P = 3x 2+7x + 8, Q= 2x 2+x-9 and R= -5x 2-8x+1, Show that P+Q+R= 0

The value of a  is 4 , b is 2 and c = -3 after factorising 8t² - 14t + 3

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number.

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.

The function is 8t² - 14t + 3

so factorising :

8t² - 14t + 3 = 8t² - 12 t - 2t + 3 = 4t(2t - 3) - (2t - 3)

= (4t - 1)(2t -3)

The value of a  is 4 , b is 2 and c = -3

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The future value is $7,689,500.

The worth of a current asset at a future date based on an estimated rate of growth is known as future value (FV). Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future.

The future value formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment.

Given that,

P = 3500

R = 12%

T = 3 years

Future value (FV) = [tex]I*(1+R)^{T}[/tex]

where:

I=Investment amount

R=Interest rate

T=Number of years

Substituting the values in the formula given:

FV = 3500*(1+12)³= 3500*2197 = 7689500

Thus, the future value is $7689500

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The number that should be added to the expression x²+4x to change it into a perfect square trinomial is 4.

The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.

It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.

Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.

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Complete Question: –

What will make the expression x²+4x a perfect square trinomial?

Answer:

f(-2) = -6

Step-by-step explanation:

f(x)=2x^2+7x        f(-2)

We put -2 in for x and solve

f(-2) = 2(-2)^2 + 7(-2)

f(-2) = 2(4) - 14

f(-2) = 8 - 14

f(-2) = -6

Pedro is initially 700 ft higher than Naomi  

Pedro decended at a greater speed and it was 800 ft/ hr

Pedro reaches the bootom faster than Naomi.

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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

Equations can be divided into three categories based on their degree. The three categories of mathematical equations are as follows:

Linear Equations

Quadratic Equations

Cubic Equations

Pedro's Elevation in feet equation

E = 4200 - 800h

So, initial elevation at h = 0 is

E = 4200 ft for Pedro

Now Naomi's Initial Elevation is 3500 ft.      

So, Pedro is 4200 - 3500 = 700 ft higher than Naomi                                            

at h = 1hr

Pedro's Elevation = 4200 - 800*1 = 3400 ft

and Naomi's Elevation = 2900 ft

Speed of desending of Pedro is = total distance/ total time

= (4200 - 3400)/1 = 800 ft/hr

Speed of desending of Naomi is = total distance/ total time

(3500 - 2900)/1 = 600 ft/hr

For Elevation = 0 for Pedro

0 = 4200 - 800h

h = 4200/800 = 5.25 hr

Naomi's elevation when time is 5.5 is 200 ft  

So, Pedro reaches the bootom faster than Naomi.

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A table gives the pairs input-output generated by the function.

We can define a general function as:

y = f(x)

where x is the input that we "feed" into the function, and the function gives y as the outcome.

A pair of input, output is written in a general form as (x, y).

If you have enough of these points, you can make a table:

inputs    outputs

x₁               y₁

x₂               y₂

x₃              y₃

...

That means that:

f(x₁) = y₁

f(x₂) = y₂

etc...

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Answer: 16%

Step-by-step explanation: If 80% of customers purchased regular gas and 10% of those who purchased regular gas paid in cash, then 8% paid in cash. If 100-80=20% of customers purchased something other than regular gas and 40% of those who did paid in cash, than another 8% paid in cash. 8+8=16, so (c 16 is the answer.

The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.

Let L be a giant dog and s be a tiny dog. What we do know is this:

s + L = 9 (9 dogs walked) (9 dogs walked)

(Money received from walking dogs is $51; 5s + 8L = 51)

To address a problem, we can employ substitution or elimination. I'll substitute in this situation (remove L from both sides):

s = 9 - L

5(9 - L) + 8L = 51

Distribute

45 - 5L + 8L = 51

45 + 3L = 51

Subtract 45:

3L = 6

Divide by 3:

L = 2

s = 9 - 2

s = 7

check:

5 * 7 + 8 * 2 = 51

35 + 16 = 51

51 = 51

The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.

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It would cost $224 to buy 56 party favors.

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.

If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.

we get, 56 * 4 = $224

Thus, it would cost $224 to buy 56 party favors.

Complete question: Football party favors come in packages like the one shown. How much would it cost to buy 56 party favors? Think about how you can model with math to help solve the problem. It's $4 per package.

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Answer:

a₄ = 67

Step-by-step explanation:

the recursive rule allows a term to be found from the previous term

using the recursive rule

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] - 2 , then

a₁ = - 3

a₂ = - 3a₁ - 2 = - 3(- 3) - 2 = 9 - 2 = 7

a₃ = - 3a₂ - 2 = - 3(7) - 2 = - 21 - 2 = - 23

a₄ = - 3a₃ - 2 = - 3(- 23) - 2 = 69 - 2 = 67

For the equation -6x + 3y = -7 , the x-intercept and y-intercept is obtained as (1.167,0) and (0,-2.333) respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

-6x + 3y = -7

To find the x-intercept, substitute the value of y = 0.

-6x + 3(0) = -7

-6x + 0 = -7

-6x = -7

Use the arithmetic operation of division -

x = -7/-6

x = 1.167

To find the y-intercept, substitute the value of x = 0.

-6(0) + 3y = -7

0 + 3y = -7

3y = -7

Use the arithmetic operation of division -

y = -7/3

y = -2.333

So, the x-intercept is obtained as x = 1.167 and y-intercept is obtained as  y = -2.333.

A graph can also be plotted to find the intercepts.

Therefore, the intercepts are x = 1.167 and y = -2.333.

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Answer: Goran will run at most 27 miles this week, and he has already run 13 miles, so the number of additional miles he will run is given by the difference of 27 - 13 = T.

Therefore, T = 27 - 13 = 14 miles

We can express this as an inequality:

T <= 14

This inequality represents that T, the number of additional miles he will run, can be any number less than or equal to 14.

Another way to express this is T <= 27-13

So the possible numbers of additional miles he will run are T <= 14.

Step-by-step explanation:

If the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.

Triangles with the same form but different sizes are referred to as comparable triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.

If two triangles have an equal number of corresponding sides and corresponding angles, they can be compared. Similar figures are objects that have the same shape but various sizes, like two or more figures.

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For x^2 * 5x to end in 5, x must be an odd number.

The last digit of a number is determined by its units digit. For example, the last digit of 123 is 3, the last digit of 789 is 9, and so on.

When you multiply two numbers, the last digit of the product is determined by the last digit of each factor. For example, the last digit of 3 * 4 is 2, the last digit of 6 * 7 is 2, and so on.

In this case, x^2 * 5x is a product of two numbers, x^2 and 5x. To find the units digit of x^2, we can square the units digit of x. The units digit of 5x is the units digit of x.

So, since we want x^2 * 5x to end in 5 , the last digit of x^2 * 5x has to be 5. The last digit of x^2 is the square of the last digit of x, and the last digit of 5x is 5 if x is odd and 0 if x is even.

--The question is not readable, answering to the question below--

"For what value of (x^2) * 5x ends in 5?"

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Answer:

The point is in the second quadrant.

Substitute 6 for r.

The value of y is approximately 5.196.

Step-by-step explanation:

To convert polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

The point is in the second quadrant.

-This statement is true because the polar angle (120°) is in the range of 90° < θ < 180° which correspond to the second quadrant in the cartesian plane.

Start by adding 180° to θ.

This statement is False, because when converting from polar coordinates to rectangular coordinates we don't need to add 180° to the angle, we use the given angle as it is.

Substitute 6 for r.

This statement is true. In this case, the given polar coordinates are (6, 120°), so we substitute 6 for r in the formulas.

The value of x is 3.

This statement is False, to calculate x we use the formula x = r * cos(θ), so in this case x = 6 * cos(120°) = -3, which is not equal to 3.

The value of y is approximately 5.196.

This statement is true, to calculate y we use the formula y = r * sin(θ), so in this case y = 6 * sin(120°) = 6 * 0.866 = 5.196, which is approximately equal to 5.196

Answer:

The point is in the second quadrant

Step-by-step explanation:

The multiplication rule example is calculating the probability that both the balls drawn are red from an urn containing 30 red and 10 blue balls. Two balls are pulled from a bag one after the other without replacement.

As per the multiplication rule, the probability of events A and B happening is equal to the product of the probability of B happening and the conditional probability that event A happens if event B occurs.

If A and B are dependent events, then the probability of both events happening simultaneously is given by:

P(A ∩ B) = P(B).P(A|B)

If A and B are two independent events in an experiment, then the probability of both events happening simultaneously is given by:

P(A ∩ B) = P(A).P(B)

Let's solve our given example

Let A and B represent the events that the first and the second balls are pulled, which are red balls. Now, we have to calculate P(A∩B) or P(AB).

P(A) = P(red balls in first draw) = 30/40

Now, only 10 balls of blue colour and 29 balls of red colour are left in the bag. The probability of pulling a red ball in the second draw is also an example of conditional probability, where the drawing of the second ball depends on the drawing of the first ball.

Hence Conditional probability of B on A will be,

P(B|A) = 29/39

By multiplication rule of probability,

P(A∩B) = P(A) × P(B|A)

P(A ∩ B) = 30/40 × 29/39 = 29/52

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The number 48.050 has five significant figures.

What do you mean by an Significant figures?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Significant figures, also known as significant digits, are the digits in a measurement or a number that carry meaning contributing to its precision. In this case, the number 48.050 has four non-zero digits (4,8,0,5) and one zero (0) between two non-zero digits, which are significant figures.

The trailing zero after the decimal point does not affect the significant figures, it is simply a placeholder to indicate the number is less than one and has a magnitude of 0.050.

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The number of miles that the crew has left to lay after 19 days is given as follows:

54 miles.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The parameters for this problem are given as follows:

m = -6, b = 168.

Hence the function is:

y = -6x + 168.

The amount of miles left after 19 days is obtained as follows:

y = -6(19) + 168

y = 54 miles.

The text of the problem is:

"A railroad crew can lay 6 miles of track each day. They need to lay  168 miles of track. "

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The numbers are 2 and 4.

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers. It tells us by how much a number differs from the other.

Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.

Here we have,

The difference in two numbers is 2.

2 and 4 are two numbers away from each other.

The sum of the same two numbers is 6.

2+4=6

Hence, In least to greatest order they would be written 2, 4.

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The Sum of 4 is a concept that emphasizes the fact that there are multiple, if not infinite, ways to reach certain results, goals, dreams, or destinations.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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Step-by-step explanation:

First you show that the triangles are congruent.

Then you show that the segments are congruent by CPCTC (Corresponding parts of congruent triangles are congruent.)

Given:

Segment KM is congruent to segment JM

<L is congruent to <H

We now have 1 pair of sides and 1 pair of angles that are congruent.

Angles KML and JMH are vertical angles, so they are congruent.

Now we have 2 pairs of congruent angles and 1 pair of not included congruent sides.

By AAS, triangle KML is congruent to triangle JMH.

By CPCTC, segment KL is congruent to segment HJ.

27m^3-64 = (3m)^3 - (4)^3

= (3m-4)((3m)^2 + (3m)(4) + (4)^2)

= (3m-4)(9m^2 + 12m + 16)

The factored form of 27m^3-64 is (3m-4)(9m^2 + 12m + 16)

Answer:

(3m−4)(9m2+12m+16)

Step-by-step explanation:

this is difference of cubes (3m)^3 - (4)^3

now, apply difference of cubes formula

a^3−b^3 = (a−b)(a2+ab+b2)

where a=3m and b=4

(3m−4) ( (3)^2×(m)^2 + 4×3m + (4)^2)

(simplify)

(3m−4)(9m2+12m+16)

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles.

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles. Then, we have to check the proportionality of the sides. If these triangles are equal, then VT/QR=UT/RS. If we calculate it, 28/7=44/11=4. This last number is the similarity ratio and since we have proportionality, ΔQRS ~ ΔVTU.

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Answer:

G to the power of 5

Step-by-step explanation:

Since there are 5 Gs, the exponent would be 5

Answer: [tex]G^5[/tex]

Step-by-step explanation: G times G times G times G times G is G times itself 5 times, which can be rewritten as [tex]G^5[/tex]

Answer:36/(x+3)^2*(x-3)^2

Step-by-step explanation:

Step-by-step explanation:

1) 2t + 5t + 2 = 0

Add 2t + 5t = (2+5)t = 7t

7t + 2 = 0

Substract 2 from both sides

7t + 2 - 2 = 0 - 2

7t = -2

Divide both sides by 7

7t/7 = -2/7

[tex] \sf \: t = \frac{ - 2}{7} [/tex]

[tex] \sf --------------------------------------------[/tex]

Y+2y+1=25

3y + 1 = 25

3y = 25 - 1

3y = 24

y = 24/3

y = 8

[tex] \sf --------------------------------------------[/tex]

9−36x=36x2

Step 1: Simplify both sides of the equation.

−36x+9=36x2

Step 2: Subtract 36x^2 from both sides.

−36x+9−36x2=36x2−36x2

−36x2−36x+9=0

For this equation: a=-36, b=-36, c=9

−36x2+−36x+9=0

Step 3: Use quadratic formula with a=-36, b=-36, c=9.

x=

−b±√b2−4ac/2a

x=−(−36)±√(−36)2−4(−36)(9)/2(−36)

x=36±√2592/−72

x=−1/2 + −1/2√2 or x=−1/2 + 1/2√2

A correct description of the transformation include the following: D. translation 10 units left and 4 units down.

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.

By translating the pre-image of triangle ABC vertically down by 4 units and horizontally left by 10 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 10, y - 4)

Coordinate A = (5, 2)   →    Coordinate A' (5 - 10, 2 - 4) = (-5, -2)

Coordinate B = (6, 1)   →    Coordinate B' = (6 - 10, 1 - 4) = (-4, -3)

Coordinate C = (4, 5)   →     Coordinate C' = (4 - 10, 5 - 4) = (-6, 1)

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Complete Question:

The table below shows the coordinates of a figure that was transformed.

Pre-Image Image

A(5,2) A'(-5,-2)

B(6,1) B'(-4,-3)

C(4,5) C'(-6, 1)

Which is a correct description of the transformation?

Question 4 options: Rotation 180° clockwise B. Reflection over the x-axis. Translation 5 units left and 2 units down. Translation 10 units left and 4 units down.

Answer:

Equation 1: (500×5)+75

Equation 2: (20×5)×7

Total Revenue: $1,875

Step-by-step explanation:

For equation 1 we multiply the companys $500 an hour flat rate by the number of hours the party was (5), then add the company's $75 set up fee for a total of $2,575.

For equation 2 we multiply the company's hourly pay (20) by the number of hours worked (5), after that we multiply the number of employees (7) for a total of $700.

Finally to figure out the actual revenue from the event we subtract the amount the company paid the employees ($700) from the total paycheck for hosting the party ($2,575) for a final total of $1,875.

The Nature Of roots of quadratic equation "x² + 5x - 14 = 0 " is , that the roots are real and distinct .

In order to find the Nature of Roots of a quadratic equation , we use the Discriminant ,

Suppose the quadratic is given by : ax² + bx + c = 0 ,

then it's discriminant(D) will be written as :  D = b² - 4ac,

The equation is given as : x² + 5x - 14 = 0 ;

On comparing it with the general equation , we get that ;

⇒ a = 1 , b = 5 and c = -14 .

On substituting the values ,

we get ,  D = 5² - 4(1)(-14) ;

⇒  D = 25 + 56 ;

⇒ D = 81 .

We see that the Discriminant (D) is greater than 0 , the roots will be Real and Distinct .

Therefore , the nature of roots is that they are Real and Distinct .

The given question is incomplete , the complete question is

What is the nature of roots of quadratic equation x² + 5x - 14 = 0 ?

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The value of x that makes both triangles congruent is x = -1 and x = 5

An equation is an expression showing the relationship between numbers and variables.

Two triangles are congruent if their corresponding sides are equal to each other and their angles are also equal.

Since triangle ABC is congruent to DEF, hence:

BC = EF

Substituting:

4x - 2 = x² - 7

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x(x - 5) + 1(x - 5) = 0

(x + 1)(x - 5) = 0

x = -1 and x = 5

The value of x is x = -1 and x = 5

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