use the distributive property to wrote each expression in equivalent form.

7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)

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

Now, We can factor as;

7) The factors of the expression (x² + 17x + 60) is,

⇒ x² + 17x + 60

By using quadratic formula as;

⇒ x = - 17 ± √(17² - 4×1×60 / 2

⇒ x = - 17 ± √289 - 240 / 2

⇒ x = - 17 ± √49 / 2

⇒ x = - 17 ± 7 / 2

⇒ x = - 17 + 7 / 2

⇒ x = - 10/2

⇒ x = - 5

And, x = - 17 - 7 / 2

⇒ x = - 24/2

⇒ x = - 12

Thus, The factors of the expression (x² + 17x + 60) is,

⇒ (x + 5) (x + 12)

8) The factors of the expression (x² - 6x - 27) is,

⇒ x² - 6x - 27

⇒ x² - 9x + 3x - 27

⇒ x (x - 9) + 3 (x - 9)

⇒ (x + 3) (x - 9)

Thus, The factors of the expression (x² - 6x - 27) is,

⇒ (x + 3) (x - 9)

9) The factors of the expression (2x² - 18x + 28) is,

⇒ 2x² - 18x + 28

⇒ 2 (x² - 9x + 14)

⇒ 2 (x² - 7x - 2x + 14)

⇒ 2 (x (x - 7) - 2 (x - 7))

⇒ 2 (x - 2) (x - 7)

Thus, The factors of the expression (2x² - 18x + 28) is,

⇒ 2 (x - 2) (x - 7)

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a. 8cm ( AD=BD)

b. 8cm ( BD=BC) , Triangle BCD is equilateral

c. 8 cm ( DC = BD)

d Perimeter of ABCD is AD+DC+BC+AB= 8+8+8+11=35

A triangle is a two-dimensional plane shape formed by three sides in the form of straight lines and has three angles. Besides having 3 sides or ribs and angles, the properties of a triangle have an angle of 180°.

The following are the properties of an equilateral triangle, including:

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Answer:

f(n) = 4n - 6

Step-by-step explanation:

the explicit formula for an arithmetic sequence is

f(n) = f(1) + (n - 1)d

where f(1) is the first term and d the common difference

given the recursive formula

f(n) = f(n - 1) + 4

this allows a term in the sequence to be found by adding the common difference d to the previous term.

here f(1) = - 2 and d = 4 , then explicit formula is

f(n) = - 2 + 4(n - 1) = - 2 + 4n - 4 = 4n - 6

The area of rhombus KLMN is 287.3 in²

A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

Given:

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O,

so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Thus, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Then, Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

        = 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

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The mean study time of students in Class B is less than students in

Class A.

Option E is the correct answer.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Class A:

{2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}

Mean:

(2 + 5 + 7 + 6 + 4 + 3 + 8 + 7 + 4 + 5 + 7 + 6 + 3 + 5 + 4 + 2 + 4 + 6 + 3 + 5) / 20

= 96/20

= 4.8

Arrange the numbers in order.

= 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8

Median = 5

Range = Highest - Lowest = 8 - 2 = 6

Class B:

{3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}

Mean:

= (2 + 2 +  2 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 +  4 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 7 = 84/20

= 4.2

Arrange the numbers in order.

= 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7

Median = 4

Range = Highest - Lowest = 7 - 2 = 5

Thus,

Mean of class A > Mean of class B

Median of class A > Median of class B

Range of class A > Range of class B

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Answer:

Two parallelograms can be created using these three vertices. The fourth vertex of the first parallelogram would have the coordinates (9,-2), and the fourth vertex of the second parallelogram would have the coordinates (-3,4). The other coordinates given are not valid for the fourth vertex of a parallelogram.

Answer:

three

(5,-6)

(9,0)

(-3,4)

The unsigned base 9 equivalent of the following unsigned decimal integer value is [tex](6239124)_{8} = (12658420)_{9}[/tex].

We can determine Base 9 equivalent is as follows:

Iteratively divide the integer by 9 until the quotient equals 0.

The integer value is 6239124.

Now we divide integer value 6239124 by 9 until quotient is equal to 0.

6239124 ÷ 9 = 693,236, Remainder = 0

693,236 ÷ 9 = 77,026, Remainder = 2

77,026 ÷ 9 = 8,558, Remainder = 4

8,558 ÷ 9 = 950, Remainder = 8

950 ÷ 9 = 105, Remainder = 5

105 ÷ 9 = 11, Remainder = 6

11 ÷ 9 = 1, Remainder = 2

1 ÷ 9 = 0, Remainder = 1

[tex](6239124)_{8} = (12658420)_{9}[/tex]

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The complete question is:

What is the unsigned base 9 equivalent of the following unsigned decimal integer value?

[tex](6239124)_{?} = (12658420)_{?}[/tex]

The break-even point in units can be calculated if the sales price per unit (P) is known. In conclusion, the break-even point in units is an essential calculation that helps companies understand their financial performance and determine the minimum level of sales they need to achieve to cover their costs and start generating a profit.

Break-even point in units = Fixed costs / (P - Variable expenses per unit)

= Fixed costs / (P - Variable expenses / Sales)

The break-even point is a crucial calculation in the field of business and finance, as it represents the level of sales at which a company's expenses and revenue are equal, and there is no profit or loss. In this scenario, Hurst Ltd's break-even point in units can be calculated based on its sales, variable expenses, and fixed costs.

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An equation of the line shown above in slope-intercept form is y = x/8 + 5/2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided in the graph above, we have the following data points on its line:

At data point (60, 10), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 10 = (20 - 10)/(140 - 60)(x - 60)

y - 10 = 1/8(x - 60)

y = x/8 - 7.5 + 10

y = x/8 + 5/2

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At 6% nominal interest, the amount should you receive today is (d) $1600.

The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum.

The present value of $2007 received in 5 years can be calculated using the formula:

PV = FV / (1 + r)^t

Where:

PV is the present value

FV is the future value ($2007)

r is the nominal interest rate (6%)

t is the time period (5 years)

So, PV = $2007 / (1 + 0.06)^5 = $1600

Therefore, you should receive $1600 today if you want an equivalent amount.

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Equivalent to 5(x+7)+7(x+5) is expression 12x + 70 .

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression

5(x+7)+7(x+5)

Using distributive property

= 5x + 35 + 7x + 35

Adding like terms

= 12x + 70

Hence, expression 12x + 70 is  equivalent  to 5(x+7)+7(x+5).

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Answer:

2x+y=-1

Step-by-step explanation:

I can't really explain,But the equation is AX+BY=C

This is a position a win for the next player; the first player's winning move is to remove 2 chips from the pile with size 11, and if each player is allowed to remove at most 9 chips in a single move, then this is a P-position, and the previous player has won.

(a) The outcome of a game of Nim depends on the XOR (exclusive or) of the sizes of the piles. The XOR of 9, 10, 11, and 12 is 2, which means that this is a P-position (i.e., the previous player has won).

To determine the winning first move, we must find a combination of pile sizes that results in a new XOR of 0. One way to do this is to remove 2 chips from the pile with size 11, resulting in 9, 10, 9, and 12. The XOR of these new pile sizes is 0, which means that this is an N-position (i.e., the next player will win).

The first player's winning move is to remove 2 chips from the pile with size 11.

(b) The maximum number of chips that can be removed in a single move is 9, so the players are restricted in the amount they can remove. However, the outcome of the game still depends on the XOR of the pile sizes. In this case, the XOR of 9, 10, 11, and 12 is 2, which means that this is still a P-position and the previous player has won.

The winning first move, as described above, would still be to remove 2 chips from the pile with size 11.

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The correct answer is row number 16 since the sum is 65536 in

pascal's triangle which equals to the 2 power of 16 , that is 4th option.

Pascal's triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. This triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. In any row of Pascal's triangle, the sum of the first, third, fifth, … numbers is equal to the sum of the second, fourth, sixth numbers.

(1+x)n=(n0)+(n1)x+(n2)x2+⋯+(nr)xr+⋯+(nn−1)xn−1+(nn)xn.

We know that , 2^16 = 65536

Therefore, the numbers come from the row number.16

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The  [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.

The radius of earth is 6371 km.

Let's say the length of the piece of wood is L.

The diameter of the Earth is 2 times its radius

The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.

The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.

The diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.

The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.

In scientific notation, we can express this as:

12742 km / L = [tex]1.2742*10^4 km / L[/tex]

The  [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.

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Answer:

kxh is the answer to this question

If the current loan balance is $79,000 and the house was recently appraised for $116,000, the equity in the house would be worth d) $37,000.

The home was bought at a price of $92,000 and a down payment of $11,000 was made. It is also given that the current loan balance is $79,000.

Also, the house was recently appraised for $116,000. We are asked to calculate the equity.

Now, equity is defined as the sum of money the owner of an item would receive if they sold it and all associated debts were settled is known as equity. For example, if one person owns a house which has a value of $100,000 and he has a mortgage of $40,000. Then, the equity in the home would be worth $60,000.

Here, in this question, the current debt is $79,000 and the current value of the house is $116,000.

So, the equity in the home would be:

                      Equity = 116,000 - 79000 = $37,000

Hence, the equity in the house would be worth $37,000.

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Answer: 11.2

Step-by-step explanation:

a) d= k/r

=> 7= k/8

=> k= 7x8

therefore, k=56

b) d=k/r

=> d=56/ 5

so, d= 11.2

The value of d is 7 when r = 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

d is inversely proportional to r.

This can be written as,

d ∝ 1/r

d = k/r

Now,

d = 7 when r = = 8

This means.

7 = k/8

k = 56

Now,

Substituting r = 8.

d = 56/8

d = 7

Thus,

d = 7.

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Are required 482,972.60 in^2 of metal to make the soup can

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

The formula and procedure to solve this geometry exercise is:

A= (2* π *r * h) + (2 * π * r²)

Where:

Problem information:

Using the formula of the cylinder area we get:

A= (2* π *r * h) + (2 * π * r²)

A= [2* π *(278/2) * 414] + [2 * π * (278/2)²]

A= [2* π *(139) * 414] + [2 * π * (139)²]

A= [2* π *(139) * 414] + [2 * π * (139)²]

A = 361575.18 in^2 + 121397.42 in^2

A = 482,972.60 in^2

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The measurement of the remaining two sides of the triangle be 4cm and 6cm.

Given :- Perimeter of triangle = 18m.

Area of triangle = √135m².

One side of triangle = 8m.

Triangle  is a plane figure with three straight sides and three angles.

Let the equation be Area of ∆ = 1/2bh

= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]

By using Heron's formula to get the Area of triangle,

s = (Perimeter /2) = (18/2) = 9m.

Putting values now we get :-

√(s(s-a)(s-b)(s-c) ) = √135

substitute the values in the above equation, we get

√[9(9-8)(9-b)(9-c)] = √135

Squaring Both sides we get,

9 × 1 × (9-b)(9-c) = (√135)² = 135

Dividing both sides by 9, we get,

(9-b)(9-c) = 15

81 - 9c - 9b + bc = 15

simplifying the above equation, we get

81 - 9(b + c) + bc = 15

9(b + c) - bc = 81 - 15

9(b + c) - bc = 66 -------- (1).

Also, if Rest two sides are b and c, we get,

→ 8 + b + c = 18

→ (b + c) = 18 - 8 = 10 cm. ------ (2).

Putting value of (2) in (1) , we get,

→ 9 × 10 - bc = 66

simplifying the above equation, we get

→ bc = 90 - 66

→ bc = 24 ------------ (3).

We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).

24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)

We can see (4,6) or (6,4) Satisfy the (2).

Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.

The complete question is:

the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides

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This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

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Francis made an error in writing the explicit formula. The correct formula should be an = 4 * (1/4)⁽ⁿ⁻¹⁾, not an = 4 * (1/4)ⁿ⁻¹. The exponent should be (n-1), not just n, to correctly represent the sequence where the second term is 8 and the fourth term is 2.

To determine the error in Francis' formula, we need to apply it to the known terms of the sequence and see if it produces the correct values. For example, for the second term, n = 2, so using Francis' formula:

an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)¹ = 4 * 1/4 = 1

But the second term of the sequence is 8, not 1. So the formula is incorrect.

Similarly, for the fourth term, n = 4, so using Francis' formula:

an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)³ = 4 * 1/64 = 1/16

But the fourth term of the sequence is 2, not 1/16. So the formula is still incorrect.

Therefore, we can conclude that the formula written by Francis is not correct and needs to be corrected to accurately describe the sequence.

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a)

P (gold or silver) is 0.20

b)

P (not gold) is 0.95

c)

P (silver or bronze) is 0.70

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Color          gold   silver   bronze  white

Probability 0.05   0.15      0.55     0.25

Now,

The probability that the counter is

a)

P (gold or silver)

= 0.05 + 0.15

= 0.20

b)

P (not gold)

= 1 - 0.05

= 0.95

c)

P (silver or bronze)

= 0.15 + 0.55

= 0.70

Thus,

The probabilities are given above.

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Answer:

SLAY

Step-by-step explanation:

UWU

The correct answer is 6 , that is 3! (3 factorial).

If the direction is not take into consideration then 3 students can stand in 3*2*1 =6 ways.

Like In the first place there can be any of the three, in the second place there can be either of the two left and then the last place .

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The ty plane the hypothesis of theorem are satisfied

The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.

The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.

This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.

In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.

Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.

Complete Question:

State where in the ty-plane the hypotheses of Theorem

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The positive whole numbers are 27 and 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the 5 positive whole numbers be a, b, c, d and e.

One of the numbers is a multiple of nine the other four numbers are equal.

Now, 9a+b+b+b+b=47

9a+4b=47

If b=1

9a=43

Here, we don't get whole number.

If b=2

9a=39

Here, we don't get whole number.

If b=3

9a=35

Here, we don't get whole number.

If b=4

9a=31

Here, we don't get whole number.

If b=5

9a=27

a=3

Substitute a=3 in equation 9a+4b=47

b=5

Therefore, the positive whole numbers are 27 and 5.

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Answer:-12

Step-by-step explanation: First you will have to deal with the things in parenthesis and the exponent. So after cubing the 3 and 2 the equation you will then multiply and then add them rest of the numbers to get -12

The express in the form of a + bi would be 0 + 5i.

Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to  (√-1). A pair of real and imaginary numbers combined in the form a + bi.

When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.

Let the given expression be [tex]$\sqrt{-25}$$[/tex].

We have to evaluate the expression.

[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]

The express in the form of a + bi = 0 + 5i.

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