The given functions will be graphed on the coordinate plane.

f(x)=x3+2x2−x−2

g(x)=log(x+3)

Which statement describes the relationship between the graphs of the two functions and the solutions to the equation x3+2x2−x−2=log(x+3)

Responses

The solutions are the y-coordinates of the points of intersection of the graphs.


The solutions are the x-coordinates of the points of intersection of the graphs.


The solutions are the x-intercepts of the graphs.


The solutions are the y-intercepts of the graphs.

Cameron can use the boards as they are for his corner shelves.

To determine if the triangular boards can be used for Cameron's corner shelves, check if they satisfy the condition for the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check each combination of sides:

18 inches + 18 inches = 36 inches > 24 inches (satisfied)

18 inches + 24 inches = 42 inches > 18 inches (satisfied)

18 inches + 24 inches = 42 inches > 18 inches (satisfied)

Therefore, all three combinations of sides satisfy the triangle inequality theorem, and the triangular boards can be used for Cameron's corner shelves.

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the length of the rectangle is 9 units

the width of the rectangle is 2 units

the area of the rectangle is 18 square units

the area of the triangle is 9 square units

to find the length and width just count the number of units along the bottom and along the side. To find the area of the rectangle, do the length times the width. To find the area of the triangle divide the area of the rectangle by 2

Therefore , the solution of the given problem of expression comes out to be  4(x + y) and 4y + 4x are identical expressions.

Mathematical processes like multiplying, dividing, joining, and now even removing are required. If they were merged, the following would be stated: An equation, some statistics, and a mathematical formula A statement of truth is made up of values, components, and mathematical processes like additions, subtractions, errors, divisions, and algebraic formulas. Words and sentences can be analysed and evaluated.

Here,

Yes, 4(x + y) and 4y + 4x are identical expressions.

We can use the distributive principle of multiplication over addition to understand why.

=> 4(x + y) = 4x + 4y

This is so that we can see what happens when we assign the 4 to both the x and y values enclosed in parentheses:

=> 4(x + y) = 4x + 4y

In fact, this is identical to the expression 4y + 4x, which is nothing more than the same words in a different order:

=> 4y + 4x = 4x + 4y

As a result, 4(x + y) and 4y + 4x are identical expressions.

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So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.

The first ten integers are the basic numbers in mathematics. The range of these vital values is 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

The total revenue from selling x units is given by:

R = xp

Substituting the demand equation p = 128 - 0.04x, we get:

R = x(128 - 0.04x)

R = 128x - 0.04x²

To find the prices that yield a revenue of $7840, we can set R equal to 7840 and solve for x:

7840 = 128x - 0.04x²

0.04x² - 128x + 7840 = 0

Dividing both sides by 0.04, we get:

x² - 3200x + 196000 = 0

Using the quadratic formula, we can solve for x:

x = [3200 ± √(3200² - 4(1)(196000))] / 2

x = [3200 ± √(10240000)] / 2

x = [3200 ± 3200] / 2

x = 1600 or x = 2400

Therefore, the corresponding prices that yield a revenue of $7840 are:

p = 128 - 0.04x

p = 128 - 0.04(1600) = 64 dollars

p = 128 - 0.04(2400) = 32 dollars

So the lowest price that yields a revenue of $7840 is $32 and the highest price is $64.

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The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:

The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.

Therefore, we find ƒ(-4) = -51.

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Answer:

Rosa must save at least $85 to purchase a new MP3 player.

The word "at least" indicates that the amount Rosa needs to save is not less than $85, but it could be more than $85.

Therefore, the inequality that represents the amount of money Rosa must save is:

C) m ≥ 85

This is because the amount Rosa saves, represented by "m", must be greater than or equal to $85 in order to afford the MP3 player.

Your number line can be broken apart by using a measuring thing like a scale.

What is a number line?

By aligning the numbers on a line, a number line allows you to visualize the size of the numbers. Typically horizontal in shape, a number line has zero in the center. The numbers are increasing and positive as you move to the right. The numbers rise and become more and more negative as you move to the left.

Why do we need a number line?

Number lines offer a method for mentally adding and subtracting. It's simple to imagine them as a type of support system for those in need, but this is untrue. These are crucial because they encourage effective mental arithmetic techniques, according to research.

So by using a scale you can measure the distance accurately and place the numbers in accurate positions.

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The side lengths from least to greatest are HJ, HI, IJ, JK and IK

A triangle is a three-sided polygon that consists of three edges and three vertices.

Angle H is 67 degrees

∠HIJ is 51 degrees

∠HJI is 61 degrees

Angle K is 63 degrees

∠KJI is 70 degrees

∠KIJ is 57 degrees

From least to greatest

HJ<HI<IJ<JK<IK

Hence, the side lengths from least to greatest is HJ, HI, IJ, JK and IK

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The correct answer is option C: 4 x 11/ 7 x 15.

What is the fractions?

A fraction is a numerical quantity that represents a part of a whole. It is expressed as one number, called the numerator, written above a line, and a second number, called the denominator, written below the same line.

The product of 4/7 and 11/15 is:

(4/7) x (11/15)

= (4 x 11)/(7 x 15) (Multiplying the numerators and denominators separately)

Hence, the correct answer is option C: 4 x 11/ 7 x 15.

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Therefore, there are 278,256 different ways for 5 students to form a group from a class of 34 students.

Factorial, followed by an exclamation point, is the sum of all positive integers that are less than or equal to a specific positive integer in mathematics. Factorial seven is therefore represented by the symbol 7!, which is made up of the letters 1 2 3 4 5 and 7. By definition, factororial 0 is equal to 1.

The number of ways to form a group of 5 students out of a class of 34 students can be calculated using the combination formula:

C(34, 5) = 34! / (5! (34-5)!) = (34 × 33 × 32 × 31 × 30) / (5 × 4 × 3 × 2 × 1) = 278,256.

Therefore, there are 278,256 different ways for 5 students to form a group from a class of 34 students.

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By answering the above question, we may state that As a result, $35.40 interest in simple interest is due for the use of the funds.

Divide the principal by the interest rate, the length of time, and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This method makes it easiest to compute interest. The most typical technique to figure out interest is as a portion of the principle sum. He will only pay his share of the 100% interest, for example, if he borrows $100 from a buddy and promises to pay it back with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an annual percentage of the loan total. The interest on the loan is this percentage.

For simple interest, use the formula:

I = P * r * t

where I represents the amount of interest payable, P the amount borrowed, r the interest rate, and t the length of time in years.

Inputting the values provided yields:

I = $590 * 0.03 * 2

I = $35.40

As a result, $35.40 in simple interest is due for the use of the funds.

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Answer:

Step-by-step explanation:

We can use the formula:

average speed = (speed downstream + speed upstream) / 2

We are given the speed downstream is 8 miles per hour and the speed upstream is 2 miles per hour. Therefore,

average speed = (8 + 2) / 2 = 5 miles per hour

So the answer is (B) 5.0 miles per hour to the nearest tenth.

As a result, length of a side is around 1347.1 inches to the nearest 10th of an inch.

The Law of Sines, which states that the ratio of the length of a side to the sine of the angle opposite that side is equal for all sides and angles in a triangle, can be used to determine the length of side an in ABC.

The following equation can be created by applying the Law of Sines:

C/sin(31°) = a/sin(74°)

If we are aware that c = 720 inches, we can use a calculator to determine sin(31°):

sin(31°) ≈ 0.51504

As a result, we can find a:

A is equal to sin(74°)*c/sin(31°)

a ≈ 0.96231 * 720 / 0.51504 \sa ≈ 1347.11

With a 10th-inch precision, we obtain:

1354.7 inches

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Answer:

its actually 1343.8

Step-by-step explanation:

A. The probability that he'll win both seats is 0.48.

B. The probability he'll loose both seats is 0.52.

C. The probability he'll win one seat is 0.92.

The probability of an event is calculated using the mathematical notion of probability. We can only use it to determine the likelihood that an event will occur. On a scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.

We are given that a candidate is contesting for both national and provincial seats.

Event A = Winning national seat

Event B = Winning provincial seat

A. The probability that he'll win both seats is

P(A) × P(B) = 0.8 × 0.6 = 0.48

B. The probability he'll loose both seats is

1 - 0.48 = 0.52

C. The probability he'll win one seat is

Probability = 0.8 + 0.6 - 0.48

Probability = 0.92

Hence, the required probabilities have been obtained.

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Question: a candidate is consisting for both national and provincial assembly seats. the probability that he will win the national seat is 0.8 and will win the provincial seat is 0.6. what is the probability that

a) he will win both seats

b) he will lose both the seats

c) he will win at least one seat

Using the given ratio we will see that each kilogram costs 15 dollars.

We know that coffee at $12 per kg is mixed with coffee at $16 per kg in the ratio of 1: 3.

Then we have 4 kilograms, and the total cost of these 4 kg is:

1*$12 + 3*$16 = $60

Dividing that between the 4 kilograms:

$60/4 = $15

Each kilogram costs 15 dollars.

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Answer:

Step-by-step explanation:

To start, let's use algebra to set up some equations based on the information we have. We know that Trip has a total of 15 coins and their total value is 95 cents. Let's call the number of nickels Trip has "n" and the number of dimes "d". Then we can write:

n + d = 15 (since Trip has a total of 15 coins)

0.05n + 0.1d = 0.95 (since the total value of the coins is 95 cents)

Next, we know that four of the coins are each worth twice as much as the rest. Let's call the value of the "rest" coins "x". Then the value of the four coins that are worth twice as much is 2x. We can set up an equation based on the total value of the coins using these values:

4(2x) + 11x = 95

Simplifying this equation, we get:

19x = 95

x = 5

Now we know that each of the "rest" coins is worth 5 cents. We can substitute this value into the equation for the total value of the coins to get:

4(2*5) + 11(5) = 95

Simplifying this equation, we get:

40 + 55 = 95

So our values for n and d are correct: Trip has 11 nickels and 4 dimes.

To justify this argument, we can use a proof by contradiction. Suppose that Trip had a different number of nickels or dimes. If Trip had more than 11 nickels, then the total value of the nickels alone would be greater than 55 cents, which is impossible since the total value of all the coins is only 95 cents. Similarly, if Trip had more than 4 dimes, then the total value of the dimes alone would be greater than 40 cents, which is also impossible. Therefore, Trip must have exactly 11 nickels and 4 dimes, and our argument is justified.

The recursive formula for an, the nth term of the sequence 4,2,1,1/2... is a(n) = a(n-1) / 2 where a(1) = 4.

A recursive formula is simply a way to define a sequence by explicitly defining one or more initial terms, and then providing a formula that allows us to calculate any term in the sequence using one or more previous terms.

In other words, to find the nth term of a sequence defined recursively, we need to know the (n-1)th term or the (n-2)th term, and so on.

Given the sequence in the questionis 4,2,1, 1/2,…

In the sequence 4, 2, 1, 1/2, we can observe that each term is half of the previous term.

So, to write a recursive formula for this sequence, we can say:

a(1) = 4 (the first term is 4)

a(n) = a(n-1) / 2

(each subsequent term is half of the previous term)

Therefore, the sequence is a(n) = a(n-1) / 2 where a(1) = 4

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The probability of obtaining the value P(9) is fraction 1/4.

Equally probable occurrences are those that have the same theoretical probability (or likelihood) of taking place. For instance, after a very high number of flips, the relative frequency of Head and Tail is equal. In light of the fact that Head and Tail are both equally likely possibilities, flipping a coin is a fair and impartial way to choose between two choices.

Given that, the spinner spins the dial.

The probability of obtaining the value P(9) is:

P (9) = 1 / 4

Hence, the probability of obtaining the value P(9) is fraction 1/4.

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The complete question is:

Answer:

. 1.75x+7.50 ≥ 100

Step-by-step explanation:

The solution of the evaluated expression, 1 / 3 x² for x = 6 is 12.

An expression is a combination of numbers, variables and operations such as addition, subtraction, multiplication, division etc.

To evaluate an expression means to find the value of the expression when the variable is replaced by a given number.

Therefore, let's evaluate the expression as follows:

1 / 3 x² for x = 6

Hence, let's substitute the value of x in the expression.

1 / 3 (6)² = 1 / 3 (36) = 12

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Answer:

[tex]( \frac{1}{2} + a) {}^{2} [/tex]

Step-by-step explanation:

There's your answer

On solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

What is meant by the system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system. A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations. A group of equations that are all satisfied by the same set of variables are referred to as a system of linear equations.

The given system of equations is:

2x + 2y = 14

4x - 2y = 10

To solve this, we have to first get rid of one variable.

Here the coefficient of variable y is the same.

So adding the equations, we get

6x = 24

x = 4

Now substituting this value of x in any one of the equations we get y.

2*4 + 2y = 14

8 + 2y = 14

2y= 6

y = 3

Therefore on solving the given system of equations, we found the values of the variables x and y as 4 and 3 respectively.

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Answer:

Step-by-step explanation:

Here are the step-by-step instructions to find the number of ear cleanings that the groomer gave:

Start with the given number of nail trims, which is 15.

Divide the number of nail trims by 5 to find out how many groups of 5 nail trims there are. This gives us: 15 ÷ 5 = 3.

Multiply the number of groups of 5 nail trims by the corresponding ratio of ear cleanings per 5 nail trims, which is 3. This gives us: 3 × 3 = 9.

This means that for every 5 nail trims, the groomer gave 3 ear cleanings, and since the groomer gave 15 nail trims, they gave 9 ear cleanings in total.

So, the pet groomer gave 9 ear cleanings in total.

Answer:

We can start by setting up a ratio of the number of fruit skewers made to the number of liters of milkshake made:

fruit skewers : milkshake = 202020 : 444

Simplifying this ratio by dividing both sides by 444, we get:

fruit skewers : milkshake = 455 : 1

This means that for every 1 liter of milkshake made, Atilio makes 455 fruit skewers. Therefore, if Atilio makes 202020 liters of milkshake, they would make:

202020 x 455 = 91919100

So, Atilio would make 91919100 fruit skewers for the party.

Step-by-step explanation:

The exponential model for the data is y=0.646(1.087)ˣ.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

From the table we have, (8, 1.26), (10, 1.49)

We know that, the general form of exponential model is y=abˣ.

Here, substitute (8, 1.26) in y=abˣ, we get

1.26=ab⁸ -------(i)

a=1.26/b⁸

Here, substitute (10, 1.49) in y=abˣ, we get

1.49=ab¹⁰ -------(ii)

a=1.49/b¹⁰

1.26/b⁸ = 1.49/b¹⁰

1.26=1.49/b²

b²=1.49/1.26

b=1.087

Substitute b=1.087 in equation (i), we get

1.26=a(1.087)⁸

1.26=a(1.95)

a=1.26/1.95

a=0.646

So, the equation is y=0.646(1.087)ˣ

Therefore, the exponential model for the data is y=0.646(1.087)ˣ.

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the trigonometric identity is proven below

cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)

tan(α) = sin(α) / cos(α)

sec(α) = 1 / cos(α)

therefore:

cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.

From the question:

The following trigonometric identities can be used to demonstrate the trigonometric identity cos(α) - tan(α) - cos(3x/2 - α) = sec(α)

cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)

tan(α) = sin(α) / cos(α)

sec(α) = 1 / cos(α)

When we enter these identities into the equation's left-hand side (LHS), the following results:

cos(α) - tan(α) - cos(3x/2 - α)

= cos(α) - sin(α)/cos(α) - cos(3x/2)cos(α) - sin(3x/2)sin(α)

By locating a common denominator for the first two terms, we can reduce the expression:

[tex]cos(\alpha ) - sin(\alpha )/cos(\alpha )[/tex]

= [tex](cos^2(\alpha ) - sin^2(\alpha )) / cos(\alpha )[/tex]

= [tex]cos(2\alpha ) / cos(\alpha )[/tex]

Reintroducing this into the LHS results in:

[tex]cos(\alpha ) - tan(\alpha ) - cos(3x/2 - \alpha )= cos(2) / cos(\alpha ) - cos(3x/2)cos(\alpha ) - sin(3x/2)sin(\alpha )[/tex]

Using the identity [tex]cos(2\alpha ) = 1 - 2sin^2(\alpha ),[/tex] we can simplify the expression further:

cos(α) - tan(α) - cos(3x/2 - α)

= [tex](1 - 2sin^2(\alpha )) / cos(\alpha ) - cos(3x/2)cos(\alpha ) - sin(3x/2)sin(\alpha[/tex])

= [tex](1 - 2sin^2(\alpha ) - cos^2(3x/2 - \alpha ))[/tex] / cos(α) (using the identity[tex]sin^2(x) + cos^2(x) = 1)[/tex]

Using the identity, we can now reduce the complexity of the equation in the numerator:

cos(3x/2 - α) = cos(3x/2)cos(α) + sin(3x/2)sin(α)

Substituting this identity into the numerator, we get:

[tex]1 - 2sin^2(\alpha ) - cos^2(3x/2)cos^2(\alpha ) - 2sin(3x/2)cos(3x/2)sin(\alpha )cos(\alpha )[/tex]

In order to further simplify the expression, we can use the identity

sin(2x) = 2sin(x)cos(x):

[tex]1 - 2sin^2(\alpha ) - cos^2(3x/2)cos^2(\alpha ) - sin(3x)sin(\alpha )[/tex]

Now, using the identity[tex]cos^2(x) + sin^2(x) = 1,[/tex] we can simplify the expression to:

[tex]cos^2(\alpha ) - sin^2(\alpha ) - cos^2(3x/2) + cos^2(3x/2)sin^2(\alpha )[/tex]

Using the identity[tex]cos(2x) = 1 - 2sin^2(x)[/tex], we can further simplify the expression to:

[tex]cos(\alpha )cos(2\alpha ) - cos^2(3x/2)(1 - sin^2(\alpha ))[/tex]

[tex]= cos(\alpha )(1 - 2sin^2(\alpha )) - cos^2(3x/2)cos^2(\alpha )sin^2[/tex]

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Answer:

Below

Step-by-step explanation:

Slope,m, is the 'x' coefficient =  -1   for this line   y = -x+4-2

Answer:

The answer could be any number, with the variable x (not x^2, x^3, x^#). So it can be, for example, 6x, 8x, 109x, etc., as long as the variable is the same in each number.

Bank A's CD would earn a greater amount of interest than Bank B's CD.

The interest is greater by $369.91

To determine which CD will earn the greater amount of interest, we can calculate the interest earned by each CD over the 3-year period.

For Bank A's CD, the interest earned would be:

I = P * r * t

I = $12,000 * 0.03 * 3

I = $1,080

For Bank B's CD, the interest earned would be:

A = P * (1 + r/n)^(nt)

A = $12,000 * (1 + 0.025/12)^(123)

A = $12,710.09

The interest earned on Bank B's CD would be the difference between the total amount earned and the original principal:

I = A - P

I = $12,710.09 - $12,000

I = $710.09

Hence, Bank A's CD would earn a greater amount of interest

The interest is greater by

$1,080 - $710.09

= $369.91

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