(m² - 7m - 11) ÷ (m-8)


By diving polynomials

The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1

From the question, we have the following parameters that can be used in our computation:

Let f(x) = log base 3 of x and g(x) = 3^x.

Express the equations properly

So, we have the following representations

f(x) = log₃(x) and g(x) = 3ˣ

Calculating the composite function [f(g(f(f(f(g(27))))))], we have

[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]

Next, we have:

[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]

This gives

[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]

For f(27), we have

[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]

For f(3), we have

[f(g(f(f(f(g(27))))))] = [f(g(1))))]

Calculating g(1), we have

[f(g(f(f(f(g(27))))))] = f(3)

Lastly, we have

[f(g(f(f(f(g(27))))))] = log₃(3)

Evaluate

[f(g(f(f(f(g(27))))))] = 1

Hence, the solution is 1

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Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.

A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.

[tex]m = \frac{y2-y1}{x2 - x1}[/tex]

given

the graph is,(0,8) and (9,2)

The slope of the line is,

m = 1/2

Because it crosses the y-axis at the point where the intercept C is equal to 8,

The equation of the line will be :

⇒ y = mx + c

⇒ y = (1/2)x + (8)

⇒ y = x/2 + 8

Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.

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A polynomial is an expression involving variables and coefficients, which is formed by adding, subtracting, multiplying, and taking non-negative integer exponents of the variables. A mathematical statement that two expressions are equal is known as an equation.

A mathematical statement that two expressions are equal is known as an equation.

Example of a polynomial:

2x^2 + 3x + 5

Example of an equation:

2x^2 + 3x + 5 = 0

Let's say we are solving the equation 2x^2 + 3x + 5 = 0

Step 1: Subtract 5 from both sides.

2x^2 + 3x = -5

Step 2: Divide both sides by 2.

x^2 + 3/2 x = -5/2

Step 3: Use the quadratic formula to solve for x.

x = (-3 ± √17) / 4

Step 4: Simplify the answer.

x = (-3 ± 4.12) / 4

Step 5: Solve for the two values of x.

x = -0.78 or x = 3.28

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Trejo is correct, because if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

A relation between a set of inputs having one output each is called a function.

Given that;

Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

But, Hilary disagrees, She says you know the intercepts but that is all you know for sure.

Now,

We know that;

In a function, If if you know the x-intercepts, y-intercepts, domain, and range of a function then you automatically know the x- intercepts, y-intercepts, domain, and range of its inverse.

Thus, The Trejo is correct.

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The probability that at least 12 buy their lunch =  0.887

Given that 73% of students buy their lunch.

⇒ p = 0.73

And q = 1-p

q =  0.27

sample size (the number of student selected) n = 19

We need to calculate the probability that at least 12 buy their lunch.

i.e., P(x ≥ 12)

We use binomial distribution formula, P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X ≥ 12)

= P(X= 12) + P(X= 13) + P(X= 14) + P(X= 15) + P(X= 16) + P(X= 17) + P(X= 18) + P(X= 19) [tex]=~ ^{19}C_{12}(0.73)^{12}(0.27)^{7} + ^{19}C_{13}(0.73)^{13}(0.27)^{6}+ ^{19}C_{14}(0.73)^{14}(0.27)^{5} + ^{19}C_{15}(0.73)^{15}(0.27)^{4} + ^{19}C_{16}(0.73)^{16}(0.27)^{3} + ^{19}C_{12}(0.73)^{17}(0.27)^{2}+ ^{19}C_{12}(0.73)^{18}(0.27)^{1}+ ^{19}C_{12}(0.73)^{19}(0.27)^{0}[/tex]

= 0.1207 + 0.1757 + 0.2036 + 0.1835 + 0.1240 + 0.0592 + 0.0178 + 0.0025

= 0.887

The required proability is  0.887

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The odds against exactly 5 cars passing over the bridge in that time are given as follows:

5.25:1.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

An odd, conversely, is calculated as the division of the number of desired outcomes by the number of non-desired outcomes.

The probability(in favor) that 5 cars will pass over a small bridge in a 4-minute period is 0.16, hence the odds are given as follows:

0.16 : (1 - 0.16) = 0.16 : 0.84.

To obtain the odds against, we must exchange the desired and the non-desired outcomes, meaning that the odds against is then given as follows:

0:84 : 0.16.

As the quotient of 84 by 16 is of 5.25, the simplified odd is given as follows:

5.25 : 1.

Meaning that it is 5.25 times more likely that exactly 5 cars do not pass over the bridge over that time rather that they do pass.

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Answer:

(2) y = -2x² + 6x - 6

Step-by-step explanation:

Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.

Using the centroid P on the triangle, the value of QN is 25.5 and PN is 8.5

The centroid of a triangle is a point located at the intersection of the three medians (the lines that connect the vertices to the midpoints of the opposite sides). The centroid divides each median in two segments that have the same length. It is the center of gravity of the triangle and is the point at which the triangle's three medians intersect.

The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

In this triangle, the centroid is at P and the QP is 17.

a) QN

The distance between QP is two-thirds the length of QN

The length of QP = 17

QP = 2/3 QN

17 = 2/3 QN

QN = (3 * 17) / 2

QN = 25.5

b) PN

The distance between PN is calculated as;

PN = QN - QP

PN = 25.5 - 17

PN = 8.5

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Answer:

(1/3) (44.5)π cm3.

Step-by-step explanation:

The volume of the two scoops of ice cream combined with the ice cream inside the cone can be calculated as follows:

Volume of cone = (1/3) π (3/2)2h = (1/3) π (4.5)8 = (1/3) (35.5)π

Volume of scoop = (1/6) π d3 = (1/6) (3)π

Total volume = (1/3) (35.5)π + 2(1/6) (3)π = (1/3) (44.5)π cm3.

Answer:

x = $25,400 [the original price of the Junko car]

Step-by-step explanation:

The price Ben paid, $23,622, is after the 7% discount.  Let x be the original price of the Jinko car.   Ben's prices reflect a 7% discount:

 x*(1-0.07) = $23,622  [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]

(0.93)x = $23,622

x = $25,400

the probability that the card is either a queen or a diamond is: 4/13

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally probable alternatives that result in a particular occurrence.

Example: When flipping a coin, there are only two possible outcomes: either it will land on its head or on its tail.

Number of cards, n(S) = 52

Let E = Event of getting a diamond

F = Event of getting a queen

(E ∩ F) = Event of getting a diamond of queen.

Then, n(E) = 13

n(F) = 4 ,

n (E ∩ F)=1

P(E) = 13/52 = 1/4

P (F) = 4/52 = 1/13

P (E ∩ F) = 1/52

(E or F) = P(E ∪ F) = P(E) + P(F) × P(E ∩ F)

P (E or F) = 1/4 + 1/13 - 1/52

P (E or F) = (13 + 4 - 1)/52

P (E or F) = 16/52

P (E or F) = 4/13

The required probability of getting either diamond or a queen is 4/13

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Solving for W in the equation 4 = (2 + W) / 2 gives W = 6

Using the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'

This is achieved by the following procedure

clearing the fraction

4 = (2 + W) / 2,

8 = 2 + W

rearranging the equation

W + 2 = 8

subtracting 2 from both sides of the equation

W + 2 - 2 = 8 - 2

since 2 - 2 = 0 we have

W = 6

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The examples for each of the quadrant is explained below.

Quadrant in math is defined as one of the four regions or sections of the coordinate system and the quadrants are separated by the x-axis and the y-axis and these axes are perpendicular to each other.

Here we have to know the value that must be placed on each quadrant.

Here the first quadrant has both x and y-coordinates are positive.

The second quadrant has the value of the x-coordinate is negative and the y-coordinate is positive.

The third quadrant has both x and y-coordinates are negative.

The fourth quadrant has the value of the x-coordinate is positive and the y-coordinate is negative.

Therefore, the example for each of them are written as

=> Quadrant I = (1, 1)

=> Quadrant II = (-1, 1)

=> Quadrant III = (-1, -1)

=> Quadrant IV = (1, -1)

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Answer:

4

Step-by-step explanation:

This question basically asks you to substitute the value of x to find the value of function g(x).

Given x = -2,

g(-2) = -4(-2) - 4 = 8 - 4 = 4

Answer:

4

Step-by-step explanation:

g(x) = -4x - 4

Let x = -2

g(-2) = -4(-2) - 4

          = 8 -4

           =4

The missing sides of the triangle can be found by applying the Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that square of  hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex]  ;

let missing side of the Right triangle be hypotnuse ;

So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .

For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .

let , the length of side "base" be unknown.

So ,  in order to find length of side b  (base) , we substitute the  known values into Pythagoras theorem:

[tex]10^{2} =6^{2} +Base^{2}[/tex] ;

[tex]Base = 100-36[/tex] ;

So , missing side "base" is = 8 ;

Therefore , the missing side can be found by using  the Pythagoras Theorem .

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On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70

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There are seven zeroes  located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).

Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.

Let P=1/(2^5.5^8)

Multiplying and dividing the numerator by 2^3

P= 2^3/(2^5.5^8.2^3)

P=8/(2^8.5^8)

P=8/10^8

P=0.00000008

The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.

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There are three solutions to the congruence x+13=55 (mod 34).

Two figures are considered to be 'congruent' if they can be put exactly over each other. When you set one slice of bread on top of the other, you'll see that they're both the same shape and size. The phrase "congruent" refers to having exactly the same form and dimension. When two things or forms superimpose on each other, they are said to be congruent. Their shapes and sizes are identical. Line segments with the same length and angles of the same measure are congruent in the case of geometric forms.

Here,

something equaling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21

do you mean x+13=21 (mod 34) ?

clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100

The congruence x+13=55 (mod 34) has three solutions.

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The final statement is: y=16

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The exponential function y=4×2ˣ

Therefore for x=2 we get

y=4×2²

y=16

Hence, The value of y at x equal to 2 is 16

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The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

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Answer: Ball A, B, C, F, E, D

Step-by-step explanation:

An object has the greatest amount of Gravitational Potential Energy when it is furthest from the ground.

This means that Ball A has the most gravitational potential energy. This is followed by Ball B and Ball C. Then, Ball F is farthest from the ground, followed by Ball E. Ball D has the least gravitational potential energy.

So, the order is as follows: Ball A, B, C, F, E, D

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

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Answer: A

Step-by-step explanation:

Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.

A: correct

Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.

B: incorrect

Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.

C: incorrect

Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.

Therefore, A is the correct answer.

Answer:

alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25

Step-by-step explanation:

Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

Answer:

120x - 96y + 32

Step-by-step explanation:

12 (10x + 3 -8y)

We use the distributive property to solve

120x - 96y + 32

One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is

120x - 96y + 32

Answer:

01?

Step-by-step explanation:

I didn't see a picture so maybe just one

The area of the isosceles triangle having two sides 12.5 cm and another 20cm is 75cm².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know that an isosceles triangle has two sides having the same length and the third one is different.

We also know that the area of an isosceles triangle is (1/2)×b×√(a² - b²/4),

where b is the value of the third side and a is the value of two similar sides.

Therefore, The area of the isosceles triangle having side lengths of two similar sides is 12.5 cm and the third side is 20 cm is,

= (1/2)×20×√((12.5)²- (20)²/4) cm²,

= 10×√(156.25 - 100) cm².

= 10×√(56.25) cm².

= 10×7.5 cm².

= 75 cm².

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Therefore , the solution of the given problem of combination comes out to be  there were 182 games played in all.

Combinations are operations in mathematics that count the number of possible combinations that can be created from a set of items, where the selection's direction is immaterial. You are free to select any arrangement of the parts. Permutations and combinations can be mixed up.

Here,

There still are 14 teams in all, but each team plays the other twice.

Every team plays almost every team twice, hence the total amount of games played is simply the permutations of 2 out of 14, which is determined by:

₁₄P₂

=14!/((14-2)!)

= (14×13×12!)/ 12!

= 14×13

=182

Consequently, there were 182 games played in all.

Therefore , the solution of the given problem of combination comes out to be  there were 182 games played in all.

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Answer:

2.35 + 0.55 × 15 = 10.6

Therefore, she can go 10.6 miles.

Answer:

10.6

Step-by-step explanation:

2.35 + 0.55 x 15 = 10.6