2x _ 2 +9x _−5 . factor trinomials (a>1) level 2

The coordinates of point W which is equidistant from M and N ( 7, 1 / 2).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the points are M(3, 7) and N(11, -6). The coordinates of the midpoints are,

W = ( x₁ + x₂ ) / 2, ( y₁ + y₂ ) / 2

W = ( 3 + 11 ) / 2, ( 7 - 6 ) / 2

W = 14 / 2, 1 / 2

W = 7, 1 / 2

Hence, the value of the coordinate of the midpoint is ( 7, 1 / 2 ).

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Answer:

To find the quarterly rate of population increase, we first need to find the annual rate of population increase in decimal form, which is 2.8% expressed as 0.028.

To find the quarterly rate, we need to divide the annual rate by 4, since there are 4 quarters in a year:

0.028 / 4 = 0.007

Therefore, the quarterly rate of population increase is 0.007 or 0.7%

Answer:

Abc

Step-by-step explanation:

2b + c + 3a = Abc

The length of RT is 13 units

A triangle is a three-sided polygon that consists of three edges and three vertices.

As T is the centroid of the given triangle.

TN=TP

x+10=4x-17

Now solve for x

27=3x

x=9

Now TP=4(9)-17

TP=36-17

TP=19

Now from pythagoras theorem we find the length of RT

19²=14²+RT²

361-196=RT²

165=RT²

Take square root on both sides

RT=13

Hence, the length of RT is 13 units

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The missing value using concept of similar triangle ratio is; 35

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Using the concept of similar triangles on the given diagram, we have;

p/(30 + 20) = 14/20

p = (14 * 50)/20

p = 35

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The scale floor's perimeter is 34 inches.

To solve, we can set up fractions:

21/7 = 30/x

Cross multiply and you get:

21x = 210

Divide each side by 21:

x = 10

You can apply the following equation since you're attempting to determine the floor's perimeter:

2w + 2l = p

Substitute to solve:

2 ( width = 10 )

2 ( length = 7 )

2 (7) + 2 (10) = p

14 + 20 = p

34 = p

The complete question is:

The rectangular floor of a classroom is 21 feet in length and 30 feet in width. A scale drawing of the floor has a length of 7 inches. What is the perimeter, in inches, of the floor in the scale drawing?

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Answer:

-1.33333333333

Step-by-step explanation:

Answer:

-1 1/3

Step-by-step explanation:

Answer:

18.4 degrees

Step-by-step explanation:

a complementary angle is 90 degrees and 90 - 71.6 is 18.4. So, the answer is 18.4 degrees.

The difference in housing prices in the fifth year is $7,125.

Price is the amount of money one has to pay for goods or services. It is also the return on an investment or the cost of borrowing money. Price is determined by the supply and demand of a product or service. It is also influenced by market forces such as competition, production costs, and availability of resources. Price is a key factor in determining the success of a business, as it can affect consumers' buying decisions and profitability.

$M(5) - G(5) = (1.7(5)³- 6.5(5)²+ 212) - (1.6(5)²- 14(5) + 165) = $7,125
Therefore, the difference in housing prices in the fifth year is $7,125.

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Answer:

F (x)=-x^2

Step-by-step explanation:

The required five million four thousand three hundred in standard form is 5,004,300.

A number system is described as a technique of composing to represent digits. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the question, we are asked to write the word of the number five million four thousand three hundred in standard form.
So,
five million four thousand three hundred = 5,004,300
Since

1 million = 1000, 000
1 thousand = 1000
1 hundred = 100

Thus, the required five million four thousand three hundred in standard form is 5,004,300.

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The process of finding the value of a numerical or algebraic expression is called evaluation.

Evaluation involves substituting the given values of the variables in the expression and then simplifying the expression using the order of operations (PEMDAS).

For example, if we are asked to evaluate the expression 3x + 2y when x=4 and y=5, we would substitute these values to get 3(4) + 2(5), which simplifies to 12 + 10 = 22. Therefore, the value of the expression 3x + 2y when x=4 and y=5 is 22.

In algebra, evaluation is an important process because it allows us to find the value of an expression for specific values of the variables, which can help us to solve equations or inequalities, and to simplify expressions.

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The binary number will be equal to 14 in base 6

1001₂ = 14 (base 6)

Base is defined as a set of digits used to represent numbers. There are different number systems which make use of different combinations of digits as the base.

One of the most common which is the binary number system uses only 2 digits, i.e., 0 and 1 to represent numbers, while the Octal number system uses 8 digits, i.e., 0 to 7, to represent numbers.

The most common number system that is in use is the decimal number system that uses the base 10, which includes digits from 0 to 9 for writing numbers.

1001₂ = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

1001₂ = 1 x 8 + 1 x 1

1001₂ = 8 + 1

1001₂ = 9

Converting 9 into base 6

6 9

6 1 r 3

  0 r 1

From downwards pointing up

9 = 13 (base 6)

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Answer:

11 feet long

Step-by-step explanation:

20+20=40

62-40=22

22÷2=11

check

11+11+20+20=62

Answer:

g=4f-k+h

Step-by-step explanation:

f=g-h+k

4

4f=g-h+k

4f-k=g-h

4f-k+h=g

The probability P(red pen, purple pen) without replacement is 10/33.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that a container holds 5 red pens, 4 purple pens and 3 blue pens.

We need to find the probability P(red pen, purple pen) without replacement.

P(red pen, purple pen) = (number of ways to select a red pen and a purple pen) / (total number of ways to select two pens)

Total number of ways to select two pens=¹²C₂=66 ways.

Number of ways to select a red pen and a purple pen = (number of ways to select a red pen) x (number of ways to select a purple pen from the remaining pens)

Number of ways to select a red pen = 5

Number of ways to select a purple pen from the remaining pens = 4

Therefore, the number of ways to select a red pen and a purple pen without replacement is:

Number of ways to select a red pen and a purple pen = 5 x 4 = 20

P(red pen, purple pen) =20/66

=10/33

Hence, the probability P(red pen, purple pen) without replacement is 10/33.

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Answer:

32

Step-by-step explanation:

Substitute values given into the expression :

3[2(1)+(3)]-4[((1)-(3)]+(3)²

3[5]-(-8)+9

15+8+9 =

32

Hope this helped and have a good day

From the given information provided, the cube root of 12,167 by prime factorization method is approximately 23.

You can find the cube root of 12,167 using a calculator or by using the prime factorization method.

Using the prime factorization method, we can express 12,167 as the product of its prime factors:

12,167 = 19 × 641

Since the cube root of a product is equal to the product of the cube roots of the factors, we can find the cube root of 12,167 as follows:

∛12,167 = ∛(19 × 641)

∛12,167 = ∛19 × ∛641

∛12,167 = 2.7144 × 8.0186

∛12,167 = 23.1649 (rounded to four decimal places)

Therefore, the cube root of 12,167 is approximately 23.

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The original fraction described in the question is; 25/31

Let the numerator be x and let the denominator be y.

We are told that the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. Thus;

4x/(y - 2) = 4

4x = 4y - 8

4x - 4y = -8   -----(1)

The numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Thus;

(x + 15)/(2y - 2) = 5/4

4x + 60 = 10y - 10

4x - 10y = - 70   ----(2)

Subtract eq 2 from eq 1 to get;

6y = 62

y = 31/3

Thus;

4x - 4(31/3) = -8

Multiply through by 3 to get;

12x - 124 = -24

12x = 100

x = 25/3

Thus, the fraction is;

(25/3)/(31/3) = 25/31

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Answer:

-72

Step-by-step explanation:

Answer:

-72

Step-by-step explanation:

multiply-12 x3^2 and then add 36

The area of the basement will be 576 square feet.

The area is defined as the space covered by the object in a two-dimensional plane. The area of the rectangle is calculated by the multiplication of the length and the width.

Given that a basement floor plan for a house is being created by an architect. He drew the plans as they are seen. On the plan, one-fourth of an inch corresponds to four feet in the house.

The area of the basement will be calculated as:-

Area = 12 x 6

Area = 72 square inches

Area = 72 x 8 feet

Area = 576 square feet

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A) By using the change of base formula, the solution of the expression is,

⇒ x = - 2/3

B) The solution of the expression is,

⇒ x = - 2/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

Now, We have the change of base formula,

⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]

Here, The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

Take log on both side,

⇒ log 5³ˣ⁻² = log 5⁶ˣ

⇒ (3x - 2) log 5 = 6x log 5

⇒ 3x - 2 = 6x

⇒ - 2 = 6x - 3x

⇒ 3x = - 2

⇒ x = - 2/3

B) By using another method as;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

By comparing we get;

⇒ 3x - 2 = 6x

⇒ - 2 = 6x - 3x

⇒ 3x = - 2

⇒ x = - 2/3

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Answer:

Ann will owe $15,258.23 after 6 years, assuming she makes no payments.

What is Compound Interest ?

Compound interest is a method of calculating interest on a loan or investment, where interest is earned on both the initial principal amount and on any interest that has already been earned. In other words, interest is added to the principal, and then interest is calculated on the new total amount (the principal plus the previously earned interest). This results in the interest earned growing exponentially over time.

According t o given condition :

To calculate the amount Ann will owe after 6 years, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

where:

A = the amount Ann will owe after 6 years

P = the initial principal amount borrowed, which is $8000 in this case

r = the annual interest rate as a decimal, which is 15% or 0.15

n = the number of times interest is compounded per year, which is once annually in this case

t = the number of years, which is 6 in this case

Plugging in these values, we get:

A =

A =

A = $15,258.23

Therefore, Ann will owe $15,258.23 after 6 years, assuming she makes no payments.

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The x-intercept and the y-intercept of the line 5x - 2y = 10 include the following ordered pairs:

x-intercept = (2, 0).

y-intercept = (0, -5).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value (base value) and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

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Answer:

Infinitely Many

Step-by-step explanation:

Both answer are equal to each other

The system of inequalities is.

x + y ≤ 20

x*7.5 +  y*6 ≥ 90

And some solutions can be:

(10, 5)

(11, 5)

(12, 6)

Let's define the variables we will be using:

x = number of hours dog-waling

y = number of hours at the car wash.

We know that you can work at most 20 hours, then:

x + y ≥ 20

And you need toearn at least $90, then wecan write:

x*7.5 +  y*6 ≥ 90

The system of inequlities is:

x + y ≤ 20

x*7.5 +  y*6 ≥ 90

And the graph is the one below. The solutions are all the points in the dark blue region, some solutions we can see there are:

(10, 5)

(11, 5)

(12, 6)

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a) There are 36 sample points that are possible.

b) The probability of obtaining a value of 7 is 1/12.

c) The probability of obtaining a value of 8 or greater is 1/6.

(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.

(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.

(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.

Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.

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Answer:

(2.4, 2)

(4, -3.4)

Step-by-step explanation:

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Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer.

The equation is typically written in algebraic form and includes numerical values.Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer. For example, if an individual is asked to verify the identity [tex]sin^2x + cos^2x[/tex]= 1, they will be given numerical values to plug into the equation. For example, if they are given x = 60, they would enter[tex](sin60)^2 + (cos60)^2[/tex] into the calculator and solve. This should result in an answer of 1, proving the equation is accurate.

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The shape with two pairs of parallel sides is called a parallelogram.

A parallelogram is a shape that has four sides, in which the two opposite lengths are:

As there are four sides, divided two by two, the shape has two pairs of parallel sides, and is called a parallelogram.

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