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Expressions → Type of factoring

3x³ + 15x² + 2x + 10 → Grouping

x³ + 27 → Sum of cubes

2x² + 6x → Greatest common factor

x² - 25 → Difference of squares

x² + 6x + 8 → Unfoil

x³ - 1 → Difference of cubes

'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

Given expressions

Using grouping method

= (3x³ + 15x²) + (2x + 10)

= 3x²(x + 5) + 2(x + 5)

Factoring out common term

= (x+5)(3x² + 2)

It can be written as

= x³ + 3³

Which is sum of cubes

it can be written as

= 2x.x + 2x.3

GCF (greatest common factor) = 2x

= 2x (x + 3)

It can be written as

= x² - 5²

which is difference of squares

= x² + 4x + 2x + 8

= x(x + 4) + 2(x + 4)

= (x + 4) (x + 2)

Which is unfoil.

it can be written as

= x³ - 1³

which is difference of cubes.

Hence, the factoring of expressions 3x³ + 15x² + 2x + 10, x³ + 27,  2x² + 6x, x² - 25, x² + 6x + 8, x³ - 1 refers to grouping, sum of cubes, greatest common factor, difference of squares, unfoil and difference of cubes respectively.

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Answer:

x <= 1.

Step-by-step explanation:

Let x be the number of jeans Jordan can purchase.

We know that the total cost of the leather jacket, hat and jeans is $45 + $10 + $35x = $45 + $10 + $35x.

We also know that the total cost cannot exceed the amount of money Jordan has, which is $90.

So we can write the inequality: $45 + $10 + $35x <= $90

Solving for x, we get: $35x <= $35

x <= 1

So the number of jeans Jordan can purchase is x <= 1.

The slope of the linear equation perpendicular to:

x - 6y = 24

is a = -6.

A general line can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, two lines are perpendicular if the product between their slopes is equal to -1.

Here we want to find a line perpendicular to:

x - 6y = 24

First, we need to find the slope of this line.

x - 6y = 24

-6y = -x + 24

y = (-1/6)*-x - 24/6

y = (1/6)*x - 3

The slope is 1/6, then if the slope of the perpendicular line is a, the slope must be a solution of:

a*(1/6) = -1

a = -6

The slope of the perpendicular line is -6.

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Answer:

67,43/10 = 6.743

When dividing any number by 10, you just move the decimal to the left. When multiplying, you move it to the right.

Step-by-step explanation:

Hope it helps! =D

Therefore , the solution of the given problem of unitary method is Boat is travelling at a speed of 21.6 miles /hour.

The unit method is a way of problem-solving where you first calculate the worth of a single group, subsequently multiply that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint or reciprocal are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators)

Here,

A boat has a speed = 36 km/hour

a km is about 60% of a mile.

1 km = 60/100 mile = 0.6 mile

the boat has a speed = (0.6 × 36) mile/hour

                                   = 21.6 miles/ hour

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The answer is pint of milk

A mixture refers to the mix that is derived as a result of mixing two or more items or substances in a certain ratio or proportion.

Given here: 1 tablespoon of grape juice is mixed into the milk and 1 tablespoon of this mixture is mixed with grape juice.

Thus the milk is more contaminated as the latter mixture contains some amount of grape juice and as a result the grape juice mixture is not contaminated to the extent of the pint of milk.

Hence, The answer is pint of milk

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A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution. A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

A sigma value, typically represented by the Greek letter or lower case s, is a measure of how far a sample or point of data is from its mean. It is given in standard deviations.

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Answer:

D

Step-by-step explanation:

26+169=0

For you to make 5 pecan pies, it would be necessary to buy 1.9 pounds of pecans.

Based on the information displayed on the label 1 cup of pecans is equal to 99 grams.

We know 1 pecan pie requires  1 3/4 cups or 1.75 cups (3/4 = 0.75)

1.75 x 5 = 8.75 cups in total

Now, let's calculate this in grams:

8.75 x 99 = 866.22 grams

Finally, let's calculate the pounds

1 pound = 453

 x           = 866.22

x = 866.22 / 453 = 1.9

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Answer:33

Step-by-step explanation:

49-16=33

Using Pythagoras theorem, the altitude a is √33.

The Pythagorean theorem, a cornerstone of Euclidean geometry, connects the side lengths of a right triangle via the straightforward formula a² + b² = c². Ancient scholars and architects from Babylon, Egypt, China, and India were aware of the connection.

While Pythagoras lived and wrote between 569 and 475 BCE, the work that bears his name first appeared on clay Babylonian tablets around 1800 BCE. Early Chinese scholars were also aware of the Pythagorean theorem, and it was mentioned in ancient Indian sacred texts that dealt with the construction of altars.

To solve a,

We can see a right triangle forming by those 3 squares

Lets take theirs sides as the base, altitude and hypotenuse

Hypotenuse = 7

Base = 4

Altitude = to find

Using Pythagoras theorem

[tex]a^2 + b^2 = c^2[/tex]

[tex]\Rightarrow a = \sqrt{c^2 - b^2 }[/tex]

[tex]\Rightarrow a = \sqrt{7^2 - 4^2 }[/tex]

[tex]\Rightarrow a = \sqrt{49 - 16 }[/tex]

[tex]\Rightarrow a = \sqrt{33 }[/tex]

Thus, Using Pythagoras theorem, the altitude a is √33.

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The Gold Standard was a system under which nearly all countries fixed the value of their currencies in terms of a specified amount of gold, or linked their currency to that of a country which did so.

Step-by-step explanation:

Answer:

No longer used.

Step-by-step explanation:

Due to too much paper money being printed, some countries did not have enough gold reserves to exchange for the excessive amounts of paper promissory notes. (China's overprinting of printed money during the 9th and 15th centuries foreshadowed England's overprinting during WWI some 200 years later.) This rendered the paper money worthless. (One of the causes of the Great Depression.)

The gold standard is no longer used now, but the system it inspired is currently used between nations.

The quadratic equation are y= 5x-3/2+x^2, y= x^2+5x-2 and y= x-1/x.

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 x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

Here,

A. y= 5x-3/2+x^2

It has a degree is 2, So quadratic equation.

B. y= x^2+5x-2

It has a degree is 2, So quadratic equation.

C. y=-x+2

It has a degree is 1, So it's not quadratic equation.

Hence the value of k is 0.33.

D. y= x-1/x

y = x² -1/x

It has a degree is 1, So it's not quadratic equation.

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Answer:

Text are too tiny for me to see sorry

Answer:

2.5

Step-by-step explanation:

P=29

w+w=4+4=8(rule of perimeter is 2w+2L)

29-8=21

21-16=5(L+L=8+8=16)

5 will be over 2 since it's for the 2 sides so 5÷2=2.5

your welcome

The Perimeter of the space that is not filled with cheese tart is 44 cm.

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The hourly pay that was charged for the repairs to Victor's car was $ 57.14

To find the hourly wage, find the total labor wages that were charged as a cost to Victor's repairs. This cost would be:

= 272 - 6 - 28. 50 - 20 .00 - 15. 00 - 2. 50

= $ 200

The total hourly wage charged was $ 200 for 3 . 5 hours of work.

This means that the hourly pay charged was :

= Total labor wages / Number of hours

= 200 / 3 . 5

= $ 57.14

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The comparison that can be be made between population of city A and B is City A < City B

The population of city A is eighty-four thousand two hundred-six

This is written in numerals as : 84,206

For Population B the size is said to be:

80,000 + 4000 + 200 + 10 +6

we would have to add this up

= 84216

Now we are to compare the value that is greater

84216 is greater than 84206

hence we would say that City A has a less population compared to City B which is greater

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Answer:

a = 15 , b = [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

the equation of proportion is

y = kx ← k is the constant of proportion

to find k substitute x = 0.7, y = 2.1 , values from the table into the equation

2.1 = 0.7k ( divide both sides by 0.7 )

3 = k

y = 3x ← equation of proportionality

then using x = 5

a = 3 × 5 = 15

using y = [tex]\frac{2}{3}[/tex]

[tex]\frac{2}{3}[/tex] = 3b ( multiply both sides by 3 to clear the fraction )

2 = 9b ( divide both sides by 9 )

[tex]\frac{2}{9}[/tex] = b

The x-intercepts of the graph of the equation are (8,0) and (-6,0).

What are intercepts?

A point on the y-axis known as an intercept is where the line's slope passes.

X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.

Now, in order to find the x- intercepts, we need to put y=0 because at that point the line crosses the x- axis and therefore, y=0 at that point.

So,

x^2-2x+(0)^2-3(0)=48

⇒x^2-2x=48

⇒x^2-2x-48=0

⇒x^2+6x-8x-48=0

⇒x(x+6)-8(x+6)=0

⇒(x-8)(x+6)=0

So, x= 8,-6

Hence, the x-intercepts of the graph of the equation are (8,0) and (-6,0).

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The amount of pints of punch that Jason served is; 52 pints

Algebraic word problems are defined as the questions that require translating sentences to equations, then solving those equations. and a single variable.

We are given that;

Amount of punch made = 8 gallons

Amount of punch left after serving = 12 pints

Now, conversion of pints to gallon is;

1 pint = 0.125 gallons

Thus;

12 pints = 1.5 gallons

Thus;

Amount of pints served = 8 - 1.5 gallons

= 6.5 gallons

Converting to pints gives 52 pints

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Answer: The solution to the expression is the result of the mathematical operations being performed in the correct order. The order of operations is: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

5/34 is a fraction, 22 2/3 is a mixed number, and 2 1/9 is also a mixed number. To perform the operations, we need to convert all these mixed numbers to fractions.

So, 22 2/3 is equal to (223+2)/3 = 68/3

and 2 1/9 is equal to (29+1)/9 = 19/9

Now the expression become 5/34 x 68/3 - 19/9

We can now perform the operations:

5/34 x 68/3 - 19/9

= (568)/(343) - 19/9

= 340/102 - 19/9

Now we have to perform subtraction, for this we need to have a common denominator:

= (3409 - 19102)/(102*9)

= 2861/918

The solution is 2861/918 which can be simplified to 3 3/34

Step-by-step explanation:

Answer: 48.6 minutes

Step-by-step explanation:

First find the total square feet:

9 x 9 = 81

Next, divide this by the increments give:

81 / 75 = 1.08

Now, the increments were each 45 minutes, so multiply this by the product:

45 x 1.08 = 48.6

a. The probability that X is less than 95 is approximately 0.0668

b. The probability that X is between 95 and 97.5 is approximately 0.1359

c. The probability that X is above 102.2 is approximately 0.0228

d. The value of X for 65% chance is 99.23

We know, z=(X-mean)/ (S.D./sqrt N)

Thus, putting in the values for the respective cases, we get

(a) z value corresponding to X=95 is,

z=(95-100)/(10/sqrt 25)= -2.5

Therefore, required probability= area under the standard normal curve left to

z= -2.5 = 0.5000- 0.4938= 0.0062

(b) z value corresponding to X=95 is -2.5 and X=97.5 is,

z=(97.5-100)/(10/sqrt 25)= -1.25

Therefore, required probability= area under the standard normal between

z= -2.5 and z= -1.25= 0.4938- 0.3944= 0.0994

(c) z=(102.2-100)/(10/sqrt 25)= 1.1

Therefore, required probability= area under the standard normal curve right to

z= -2.5 = 0.5000- 0.3643= 0.1357

(d) 65%= 0.6500 is an area on the left side of the z value.

Or, we can say 35%= 0.3500 is on the right side of the z value.

therefore, the corresponding z value is -0.385 approximately.

Thus, for X value,

-0.385= (X-100)/(10/sqrt 25)

-0.385= (X-100)/2

-0.77= X-100

X= 99.23

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Price of gasoline is with Time:

The term "rate of change" (ROC) describes the rate which something alters over time.

For the stated graph.

Price of gasoline is fixed for Time: A , C, E, and G.

Price of gasoline is increasing rate for Time: D

Price of gasoline is decreasing rate for Time: B, and F

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The standard deviation of the data-set is given as follows:

2.24.

The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

The sum of the differences squared between each observation and the mean is given as follows:

4 x (6 - 9.28)² + 5 x (7 - 9.28)² + (8 - 9.28)² + 4 x (9 - 9.28)² + 5 x (10 - 9.28)² + 4 x (11 - 9.28)² + 6 x (12 - 9.28)² = 144.75.

Dividing by the number of values, we have that:

144.75/(4 + 5 + 1 + 4 + 5 + 4 + 6) = 5.

Taking the square root, the standard deviation is given as follows:

2.24.

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The expression is equal to f(x) g(x) is 77x⁷ + 78x⁶ - 27x⁵

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

In order to find which expression is equal to f(x) g(x), multiply (11x³ - 3x²) by (7x⁴ + 9x³). That is:

f(x) g(x) = (11x³ - 3x²)(7x⁴ + 9x³)

Expand the expression:

f(x) g(x) = 11x³ × 7x⁴ + 11x³ × 9x³ - 3x² × 7x⁴ - 3x² × 9x³

f(x) g(x) = 77x⁷ + 99x⁶ - 21x⁶ - 27x⁵

Combine like terms:

f(x) g(x) = 77x⁷ + 78x⁶ - 27x⁵

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Complete Question

Select the correct answer.

Consider functions f and g.

f(x) = 11x³ - 3x²

g(x) = 7x² + 9x³

Which expression is equal to f (x) g(x)?

A. 7x⁴ + 99x³ -3x²

B.77x¹² +99x⁹- 21x⁸ - 27x⁶

C. 18x⁷ + 10x⁶ + 6x⁵

D. 77x⁷ + 78x⁶ - 27x⁵

The value of the function is 5.33

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

f(x) = 1/3 * 4^x

To find f(2), we need to substitute x = 2 into the function f(x) = 1/3 * 4^x

f(x) = 1/3 * 4^x

f(2) = 1/3 * 4^2

f(2) = 1/3 * 16

f(2) = (1/3) * 16

f(2) = 16/3

f(2) = 5.33

So the value is f(2) = 5.33

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Part (a)

[tex]\lim_{h \to 0} \frac{(h-1)^5+1}{h} \\ \\ =\lim_{h \to 0} \frac{5(h-1)^4}{1} \\ \\ =\boxed{5}[/tex]

Part (b)

[tex]y+1=5(x+1) \\ \\ y+1=5x+5 \\ \\ \boxed{y=5x+4}[/tex]

Using the substitution method, we know that the values of A is 19,200.

The substitution method is typically used in mathematics to solve an equation system.

In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

So, we know that:

I = 240

W = I / 3

A = I * W

A = ?

Now, keep substituting the values to get A as follows:

I = 240

W = 240/3

W = 80

A = I * W

A = 240 * 80

A = 19,200

Therefore, using the substitution method, we know that the values of A is 19,200.

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To calculate the average (mean) value of a function, you need to find the area under the curve of the function, divide it by the interval over which the function is defined, and then find the value of the function at the midpoint of the interval.

In this case, the function is 3t³ - t² and we need to find an interval to calculate the average (mean) value. A common interval used for this calculation is from 0 to 1.

The area under the curve of the function from 0 to 1 can be found by integrating the function from 0 to 1. However, to keep it simple, we can also use the definite integral of the function from 0 to 1, which is:

∫ (3t³ - t²) dt = 3t⁴/4 - t³/3 | from 0 to 1

= (3/4) - (1/3) = 1/4

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is: 1/4 ÷ 1 = 1/4

And the value of the function at the midpoint of the interval, which is 0.5, is: 3(0.5) ³ - (0.5) ² = 3/8 - 1/4 = -1/32

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is -1/32.

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