Is the expression (x + 18) a factor of x² - 324?

The y coordinate of the solution to this system of equations is -2

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

3x+y=-2 x-2y=4

Express properly

So, we have

3x + y = -2

x - 2y = 4

Multiply the second equation by -3

so, we have the following representation

3x + y = -2

-3x + 6y = -12

Add the equations to eliminate x

7y = -14

Divide both sides by 7

y = -2

Hence, the value of y is -2

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she can add each number one by one , and whenever she needs to carry numbers over. She can add them to the already existing numbers. she cna check with a calculator

The limited precision of floating-point arithmetic in computers can cause rounding errors, leading to unexpected results such as the value 0.7999999999999999 instead of 0.8. This occurs because certain decimal values cannot be accurately represented in binary form.

This is due to the way floating-point numbers are represented in the computer's memory.

Binary floating-point arithmetic cannot represent every decimal value exactly, so sometimes small rounding errors can occur.

In this case, the value 0.8 cannot be represented exactly in binary floating-point format, so the closest approximation is used, resulting in a slightly different value.

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According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.

To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.

To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:

n = (z² x s²) / E²

Where:

n = sample size needed

z = z-score for desired level of confidence (99% = 2.58)

s = standard deviation of the population (0.15 feet)

E = level of precision (0.025 feet)

Plugging in the values, we get:

n = (2.58² x 0.15²) / 0.025²

n = 74.83 ≈ 75

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So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.

Since the circle at each end of the court that surrounds the free throw line is the same size as the jump ball circle, they both have the same radius. Let's call this radius "r".

The diameter of the circle is equal to the width of the lane, which is the same as the width of the free throw line. Therefore, the diameter of the circle is also 12 feet (the width of the free throw line is always 12 feet).

We know that the area of a circle is given by the formula A = πr^2, so the area of each circle is πr^2.

The rectangle (or lane) has a length of 19 feet and a width of 12 feet. Therefore, its area is simply the product of its length and width, which is:

A = 19 feet * 12 feet

A = 228 square feet

Since there are two circles, the total area of the circles is 2πr^2.

We know that the diameter of the circle is equal to the width of the lane, which is 12 feet. Therefore, the radius is half of the diameter, or:

r = 12 feet / 2

r = 6 feet

Now we can calculate the area of the circles:

A = 2πr^2

A = 2π(6 feet)^2

A = 72π square feet

Therefore, the total area of the rectangle and circles (or lane and circles) is:

A_total = A_rectangle + A_circles

A_total = 228 square feet + 72π square feet

A_total ≈ 450.39 square feet

So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.

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Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.

When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.

Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.

Therefore, we can set up the following equation:

x + y = 180

This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:

y = 180 - x

This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:

2x = 180

Solving for x, we find that x = 90.

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To determine the probability of the coin flip and the cube roll describing the pizza crust and topping combination made at Mario's Pizzeria, we need to consider the total possible outcomes of these events.

There are 2 types of crust, so the coin has 2 sides (heads for one crust type and tails for the other). For the toppings, there are 6 options, represented by the numbers 1 to 6 on the number cube.

First, we find the total possible outcomes by multiplying the number of crust options (2) by the number of topping options (6):
Total possible outcomes = 2 crust options * 6 topping options = 12 combinations

Since there is only one specific combination that Mario's Pizzeria just made, the probability of the coin flip and the cube roll describing this specific combination is:
Probability = 1 (specific combination) / 12 (total possible outcomes)

To express this as a decimal rounded to the nearest thousandth, divide 1 by 12:
Probability ≈ 0.083

So, the probability that the coin flipped and the cube rolled will describe the pizza crust and topping combination that Mario's Pizzeria just made is approximately 0.083, or 8.3%.

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The two contradictory statements are "triangle LMN is a right triangle" and "triangle LMN is equilateral."

An equilateral triangle has all three sides and angles congruent. Therefore, if triangle LMN is equilateral, all angles in the triangle must be congruent and equal to 60 degrees. However, the statement "triangle LMN is a right triangle" implies the presence of a 90-degree angle, which contradicts the requirement for all angles to be 60 degrees in an equilateral triangle.

Additionally, the statement "angle L ≅ angle N" suggests that angles L and N are congruent. In an equilateral triangle, all angles are congruent, so if angles L and N are congruent, it further supports the claim that triangle LMN is equilateral.

In conclusion, the statement "triangle LMN is a right triangle" contradicts the statement "triangle LMN is equilateral" because a right triangle cannot be equilateral.

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The 95 percent confidence interval for the population mean is $65.59 to $74.41.

To calculate a 95% confidence interval for the population mean, we will use the sample mean, population standard deviation, and sample size provided. The formula for the confidence interval is:

CI = X ± (Z * (σ / √n))

Where:
- X is the sample mean, $70.00
- Z is the Z-score for a 95% confidence interval, 1.96
- σ is the population standard deviation, $17.50
- n is the sample size, 60

CI = $70.00 ± (1.96 * ($17.50 / √60))

Calculate the margin of error:

Margin of Error = 1.96 * ($17.50 / √60) ≈ $4.41

Now, calculate the confidence interval:

Lower Limit = $70.00 - $4.41 ≈ $65.59
Upper Limit = $70.00 + $4.41 ≈ $74.41

So, the 95% confidence interval for the population mean is approximately $65.59 to $74.41.

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I'm sorry, but I cannot answer your question without a net or a description of the solid figure. Can you please provide more information or context?

The solution of the inequality 4x-1 grater then -5 is x > -1

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

4x-1 grater then -5

Express properly

so, we have the following representation

4x - 1 > -5

Add 1 to both sides of the inequality

so, we have the following representation

4x > -4

Divide both sides by 4

x > -1

Hence, the solution of the inequality is x > -1

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To differentiate x^6y^9 with respect to x, we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function multiplied with the second function, plus the first function multiplied with the derivative of the second function.

Step 1: Identify the functions
Function 1 (u): x^6
Function 2 (v): y^9

Step 2: Find the derivatives
u' (du/dx): Differentiate x^6 with respect to x, which gives 6x^5
v' (dv/dx): Differentiate y^9 with respect to x, which gives 9y^8 * (dy/dx) = 9y^8D (since D = dy/dx)

Step 3: Apply the product rule
d/dx (x^6y^9) = u'v + uv'
= (6x^5)(y^9) + (x^6)(9y^8D)
= 6x^5y^9 + 9x^6y^8D

So, the derivative of x^6y^9 with respect to x is 6x^5y^9 + 9x^6y^8D.

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Answer:

I'm assuming that A and B are two different items, and you want me to work with the same data set for both items. Here are the calculations:

1. Mean price of milkshake:

To find the mean price of a milkshake, you need to add up all the prices and divide by the total number of prices:

(4 + 2 + 9 + 14 + 6) / 5 = 7

Therefore, the mean price of a milkshake is $7.

2. Median price of milkshake:

To find the median price of a milkshake, you need to put the prices in order from lowest to highest:

2, 4, 6, 9, 14

The median is the middle value. Since there are five values, the middle value is the third value, which is 6.

Therefore, the median price of a milkshake is $6.

3. Mode of price of milkshake:

To find the mode of the price of a milkshake, you need to find the price that appears most frequently in the data set. In this case, there is no price that appears more than once, so there is no mode.

Therefore, there is no mode for the price of a milkshake.

I hope that helps! Let me know if you have any further questions.

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When the base of a triangle is doubled, the height must be halved to maintain the same area. This is because the area of a triangle is proportional to the product of its base and height. Area of the new triangle is b₁h₂.

Given that a triangle has base b and height h, and the base is doubled. We need to find how the height must change so that the area remains the same.

The area of the original triangle is (1/2) b₁h₁.

Let's assume that the original base is b₁ and the original height is h₁.

Now, the base is doubled, so the new base is 2b₁.

Using the formula for the area of a triangle, we can find the area of the new triangle as

Area of the new triangle = (1/2) × base × height

= (1/2) × 2b₁ × h₂

= b₁h₂

where h₂ is the new height of the triangle.

Since we want the area of the new triangle to be equal to the area of the original triangle, we can equate the two expressions for the area

b₁h₁ = b₁h₂

Simplifying, we get

h₂ = h₁/2

Therefore, the height must be halved when the base is doubled to keep the area of the triangle constant.

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--The given question is incomplete, the complete question is given

"  A triangle has base b and height h. The base is doubled. Complete the description of how the height

must change so that the area remains the same. Complete the explanation of the reasoning.

The area of the original triangle is (1/2) b₁h₁. The area of the new triangle is 1/2 (2b₁)h₂ =_____ This must equal the original area (1/2) b₁h₁. Therefore, the height must be_____"--

The rent for the apartment using exponential equation in 2017 was $8,029.91.

To find the rent of the apartment in 2017, we will use an exponential equation. An exponential equation is a mathematical expression where a variable is raised to a power, often used to model growth or decay. In this case, we will model the growth of the rent over time.

1. Identify the initial rent, the growth rate, and the number of years that have passed since 2012.
Initial rent (A0): $6,600
Growth rate (r): 4% = 0.04
Number of years (t): 2017 - 2012 = 5

2. Write the exponential equation for the rent increase:
At = A0 * (1 + r)^t

3. Plug in the given values and calculate the rent in 2017:
At = $6,600 * (1 + 0.04)^5

4. Calculate the rent:
At = $6,600 * (1.04)^5
At = $6,600 * 1.2166529
At = $8,029.91

The rent for the apartment in 2017 was $8,029.91. This was calculated using an exponential equation, which allowed us to account for the 4% annual increase in rent over the 5 years since 2012.

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The calculated value of X when Y equals four is four

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

Using the above as a guide, we have the following:

y = kx

Where

k = constant of variation

When Y equals eight when X equals eight, we have

8k = 8

So, we have

k = 1

This means that the equation is

y = 1 * x

Evaluate

y = x

When the value of y is 4, we have

4 = x

This gives

x = 4

Hence, the value of X when Y equals four is four

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If FY varies directly as X, we can write the equation as:

FY = kX

where k is the constant of variation. To find the value of k, we can use the fact that "Y equals eight when X equals eight":

8 = k(8)

Simplifying this equation, we get:

k = 1

Now we can use this value of k to find the value of X when Y equals four:

4 = 1X

Solving for X, we find that

X = 4

Therefore, when Y equals four, X equals 4 as well...

The prime number values of a, b and c that satisfy the equation a⁴ + b⁴ + c⁴ + 54 = 11abc are a = 3, b = 2, and c = 5.

Let's consider the equation a⁴ + b⁴ + c⁴ + 54 = 11abc. Due to the fact that the total of four even numbers is also even, the left-hand side is always even. As a result, since 2 is the only even prime, one of the factors a, b, or c must be 2 for 11abc to likewise be even.

Let's examine each instance,

Case 1: a = 2

Substituting a = 2 into the equation, we get,

16 + b⁴ + c⁴ + 54 = 22bc

b⁴ + c⁴ - 22bc + 38 = 0

Since b and c are primes, they must be odd. Let b = 3 and c = 5, we have,

3⁴ + 5⁴ - 2235 + 38 = 0

81 + 625 - 330 + 38 = 0

Case 2: b = 2

Substituting b = 2 into the equation, we get,

a⁴ + 16 + c⁴ + 54 = 22ac

a⁴ + c⁴ - 22ac + 70 = 0

Since a and c are primes, they must be odd. Let a = 3 and c = 5, we have,

3⁴ + 5⁴ - 2235 + 70 = 0

Case 3: c = 2

Substituting c = 2 into the equation, we get,

a⁴ + b⁴ + 16 + 54 = 22ab

a⁴ + b⁴ - 22ab + 70 = 0

However, for any odd number x, x⁴ mod 16 = 1, which means that a⁴ and b⁴ are both corrosponds to 1 mod 16. So, as the conclusion, a = 3, b = 2, and c = 5.

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The answer is 2, which represents the sum of the values of x for which f'(x) = 0.

To find the critical points of f(x), we need to find the derivative of f(x):

Setting f'(x) = 0 and solving for x, we get:

We can use the Rational Root Theorem to find possible rational roots of the equation. The possible rational roots are:

We can use synthetic division or long division to check which of these roots are actually roots of the equation. We find that the only real root is x = 5/4, and it has multiplicity 2.

The sum of the values of x for which f'(x) = 0 is simply the sum of the critical points of f(x). In this case, we only have one critical point: x = 5/4.

We first find the derivative of the given function and set it equal to zero to find the critical points. We use the Rational Root Theorem to find the possible rational roots of the equation, and then we use synthetic division or long division to check which of these roots are actually roots of the equation. In this case, we find that the only critical point of the function is x = 5/4 with multiplicity 2.

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Answer:

∠ a = 125°

Step-by-step explanation:

the measure of chord- chord angle a is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

∠ a = [tex]\frac{117+133}{2}[/tex] = [tex]\frac{250}{2}[/tex] = 125°

The function f(x) = -4x² + 12x - 4 attains an absolute maximum of 3 at x = 1/2 and an absolute minimum of -8 at x = 2 on the interval [1/2, 2].

To help you verify and find the absolute maximum and minimum values of the function f(x) = -4x² + 12x - 4 on the interval [1/2, 2].

Step 1: Find the critical points by taking the derivative of f(x) and setting it to 0.
f'(x) = -8x + 12

Step 2: Solve f'(x) = 0 to find critical points.
-8x + 12 = 0
x = 3/2

Step 3: Evaluate the function f(x) at the critical point and the interval's endpoints.
f(1/2) = -4(1/2)^2 + 12(1/2) - 4(1/2) = 3
f(3/2) = -4(3/2)^2 + 12(3/2) - 4(3/2) = 1
f(2) = -4(2)^2 + 12(2) - 4(2) = -8

Step 4: Compare the function values and determine the absolute maximum and minimum values.
The absolute maximum value is 3 at x = 1/2.
The absolute minimum value is -8 at x = 2.

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The 10 breeding pairs of spotted owls in Cascade National Park studied by the researcher represent a selected sample. So, the correct answer is A)

The 10 breeding pairs of spotted owls represent a selected sample.

A sample is a subset of a larger population that is chosen for research or study purposes. In this case, the researcher is interested in studying the disappearance of spotted owls from northwestern forests, but it would be impractical to study the entire population of spotted owls in the region.

Therefore, the researcher selected a smaller group of 10 breeding pairs in Cascade National Park as a representative sample to study over the course of one year. The selected sample may help the researcher to draw conclusions about the population of spotted owls in the region. So, the correct option is A).

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--The given question is incomplete, the complete question is given

" a researcher is interested in the disappearance of spotted owls from northwestern forests. she studies 10 breeding pairs of spotted owls in cascade national park for one year. the 10 breeding pairs are the: group of answer choices

selected sample

snowball sample  

stratified sample

target population"--

The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .

It can be evaluated applying the formula

Lower Bound = Sample Proportion - Z-Score × Standard Error

Here

Sample Proportion
= 200/371 = 0.539

Z-Score = 1.96 (for a 95% confidence interval)

Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,

Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.

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Answer: 20 kg

Step-by-step explanation:

You follow the line of best fit until 50cm

Then you trace across and look at the x-axis.

There you will find that the dog will be 20kg at 50cm using the line of best fit.

In this prism, lateral Area =  858.54 m² and surface area = 890.54 m².

Firstly, we will find the lateral area of the prism by applying the formula:

Lateral  area = perimeter × height

Perimeter = sum of all the sides of prism

= 4 + 8 + 8.94  = 20.94 m

Lateral Area = 20.94 * 41  =  858.54 m²

Now, we have to find the surface area of the prism.

Surface area = Lateral Area + 2 × ( Base Area)

Base Area = the area of a triangle with sides 4, 8, and 8.94.

Now, we will calculate the area of the triangle

Firstly, we will find s for calculating the area of triangle and then apply the formula.

s = ( 4 + 8 + 8.94)/2 = 10.47 m

Area of triangle =  [tex]\sqrt{ (10.47 (10.47 - 4)(10.47 - 8)(10.47 - 8.94))}[/tex]

= [tex]\sqrt{(10.47 (6.47)(2.47)(1.53))}[/tex]

= 16 m²

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Correct question:

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.

14 revolutions per second can be expressed as 28π radians per second.

A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.

1 revolution per second is expressed as 2π radians per second.

To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.

14 revolutions per second = 14 * 2π

= 28π radians per second

Thus, the answer to the given question comes out to be 28 π radians per second

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Correct option is A)

The arrangement of electrons in different energy levels around a nucleus is called electronic configuration. The periodicity in properties of elements in any group is due to repetition in the same valence shell electronic configuration after a certain gap of atomic numbers such as 2, 8, 8, 18, 18, 32.

The atomic number of Al is 13 and its electronic configuration is 2, 8, 3. So, the electronic configuration of [tex]\text{Al}^3+[/tex] is 2,8.

The total number of problems he solved is 36 if after completion of 27 problems he has completed 75% of the assignments.

Percentage of completion = 75 % of the work

The percentage can be converted to decimal by dividing the percentage by 100.

Thus, the part that has been completed = 75% = 0.75 of the work

The number of questions done = 27

Let the total number of questions be x

Thus, 75% of x is given as 27

75% of x = 27

0.75 * x = 27

0.75x = 27

x = 27/0.75

x = 36

Thus, the total number of questions is 36.

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The only line on the graph with a unit rate less than 2 is the horizontal line passing through y=8.

To identify the unit rates on the graph, we need to find the slope of the line connecting each pair of points. We can use the formula:

slope = (change in y) / (change in x)

For example, the slope between the first two points (7,8) and (14,16) is:

slope = (16-8) / (14-7) = 8/7

Similarly, we can find the slopes for the other pairs of points:

- between (7,8) and (21,24): slope = (24-8) / (21-7) = 16/14 = 8/7
- between (14,16) and (21,24): slope = (24-16) / (21-14) = 8/7

Notice that all three slopes are equal, which means the graph represents a line with a constant unit rate of 8/7.

To find lines with unit rates less than 2, we need to look for steeper lines on the graph. Any line with a slope greater than 2/8 (or 1/4) will have a unit rate greater than 2.

One way to see this is to note that a slope of 2/8 means that for every 2 units of increase in y, there is 8 units of increase in x. This is equivalent to saying that the unit rate is 2/8 = 1/4. If the slope is greater than 2/8, then the unit rate is greater than 1/4, and therefore greater than 2.

Looking at the graph, we can see that the steepest line has a slope of 2/3, which means it has a unit rate of 2/3. Therefore, any line with a slope greater than 2/3 will have a unit rate greater than 2, and any line with a slope less than 2/3 will have a unit rate less than 2.

To summarize:

- The graph represents a line with a constant unit rate of 8/7.
- Any line with a slope greater than 2/3 has a unit rate greater than 2.
- Any line with a slope less than 2/3 has a unit rate less than 2.

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First, using the Pythagorean theorem, we get the hypotenuse = 12.

sin = opposite/hypotenuse = [tex]\frac{6\sqrt{3} }{12} = \frac{\sqrt{3} }{2}[/tex]

cos = adjacent/hypotenuse = [tex]\frac{6}{12} =\frac{1}{2}[/tex]

tan = opposite/adjacent = [tex]\frac{6\sqrt{3} }{6} = \sqrt{3}[/tex]

csc = hypotenuse/opposite = [tex]\frac{12}{6\sqrt{3} } =\frac{2}{\sqrt{3} }[/tex]

sec = hypotenuse/adjacent = [tex]\frac{12}{6} =2[/tex]

cot = adjacent/opposite = [tex]\frac{6}{6\sqrt{3} } = \frac{1}{\sqrt{3} }[/tex]