would be

The cars traveling east divided by the total numbers of cars time s100%.

= (189/486 + 189)×100%.

= (189/675)×100%.

= 0.28×100%.

= 28%.

So, 28% of the total cars traveling east.

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Answer:

9 ft

Step-by-step explanation:

assuming the 3 was a mistake T'T volume is l x w x h so if the base is l x w then 12 x 14 (168) is the base then divide the volume from the base (1512 / 168) the answer is 9 ft

The interquartile range of the data decreases when the eighth day's amount is included in the data is true.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Joanna set a goal to drink more water daily.

The number of ounces of water she drank each of the last seven days is

60, 58, 64, 64, 68, 50, 57

On the eighth day, she drinks 82 ounces of water.

Raw data:      [60,58,64,64,68,50,57,82],

Sorted data:  [50,57,58,60,64,64,68,82]

Sample size = 8 (even)

mean  = 62.875

median  = (60+64)/2 = 62

1st quartile   = (57+58)/2 = 57.5

3rd quartile  = (64+68)/2 =  66

IQR = 66 - 57.5 = 8.5

Data without the eight day's measurement.

Raw data:      [60,58,64,64,68,50,57]

Sorted data:  [50,57,58,60,64,64,68]

Sample size = 7 (odd)

mean            = 60.143

median         = 60

1st quartile   = 57

3rd quartile = 64

IQR = 64 -57 = 7

Hence, the interquartile range of the data decreases when the eighth day's amount is included in the data is true.

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Answer: It's just

The interquartile range of the data decreases when the eighth day's amount is included in the data.

Step-by-step explanation: The question asks you to select ALL correct answers, but there is only one correct answer.

Answer:B or A depending on if it went per year or overall

Step-by-step explanation:100 137, 137-100=37

37/5=7.4

The algebraic expression for the sequence 1, 10, 19, is given as a(n) = 1 + (n-1) 9.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

For the given sequence the common difference between two consecutive terms is 19 - 10 = 9.

The general form of the nth term of an arithmetic sequence is given as:

a(n) = a + (n-1) d

Since, the value of a = 1 and the common difference d =9, the resulting expression is:

a(n) = 1 + (n - 1) 9

Hence, the algebraic expression for the given sequence is a(n) = 1 + (n - 1) 9.

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If the square base with perimeter 24 inches then the height  of the right pyramid be 8.485 - inches.

A right pyramid is one whose apex is located exactly above the centroid of the base. As a result, a right pyramid is a special instance of a regular pyramid.

It is referred to as the right pyramid if the pyramid's apex lies immediately above the base's center. If not, the pyramid is known as the oblique pyramid.

A right-triangular pyramid is a three-dimensional object that has a base that is a right-angle triangle and extends up to a single point.

Right pyramids have apex points that are immediately above the centroid of their base. Oblique pyramids are referred to as non right pyramids. An implied right pyramid is a regular pyramid since it has a regular polygon base.

24 / 4 = 6 inches - the edge length of the square base

9² = 3² + Height²

simplifying the above equation, we get

Height² = 9² - 3²

Height² = 72 take the square root of both sides

Height = ~8.485 - inches - the height of the pyramid.

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If the square base with perimeter 24 inches then the height  of the right pyramid be 8.485 - inches.

The centroid of the base is exactly where the top of a right pyramid sits. Consequently, a right pyramid is a unique example of a standard pyramid.

If the top of the pyramid sits directly above the centre of the base, it is referred to as the right pyramid. If not, the structure is referred to as an oblique pyramid.

A right-triangular pyramid is a three-dimensional object with a base that rises to a single point from a right-angle triangle.

Apex points of right pyramids are located directly above the centroid of their base. Non-right pyramids are another name for oblique pyramids. Given that its base is a regular polygon, an implied right pyramid is a typical pyramid.

24 / 4 = 6 inches - the edge length of the square base

9² = 3² + Height²

simplifying the above equation, we get

Height² = 9² - 3²

Height² = 72 take the square root of both sides

Height = ~8.485 - inches - the height of the pyramid.

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The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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At least 30 of the households have 0 to 4 pets.

What is Chebyshev's theorem?

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied to this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Here,

we have a sample size of n = 40.

The mean number of pets per household is 2 and the standard deviation is 1.

We need to determine at least how many of the households have 0 to 4 pets.

By using Chebyshev’s inequality rule with k = 2(that is ) then,

= 100(1- (1/k²))%

= 100 (1- (1/2²))%

= 100 (1- (1/4))%

= 75%

The corresponding number of households is the percentage multiplied by the sample size.

= 75% × 40 = 30

Hence, at least 30 of the households have 0 to 4 pets.

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To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.

Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.

The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.