Determine which consecutive integers do not have a real zero of f(x)=x²-4x²-4x+15 between them.
a. (4, 5)
C. (-2,-1)
b.
(1, 2)
d.
(-3,-2)

A.) f(x-2)+f(2x)

To find this expression, we can substitute the definition of f(x) into the expression and simplify:

f(x-2)+f(2x) = [10(x-2)-4] + [10(2x)-4]

= 10x - 20 - 4 + 20x - 4

= 30x - 28

Therefore, f(x-2)+f(2x) = 30x - 28.

Given f(x) = 10x - 4, we need to find f(2a) - f(a).

f(2a) = 10(2a) - 4 = 20a - 4

f(a) = 10a - 4

Therefore,

f(2a) - f(a) = (20a - 4) - (10a - 4)

= 10a

Answer: f(2a) - f(a) = 10a. This means that the difference between the function evaluated at 2a and a is simply 10 times a.

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Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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The exact measure of an angle whose measure is 18° in radians is; pi over 10.

Recall, it follows from angle measurements that;

π radians ==== 180°

Hence, it follows from proportion that the measure of 18° in radians, x can be determined as follows;

x = 18 π radians / 180

x = π / 10 radians.

Ultimately, the required measure of 18° in radians as required is; π / 10.

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Answer:

Based on the information given, it seems like Messi and Ronaldo were asked to shoot the ball at two targets, target 1 and target 2, and the points they earned would be based on which target they hit.

In Test 1, Messi's first shot followed the equation 3(3x-4) = 24. To determine which target he hit, we need to solve for x. Using algebra, we can simplify the equation to 9x - 12 = 8, and then add 12 to both sides to get 9x = 20. Dividing both sides by 9, we find x = 2.2. Since x represents the number of points earned, this means Messi earned 2.2 points with this shot.

For Messi's second shot, the equation is 6.8 (2.3x + 5.7) = 132.6. To solve for x, we can start by dividing both sides by 6.8 to get 2.3x + 5.7 = 19.5. Subtracting 5.7 from both sides, we find 2.3x = 13.8. Dividing both sides by 2.3, we find x = 6.

In Test 2, Ronaldo's first shot followed the equation (6y-18) = 12. To solve for y, we can add 18 to both sides to get 6y = 30, and then divide both sides by 6 to get y = 5. This means Ronaldo earned 5 points with this shot.

For Ronaldo's second shot, the equation is 8.2 (-5) = -16.4. To solve for y, we need to determine the value of x. Since the equation is just a constant times a negative number, we can simplify it to 8.2 * -5 = -41. This means Ronaldo earned -41 points with this shot.

It's important to note that negative points are not possible in this scenario, as the targets only have positive point values.

Step-by-step explanation:

Answer:

You will pay 81.25

Step-by-step explanation:

If the cost is 35% off, you will need to pay 100% - 35% = 65%

125 * 65 %

125 *.65

81.25

You will pay 81.25

The solution is:  (A) y+4=-3(x+6), is the equation of the line in point-slope form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:

y-y1 = m (x-x1)

Given the point:

(x1,y1) = (-6, -4)

Slope, m= -3

x1 = -6,

y1 =-4

Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:

we get,

y+4=-3(x+6)

The correct option is A.

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complete question:

The graph of a line has a slope of -3 and passes through the point (-6,-4).

What is the equation of the line in point-slope form?

Oy + 4 = -3(x + 6)

y + 6 = -3(x + 4)

y-4 = -3(x-6)

y-6 = -3(x – 4)

The total mass of all three boxes to be delivered by the mail carrier is 180,000 grams.

Given the data in the question;

Mass of the boxes carried by the mail carrier.

Mass of first box = 80kg

Mass of second box = 40kg

Mass of third box = 60kg

First, we convert from kilograms to grams.

Note: 1 kg = 1000g

Hence;

Mass of first box = 80kg = ( 80 × 1000 )g = 80000g

Mass of second box = 40kg = ( 40 × 1000 )g = 40000g

Mass of third box = 60kg = ( 60 × 1000 )g = 60000g

Now, we add the mass of the boxes in gram.

80000g + 40000g + 60000g

180,000 grams

Therefore, the total mass is 180,000 grams.

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Answer:

Step-by-step explanation:

(1/3) x 81=27 people

Answer:57.6^3

thats t

Answer:

The correct answer is D. 7 pounds.

Step-by-step explanation:

The weight of the baby when its born is 7 pounds.

The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.

To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:

Using the formulas, we get:

Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20

= 377.5 meters

Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)

= 7007.5 meters^2

Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters

Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.

To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:

Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))

Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.

substituting the values, we get:

Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))

= 377.5 ± 37.0

Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.

The assumptions needed for this inference to be valid are:

The sample is a random sample from the population of skidding distances along the road.

The skidding distances follow a normal distribution in the population.

The sample size is large enough (at least 30) or the population standard deviation is known.

To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.

To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.

Using the formula for the t-statistic, we get:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

= (377.5 - 425) / (83.7 / sqrt(20))

= -3.61

From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.

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Let's call the tens digit "x" and the units digit "y". We know that the number is a multiple of 9, so:

x + y = 9

and the ratio of the units digit to the tens digit is 1:2, so:

y = 2x

Substituting the second equation into the first, we get:

x + 2x = 9

3x = 9

x = 3

So the tens digit is 3 and the units digit is 2 times that, or 6. The number is 36.

Answer:

63

Step-by-step explanation:

___________________

First, let's list all the 2-digit multiples of "9":

______________________________________________________

18, 27, 36, 45, 54, 63, 72, 81, 90, 99.

______________________________________________________

From this list, the only answer that has a ratio in which its "units digits to its tens digits" is "1:2" is: "63" . "3:6" = "1:2" .

the  solution of the given equation will be x =1

What is a System of Equations?

A system of equations in algebra is made up of two or more equations that are solved together. "A group of equations satisfied by the same set of variables are called a system of linear equations. Finding the values of the variables employed in the system of equations is the first step towards solving it. While maintaining the balance of the equations on both sides, we compute the values of the unknown variables. Finding a variable whose value makes the condition of all the given equations true is the primary goal of solving an equation system.

The given equation x -5 = -4

add +5 in both side we get

x = -4+5

x=1.

Hence the solution of the given equation will be x =1

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If the r-value, or correlation coefficient, of a data set is 0.934, the

coefficient of determination to three decimal places is:  A. 0.872.

The coefficient of determination (R-squared) is the square of the correlation coefficient (r) and represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).

So, to find the coefficient of determination, we need to square the correlation coefficient:

R-squared = r^2

= 0.934^2

= 0.872 (Rounded to three decimal places)

Therefore, the answer is (A) 0.872.

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the solution:

Calculate the government deposit: For every $1.00 you deposit, the government deposits $2.00. So if you deposit the maximum of $100.00 each month, the government deposit would be $100.00 * $2.00 = $200.00.

Calculate the total deposit each month: The total deposit each month is the sum of your deposit and the government deposit, so it would be $100.00 + $200.00 = $300.00.

Calculate the number of months: You started with $100.00 and made the maximum deposit of $100.00 each month for 5 years. Five years is 5 * 12 = 60 months.

Calculate the total deposit over 5 years: Over 5 years, you made 60 deposits of $300.00 each, so the total deposit over 5 years would be 60 * $300.00 = $18,000.00.

Calculate the final balance: Adding the initial deposit of $100.00 to the total deposit over 5 years, the final balance in your account after 5 years would be $18,000.00 + $100.00 = $18,100.00.

So, at the end of 5 years, if you deposited the maximum of $100.00 each month into the College Savings fund, you would have $18,100.00 in your account.

Given the information that the average of the ages of 5 women is 47 years and that their ages are 48, y, 52, 50, and (2y-5), we can set up the following equation:

(48 + y + 52 + 50 + 2y - 5) / 5 = 47

Expanding the equation and simplifying, we get:

5y = 244

y = 48.8

So the age of the woman whose age is represented by the variable y is 48.8 years.

The oldest woman is represented by the age of 52 years, which is the largest of all the ages.

Therefore, the age of the oldest woman is 52 years.

Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).

As h gets smaller, the distance between the two points gets smaller.

The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = sin(x) using first principles, substitute f(x + h) = sin(x + h) and f(x) = sin(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x+h)-\sin(x)}{(x+h)-x}\right][/tex]

Use the sin addition formula to expand sin(x + h).

[tex]\boxed{\sin(A + B) = \sin A \cos B + \cos A \sin B}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)+\cos(x)\sin(h)-\sin(x)}{(x+h)-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)-\sin(x)+\cos(x)\sin(h)}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)+\cos(x)\sin(h)}{h}\right][/tex]

Separate the sin(x) and cos(x) terms into two fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)}{h}+\dfrac{\cos(x)\sin(h)}{h}\right][/tex]

When h gets really small, we can use the small angle approximation to rewrite cos(h).

[tex]\boxed{\cos (h) \approx 1-\dfrac{1}{2}h^2}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(1-\dfrac{1}{2}h^2-1\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(-\dfrac{1}{2}h^2\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[-\dfrac{1}{2}h\sin(x)+\cos(x)\right][/tex]

As h → 0, the first term → 0:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

The length of the caple is √3125 cm. (option C)

The caple and the tower would form a right triangle. The caple would be the hypotenuse. The tower would be the length and the distance from the base of the tower would be the base.

In order to determine the length of the caple, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:

c² = 25²  + 50 ²

c² = 625 + 2500

c² = 3125

c= √3125 cm

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If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:

a. The first 50 students leaving the cafeteria. Not representative

b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative

c. Ten students randomly chosen from each of the 5 areas of campus. Representative

d. Five students from 10 teachers' classes. Representative

A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.

Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.

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The company’s revenue (R) from a particular distributor that buys x units is R(x) = 8999.93x

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Given:

original price = $9000 per unit.

let the number units bought be x

then amount= 9000x.

If the price reduces the list price by seven cents times the number of units bought .

7cents= 0.07 dollar

Then,

R(x) = 9000x - 0.07x

R(x) = 8999.93x

Hence, R(x) = 8999.93x.

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7x² + 48xy - 7y² is the simplified expression

Polynomial is an equation described as the sum of terms in the form of

k[tex]x^n[/tex].

where,

k and n =  positive integers.

Example:

2x³ + 4x² + 3x + 5 is a polynomial.

We have,

(x + 7y) (7x − y)

Distribute the addition over subtraction.

x (7x - y) + 7y (7x - y)

7x² - xy + 49xy - 7y²

Add like terms.

7x² + 48xy - 7y²

We can not further simplify.

So,

7x² + 48xy - 7y² is the final expression.

Thus,

7x² + 48xy - 7y² is the simplified expression

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The complete question.

Find the product (x+7y) (7x−y)

Using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

The process of addition involves combining two or more numbers to determine their sum.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 + 7 equals 14.

So, we can get the total time using addition as follows:

= 0.6 + 2.4 + 5.2 + 1.4 + 1.8

= 11.4 hours

Therefore, using addition we can conclude that the total time taken for the setup of the machine would be 11.4 hours.

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The population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

percentage, a relative value indicating hundredth parts of any quantity.

First, we can find the population of chickadees by multiplying the population of phoebes by 0.7 (100% - 30%):

Population of chickadees = 0.7 x 12,000 = 8,400

Next, we can find the population of blue jays by multiplying the population of phoebes by 0.3:

Population of blue jays = 0.3 x 12,000 = 3,600

Therefore, the population of chickadees in the region is 8,400 and the population of blue jays is 3,600.

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The quotient and remainder, written as partial fractions, of 15x²+52x+43/3x²+5x-8 would be  A/(3x + 8) + B/(x - 1) where A is -8/3 and B is 1.

What in mathematics is a partial fraction?

The fractions that are utilized to break down a rational expression are called partial fractions.

                     Any component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.

15x²+ 52x + 43/3x²+5x-8

15x²+52x +43/3x² + ( 8 -3)x - 8

15x²+52x +43/3x² + 8x -3x - 8

15x²+52x +43/3x(x - 1) +8(x - 1 )

15x²+52x +43/(3x + 8)(x -1 )

A/(3x + 8) + B/(x - 1)

To find the value of A;

3x + 8 = 0

x = -8/3

To find the value of B;

x - 1 = 0

x = 1

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The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',

We are asked to select the correct composition of similarity transformations,

According to the graph, there is a scale factor of 1/2 which is smaller than 1,

Also, the polygon is dilating and then reflected.

Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

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The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.

We need to find a number that is divisible by at least 3, but less than 10.

We can start by listing out the multiples of 3 and see which one is closest to 1,932:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

3 × 7 = 21

3 × 8 = 24

3 × 9 = 27

We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.

We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.

Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.

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Answer:

C = 60t + 100

Step-by-step explanation:

our flat fee is 100 dollars, meaning you're charged straight up $100, and then for each hour the electrician works, you're charged another $60

this means that 100 stays constant, while the amount of times you multiply 60 changes based on the amount of hours the electrician works

therefore, our equation will be C = 60t + 100, where C represents the total cost while t represents the hours the electrician works

for our table, we can use the equation we just found to make one

the easiest and most reasonable numbers will be 1, 2, 3, 4, and 5, because it's unreasonable to charge a proportional amount for something such as 1.2948 hours

using the equation, we plug 1, 2, 3, 4, and 5 into C = 60t+100 to find C for t

C = 160, 220, 280, 340, 400

T = 1, 2, 3, 4, 5

No, the marked price of $73.25 is not correct.

To calculate the sale price, we start by multiplying the original price by the discount percentage:

$95.00 * 0.25 = $23.75

This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:

$95.00 - $23.75 = $71.25

Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.