1. Use the FOIL method to solve the following problems.
a. (a + b)(2a-3b²) = ?
b. (k-8)(4k+ b) = ?
c. (7x15)(2x + 2) = ?
d. (3ab - 1)(2ab + 6) = ?

Answer:

41(2) or just 82

Step-by-step explanation:

First, you would combine like terms, 9* and 32* then you would time by 2.

The name of the polygon is triangle with the points (4, 1), (2, -2), and

(-3, -3).

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The points (4,1), (2, -2), and (-3, -3) are vertices of a polygon.

Here, All the points are collinear points.

Hence, The name of the polygon is triangle with the points (4, 1), (2, -2), and (-3, -3).

Thus, The polygon is triangle.

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Answer:

100

Step-by-step explanation:

you divide 220 by 2.2 which is equal to 100.

so.. 100 would be your answer

Answer:

Missing factor = 100

Step-by-step explanation:

The answer can be found, simply by dividing both sides of the equation by 2.2, to get ___ = 100, or 100 = 100

The value of the equation is A = ⁵√32,768 is A = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ⁵√32,768   be equation (1)

On simplifying the equation , we get

A = 8 x 8 x 8 x 8 x 8 = 32,768

So , the 5th root of ( 32,768 ) is 8

Therefore , the value of A = 8

Hence , the equation is A = 8

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The picometer  is a unit of length in the International System of Units (SI), equal to 1×10−12 m, or one trillionth (11000000000000) of a metre, which is the SI base unit of length.

In the International System of Units (SI), the picometer is a unit of length that is equal to 11012 m, or one trillionth (11000000000000) of a metre, the SI base unit of length.

The International Bureau of Weights and Measures uses its international spelling.

In the International System of Units (SI), the picometer is a unit of length that is equal to 11012 m, or one trillionth (11000000000000) of a metre, the SI base unit of length.

The International Bureau of Weights and Measures uses a different international spelling for it, and its SI sign is pm.

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The proof of the sum of the lengths of the medians of a triangle is greater than half the perimeter is shown below.

In Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side;

Given:

We have

In ΔABC

let AB = c , BC = a , CA = b and M is the Median

Now, In ΔCMA using Triangle Inequality

b < m + c/2

and,  In ΔCMB using Triangle Inequality

a < m + c/2

Now, adding above two equation we get

a + b < 2m + c  (1)

Similarly we can write for other two medians

a+ c < 2n + b (2)

b+ c < 2o+ a (3)

Now, adding (1), (2) and (3) we get

2 (a+b + c)< 2(m + n+ o) + ( a+ +b+ c)

(m+ n + o)> (a+ +b+ c)/ 2

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The big-O limit lemma states that if f(n) = O(g(n)) as n approaches infinity, then lim n→∞ f(n)/g(n) = C for some constant C.

We must demonstrate that for any constant C > 0, there exists an N such that for all n > N, |log(n)| C*n in order to demonstrate that log(n) = o(n). Here's how to go about it:

For any constant C > 0, choose N = e^C. Then, for all n > N, we have:

log(n) < C

So, |log(n)| < C

And, |log(n)| < C*n

This means that log(n) = o(n), as required.

To show that n^x log(n) = o(n^x) for any constant x, we use the big-O limit lemma. Since log(n) = o(n), we have:

lim n→∞ (n^x log(n))/(n^x) = lim n→∞ log(n)/n^(x-1) = C for some constant C.

Since the limit of the right side is a finite constant, we can conclude that n^x log(n) = o(n^x), as required.

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Answer:

5th term is 9, 30, and -20.3 and the 23rd term is 45, 174, and -132.9

Step-by-step explanation:

The given pattern consists of three mathematical expressions: 2x + 1, 8x - 2, and -6.2x + 4.5. To find the 5th and 23rd term of the pattern, we need to substitute x with the corresponding value and evaluate the expressions for each of the terms.

For the 5th term:

x = 5-1 = 4

So, the 5th term would be:

2x + 1 = 2 * 4 + 1 = 9

8x - 2 = 8 * 4 - 2 = 30

-6.2x + 4.5 = -6.2 * 4 + 4.5 = -24.8 + 4.5 = -20.3

For the 23rd term:

x = 23-1 = 22

So, the 23rd term would be:

2x + 1 = 2 * 22 + 1 = 45

8x - 2 = 8 * 22 - 2 = 174

-6.2x + 4.5 = -6.2 * 22 + 4.5 = -136.4 + 4.5 = -132.9

Therefore, the 5th term is 9, 30, and -20.3 and the 23rd term is 45, 174, and -132.9 for the given pattern of mathematical expressions.

The two possible non-zero values of k in terms of a and b for the given differential equation is √(-b/a) and -√(-b/a).

The characteristic equation of the differential equation is given by:

a*k^2 + b = 0

Solving for k, we get:

k = +/- sqrt(-b/a)

The general solution to the differential equation ay'' + by = 0 is given by

y = C1 * cos(sqrt(b/a) * t) + C2 * sin(sqrt(b/a) * t)

where C1 and C2 are constants determined by the initial conditions.

So, the two possible values of k in terms of a and b are:

k = ± √(b/a)

--The question is incomplete, answering to the question below--

"If the function y = sin(kt) solves the differential equation ay" + by = 0, where a, b > 0, what are the two possible values of k in terms of a and b?"

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Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

Given data :

60 mph for 3 hours = 180 miles

55 mph for 4 hours = 220 miles

Total distance covered = 220 + 180

Additional Hours needed for the average speed of the entire trip to decrease to 54 mph = 400/ 54 = 7 hours and 40 minutes.

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The percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Let the percent of the real fruit in the first brand = x

Given that number of gallons of  real fruit in the first brand = 9 gallons

Given that percent of the real fruit in the second brand = 48%

Given that number of gallons of  real fruit in the second brand = 8 gallons

Given that  percent of the real fruit in the mixture = 30%

then number of gallons of  real fruit in the mixture = (9+8) = 17 gallons

Then we get equation:

[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]

9x+48(8)=30(17)

9x+384=510

9x=510-384

9x=126

x=126/9

x=14

Therefore, the percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14.

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The percentage of real fruit juice in the first brand if the mixture contained 30% real fruit juice is 14%.

Let the percentage of real fruit juice in the first brand = a

Given number of gallons of real fruit in first brand = 9 gallons

Given the percent of real fruit juice in the second brand = 48%

Given number of gallons of real fruit in second brand = 8 gallons

Given the percent of the real fruit in total mixture = 30%

Total mixture of gallons of real fruit = 17 gallons

a% of 9 + 48% of 8 = 30% of 17

9a+48(8)=30(17)

9a+384=510

9a=510-384

9a=126

a=14

Therefore the percent of real fruit in the first brand =a=14%

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1 pints = 473.176475 milliliters

Step-by-step explanation:

1pt (US)=473.176479mL

1mL=0.0021133764 pt (US)

for example

covert 15 pt (US) to mL:

15pt (US)= 15 x 473.176473 mL

               = 7097.647095 mL

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1 pints  is equal to 473.176475 milliliters

How to Convert Pint (US) to Milliliter?

1pt (US)=473.176479mL

1mL=0.0021133764 pt (US)

for example

convert 15 pt (US) to mL:

15pt (US)= 15 x 473.176473 mL

               = 7097.647095 mL

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Helena would need to babysit at least 4 kids.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Helena will receive $53 plus $4 per kid for babysitting this afternoon.

Let x be the number of kids that she babysit.

Given the inequality can be written as,

4x + 53 ≥ 68

4x ≥ 68 - 53

4x ≥ 15

x ≥ 3.75 ≈ 4

Hence Helena should babysit 4 kids in order to get at least $68.

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The probability that she will choose a fruit snacks, put it back and choose a granola bar will be 5/36.

The number of sections that need to be colored purple will be 2.

The probability that she will choose a fruit snacks, put it back and choose a granola bar will be:

= 5/12 × 4 / 12

= 5 / 36

The number of sections that need to be colored purple will be 2. This will be:

= p(head) × P(purple)

= 1/2 × 2/8

= 1/8

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Answer:

Step-by-step explanation:1500-1322=178

178:60=2.9... =>3h

They need to drive for approximately3 hours, to cover the remaining 178 miles and reach their goal of the 1,500-mile mark by the end of the day tomorrow.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,

To reach the 1,500-mile mark, Henrietta's family needs to travel an additional 1,500 - 1,322 = 178 miles.

Since they averaged a speed of 60 miles per hour so far, we can use the formula:

distance = speed × time

To find out how long they need to drive to cover the remaining 178 miles. Solving for time, we get,

time = distance/speed

time = 178 miles ÷ 60 miles per hour

time = 2.967 hours

This means they need to drive for approximately3 hours, to cover the remaining 178 miles and reach their goal of the 1,500-mile mark by the end of the day tomorrow.

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The point on the x-axis that lies on the line passing through point C and parallel to line AB is (4, 0).

A line that is parallel to line AB and passes through point C has the same slope as line AB. The slope of line AB can be found using the formula:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

In this case, (x1, y1) = (negative 4, 0) and (x2, y2) = (2, negative 3).

Substituting these values into the formula, we get:

m = (-3 - 0) / (2 - -4) =  -3 / 6 = -1/2

Since the slope of line AB is -1/2,

the slope of the line through point C and parallel to line AB is also -1/2.

A line with slope -1/2 and passing through (negative 2, 2) has the equation:

y - 2 = -1/2 (x - -2),

Rearranging this equation to solve for y, we get:

y = -1/2 x + 2

The x-axis has y-coordinate 0, so substituting 0 for y in the equation, we get:

0 = -1/2 x + 2

Solving for x, we get:

x = 4

hence the point is (4, 0)

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The volume of the given cone is V= 10512.72 cm^3.

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.

here, we have,

Volume =  ⅓ r²h

given that,

r=18

h=31

i.e. V= 10512.72 cm^3

Hence, The volume of the given cone is V= 10512.72 cm^3.

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A least squares regression line is one that best fits the linear relationship, and the answer is D. none of the above.

A least-squares regression line, which minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relationship between two variables when the data indicates such a relationship. Because it is the smallest sum of squares of errors, also known as the "variance," the phrase "least squares" is used to describe it.

A east squares regression line is one that best fits the linear relationship.

Hence, none of the options given are correct and answer D. none of the above is the correct answer.

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The area of r is 18.

1. First, we need to find the intersection of the curve and the line y = 6. We can do this by setting the two equations equal to each other and solving for x.

y = x−−√

y = 6

x = 6

2. Next, we need to calculate the area of the region. We can do this by using the formula for the area of a triangle.

A = 1/2 * base * height

A = 1/2 * 6 * (6 - √6)

A = 18

Therefore, the area of the region r is 18.

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Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.

These equations are used to model a wide range of physical, biological, and chemical processes. The seventh edition of Fundamentals of Differential Equations and Boundary Value Problems by R. Kent Nagle, Edward B. Saff, and Arthur David Snider is a comprehensive textbook that covers the fundamentals of these equations.Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.  It includes topics such as first order equations, higher order linear equations, systems of equations, Laplace transforms, Fourier series, and numerical methods. It also contains a variety of worked examples, exercises, and applications to help students understand the material. Examples include solving initial value problems, boundary value problems, and inverse problems. The book also provides a step-by-step approach to solving problems, including the use of formulas such as the Euler-Cauchy formula, the Picard-Lindelof formula, the Runge-Kutta formula, the Laplace transform, and the Fourier series.

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Complete question:

Find the solution to the differential equation dy/dx + 4y = 0, given the boundary values y(0) = 2 and y(2) = 0.

There are three values in the interval [60,65) which satisfy the mentioned criteria.

The number of times, a data point occurs in the data set is called its frequency .

For eg - If I visit market twice a week, so my frequency of going to the market in a week is 2.

Now, here given 4 data column and data points in interval [60,65) means that 60 and less than 65 will included included but 65 not included in interval i.e. its an open interval at 65 and a closed interval at 60.

So, from the given data we can say that the values  (64.1, 60, 64.83) are lying in the interval [60,65).

So, the frequency is 3.

Therefore, there are three values in the interval [60,65) which satisfy the mentioned criteria.

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There are three values in the interval [60,65) that satisfy the mentioned criteria.

The number of times, a data point occurs in the data set is called its frequency.

For eg - If I visit the market twice a week, so my frequency of going to the market in a week is 2.

Now, here given 4 data columns and data points in the interval [60,65) means that 60 and less than 65 will be included but 65 is not included in the interval i.e. it's an open interval at 65 and a closed interval at 60.

So, from the given data we can say that the values  (64.1, 60, 64.83) are lying in the interval [60,65).

So, the frequency is 3.

Therefore, there are three values in the interval [60,65) that satisfy the mentioned criteria.

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a) Note that the points in the interior region of the circle are given as follows;

b) the name of the point(s) in the interior region of the triangle are:

c)  the name of the line(s) in the interior region of the triangle is:

d) Another name for the Line [tex]\overline{P}[/tex] is: [tex]\overline{HD}[/tex]

A line is an endlessly long object with no breadth, depth, or curve in geometry.

Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.

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The Z-value represents the number of standard deviations away from the mean a particular value is. To find the Z-value when x is 10, given the population mean and standard deviation of 7 and 3, respectively, we use the following formula:

Z = (X - μ) / σ

Where:

X = 10 (the value of x)

μ = 7 (the population mean)

σ = 3 (the population standard deviation)

Plugging in the values, we get:

Z = (10 - 7) / 3 = 3 / 3 = 1

So the Z-value when x is 10 is 1, which means that x is 1 standard deviation above the mean.

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Answer:

Step-by-step explanation:

To find the height of the hill, we can use the tangent function. Let h be the height of the hill and x be the distance from the person to the base of the hill. We know that:

tan 1.5° = 127 / x

and

tan 25° = h / x

We can use the first equation to find x:

x = 127 / tan 1.5°

And then substitute x into the second equation to find h:

h = x * tan 25° = (127 / tan 1.5°) * tan 25°

This gives us the height of the hill. You can use a calculator to find the value of h.

On solving the provided question we cans ay that we know that sum of all angles in a triangle is 180 => 55+68 +x = 180 => x = 57

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

in the given triangle,

we have 2 angles given, and

we know that sum of all angles in a triangle is 180

55+68 +x = 180

x = 180 -55-68

x = 57

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The required expression that represents the area of a sector of circle  A is 120/360 × 100π.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr²

From the quesiton, we have circle A with a radius of 10 units.
The angle of the sector is not defined in the question,
Let the angle of sector Ф = 120°

Formula of area of sector = Ф/360 × πr²,

Assign the value in the above expression,
Area of the sector of circle A = 120 / 360 × π (10)²

Area of th sector of circle A = 120/360 × 100π

Thus, the required expression that represents the area of a sector of circle  A is 120/360 × 100π.

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Answer:

0.05

Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

0.05

1. An extraneous solution is a solution that is outside the domain of a function.

2. In a rational function, the solutions must be checked if they belong to the domain, that is, if they do not make the denominator of the function zero.

3. Mikael is wrong as y = -6 is an extraneous solution, as it makes the denominator of y/(y + 6) zero.

An extraneous solution is a solution that is outside the domain of a function, and examples are given as follows:

A rational function is a function with a variable in the denominator, and the domain of the function is that the denominator cannot assume a value of zero. Hence, each solution must be checked to ensure that it does not make the denominator assume a value of zero.

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The algebraic representation of the verbal expression is given by (j + m) / 7.

Number of crackers jaylen bought = j

Number of crackers Marvin bought = m

Number of friends shared with = 7

Algebraic expression:

(j + m) / 7

Ultimately, the verbal expression is represented by (j + m) / 7

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Answer:

1/6

Step-by-step explanation:

convert the 1 1/2 into a mixed fraction (3/2).  Then take the reciprocal of 3/2 (2/3).  This becomes 1/4 times 2/3.

1/4 x 2/3 = 2/12

2/12 = 1/6