Factoring Polynomials Formative
QUESTION 1
Solve the following by factoring:
y³ - 6y² = 0

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

We have,

We need to standardize the IQ score using the formula:

z = (x - μ) / σ

So,

For x = 99,

z = (99 - 100) / 15

z = -0.067

We can then use a standard normal distribution table or calculator to find the probability of a z-score less than -0.067.

Using a standard normal distribution table, we find that the probability of a z-score less than -0.067 is 0.4729

Therefore,

The probability of a random person on the street having an IQ score of less than 99 is 0.4729.

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Answer:

10

Step-by-step explanation:

1 acre = 43560 ft²

3/4 acre = 3/4 × 43560 ft² = 32670 ft²

The lawn is 32670 ft².

Each bag covers 3500 ft².

number of bags needed = 32670/3500 = 9.33

You need approximately 9 1/3 bags, but since you must buy full bags, you must buy 10 bags.

Answer: 10

The average team score for the first five basketball games is 46 points.

To find the average team score for the first five basketball games, we simply use Mean.

Mean is the sum of the scores and divide it by the number of games.

Given scores:

Game 1 score = 54

Game 2 score = 60

Game 3 score = 28

Game 4 score = 42

Sum of scores = 54 + 60 + 28 + 42

                        = 184

Number of games = 4 (since we have scores for only four games)

Average team score (Mean) = Sum of scores / Number of games

                                               = 184 / 4

                                               = 46

Therefore, the average team score for the first five basketball games is 46 points.

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Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

One hundred US dollars are equivalent to 834.3664 French francs at the exchange rate on Tuesday. Accordingly, you can swap eight hundred forty-three point 64 years old French francs for every one hundred dollars in the United States.

1. From the tables, the Tuesday rate is 0.119 US dollars to 1 French franc.

2. To find the exchange rate, multiply the number of US dollars by the exchange rate: 100 x 0.119 = 11.90.

3. To find the amount in French francs, divide the US dollars by the exchange rate: 11.90 / 0.119 = 843.64 French francs. Based on the Tuesday rate, $100 United States dollars is equal to 843.64 French francs.

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The value of n on the series 5 + 10 + 20 + ... = 5115 is 10

The given sequence is 5, 10, 20, ... is a geometric progression (GP) with

first term a = 5 and

common ratio r = 2

formula for the sum of the first n terms of a GP

Sn = a(rⁿ - 1) / (r - 1)

Substituting the values we have

5115 = 5(2ⁿ - 1) / (2 - 1)

Simplifying and multiplying both sides by 1

1023 = 2ⁿ - 1

2ⁿ = 1024

2ⁿ = 2¹⁰

Equation powers

n = 10

Therefore, the value of n is 10.

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Answer:

52° is approximately 0.907 radians

Step-by-step explanation:

To find the equivalent radian measure for an angle that measures 52°, we need to convert 52° to radians using the formula:

radians = degrees × π/180

Substituting the value of 52° into the formula, we get:

radians = 52 × π/180

radians ≈ 0.907

Therefore, the equivalent radian measure for an angle that measures 52° is approximately 0.907 radians.

The 6-digit number A is 419065.

To find the least 6-digit number A that is divisible by 495, we need to follow these steps:
Step 1: Find the prime factors of 495.
495 = 3 × 3 × 5 × 11 = 3^2 × 5 × 11
Step 2: Determine the lowest 6-digit number divisible by the prime factors.
The lowest 6-digit number is 100000, so we find the next multiple of 495 above 100000.
100000 ÷ 495 ≈ 202.02
The next integer value is 203, so:
203 × 495 = 100485
Step 3: Substitute the given digits (4, 9, and 6) into the 6-digit number.
The least 6-digit number divisible by 495 is 100485. To make A the smallest possible number, we will place the given digits in the following order: 4, 9, and 6. The missing digits in A are 1, 0, and 5.
So, the 6-digit number A is 419065.

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The evaluation of the value of the arithmetic operation based on the place value of the numbers indicates;

1. The number in the thousands place is; 7

The number is od

2. The difference between the predecessor and successor of the set of integers is; 8 - 6 = 2

Arithmetic operations are operations including, addition, subtraction, division and multiplication.

1. The numbers to be added are; 600, 5800, and 685

The sum of the numbers is; 600 + 5800 + 685 = 7085

Therefore, the place value in the thousands place is 7

The last digit of the number 7085 is 5 indicating that the number is an odd number

2. The predecessor of a number is the number that comes before the number.

The successor of the number is the number that comes after the number

The difference between the predecessor and the successor of a number therefore is; n + 1 - (n - 1) = n + 1 - n + 1 = 2

Example; 8 - 6 = 2

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Answer:

so you start with D-6>4

then you add 6 to both sides now you have D>10

the answer is D

The distance d between A and B is √(68), and the square of the distance in the y direction is 64.

To find the distance d between points A and B, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values of A and B, we get:
d = sqrt((4 - 2)^2 + (5 - (-3))^2)
d = sqrt(2^2 + 8^2)
d = sqrt(4 + 64)
d = sqrt(68)
Next, to calculate the square of the distance in the y direction, we need to find the difference between the y-coordinates of A and B and square it. So:
(y2 - y1)^2 = (5 - (-3))^2 = 8^2 = 64
Therefore, the square of the distance in the y direction is 64.
I'm here to help you with your question. To find the distance d between two points A(x1, y1) and B(x2, y2), we can use the distance formula:
d = √((x2-x1)² + (y2-y1)²)
Given the points A(2, -3) and B(4, 5), let's plug in the values:
d = √((4-2)² + (5-(-3))²)
Now, calculate the difference for each coordinate:
d = √((2)² + (8)²)
Next, square the differences:
d = √(4 + 64)
Finally, calculate the square root:
d = √(68)
ow, let's find the square of the distance in the y direction, which is (y2-y1)²:
(y2-y1)² = (5-(-3))²
Calculate the difference:
(y2-y1)² = (8)²
Square the difference:
(y2-y1)² = 64
So, the distance d between A and B is √(68), and the square of the distance in the y direction is 64.

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Using the concept of exponential decay, the predicted number of people is  233,176,000

To predict the number of gas-powered cars on the road in 10 years, we'll apply the given annual decrease rate of 1.9% to the initial count of 286 million.

First, let's calculate the decrease rate per year:

Decrease rate = 1.9% = 1.9/100 = 0.019

Next, we'll calculate the predicted count after 10 years using the formula for exponential decay:

Predicted count = Initial count * (1 - Decrease rate)^Number of years

Substituting the values:

Predicted count = 286 million * (1 - 0.019)^10

Calculating the value:

Predicted count ≈ 286 million * (0.981)^10

Rounding the answer to the nearest whole number:

Predicted count ≈ 286 million * 0.816

Predicted count ≈ 233,176,000

Therefore, the best prediction for the number of people driving gas-powered cars in 10 years, based on the given information, is approximately 233,176,000.

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Answer:

Step-by-step explanation:

To calculate the amount of wrapping paper needed to cover the package, we need to find the area of each face of the trapezoidal prism and add them together.

First, we can find the area of the trapezoidal front and back faces. The formula for the area of a trapezoid is:

Area = (a + b) / 2 * h

where a and b are the lengths of the parallel sides, and h is the height. For the front and back faces, we have:

Front/back area = ((6 + 12) / 2) * 15 = 135 square inches

Next, we can find the area of the top and bottom faces, which are rectangles. The formula for the area of a rectangle is:

Area = length * width

For the top and bottom faces, we have:

Top/bottom area = 4 * 12 = 48 square inches

Finally, we need to find the area of the two slanted faces. These faces are parallelograms, and the formula for the area of a parallelogram is:

Area = base * height

where the base is the distance between the two parallel sides, and the height is the perpendicular distance between the two parallel sides. For the slanted faces, we have:

Slanted face area = 1/2 * (12 + 4) * 10 = 80 square inches

Now we can add up all the areas to get the total amount of wrapping paper needed:

Total area = Front/back area + Top/bottom area + 2 * Slanted face area

Total area = 135 + 48 + 2 * 80

Total area = 343 square inches

Therefore, the minimum amount of wrapping paper needed to cover the package is 343 square inches.

The derivative of the inverse trigonometric function is equal to f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ). (Correct choice: D)

In this problem we find the case of the inverse trigonometric function, whose derivative must be found. This can be done by means of derivative rules and chain rules. First, write the entire function:

f(x) = sin⁻¹ (e²ˣ)

Second, find the derivative of the inverse trigonometric function:

f'(x) = [1 / √[1 - (e²ˣ)²]] · (2 · e²ˣ)

f'(x) = (2 · e²ˣ) / √(1 - e⁴ˣ)

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a. The concentration of the drug after 8 hours is equal to 24 mg/L.

b. The interval over which the concentration increases is 0 < t < 2. The interval over which the concentration decreases is 2 < t < ∞.

c. The drug is at its maximum concentration when t = 2 hours and the maximum concentration is 64 mg/L.

d. After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L is 8 hours.

e. After 1 week and 1 month, we can predict that the concentration of the drug kept decreasing after reaching 20 hours.

f. After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L.

By critically observing the graph, the time and concentration of the drug after 8 hours is represented by the order pair (8, 24). Therefore, the concentration is equal to 24 mg/L.

Part b.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value is increased, then, the function is generally referred to as a decreasing function.

For any given function, y = f(x), if the output value (range) is increasing when the input value is increased, then, the function is generally referred to as an increasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce the following:

Part c.

The vertex (2, 64) of the graph represent the point where the drug is at its maximum concentration, which is time (t) = 2 hours and the maximum concentration is y = 64 mg/L.

Part d.

After the drug reaches its maximum concentration, the number of hours that are required for the concentration to decrease to 16 mg/L can be calculated from the graph as follows;

Number of hours = 10 - 2

Number of hours = 8 hours.

Part e.

After 1 week and 1 month, it can be predicted that the concentration of the drug kept decreasing after reaching 20 hours.

Part f.

After the drug is taken orally, it took exactly 2 hours to reach a maximum concentration of 64 mg/L. Subsequently, the level of the drug in the bloodstream drops after reaching its maximum concentration, reaching approximately 10 mg/L after 12 hours.

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If the temperature of a chemical mixture is tan√x degree celsius after x hours then the rate of change of temperature after π /4 hours is 0.141099

We are given that the temperature of the chemical mixture after x hours is given by:

T(x) = tan(√x)

To find the rate of change of temperature after π/4 hours, we need to find the derivative of T(x) with respect to x and evaluate it at x = π/4.

T'(x) = sec²(√x)/2√x

So, the rate of change of temperature after π/4 hours is given by:

T'(π/4) = sec²(√(π/4))/2√(π/4)

= sec²(π/2)/2√(π/4)

= 1/2√(π/4)

We can simplify this expression as:

T'(π/4) = 1/2(π/2)⁰⁵

= 0.141099

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Answer:

The equation of a line that is perpendicular to y = 3x + 3 is option A y equals negative one-third times x plus 1(-1/3x + 1)Given,The equation of line, y = 3x + 3The line passes through (-6, 3)We have to find the equation of the line that is perpendicular to y = 3x + 3Slope of the line, m = 3Here, in perpendicular case, slope is negative of its reciprocal.That is, m = -1/3Now, we can find the equationy - y₁ = m(x - x₁)

Here,

y₁ = 3x₁ = -6m = -1/3

So,y - 3 = -1/3(x - (-6))

y - 3 = -1/3(x + 6)

y - 3 = -1/3x + -1/3(6)

y - 3 = -1/3x - 6/3

y - 3 = -1/3

x - 2y = -1/3

x - 2 + 3

y = -1/3x + 1

That is, the equation of a line that is perpendicular to y = 3x + 3 is y equals negative one-third times x plus 1(y = -1/3x + 1)

Step-by-step explanation:

Answer:

the answer is: 258

How?:

Area:

2(wl+hl+hw)

2(9×6 + 5×6 + 5×9) = 258

Answer:

f(- 5) = 10

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

given

f(x) = 5 + | x |

to find f(- 5) substitute x = - 5 into f)x)

f(- 5) = 5 + | - 5| = 5 + | 5 | = 5 + 5 = 10

Answer: 314 mi

Step-by-step explanation:

Area of a circle = (pi) * (radius)^2

Radius is 1/2 the diameter

Radius = 10

10^2 = 100

100*3.14 = 314

The trinomial expression when factored is (3x - 3)² & A = 3 and B = 3

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

9x² - 18x + 9 = (Ax − B)²

Factor out 9 in the expression

So we have

9(x² - 2x + 1) = (Ax − B)²

When the above expression is factored

We have

9(x - 1)² = (Ax − B)²

Express 9 as 3²

3²(x - 1)² = (Ax − B)²

So, we have

(3x - 3)² = (Ax − B)²

This means that

A = 3 and B = 3

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A(5,0), B(3,2), C(0,5), and D(-6,1) are all located in the first quadrant. D(-6,1) is located within the second quadrant.

A coordinate system within geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points and other geometrical objects over a manifold, such Euclidean space. The order of the coordinates is crucial, and they are frequently identified by their position within an arranged tuple or through a letter, such as "the x-coordinate."  Within the first quadrant is A(5,0). The first quadrant is occupied by B(3,2), followed by C(0,5) with the first quadrant, D(-6,1) with the second quadrant, E(-4,4) from the second quadrant, and F(2,-3) with the fourth quadrant.

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The required forms of the equation are;

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

Completing the square is a method used to rewrite a quadratic expression in standard form by adding and subtracting a constant to make it a perfect square trinomial. Completing the square is a useful method to solve quadratic equations and to rewrite quadratic expressions in standard form.

The standard form of a quadratic equation  is ax² + bx + c = 0

We have that;

x²-8x+5=0

(x+(-4))²= - 5 + ((-4))²

(x -4)²= 11

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The segment lengths are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

Considering the geometric mean theorem, the triangle has bases of 7 and 14 - 7 = 7, hence the altitude BD is given as follows:

BD² = 7 x 7

BD² = 7²

BD = 7.

The segment BC is the hypotenuse of a right triangle of two sides with length 7, hence:

(BC)² = 7² + 7²

[tex]BC = \sqrt{2 \times 49}[/tex]

[tex]BC = 7\sqrt{2}[/tex]

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The coordinates of the image after the rotation are given as follows:

The five more known rotation rules are given as follows:

The coordinates of the original image are given as follows:

The rotation is a 90º counterclockwise about the origin, hence the rule is given as follows:

(x,y) -> (-y, x).

Meaning that the coordinates of the rotated image are given as follows:

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To use the substitution method to solve the system, we need to solve one of the equations for x or y in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable that we can solve.

Let's solve the first equation for x in terms of y:

x + 4y = -9

x = -4y - 9

Now we substitute this expression for x into the second equation:

2x + 5y = -6

2(-4y - 9) + 5y = -6

Simplifying this expression, we get:

-8y - 18 + 5y = -6

-3y = 12

y = -4

Now we can substitute this value of y into either of the original equations to find x. Let's use the first equation:

x + 4y = -9

x + 4(-4) = -9

x - 16 = -9

x = 7

Therefore, the solution to the system is x = 7, y = -4.

Now let's look at the answer choices and see which one matches the equation we got by substituting x = -4y - 9 into the second equation:

A) 2(4-9)+ 5y-6 = -10 + 5y - 6 = 5y - 16

B) 21-4y-9)+5% -6 = -4y + 6

C) 2x+5(4-9)=-6 = 2x - 25 = -6

D) 2x+5(-4y-9)=-6 = 2x - 20y - 45 = -6

The answer choice that matches our equation is D), 2x + 5(-4y - 9) = -6.

Answer: 15cm?

Step-by-step explanation: I am doing this assignment right now, after i submit it i will reply with the answer. Edit: 15cm is correct.

The distance from point A (tangent point on clock) to point B (the hanger) is approximately 10 cm, based on the principles of right-angle triangles and Pythagorean theorem.

In this geometry problem, we're looking at a situation where a circular clock is hung by wires connected to a tangential point on the clock. By using right-angle triangle principles and the given radius of 15 cm from E to D, it''s key to recognize that triangle AED is a right triangle (since a radius perpendicular to a tangent at its point of contact forms a right angle).

So, the distance from A to E (the radius) is 15 cm. The distance from E to D is also a radius, hence is 15 cm as well. Now, by Pythagoras theorem for right triangle AED, the distance AD (the hypotenuse) is square root of (15^2 + 15^2), which is approximately 21.21 cm.

The distance BD from the top of the clock at point D to the hanger at point B is given as 10 cm. Since the clock is hanging from point B, this creates another right triangle ADB. The length from point A to B is found by subtracting BD (10 cm) from the hypotenuse AD (21.21 cm), which is roughly 11.21 cm. However, this option is not offered in the question, meaning a rounding must be made, so the answer is approximately 10 cm.

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The probability for the dial stops on a red or blue slice is,

P = 7/8.

Since, We know that;

Probability is to measure of the likelihood of an event occurring.

Hence, It is a number between 0 and 1,

Since, The closer the probability is to 1, the more likely the event is to occur.

Hence, Probability can make predictions and decisions in various fields, including finance, statistics, etc.

Since, There are 4 red and 3 blue slices,

Hence, a total of slices,

= 4 + 3

= 7 slices that are either red or blue.

So, The probability of the dial stopping on a red or blue slice,

Probability = ( red or blue slices) / (total of slices)

Probability = 7/8

Therefore, the probability for the dial stops on a red or blue slice is 7/8.

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Complete question is,

A spinner with 8 equally sized slices has 4 red slices, 3 blue slices, and 1 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red or blue slice?

Write your answer as a fraction in the simplest form.