5.
Factorise each of the following.
(a)-15ab-6ab²
(b) 6x(2y-5)-3(5-2y)

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.

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For the above set of similar triangles, the value of x is 23 units.

Similar triangles have the same proportionate side lengths and related angle measurements. Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion). Similar triangles will have the same form but may or may not have the same size. Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Here,

Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion).

x-10/39=12/36

x-10=13

x=23

The value of x for given set of similar triangles is 23 units.

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Answer:

The cost at Pauline's print store can be described with the following equation, where y represents the cost in dollars of x copies:

y = 0.05x, because 1.25/25 = 2.75/55 = 90/4.50 = 0.05

Carla's Copy Shop charges a higher unit right

and it is $0.04 higher per copy

Step-by-step explanation:

Hope this helps. Much appreciated if Brainlisest.

The series of transformation that would map the quadrilateral in figure G to the quadrilateral in figure H are A reflection about the y-axis and A translation of three units left.

A geometric figure can undergo a geometric transformation by changing its position, size, orientation, or any combination of these.

The potential polygon in the question, which was produced in MS Excel using data from a related web question, is attached;

The polygon's vertices are;

Figure G's vertices' coordinates are (-2, 7), (-6, 3), (-1, 5), and (-1, 1)

Figure H's corresponding vertices' coordinates are (5, 7), (9, 3), (4, 5), and (9, 3). (4, 1)

Figures G and H have identical y-values, but their x-values have different values and signs.

Following a reflection about the y-axis, the coordinates of the point (x, y) are the point (-x, y)

The transformation that maps the image produced by the reflection and figure H are;

Transformation (5 - 3, 7 - 7) = (3, 0)

(9 - 6, 3 - 3) = (3, 0)

(4 - 1, 5 - 5) = (3, 0)

(4 - 1, 1 - 1) = (3, 0)

The transformation that maps the image of figure G to figure H is therefore T₍₃, ₀₎, which is a translation of 3 units to the right.

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The equations equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

The correct answer is option B and C

2.3p – 10.1 = 6.5p – 4 – 0.01p

collect like terms

2.3p - 6.5p + 0.01p = -4 + 10.1

-4.19p = 6.1

p = 6.1/-4.19

p = -1.46

2.3p – 10.1 = 6.5p – 4 – 0.01p

= 2.3p – 10.1 = 6.49p – 4

Given options:

2.3p – 10.1 = 6.4p – 4

False

2.3p – 10.1 = 6.49p – 4

True

230p – 1010 = 650p – 400 – p

divide through by 100

= 2.3p – 10.1 = 6.5p – 4 – 0.01p

True

23p – 101 = 65p – 40 – p

False

2.3p – 14.1 = 6.4p – 4

False

Therefore, 2.3p – 10.1 = 6.49p – 4; 230p – 1010 = 650p – 400 – p are equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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Answer:

Domain of inverse = Range of f = x>-4

Hence B

Answer:

560

Step-by-step explanation:

A bottle of Water is x=80

A Pack Of Peanuts is y=?

x+2y=200

y= 200-80 divided by 2 =60

4x+4y= 4x80 + 4x60 = 560

Yes, 1 is a monomial, a unique type of polynomial.

You must first understand what a word is. A term is a real number multiplied by one or more variables, each of which has been raised to a power. Remember that a constant might appear in a phrase when a variable is multiplied by itself to the power of 0. (which is 1). A polynomial is just the sum of one or more terms that meet the criteria listed below:

1] There are no variables to split the words into.

The variables' exponents are whole numbers, e.g. 0, 1, 2, 3, etc.

Thus, 1 is just 1*(x0).

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Answer:

This theory states that the concentric circles are based on the amount that people will pay for the land.

Step-by-step explanation:

I swear this is the answer because I had the same question and I think this was my answer .

The concentric circle model illustrates nested relationships or boundaries.

We have,

The concentric circle model illustrates the concept of nested or concentric circles.

It represents a series of circles that share the same center point but have different radii.

These circles are placed one inside the other, with each circle contained within the previous one.

The concentric circle model is often used to visualize or explain various concepts, such as:

- Levels of influence or impact

- Zones or boundaries

- Relationships or proximity

- Targeting or segmentation

Thus,

The concentric circle model helps visually represent hierarchical or nested relationships, boundaries, proximity, or segmentation in various contexts.

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Step-by-step explanation:

he needs two pairs of jeans and 4 shirt for him to spend 4 days at the camp

Answer:

-5

Step-by-step explanation:

2(-1) - 3

-2 - 3

-5

Therefore ,In light of this, the answer to the above equation issue is 

be 8.

An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.

Here,

Replace -3 with the following in the above quadratic equation.

(-3)² - 5(-3) + c = 0

measuring c:

c = -24

a quadratic equation that looks like this

x² - 5x - 24 = 0

x's value can be determined using the quadratic formula as follows:

x = [-b ±√(b² - 4(a)(c))]

/2a

x = [-(-5) ± √((-5)² - 4(1)(-24))] /2(1)

x = 8, -3

Therefore ,In light of this, the answer to the above equation issue is 

be 8.

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The function rules for each table are given as follows:

7. y = 5x - 2.

8. y = x³.

9. y = x³ + 1.

For item 7, when x increases by one, y is increased by 5, hence the function is a linear function with slope 5, as follows:

y = 5x + b

When x = 6, y = 28, hence the intercept b is given as follows:

28 = 5(6) + b

b = 28 - 30

b = -2.

Hence the function is:

y = 5x - 2.

For item 8, the each term is cubed, hence the function is given as follows:

y = x³.

For item 9, the function is one added to the function in the previous problem, hence:

y = x³ + 1.

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Answer:

<UVS and <WVX

Step-by-step explanation:

They are both supplementary to the same angle. (<SVW)

Otherwise, you could just see if they are across from each other.

The following is a basic formula to find the scale factor of a dilated figure is:  :  Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Sizing Factor (Dilation) The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object). An expansion happens when the scaling factor's absolute value exceeds one.

Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.

In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is the ratio of the original figure's and dilated figure's sizes.

You can use r or k to represent the scaling factor.

If the scale factor is more than 1 (k > 1), the image is expanded.

If the scale factor is less than 1 (0 k 1), the image is condensed.

If the scale factor is 1 (k = 1), the image doesn't change.

It should be noted that the scale factor's magnitude is taken into account and that it cannot be 0.

An object's size can change depending on the scale factor, either growing or shrinking. The following is a basic formula to determine a dilated figure's scale factor:

Another approach to express this formula that aids in determining the new shape's dimensions is as follows:

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The integral rate law for a first-order reaction has the following exponential form: [A] = [tex][A]_{0}e^{-kt}[/tex]

If there are constants c, M > 0, and T > 0 such that |f(t)| ≤ Mect for all t>T, then a function f is said to be of exponential order c.

It is helpful to keep in mind the exponential's definition and characteristics since they serve as the foundation for the solution of first-order linear differential equations.

The Concentration of the Reactant Decreases Exponentially with Time in First-Order Reactions. A plot of the natural logarithm of the concentration is a linear function of time according to this form.

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a) The percentage abundance Shows us the amount of the substance in the element

b) The relative atomic mass for the element X has been obtained as 122.5 amu

c) The Rutherford's model explained showed the movement of the electrons.

The isotopes of an elements are the atoms of the elements that have the same atomic number but do not have the same mass number. We know that the atoms of the isotopes of the element that we have are important as we try to determine the relative atomic mass of the element as we have the element X in this case.

Now we have that;

Relative atomic mass = Weighted average of all the isotopes

As such we have;

(121 * 0.432) + (123 * 0.531) + (129 * 0.0370)

52.27 + 65.31 + 4.773

=122.35 amu

The Rutherford model of the atom shed light on the manner in which the electrons move around the nucleus of the atom of the element that we have in the atom.

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a/a+b is the same as a/(a+b). This is because the division of two numbers is represented by the symbol '/', and when a and b are being divided, it is written as a/b.

In this case, a and b are being divided by a+b, so it is written as a/(a+b). This is known as a fraction, which represents a ratio of two numbers. This fraction represents the proportion of a to the total of a+b. The numerator (a) represents the part of the total that you are interested in, and the denominator (a+b) represents the entire quantity.

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Answer:

They might include variety of nuts, raisins, and healthy sweets

Step-by-step explanation:

To classify a quadrilateral by its sides, we need to calculate the distance between each pair of its vertices.

The distance between Q and R is the square root of ((1-(-2))^2 + (5-(-1))^2) = square root of (3^2 + 6^2) = square root of (9+36) = square root of 45 = 6.7

The distance between R and T is the square root of ((-8-1)^2 + (-4-5)^2) = square root of (9+81) = square root of 90 = 9.5

The distance between Q and T is the square root of ((-8+2)^2 + (-4+1)^2) = square root of (10+5) = square root of 15 = 3.87

If the quadrilateral is a rectangle, two sides of it have to be equal, so in this case, AQRT is not a rectangle.

If the quadrilateral is a rhombus, all four sides have to be equal, so in this case, AQRT is not a rhombus.

If the quadrilateral is a square, all four sides have to be equal, so in this case, AQRT is not a square.

If the quadrilateral is a trapezoid, two adjacent sides are parallel, so in this case, AQRT is not a trapezoid.

If the quadrilateral is a parallelogram, two pairs of opposite sides are parallel, so in this case, AQRT is not a parallelogram.

If the quadrilateral is a kite, two pairs of sides have the same length, so in this case, AQRT is not a kite.

So the only possible classification is that AQRT is a general quadrilateral.

so we have:

QR = 6.7

RT = 9.5

QT = 3.87

The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

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A parabola is the form of a quadratic function's graph because the vertex of a parabola is the location where the axis of symmetry of the curve crosses.

f(x) = ax^2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the form of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.

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The missing number of points scored in the last basketball game is 13.

What is the meaning of the data set?

A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.

Given that,

the number of points scored in the last basketball game by each player on the Dragons basketball team are 7, 5,8,11,7,5,?.

Assume that the missing point is x.

The sum of points is 7+5+8+11+7+5+x = 43 + x.

The number of points is 7.

The mean is the sum of points/number of points

= (43+x)/7

Given that the mean of the data set is 8 points.

Therefore,

(43+x)/7 = 8

Multiply both sides by 7:

43+x = 8×7

43 + x = 56

x = 56 - 43

x = 13

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The probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

The event of getting a "2" and the event of getting a "5" on the first roll of a die are mutually exclusive events because they cannot both occur in the same trial. The probability of either of these events occurring is P(A) = 0.16, and the probability of both events occurring at the same time is P(A ∩ B) = 0.00.

The event of getting a "2" on the first roll and the event of getting a "5" on the second roll of a die are independent events. This can be confirmed using the formula P(A ∩ B) = P(A)P(B). The probability of getting a "2" on the first roll is P(A) = 0.16 and the probability of getting a "5" on the second roll is P(B) = 0.16. Thus, the probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

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The additive inverse of 2 /- 7 is -2 /+ 7.

An additive inverse is a number that when added to the number in question, the sum is equal to zero. This can be expressed by the formula x + (-x) = 0, where x is the number in question. In this case, x is 2 /- 7. So, when 2 /- 7 is added to its additive inverse, -2 /+ 7, the sum is 0. This can be expressed mathematically as 2 /- 7 + (-2 /+ 7) = 0. Calculating this equation, we get 2 /- 7 + (-2 /+ 7) = -2 /+ 7 + (-2 /+ 7) = -4 /+ 14 = 0. Therefore, the additive inverse of 2 /- 7 is -2 /+ 7.

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Answer: so the column on the left are expressions, you simplify them by combining like terms, in this case, the variable x. And the row across the top are the simplified expressions. Once you finished simplifying it, you check mark the simplified expression it matches under the column.

Step-by-step explanation:

For example, the first one you’d do this;

The simplified version of 1/3x + 1/4 -2/3x is -1/3x + 1/4

The Total Pay for the following Day is $136 in this algebra question.

A time card is a piece of cardboard with the hours worked by an employee for a given work week printed on it. The time an employee starts and stops working is often printed on the card when it is entered into a time clock. It is used by the payroll staff to calculate the hours for which an employee shall be paid.

On Monday Morning the work time is from 8:15 to 12:15 is equal to 4 hours.

On Monday Afternoon the work time is from 13:00 to 17:30 is equal to 4.5 hours.

So, total work time is = (4+4.5)hours = 8.5 hours

SInce the given wage is $16/hr

Therefore,    

Total Pay for he following day is = 8.5 x 16=$136.

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