the logarithm is the ____ of a specified base

Please i need help!!!!!

The  polynomial function that could be represented by the graph is; f(x) = x³ + x² - 6x

Let us find the zeros of the polynomial from the graph. The zeros of the polynomial will be the points where the graph crosses the x-axis.

Thus, we see that the graph crosses the x-axis at x = -3, 0 and 2. Thus, the factors of the polynomial are;

(x - 0), (x + 3) and (x - 2)

Therefore, the equation of the polynomial is;

f(x) = x(x - 2)(x + 3)

Expanding this gives us;

f(x) = x(x² + x - 6)

f(x) = x³ + x² - 6x

We conclude that is the equation of the polynomial represented by the graph.

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BC is equal to 24cm.Now, by applying the Pythagoras theorem i.e. in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides, we can find BC.

Find BC ?

So, we can apply the Pythagoras theorem here, if it is right-angled at C then the side opposite to C will be the hypotenuse of the triangle that is AB = 25 cm, and the other two sides are AC = 7 cm and BC.

AB = 25 cm, AC = 7 cm and BC =?

In triangle ACB, By Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2

AB)2 = (AC)2 + (BC)2

(25)2 = (7)2 + (BC)2

625 = 49 + (BC)2

(BC)2 = 625 – 49

(BC)2 = 576

BC = 24 cm

Thus, BC is equal to 24cm

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The system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics.

Here,

Given data:

Time taken by Latanya to solve a problem = 1.5 minute.

Time to read one page = 2 minutes.

Number of problems completed = x problems.

Total time used for reading = y  minutes.

Using the data to consider:

Let x be the the number of math problems that Latanya solved.

Let y be the number of pages that Latanya read.

thus,

1.5x +2 y = 48

and

x = 4 + y

Thus, we can conclude the the system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

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Answer: x= 4/k

Step-by-step explanation:

Answer:

B.) [tex]\frac{4}{k}[/tex]

Step-by-step explanation:

[tex]3kx+24=9kx\\3(kx+8)=9kx\\\frac{3(kx+8)}{3}=\frac{9kx}{3}\\kx+8=3kx\\(kx+8)-kx=(3kx)-kx\\8=2kx\\\frac{8}{2k}=\frac{2kx}{2k}\\\frac{4}{k}=x[/tex]

According to the calculation used to compute it, [tex]3\frac{1}{3}[/tex] liters of water are required to water all the indoor plants.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. An expression in mathematics is a combination of digits and operations. A mathematical expression that performs an operation has the following components: Operations and Operands

The amount of water needed to water all the indoor plants is 1/3 liter, according to the calculation used to determine this.

[tex]= 4/3 / 2/5\\ = 4/3 X 5/2\\ = 3\frac{1}{3}[/tex]

Consequently, 3 1/3 liters are needed.

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No, 1 is not a real number.

Real numbers are numbers that can be used to measure or describe anything, such as a quantity or distance. Real numbers can be either rational (e.g. fractions, decimals, and integers) or irrational (e.g. roots and pi). Real numbers are usually represented on a number line, where points to the right of 0 represent positive numbers and points to the left of 0 represent negative numbers.

Real numbers include all the rational and irrational numbers. They can be integers, fractions, decimals, and even imaginary numbers. 1 is an integer, so it is not considered a real number. Real numbers are those that have a decimal representation, which 1 does not.
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Answer:

Three and four  and five  and zero.

Step-by-step explanation:

Answer:

3 and 4

Step-by-step explanation:

The value of polynomial 5x - 4x² + 3 at x=0 is equal to 3

Given that,

The polynomial is 5x - 4x² + 3

To find : The value of polynomial 5x - 4x² + 3 at x=0

A combination of more than two algebraic expressions, particularly when they each contain a distinct power of the same variable (s).Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Given : x = 0

→ 5x - 4x² + 3

→ 5 ( 0 ) - 4 ( 0) ² + 3

→ 0 - 0 + 3   ( ∵ here + 0 - 0 cancels )

→ 3

Therefore, The value of polynomial 5x - 4x² + 3 at x=0 is 3.

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It was first called "pi" in 1706 by William Jones, because pi is the first letter in the Greek word perimitros, which means "perimeter."

2 is a  prime number because it has only two factors (1 x 2).

A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.

Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.

Given why 2 is prime,

The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.

so 2 has only two multiple

1 and 2,

Hence 2 is a prime number.

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The probability that the sample proportion is more than 40% is approximately .0001.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To find the probability that the sample proportion is more than 40%, we need to use the normal distribution and the central limit theorem.

The central limit theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To find the probability that the sample proportion is more than 40%, we need to first calculate the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion (38%), and the standard deviation of the sample proportion is equal to:

  [tex]standard\ deviation = sqrt((population\ proportion * (1 - population\ proportion)) / sample\ size)\\\\= \sqrt{((.38 * .62) / 400)}\\\\= .048[/tex]

Next, we need to standardize the sample proportion of 40% by subtracting the mean and dividing by the standard deviation:

z = (40% - 38%) / .048 = 4.17

The probability that it is less than or equal to 40% is approximately .9999.

The probability that the sample proportion is more than 40% is then equal to 1 - .9999 = .0001.

So, The probability that the sample proportion is more than 40% is approximately .0001.

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The state income tax owed on the $40,000 salary should be $1,800.

An income tax is a tax levied on persons or companies based on their earnings or profits. In most cases, income tax is calculated as the result of a tax rate multiplied by the taxable income. Taxation rates may differ depending on the taxpayer's attributes and the source of income.

Given:

Income Progressive Range ($)                  Tax Rate

                        0-  10,000                                 3%

                       10-001- 50000                           5 %

                      50001- 100000                          5.5%

The calculation of the state income tax owed on $40,000 salary

= 3% of $10,000 + 5% of $30,000

= $300 + $1,500

= $1,800

Hence, the state income tax owed is $1,800.

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An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

Given that,

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The pipe is located 9 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 9 inches from the vertex (0,0)

9 inches is the focus of the mirror

The distance between the vertex and the focus = 9

Since parabola is upwards and vertex is (0,0) we use formula,

[tex]4py = x^{2}[/tex]  

Where,

p is the distance between the vertex and focus p = 9

Now,

[tex]4*9*y = x^{2}[/tex]    

[tex]36y =x^{2}[/tex]

Now isolate y by dividing 36 on both sides, we get

y = [tex]\frac{x^{2} }{36}[/tex]

Therefore,

An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

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Answer:

Below

Step-by-step explanation:

From the graph, the zeroes are at -4 and - 0.5 so the equation starts like this:

a (x+4)(x+.5) = 0    now ya need to sub in a point to calculate 'a'

 ......  point 0,4 results in this:

a (0+4)(0+.5) = 4

 2a = 4

   a = 2

so the equation becomes  2 ( x+4)(x+.5) = 0

                                2 ( x^2 + 4.5x +2) = 0

                                   2 x^2 + 9x + 4 =0  

Answer:

Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased

Step-by-step explanation:

Domain is the input of a function and range is the output of a function, for f(x) = sin(x), domain will be (-inf, +inf) and range will be [0,1].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain is the input of a function and range is the output of a function.

Examples:

f(x) = sin(x), domain =  (-inf, +inf) and range = [0,1].

f(x) = cos(x), domain =  (-inf, +inf) and range = [0,1].

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Identify the denominator of the function and set it equal to zero. Solve the equation to find the x-values of the asymptote. Substitute the x-values found in step two into the original equation to determine if the vertical asymptote is a true asymptote.

The first step when finding vertical asymptotes is to identify the

denominator of the function and set it equal to zero. This creates an equation which can then be solved to find the x-values of the asymptote. The second step is to solve the equation, using methods such as factoring or completing the square, to find the x-values of the asymptote. The final step is to substitute the x-values found in step two into the original equation and determine if the vertical asymptote is a true asymptote. If the limit of the function as x approaches the x-value found in step two is either positive or negative infinity, then the vertical asymptote is a true asymptote. If, however, the limit of the function as x approaches the x-value found in step two is not infinity, then the vertical asymptote is not a true asymptote. This process of finding vertical asymptotes can be used to find the vertical asymptotes of any function.

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The solutions to the equation 2x^2 = 100 is  [tex]x=\pm 5 \sqrt{2}[/tex].

How do you find all solutions of a quadratic equation?

The solutions of a quadratic equation ax2 + bx + c = 0 are given by the quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula, just get the equation into standard form ax2 + bx + c = 0, and apply the quadratic formula.

[tex]$$2 x^2=100$$[/tex]

Divide both sides by 2

[tex]\frac{2 x^2}{2}=\frac{100}{2}$$[/tex]

Simplify

[tex]x^2=50$$[/tex]

For [tex]$x^2=f(a)$[/tex] the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]

[tex]$$x=\sqrt{50}, x=-\sqrt{50}$$[/tex]

[tex]$$\begin{aligned}& \sqrt{50}=5 \sqrt{2} \\& -\sqrt{50}=-5 \sqrt{2} \\& x=5 \sqrt{2}, x=-5 \sqrt{2}\end{aligned}$$[/tex]

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The initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours  of flight.

The linear model that can be used to predict the amount of jet fuel present on the Boeing 747-8 Intercontinental jet after 18 hours of flight without refueling is given by the equation

F = 63,500 - (800 x 18),

where F is the amount of jet fuel in gallons and 18 is the number of hours of flight. This equation indicates that after 18 hours of flight, the jet would have an estimated amount of jet fuel of 42,400 gallons remaining. This amount is significantly lower than the initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.

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The mode of a set of numbers is the number that appears most often in the set. In the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there is no number that appears more often than any other, so the mode of this set is not defined.

The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group. The mode is the one that is most prevalent.

The value that appears most frequently in a set of values is referred to as the mode. It is the value that shows up the most frequently. Example: Since the number 5 appears twice in the provided data set of 2, 4, 5, 6, and 7, it is the mode of the data set. 2

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The Nature of roots of the quadratic equation "5x² -3x +2 = 0" is  imaginary and conjugate   .

To find the Nature Of Roots of the Quadratic Equation ax² + bx + c = 0 , we find the discriminant(D) by the formula ; D = b² - 4ac .

the quadratic equation is given as 5x² -3x +2 = 0 ;

On comparing , we get , a = 5  , b = -3 and c = 2 .

Substituting the values in the Discriminant formula mentioned above , we get

D = (-3)² - 4×5×2

= 9 - 40

= -36 .

Since the value of the discriminant is less than 0 ,

Therefore  , the roots will be imaginary and conjugate .

The given question is incomplete , the complete question is

What is the nature of the roots of the equation 5x² -3x +2 = 0  ?

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The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let us find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 399

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 399

3X + 3 = 399

3X + 3 - 3 = 399 - 3

3X = 396

3X/3 = 396/3

X = 132

Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.

Hence , The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

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Answer:

3x + 2y = 6

Step-by-step explanation:

When you solve for y in this equation, it is in the same format as the slope-intercept equation.

3x + 2y = 6

2y = -3x + 6

y = -3/2 x + 3  

The slope intercept equation is ...

y = mx + b

(m can be any number)

The slope-intercept equation is for linear functions!

The answer to the expression -( 7 4x )= 9 is -7, since subtracting 7 from both sides of the equation leaves us with 4x = 2, and then dividing both sides of the equation by 4 gives us x = -7.

The expression -( 7 4x ) = 9 can be solved by using basic algebraic operations. First, we subtract 7 from both sides of the equation to obtain -4x = 2. This is because when subtracting a number from both sides of an equation, we are essentially adding the opposite of that number to both sides. Then, we divide both sides of the equation by 4 to obtain x = -7. This is because when dividing both sides of the equation by a number, we are essentially multiplying both sides by the inverse of that number. Therefore, the answer to the expression is -7.

-(7 4x ) = 9

-7 - 4x = 9

-4x = 2

x = -7

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The equation of the line that passes through the points (0,3) and (2,7) in slope intercept form is y = 2x + 3  .

The Slope Intercept form of the line is written as y = mx + c ; where c is the y intercept and m is the slope of the line .

to find the equation , we first need to find the slope ,

So , slope (m) = (7-3)/(2-0) = 4/2 = 2 ;

next we need to find the y intercept ;

So , putting the values , we get ;

3 = 2(0) + c

c = 3 .

putting the values of y intercept and slope in the equation ,

we get ;

the equation as ; y = 2x + 3 .

Therefore , the equation of the line is y = 2x + 3 .

The given question is incomplete , the complete question is

How do you write an equation of a line that passes through the points (0,3) and (2,7) in slope intercept form ?

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Answer:

320 teenagers

Step-by-step explanation:

10% = 0.1

Take 3200 times 0.1 = 320

So, there are 320 teenagers attended the football game.

The amount of fabric used on the headband and wristband for each player is 27.64 inches.

The operations that we use in particular actions like adding and taking away things or adding multiple times, diving things, etc.

The four basic Mathematical operations are addition, subtraction, multiplication, and division.

Here in this problem, we use divisions to solve the problem,

Given that,

Nancy uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. 378.83 inches of fabric used on wristbands for the players only.

Number of headbands made with 866.18 inches

= 43 (player's) + 3 (coach's)  

= 46 headbands

The amount of fabric used for 1 head band = (866.18)/46 = 18.83 in

378.83 inches of fabric used on wristbands for the players only.  

The amount of fabric used for each wristband = 378.83/43 = 8.81 in

Amount of fabric used on headband and wristband = 18.83 + 8.81

= 27.64 inches

Therefore,

The amount of fabric used on the headband and wristband for each player is 27.64 inches.

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On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)

The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.

The answer to the question is that all real numbers or (−∞,∞)

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Answer:440

Step-by-step explanation:

Answer:

To find the number of nickels in $22, we need to first convert the amount of money from dollars to cents and then divide this number by the value of a nickel in cents. Since 1 dollar is equal to 100 cents, we can convert $22 to 2200 cents.

Next, we need to find the value of a nickel in cents. Since a nickel is worth 5 cents, the value of a nickel in cents is 0.05 * 100 = 5 cents.

Finally, we can divide the total number of cents by the value of a nickel in cents to find the number of nickels:

2200 cents / 5 cents/nickel = 440 nickels

Therefore, there are 440 nickels in $22. Solving the equation 22 ÷ 0.05 gives the same result.

The cost of each pen would be 5 dollars.

What is a unit value?

When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. Context: The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities

The shopkeeper has 56 pens. and he sold them for 280 dollars

Cost of each pen = total amount/ number of pens

                            = 280/56

                            =10/2

                            = 5

Hence, the cost of each pen would be 5 dollars.

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