What is the product of 3x – 4 and 5x^2–2x+6. Write your answer in standard form.
Part a: SHOW WORK
Part b: Is the product of 3x – 4 and 5x^2–2x+6 equal to the product of 4 – 3x and 5x^2 – 2x + 6? EXPLAIN.

20 points, please show work. Thanks.

The Pythagorean triple created by the steps are (3, 4, 5) where the hypotenuse is 5

The numbers x and y

Let's choose 3 and 4 as our x and y, respectively.

How we chose x and y

We can choose any numbers for x and y.

However, we usually choose numbers such that x > y to avoid duplicates.

Finding the triple

To find the Pythagorean triple, we substitute x = 3 and y = 4 in the Pythagorean identity:

(x²- y²)² + (2xy)² = (x² + y²)²

(3² - 4²)² + (2(3)(4))² = (3² + 4²)²

(-7)² + (24)² = (9)² + (16)²

49 + 576 = 81 + 256

625 = 625

We can see that this equation is true, which means that (3, 4, 5) is a Pythagorean triple.

Why at least one leg must be even

At least one leg of the triangle represented by the Pythagorean triple must have an even-numbered length because if one of the legs is odd, then the other leg and the hypotenuse must be odd too.

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All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:

ax² + bx + c = 0.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.

The functions in standard form are:

3x² + 6x - 12 = 0

3x² + 2x + 10 = 0

5x² - 10x + 5 = 0

2x² - 4x + 6 = 0

All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are constants and a ≠ 0.

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The only true statement in the following equation are B and D.

A. When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.

To check this statement, we can use the formula for exponential growth:

P(t) = P0 * [tex]3^{(t/6)[/tex]

Where P(t) is the population at time t, P0 is the initial population, and t is the time in hours.

If P(t) = 900, we can solve for t:

900 = [tex]100 * 3^{(t/6)[/tex]

9 = [tex]3^{(t/6)[/tex]

ln(9) = (t/6) * ln(3)

t = 6 * ln(9) / ln(3) ≈ 12.68

So, it takes approximately 12.68 hours for the population to reach 900. Therefore, statement A is false.

B. Three hours after the colony is placed on the petri dish, there are 200 bacteria.

Using the formula above with t=3:

P(3) = [tex]100 * 3^{(3/6) = 200[/tex]

So, statement B is true.

C. Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.

Using the formula above with t=3:

P(3) = [tex]100 * 3^{(3/6) = 200[/tex]

So, statement C is false.

D. In the first hour the colony is placed on the petri dish, the population grows by a factor of [tex]$3^{\frac{1}{6}}$[/tex]

Using the formula above with t=1:

P(1) = [tex]100 * 3^(1/6)[/tex]

So, the population after 1 hour is 100 times the sixth root of 3. We can write this as:

P(1) = [tex]100 * (3^(1/6)) = 100 * 3^{\frac{1}{6}}[/tex]

Therefore, statement D is true.

E. Between 8 a.m. and 9 a.m., the population grows by a factor of [tex]$3^{\frac{2}{3}}$[/tex]

Between 7 a.m. and 8 a.m., the population grows by a factor of 3. Then, between 8 a.m. and 9 a.m., it grows by another factor of 3. So, between 7 a.m. and 9 a.m., the population grows by a factor of [tex]3^2[/tex] = 9. Taking the sixth root of 9 gives:

[tex](3^2)^(1/6) = 3^(1/3) = 3^{\frac{2}{6}} = 3^{\frac{1}{3}}[/tex]

So, the population between 8 a.m. and 9 a.m. grows by a factor of [tex]3^(1/3)[/tex]. Therefore, statement E is false.

In summary, the true statements are B and D.

We can employ the AC approach to factor the quadratic expression seen in the image. To achieve -6 * -15 = 90, we first multiply the coefficients of the first and last terms. The middle term's coefficient, which is -9, is then shown to be two factors of 90. Since -6 * -15 = 90 and -6 + (-15) = -21, which is the same as -9 when we factor out the GCF of 3, these factors are -6 and -15:

[tex]x^2 - 9x - 90 = (x - 15)(x + 6)[/tex]

As a result, the quadratic expression's factored form is (x - 15)(x + 6).

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Answer:

Cherry Trail Mix

Step-by-step explanation:

cherry trail mix ratio = 4:3

sunflower trail mix ration = 5:2

4 goes into 20 5 times so multiply 3 by 5 to get 15. Add them together to make 35 oz

5 goes into 20 4 times so multiply w by 4 to get 8. Add them together to make 28 oz

35 > 28

Answer:

800

Step-by-step explanation:

the answer is 800 as 1 rounds down

Answer:

If you add 5 to a, it will be greater than b

Step-by-step explanation:

i got it right

A.  The linear equation is R = -18t + 1,820

B. total reserve oil 1,568 billions of barrels

C. approximately 101.11 years

To make our equation, we'll use the form R = mt + b. M represents how many billion barrels of oil are being lost each year, which we know is 18 billion. So -18 will be our m. B is how many total barrels of oil there are, which is 1,820. So 1,820 will be our b. Now the equation looks like this:

R = -18t + 1,820

We can use this equation to answer Part B.

Replace the t with 14:

R = -18(14) + 1,820

Now solve for R:

R = -18(14) + 1,820

R = -252 + 1,820

R = 1,568

14 years from now, there will be 1,568 billions of barrels left.

To solve part C, we need to find how many years it will take for all of the oil to be used up. After it's all used up, the total amount of oil will be 0, so we can replace R with 0 and then solve for t:

0 = -18t + 1,820

Subtract 1,820 from both sides to isolate -18t:

0 - 1,820 = -18t + 1,820 - 1,820

-1,820 = -18t

Divide both sides by -18 to isolate the t:

-1,820/-18 = -18t/-18

101.11 = t

After approximately 101.11 years, all of the oil will be used up.

The complete question is-

Suppose that the world's current oil reserves is R = 1820 billion barrels. If, on average, the total reserves

is decreasing by 18 billion barrels of oil each year, answer the following:

A.) Give a linear equation for the total remaining oil reserves, R, in billions of barrels, in terms of t, the

number of years since now. (Be sure to use the correct variable and Preview before you submit.)

R

B.) 14 years from now, the total oil reserves will be

billions of barrels.

C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all

used up) approximately

years from now.

(Round your answer to two decimal places.)

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Answer:

429

Step-by-step explanation:

Answer:

Edgar will earn $3,646.30 in interest over 3 years.

Step-by-step explanation:

I'd be happy to walk you through the problem step by step!

The problem is asking how much interest Edgar will earn in 3 years on an initial deposit of $7,000 that earns 15% interest compounded annually.

To solve this problem, we need to use the formula for compound interest:

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

Where:

A = the final amount including interest

P = the principal amount (the initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years) the money is invested

We are given that:

P = $7,000

r = 15% = 0.15 (as a decimal)

n = 1 (compounded annually)

t = 3 years

Now, we can plug these values into the formula and solve for A, which is the final amount including interest:

A = $7,000(1 + 0.15/1)^(1*3)

We simplify the expression inside the parentheses first, by dividing the annual interest rate by the number of times the interest is compounded per year:

A = $7,000(1.15)^(3)

We raise 1.15 to the power of 3 using a calculator or by multiplying 1.15 by itself 3 times:

A = $7,000(1.5209)

We multiply the initial deposit by the final amount including interest to get the total amount of interest earned:

Interest = $7,000(1.5209) - $7,000

We simplify the expression:

Interest = $10,646.30 - $7,000

Interest = $3,646.30

So, Edgar will earn $3,646.30 in interest over 3 years.

Hope this helped! If it didn't, I'm sorry! If you still need more help on this, ask me! :]

The monthly periodic rate with APR 20.3% is 1.69%

APR is also known as Annual Payment Rate. And it is the cost of your mortgage credit as a yearly rate.

Annual Percentage Rate is typically higher than your interest rate because it includes your interest rate plus certain fees, such as lender and mortgage broker fees, based on the specific characteristics of your loan.

Monthly Interest Payment means the amount of interest paid on a Payment Date for the preceding Interest Period based on interest calculated for such preceding Interest Period at the Monthly Interest Rate.

If the Annual Percentage Rate is 20.3% and there are 12 months on a year , the monthly interest = 20.3/12 = 1.69 %

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If the bottle can only hold 13 ounces, then the probability the bottle will overflow is approximately 0.0032 or 0.32%.

First, we need to calculate the z-score, which is the number of standard deviations that the mean value of 12.2 ounces is away from the bottle's capacity of 13 ounces. We can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the bottle capacity (13 ounces), μ is the mean value of soda dispensed by the machine (12.2 ounces), and σ is the standard deviation (0.3 ounces).

Substituting the values, we get:

z = (13 - 12.2) / 0.3 = 2.67

The z-score of 2.67 means that the bottle capacity of 13 ounces is 2.67 standard deviations away from the mean value of soda dispensed by the machine.

Substituting the values, we get:

P(Z > 2.67) = 1 - P(Z ≤ 2.67) = 1 - 0.9968 = 0.0032

Therefore, the probability of the soda bottle overflowing is approximately 0.0032 or 0.32%.

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The probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.

To find the probability of a task taking more than 25 days to complete, given that the mean and standard deviation of the normal distribution are 20 and 3 days, respectively, one can use the Z-score formula.Z = (X - μ)/σwhere Z is the standard score, X is the observed value, μ is the mean, and σ is the standard deviation. Therefore,Z = (25 - 20)/3 = 5/3 ≈ 1.67The area to the right of Z = 1.67 on a standard normal distribution table represents the probability that the task will take more than 25 days to complete. Using a standard normal distribution table or calculator, we can find that P(Z > 1.67) = 0.0475 or approximately 4.75%.Therefore, the probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.

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From the given information, the complex zeros of the polynomial are x = -3/4, (9 + 17i)/8, (9 - 17i)/8.

To find the complex zeros of the given polynomial function, we can use the Rational Root Theorem to check for possible rational roots, and then use synthetic division or long division to factor the polynomial.

The possible rational roots of the polynomial are of the form ±a/b, where a is a factor of the constant term 33 and b is a factor of the leading coefficient 4. Therefore, the possible rational roots are:

±1/4, ±3/4, ±1/2, ±3/2, ±11/4, ±33/4, ±11/2, ±33/2.

We can check these possible roots using synthetic division, and we find that the polynomial has a rational root x = -3/4. Dividing by (x + 3/4) using synthetic division, we get:

4x³ + 3x² - 44x - 33 = (x + 3/4)(4x² - 9x - 44)

Now, we can use the quadratic formula to find the roots of the quadratic factor 4x² - 9x - 44:

x = (9 ± √(9² + 4(4)(44)))/(2(4)) = (9 ± 17i)/8.

To factor the polynomial completely, we can use the complex zeros and the linear factor we found earlier:

f(x) = 4x³ + 3x² - 44x - 33 = (x + 3/4)(x - (9 + 17i)/8)(x - (9 - 17i)/8).

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Answer:

see below

Step-by-step explanation:

2:1

Look at the image below.

Answer:

(5,1)

(7, -5)

Step-by-step explanation:

y = mx + b

The b is the y intercept.  This is where the graph crosses the y axis.  Graph this first.  The m is the slope.  It is the rise over the run.  You can make any number a fraction by putting it over 1.  From the y-intercept you use the slope (rise/run) to graph the second point.  

For example, if the slope is 1. then 1/1 would show your rise and run. Start when the y-intercept is and go up 1 and then 1 right.  Connect the two points that you have graphed.

If the slope is 2/7, then from the y-intercept go up 2 and right 7.  Graph that point and draw a line connecting that point to the point on the y-intercept.

Helping in the name of Jesus.

ANSWER OF THE FIRST TWO EQUATIONS

y = x -4

y= -x+6

both the equations represent a straight line with y intercept as -4 and 6 respectively

x-y-4 = 0. ........(equation 1)

x+y-6 = 0. .........(equation 2)

adding equation 1 and 2

2x - 10 = 0

x = 5

subtracting equation 2 from 1

-2y -2 = 0

y = 1

FINAL ANS : (5,1)

Answer:

9(5)-/y

9(5)-15/3

45-15/3

45-5

40

Neil and Joey ate a total of 15 ounces of cereal from the 24-ounce box. By subtracting the amount eaten from the total amount, we find that there are 9 ounces of cereal left in the box.

Neil has eaten 3/8 of the box, which is equal to (3/8) x 24 = 9 ounces.

Joey has eaten 1/4 of the box, which is equal to (1/4) x 24 = 6 ounces.

Together, they have eaten 9 + 6 = 15 ounces.

Subtracting the amount they have eaten from the total amount, we get:

24 - 15 = 9

Therefore, there are 9 ounces of cereal left in the box.

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If the company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by P(x)=−3(x−5) ^2+12, the maximum profit is $87 million.

The given profit function is in the form of a quadratic equation with a negative coefficient of the squared term. This means that the graph of the function is a downward-facing parabola, and the vertex of this parabola represents the maximum value of the function.

To find the vertex, we need to convert the given function into vertex form:

P(x) = -3(x - 5)^2 + 12

= -3(x^2 - 10x + 25) + 12

= -3x^2 + 30x - 63

Completing the square, we get:

P(x) = -3(x - 5)^2 + 12 + 75

= -3(x - 5)^2 + 87

The vertex of this parabola is at the point (5, 87), which represents the maximum profit the company can earn.

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According the question given above  the value of n is 21.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

Calculations and problem-solving techniques simplify the issue. The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).

Here, we have

Given : 7 = n/3

we have to find the value οf n.

We apply simplification here and we get

7 = n/3

n = 7×3

n = 21.

Hence, the value οf n is 21.

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Answer: Option A. an+1=an-4, a1=-6

Step-by-step explanation:

The greatest possible difference between David's result and Armen's result is 5.

Let's first consider the maximum number of odd shirts Armen can count. Since there are only 5 odd numbers between 1 and 9, the maximum number of odd shirts Armen can count is 1+3+5+7+9 = 25.

Now, let's consider the maximum number of even shirts David can count. Since there are only 4 even numbers between 1 and 9, the maximum number of even shirts David can count is 2+4+6+8 = 20.

Therefore, the greatest possible difference between David's result and Armen's result is

= 25 - 20

Subtract the numbers

= 5

The maximum difference occurs when Armen counts all 5 odd shirts and David counts all 4 even shirts.

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Answer:

If the model is 5cm and 1cm is equal to 2m, it means the actual rocket is 10 meters.

Step-by-step explanation:

1cm = 2m

5cm is 5 times the amount of 1cm.

10m is 5 times the amount of 2m

Answer : 10 Meters

Explanation : 2 × 5 = 10

The probability that at least 29% of the sample are from poverty-level households is 0.17% and we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that at least 29% of the sample are from poverty-level households.

To answer part (a) of the question, we can use the normal approximation to the binomial distribution. The mean of the distribution is np = 300 * 0.22 = 66 and the standard deviation is sqrt(np(1-p)) = sqrt(66 * 0.78) = 7.09. We can use the normalcdf function to find the probability that at least 29% of the sample are from poverty-level households:

normalcdf(87.5, 300, 66, 7.09) = 0.0017

So the probability is 0.17%.

For part (b) of the question, we need to determine if there is convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

Since the probability that at least 29% of the sample are from poverty-level households is 0.17%, which is very small, we can conclude that there is not convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

The small probability suggests that the observed sample result is unlikely to occur by chance if the true population proportion is 22%, so we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.

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The result, doing nothing is not a sensible approach to missing data handling.

The correct way to handle the missing values is to replace the missing values with the most frequent category.What is a variable?A variable is any feature, number, or measurement that may be measured, manipulated, or controlled in an experiment. Variables in scientific investigations are classified as dependent or independent. A categorical variable is one that may take on one of several different categories or distinct groups of data. Understanding the problem statement While attempting to understand and prepare data for further analysis, you discover that there are a small number of missing values for a categorical variable.

Since you know that retaining this variable is important for the project's success, what is the appropriate method for handling the missing values?Missing values should be replaced with the most frequent category because this is the best way to handle them.

To get a complete dataset, the missing values must be filled. The variables with missing data are imputed to improve the accuracy of your analysis.Replace missing values with the mean value (option A) - This technique is only applicable to quantitative variables.

In categorical variables, it makes no sense to replace missing data with the mean value. It might produce nonsensical data, making the whole data set unusable.Although it seems like keeping this variable is important for the success of the project, due to missing values decide to exclude this variable from the analysis (option B) - This alternative may lead to the exclusion of crucial data that can help with a future examination.

Replace the missing values with the most frequent category (option C) - The most frequent category is frequently used to replace missing data. The most common category is determined and substituted for missing data. It's a reasonable method because the data is still valuable and the categorical variable is critical for the project's success.Do nothing and proceed with further analysis (option D) - The examination results would be influenced if we use the existing data without filling in the missing information. As a result, doing nothing is not a sensible approach to missing data handling.

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Answer:

(secΘ+tanΘ-1)(secΘ-tanΘ+1)

=sec²Θ-secΘtanΘ+secΘ+secΘtan-tan²Θ+tanΘ-secΘ+tanΘ-1

=2tanΘ+(sec²Θ-tan²Θ)-1

=2tanΘ+1-1

=2tanΘ

The price of each drink is given as follows:

The price of each drink is obtained by a system of equations, for which the variables are given as follows:

He spent $37 on 7 cases of juice and 8 cases of soda, hence:

7x + 8y = 37.

Purchased an additional 7 cases of juice and 15 cases of soda, spending a total of $51, hence:

7x + 15y = 51.

Hence the system is composed by these two equations:

Subtracting the second equation by the first, the value of y is obtained as follows:

7y = 14

y = 2.

Then the value of x is obtained as follows:

7x + 15(2) = 51

7x = 21

x = 21/7

x = 3.

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Answer:

A

Step-by-step explanation:

The answer is 2x+2y+2 which is A

Answer: I think its B but I'm not quite sure

Step-by-step explanation:

Answer: the length of side c is approximately 74.3 units.

Step-by-step explanation: In a triangle with sides a, b, and c, and opposite angles A, B, and C, respectively, the Law of Cosines states that:

c^2 = a^2 + b^2 - 2ab*cos(C)

We are given the following information:

a = 55 (the side opposite angle A)

b = 50 (the side opposite angle B)

C = 90 degrees (the angle opposite side c)

Substituting these values into the Law of Cosines, we get:

c^2 = 55^2 + 50^2 - 2(55)(50)*cos(90)

c^2 = 3025 + 2500 - 0

c^2 = 5525

Taking the square root of both sides, we get:

c = sqrt(5525)

c ≈ 74.3

We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878. The number of turkeys, y, in the population at the end of t years is obtained by substituting this value into the exponential decay formula and getting the following result: y = 250(0.878)t.

The equation y = 250(1 - 0.022)t, where t is the number of years, may be used to calculate the number of turkeys, y, in this population at the end of t years.

Using the exponential decay formula, A = P(1 - r)t, where A is the final amount, P is the beginning amount, r is the rate of decay in decimal notation, and t is the duration in years, we may arrive at this function.

If we substitute the values provided, we get: 209 = 250(1 - 0.022)^8

We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878.

This value may be substituted into the exponential decay formula to obtain the number of turkeys, y, in the population at the end of t years: y = 250(0.878)t.

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Answer:

The outcomes when rolling a fair six-sided die are: 1, 2, 3, 4, 5, and 6.

a. The probability of getting a 1, 3, or a 6 is 3/6 or 1/2.

b. The probability of getting a number less than 5 is 4/6 or 2/3.

If the angle of elevation from the spot where a basketball player is standing up to the top of a 10ft high hoop is 25 degrees, the player is approximately 21.45 feet away from the base of the hoop.

To solve this problem, we can use the trigonometric function tangent, which relates the opposite side of a right triangle to its adjacent side, using the angle of elevation:

tan(25 degrees) = opposite / adjacent

where the opposite side is the height of the hoop (10 feet), and we need to find the adjacent side, which is the distance from the player to the base of the hoop.

To isolate the adjacent side, we can rearrange the equation:

adjacent = opposite / tan(25 degrees)

adjacent = 10 / tan(25 degrees)

Using a calculator, we can find that tan(25 degrees) is approximately 0.4663:

adjacent = 10 / 0.4663

adjacent ≈ 21.45 feet

We round to the nearest hundredth of a foot, which gives us the final answer of 21.45 feet.

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