Factorize the expression, 10ab (a − 2b)³ +24ab² (3a − 6b)²

A rational function is the algebraic expression y = 2 / x. (Correct choice: A)

Rational functions are algebraic expressions, whose form is described below:

R(x) = P(x) / Q(x)

Where:

Please notice that Q(x) must be a polynomial whose grade is greater than zero.

Polynomials are algebraic expressions of the form:

P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.

Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.

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Answer:

343.2

Step-by-step explanation:

156 × 2.2

= (156 × 22)/10

= 3432/10

= 343.2

Answer:

I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!

Check the picture below.

From the inventory ratios of  24 8, 33.4 and 53.8 of  Dunn and Bradstreet report. It can be concluded that

The problem is seeking expression of ratios in percentage

Ratios represents part or share of a whole while percentage refers to a fraction of hundred

Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up

= 24 8 + 33.4 + 53.8

= 108

Expressing as ratio 53.8 a percentage, we have

= 53.8/108 * 100

= 0.4981 * 100

= 49.81%

approximately 50%

We can therefore say that inventory of 53.8 or more is 50%

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Answer:

Other words for subtraction:

taking away

withdrawal

abstraction

removal

discounting

Step-by-step explanation:

Answer:

45 cars

Step-by-step explanation:

115+365+(55*5) = 755

755 - 485 =270

270/6 = 45

Answer:

To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.

The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.

The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:

Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)

Plugging in the given values, we have:

Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16

The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.

The balance of the PLUS loan at the time of repayment can be calculated using the same formula:

Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54

Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.

Step-by-step explanation:

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5² + 7 - 3 + 4

Simplify the expression, then we have

⇒ 5² + 7 - 3 + 4

⇒ 25 + 7 - 3 + 4

⇒ 36 - 3

⇒ 33

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

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Answer:c=35

Step-by-step explanation:

i just did this

Answer:

[tex]A=9\pi cm^{2}[/tex][tex]=28.27cm^{2}[/tex]

Step-by-step explanation:

If  BC= 6

then r = BC/2 = 6/2 = 3cm

[tex]A=\pi r^{2} =\pi (3)^{2} =9\pi[/tex]

[tex]A=28.27cm^{2}[/tex]

Hope this helps

Answer:

a and c are both congruent to each other i just learned about rhombuses the other day so if a and c are congruent then b and d are congruent too

Answer: $272

Step-by-step explanation: you would multiply 250 * 0.022 = 5.5

then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272

The product of 5 and 14 using the distributive property is 70.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

For three numbers a, b and c, Distributive property states that,

a (b + c) = a b + a c

We have to find the product 5 × 14 using distributive property.

5 × 14 = 5 (12 + 2)

Using distributive property,

5 × 14 = (5 × 12) + (5 × 2)

          = 60 + 10

          = 70

Hence using distributive property, we can find the product of 5 and 14 as 70.

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Answer:

102200

Step-by-step explanation:

564+458= 1022

1 decagram=100 decigram

So multiply the sum by 100

1022*100=102200

Answer:
3(y^2 + 1) + 2(y+4)

Step-by-step explanation:

2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
= 2y^2 + y^2 + 6y - 4y + 8.9 - 8.6
= 3y^2 + 2y + 8(9-6)
= 3y^2 + 2y + 24
= 3y^2 + 2y + 3.2.2.2
= 3(y^2 + 1) + 2(y+4)

Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way

Here,

Given :  complementary angle one of the angle is 35°

=>  x+ 35° = 90°

=> x = 55°

Let y be the supplement of angle x

=> x+ y = 180°

=>55° + y =180°

=>y =125°

Therefore , the solution of the given problem of angle comes out to be

x = 55° and y =125°.

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Answer:

highest 77 and lowest is 4

On solving the question, we can say that y using the given information we can prove that similar angle m ∠ABC = m ∠EDC.

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

∠EDC = ∠3 + ∠4

m ∠ABC = m ∠1 + m ∠2

m ∠EDC = m ∠3 + m ∠4

m ∠1 + m ∠2 = m ∠3 + m ∠4      

m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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Answer:

The probability of drawing a bag with bad potatoes is less than 1. True

The probability of drawing a bag with good potatoes is greater than 0. True

What is the probability of drawing a bag with bad potatoes?

The probability of drawing a bag with bad potatoes is (2 bad bags) / (20 total bags) = 0.1 or 10%.

What is the expected probability of the complement of the event?

The complement of the event of drawing a bag with bad potatoes is drawing a bag with good potatoes. The probability of drawing a bag with good potatoes is (18 good bags) / (20 total bags) = 0.9 or 90%.

Uday Tahlan

Answer:

A sample of helium was compressed at 35 °C from a volume of 0.5 L

to 0.25 L where the pressure is 500 mmHg. What was the original pressure?

Step-by-step explanation:

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).

Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:

F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)

We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:

105 = (R + F) * 3

Now we can substitute the first equation into the second equation:

105 = (R + (R + 5)) * 3

Simplifying and solving for R, we get:

R = 20 mph

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).

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1) Note that in the problem above, the complete table is given as:

Team Number:     1             2      3           4           5

Best Jump (ft)       20.6    21.5    20.9      19.4        20.2

2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.

3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.

Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.

The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.

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The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that,

The function g(x).

The graph of a function never touches the x = 1 line

At x = -1 there will be a vertical asymptote.

At x = -2 there will be a horizontal asymptote.

The equation of the function g(x) will be:

g(x) = (2x + 4)/(x + 1)

The equation of rational function is g(x) = (2x + 4)/(x + 1)

Therefore,  g(x) = (2x + 4)/(x + 1) is correct.

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Answer:

The probability of the event is 1. False

The probability of the event is 0. False

What is the expected probability of this event?

The probability of the event is (500 million successful events) / (3 billion total repetitions) = 0.1667 or 16.67%.

What is the expected probability of the complement of the event?

The complement of the event is the event not happening. The probability of the event not happening is (3 billion total repetitions - 500 million successful events) / (3 billion total repetitions) = 0.8333 or 83.33%.

Uday Tahlan

The length of AB in the line segment is 21 units.

A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.

Therefore, let's find the length AB, in the line segment AC.

Hence,

AC = AB + BC

AC = 23

AB = 2x + 7

BC = 3x - 19

Therefore,

23 = 2x + 7 + 3x - 19

23 = 5x  - 12

23 + 12 = 5x

35 = 5x

divide both sides by 5

x = 35 / 5

x = 7

Therefore,

AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21

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Answer:

y-int = 0

slope = -1

equation: y = -x

Step-by-step explanation:

The line crosses the y-axis at y = 0, so the y-intercept is 0.

Go from (0, 0) to (-1, 1).

slope = m = rise/run = 1/(-1) = -1

y = mx + b

y = -x

y-int = 0

slope = -1

equation: y = -x

The values of A and B are 2 and 4 respectively.

Given is the equation as -

(x + A)² - 3 = x² + 4x + B

We can write the given equation as -

(x + A)² - 3 = x² + 4x + B

x² + A² + 2Ax = x² + 4x + B

A² + 2Ax = 4x + B

A² + 2Ax = B + 4x

Equating both sides, we get -

A² = B

and

2A = 4

A = 2

Then B will be equivalent to 4.

B = 4

Therefore, the values of A and B are 2 and 4 respectively.

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when f(x)=4, then the value of x is 2

A relation is a function if it has only One y-value for each x-value.

Given that A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs:

The ordered pairs are (2, 4), (-3, 0), (- 1, -1), (4, 3)

We need to find value of x when f(x)=4

In the (x, y) ordered pair the x place represents the domain value and y place represents the range.

In the order pairs we have to look for the y value which has 4.

The corresponding element of 4 is the x value

So the value of x is 2 if f(x)=4

Hence, when f(x)=4, then the value of x is 2

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