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Expression: x² - 6x + 9

Factored form: (x - 3)²

Using the concept of factorization.

The breaking or breakdown of an entity (such as an integer, a matrix, or even a polynomial) into such a combination of some other unit, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

Similarly to this, factoring is a very useful technique in algebra that is utilized at all levels. Additionally, to, of course, simplify complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

Factor the expression, put each factor equal to 0, and then solve each equation to solve a quadratic equation by factoring. To do this, rearrange all terms on one side of the equation such the other side equals 0.

Given that,

x² - 6x

Now, to find the value of c = (b/2)²

divide the coefficient of x by 2.

So, divide 6 by 2 we get: ( -1.3)²

Next, multiply -1 by 3: (-3)²

Now, raise -3 to the power of 2, we get: 9

So, the expression becomes: x² - 6x + 9

Factorized form: (x - 3) (x -3)

or we can write (x - 3)²

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Answer:

The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level. Shuttles format (e.g. 9.5). The maximum laps on the PACER test is 247, which former Central Middle School student Dennis Mejia achieved, the only person to ever reach such a level.

Step-by-step explanation:

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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Their Customer Acquisition cost was $10

Customer Acquisition Cost is the cost of winning a customer to purchase a product or service. As an important unit economic, customer acquisition costs are often related to customer lifetime value. Customer acquisition cost can also be referred as the fee associated with convincing a customer to buy your product or service.

To calculate customer acquisition cost

Customer Acquisition Cost (CAC) = Customer Acquisition Cost/total marketing cost

From the question,

The business gained 50+100+150= 300 new customers

Campaign budget = $30000

Customer Acquisition Cost (CAC) = $3000/300

=$10

Hence, it cost the business $10 to acquire a new customer

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The profits last year were $2041.66

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900

                            x=4900/2.4

                            x=2041.66

Hence, The profits last year were $2041.66

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Answer:

0.05 US$=1 sar

then,1 US$=1/0.05 sar.

The percentage of people aged 20 to 34 that  have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%

Percentage simply means a proportion of the number as a fraction of 100

What percent of people aged 20 to 34 have IQs between 125 and 150?

Let X = Scores on the standard IQ test for the 20 to 34 age group

This implies that  X ~ Normal(x=110, б² = 25)

The z-score probability distribution for the normal distribution is given by;   Z  =   (x-ц)/б ~ N(0,1)

Recall that  population mean = 110 and standard deviation = 25

Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X  125)

 P(X < 150) = P(  <  ) = P(Z < 1.60) = 0.9452

 P(X  125) = P(    ) = P(Z  0.60) = 0.7258

The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.

Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%

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The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410

An arithmetic progression is when the difference between each phrase that follows another in a sequence is always the same. For instance, the sequence 5, 7, 9, 11, 13, and 15 is an example of an arithmetic progression with a 2 tolerance. A progression having a set tolerance between any two consecutive numbers is known as a "arithmetic progression" (A.P.). Two alternative types of mathematical progression exist: finite-length mathematical series A series that has a limited number of terms is a finite geometric progression. One may calculate the early, late, tolerance, and number of terms in a series using the terms in the series.

given

1) n6 = 6  where a = 5 and d = 5 = 105

2)n6 =6 where a = 9 and d = 12 = 234

3) n5= 5 where a = 5.7 and d = 1.4 = 42.5

4) a = 20 and  t₂₁ = 400 ,

= 380

Therefore, Sum of 21 terms =  4410

5) In series  a = 0 and t₁₀₀ =  99  = 4950

The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410

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Suppose we want to choose 6 letters with out replacement from 13 distinct letters.

a. The number of  ways this be done if the order of the choices is not relevant is   1,235,520  ways.

b.  The number of  ways this be done if the order of the choices is relevant is 1716 ways.

a. Number of ways if choice are not relevant

[tex]^nP_r = n!/ (n-r)![/tex]

Where:

n =13

r = 6

So,

[tex]^1^3P_6[/tex] = 13! / (13 - 6)!

[tex]^1^3P_6[/tex] =6,227,020,800 /7!

[tex]^1^3P_6[/tex] =6,227,020,800/5,040

[tex]^1^3P_6[/tex] =  1,235,520 ways

b. Number of ways if choice are relevant

[tex]^nC_r =n!/ r! (n-r)![/tex]

[tex]^1^3C_6[/tex] = 13! / 6!(13-6)!

[tex]^1^3C_6[/tex] = 13! / 6! × 7!

[tex]^1^3C_6[/tex] =6,227,020,800 / 720×5040

[tex]^1^3C_6[/tex] =6,227,020,800 / 3,628,800

[tex]^1^3C_6[/tex] = 1,716 ways

Therefore the number of ways are 1,235,520 ways  and 1,716 ways.

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The trigonometric functions are sin A = 12/13, sin B = 5/13, cos A = 5/13, cos B = 12/13, tan A = 12/5, and tan B = 5/12 as fractions.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin A = BC/AB

sin A = 12/13

sin B = AC/AB

sin B = 5/13

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos A = AC/AB

cos A = 5/13

cos B = BC/AB

cos B = 12/13

Apply the tangent ratio on the given right triangle

⇒ sin(θ) = Perpendicular/Base

tan A = BC/AC

tan A = 12/5

tan B = AC/BC

tan B = 5/12

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The number of years until the book value of the boat is $ 48, 000, can be found to be 2 years

To find the number of years till the book value of the boat is $ 48, 000, you first need to find the depreciation rate per year by the formula :

= ( Purchase price of boat - Resale value ) / Useful life

= ( 51, 000 - 42, 000 ) / 6

= 9, 000 / 6 years

= $ 1, 500 per year

In the first year, the value of the boat would depreciate to:

= 51, 000 - 1, 500

= $ 49, 500

In the second year, the value would depreciate to:

= 49, 500 - 1, 500

= $ 48, 000

It therefore takes 2 years for the book value to be $ 48, 000.

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Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet

Step-by-step explanation:

1 / 6 = 0.166666667 yards

1 yard = 0.9144 meters

0.9144 / 6 = 0.1524 meters

1 yard = 3 feet

3 / 6 = 0.5 feet

Answer:

Step-by-step explanation:

As she is baking cookies = 3/20

she egave it to her neigbour = 7/20

Remaining = ?

R = 3/20 -7/20 = -1/5

Due to the fact that element 1 relates to two distinct images, namely 3 and 5. The relationship hence is not a function.

Therefore,

(i) {(2,1),(5,1),(8,1),(11,1),(14,1),(17,1)

Every input has a single output, proving that it is a function.

The elements in the domain of the provided relation are therefore 2,5,8,11,14, and 17.

Here, domain is equal to two and range is one.

(ii) (2,1),(4,2),(6,3),(8,4),(10,5)(12,6),(14,7)

Every input has a single output, proving that it is a function.

Therefore, 2, 4, 6, 8, 10, 12, and 14 make up the domain of the provided relation.

Here, range is 1,2,3,4,5,6,7 and domain is 2,4,6,8,10,12,14.

(iii) (1,3),(1,5),(2,5)

Due to the fact that element 1 relates to two distinct images, namely 3 and 5. The relationship hence is not a function.

The complete question is:

Which of the following relations are functions? Give reasons.

If it is a function determine its domain and range

(i) (2,1),(5,1),(8,1),(11,1),(14,1),(17,1)

(ii) {(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7)

(iii) {(1,3),(1,5),(2,5)

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Therefore , the solution of the given problem of equation comes out to be  x = 38.

Equivalent is the meaning of the Latin term equ. A lot of variable words in the English language, such as adequate, equator, and equality, have Latin roots as their root words. Since both side of an equations are, by definition, "equal" to one another, the Latin root term equ makes its way into our vocabulary quite simply.

Here,

Given : m m/MTU = 38°, and m/STU = 2x + 88.

thus,

x + 50 = 2x + 88

To find the value of x:

We do,

=> x + 50 = 2x +88

=> x -2x  = 88 -50

=> -x = -38

=> x = 38

Therefore , the solution of the given problem of equation comes out to be x = 38.

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The  largest amount of money they can borrow is $$276.268.65

The main formula used in this problem is the Present Value of an annuity Formula:

P = R[1-(1+i)⁻ⁿ]/i

Where;

The maximal monthly payment that Bethany and Samuel can afford is $1,500.

The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.

This implies that

R=1,500

t=30

r=%5.1 = 5.1 /100 = 0.051

m=12, because they make the payments monthly

i=r/m=0.051/12=0.00425

n=mt = 12*30=360

That is,

i) they will make 360 monthly payments,

ii) the largest amount of money they can borrow can be found using the formula:

P = R[1-(1+i)⁻ⁿ]/i

Substituting the known values:

P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425

Therefore, $276.268.65 is the largest possible principal for the situation

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I think it's 84 I'm not good with math though I multipled 7 and 12

The simple interest for principal of 640 and rate of 3% and time of 2 years is $3.84

The Simple interest the end of 2 years is calculated using the simple interest formula

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $640

rate= 3%

time = 2 years

plugging in the values

Simple interest = Principal *  time *  rate / 100

Simple interest = 640 * 2 * 3 /100

Simple interest = 3840 / 100

Simple interest = $3.84

The simple interest  is $3.84

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Answer:

P = 59/5

Step-by-step explanation:

Answer:

Monday??????

SteP-by-step explanation:

The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).

The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.

First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.

Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).

Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.

Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).

Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:

a + 3b = 0

b = 0

-a = 0

Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.

Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).

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Answer:

60cm

Step-by-step explanation:

given:

focal length (f) = 20cm

image height (v) = ½u

object height (u) = ?

(1÷v) + (1÷u) = (1÷20)

(1÷(½u)) + (1÷u) = (1÷20)

(2÷u) + (1÷u) = (1÷20)

(3÷u) = (1÷20)

u = 20 × 3

u = 60cm

Answer:

The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.

Step-by-step explanation:

hope it helps

Answer:

588 inches

Step-by-step explanation:

First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7

7 inches/ft

Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588

588 inches

To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .

y=|x-10|-3

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Answer:

  14

Step-by-step explanation:

You want to know the size of the universal set if ...

The given sets are mutually exclusive and exhaustive, so the sum of their sizes is the size of the universal set:

  n(u) = 3 + 4 + 7

  n(u) = 14

__

Additional comment

  (r'∩s') ∪ (r'∩s) = r'∩(s' ∪ s) = r' . . . . n(r') = 3

  (r∩s) ∪ (r∩s') = r∩(s ∪ s') = r . . . . . . n(r) = 4 +7 = 11

Then r' ∪ r = u, the universal set.  . . . . n(u) = 3 +11 = 14

Answer:

- 2x +29

Step-by-step explanation:

Open up the parenthesis, then simplify

14 + 5x + 15 - 7x

5x - 7x + 14 + 15

-2x + 29

[tex]14+5(x+3) - 7x[/tex]

Distribute:

[tex]14+(5)(x)+(5)(3)-7x[/tex]

[tex]14+5x+15-7x[/tex]

Combine Like Terms:

[tex](5x-7x)+(14+15)[/tex]

[tex]\fbox{-2x + 29}[/tex]

It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet

An equation is an expression that shows the relationship between two or more numbers.

The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:

Speed = distance / time

Distance = Speed * time

The spaceships are moving at 110000 km/h

The distance covered by each in x hours is:

Distance = 110000 * x = 110000x

Since they are 7100 km apart, hence:

110000x + 110000x = 7100

220000x = 7100

x = 0.03227 hours = 116.18 seconds

It would take 116.18 seconds for the spaceships to meet.

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Answer:(0,5

Step-by-step explanation: