in the figure to the right, the two triangles are similar. what is the value of x?

Answer:

y=4/5x-3

Step-by-step explanation:

y=mx+b

Substitute the 4/5 in for x and the -3 in for the b

That gets you y=4/5x-3

It is proved that in parallelogram MNOP, MP=ON. The solution has been obtained using the ASA congruency of triangles.

What is a ASA congruency of triangles?

As per the Angle-Side-Angle rule, two triangles are said to be congruent if any two of the angles and sides that make up one triangle are equal to the corresponding two angles and sides that make up the other triangle.

We are given MN║PO and MP║NO

Since, MN║PO and angles ∠POM and ∠NMO are alternate angles

So, ∠POM≅∠NMO because alternate angles are equal

Similarly, since MP║NO and angles ∠PMO and ∠NOM are alternate angles

So, ∠PMO≅∠NOM because alternate angles are equal

Also, MO≅OM

Thus, by angle-side-angle congruency,

Triangle NMO ≅ Triangle POM

Hence, MP=ON as the triangles are congruent.

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Since, there are multiple questions so the question I answered is attached below.

The angle whose vertex is on the circle and the sides of the angle are the chords is called an Inscribed Angle .

What is an Inscribed Angle ?

An inscribed angle in the circle is formed by the two chords which have a common end point on circle and this common end point is called the vertex of inscribed angle.

The arc formed by the inscribed angle in the circle is called as the intercepted arc .

also the Inscribed Angle Theorem states that inscribed angle on the circle is half the measure of central angle that subtends the same arc .

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Since the inverse of the inverse of a positive number is that positive number back again, the fact that the product of two negatives makes a  positive number line is related to that fact.

Numbers in a straight line are represented visually as a number line. It serves as a resource for number comparison and arranging. Every whole number and natural number, as well as other real numbers, can be represented by it.

Let's understand with an example.

Suppose x and y are two positive integers. So, the negative integers will be -x and -y.

Multiplying both, we get

(-x)*(-y) = (-1 * -1) (x y)

Now, to prove that multiplication of -x and -y is positive, we need to prove that (-1)*(-1) is +1, as x and y are positive integers.

Using contradiction method, we assume that (-1)*(-1)= - 1 and see whether this holds good in distributive property of multiplication.

For this, let p, q and r be three real numbers.

(- r) (p-q)

= (- r) (p) + (- r) (- q)

= - rp + (-1*-1) (rq)

= - rp + (-1) (rq)    … (as we have assumed that -1*-1= - 1)

= - rp - rq

= - r (p+q)

Thus, LHS "- r (p+q)" is not equal to RHS "(- r) (p-q)".

This implies that the distributive property of multiplication does not work for (-1)*(-1)= - 1 .

Hence, our assumption of (-1)*(-1)= - 1 is not correct. This means that

(-1)*(-1)= + 1

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The area of the pool B shown is 2x² + 12x + 10 square unit

An equation shows the relationship between numbers and variables in an expression.

The area of a rectangle is the amount of space that it occupies. It is given by:

Area = length * width

For pool B, the length is 2x + 2 and the width is x + 2, hence:

Area = length of pool * width of pool

Substituting:

Area (A) = (2x + 2)(x + 5)

A = 2x² + 12x + 10

The area is 2x² + 12x + 10 square unit

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The difference is that the simple interest gives you interest only on the deposited amount in the account.

What is Simple interest ?

Simple interest can be defined as the ratio of product of Principal amount , time and rate and hundred.

Given ,

The difference between Simple and Compound Interest in a savings

account is that

You will always earn less than 196 interest with a simple interest savings account, You will earn more interest with a simple interest savings account, You will always earn more than 10% interest with a compound savings account and You will earn more interest with a compound interest savings account

The difference is that the simple interest gives you interest only on the deposited amount in the account while the compound interest is calculated over the deposited amount and the previous interest amount added to the deposited amount.

Hence, The difference is that the simple interest gives you interest only on the deposited amount in the account.

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Representing Ratios that describes a ratio in the table

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The surface area of the prism is 1,664mm²

Triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces connected to each other through the edges

we know that

The surface area of the triangular prism is equal to

SA = 2B +PL

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

B = 1 {24}{16}=192mm²

     2

Find the perimeter of the triangular face P

P = {24+20+20} = 64mm

 we have

L= 20mm

substitute the values

SA=2{192}+{64}{20} = 1,664mm²

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The amount of money you have left is 1.75 dollars.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

To determine the total number of quarters you have after finding more in your room, you can use the following expression:

20 + (40/100) × 20 = 20 + 8 = 28 quarters

To find the total number of quarters you take with you shopping, you can use the following expression:

28 - (75/100) × 28 = 28 - 21 = 7 quarters

In dollars, the amount you have left is 7 × 0.25 = $1.75

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We can solve two unknown angles in a triangle only if the exterior angle is already given and then put the sum of all the angles equal to 180 degrees.

We know that,

If the exterior angle of a triangle is θ and the two opposite interior angles are θ₁ and θ₂, then the sum of θ₁ and θ₂ will be equal to the θ.

⇒θ = θ₁ + θ₂

Also,

If the angles of a triangle are θ₁, θ₂ and θ₃, respectively. Then the sum of θ₁, θ₂ and θ₃ is equal to 180°.

⇒θ₁ + θ₂ + θ₃ = 180°

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Answer:

[tex]y=-4x+5[/tex]

Step-by-step explanation:

Answer: The answer to this question is

B) Wildfires can lead to worse air quality.

The value of x is 20.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Given that ΔACB≅ΔDCE

∠BAC=3x-10

∠ECD=45 degrees

∠EDC=2x+10

∠A is congruent to ∠D

∠A=∠D

3x-10=2x+10

Subtract 2x on both sides

x-10=10

Add 10 on both sides

x=20

Hence, the value of x is 20.

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The statement regarding the repayment schedule is false.

Given is the statement regarding the repayment schedule.

The given statement is -

A repayment schedule shows the distribution of interest and other charges over the life of a loan. It usually does not show the principal. The given statement is false.

Therefore, the statement regarding the repayment schedule is false.

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By calculating , The values of x are 8,4,7,1.5 respectively.

What is Quadrilateral ?

Quadrilateral can be defined in which it contains four sides and the sum of the four angles in a quadrilateral is always 360 degrees.

Given in figures ,

we have to find the value of x in which that males the quadrilateral a parallelogram.

So, in the given figure As the diagonal of quadrilateral bisects each other

so ,

4x+2 = 5x - 6

5x-4x = 6+2

x = 8

In the second figure,

similarly ,

2x+3 = x+7

2x-x = 7-3

x = 4

In the third figure ,

3x+5 = 5x- 9

5x-3x = 9+5

2x = 14

x = 14/2

x = 7

In the fourth figure ,

6x = 3x+2

3x = 2

x = 1.5

Hence, The values of x are 8,4,7,1.5 respectively.

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The expression is (10² -5)z. The variable is z. The simplest form of the expression is 95z.

What are algebraic operations?

The four fundamental algebraic operations are as follows:

Addition, Subtraction, Multiplication, Division

We always categorize the terms in our algebraic equations as like and unlike terms in each of the algebraic operations we perform.

The given sequence of operations are:

1) Raise 10 to the 2nd power

2) Subtract the result from 5

3) Then multiply z

The mathematical representation of the first statement is:

10².

Then apply the second operation:

10² - 5

Then apply the third operation:

(10² - 5)z

Now simplify the above expression:

= (100 - 5)z

= 95z

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On solving the provided question, we can say that 2 answers that would be like equations with terms with 10x are 2a and 10 as a= 5 and 2a = 2*5 = 10

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

2 answers that would be like equations with terms with 10x are

2a and 10

as a= 5

and 2a = 2*5 = 10

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The parent function of a parabola is the quadratic function y = x^2.

A parabola is a type of U-shaped curve that is the graph of a quadratic equation. The parent function of a parabola is the simplest form of a quadratic equation, which is y = x^2. This equation can be used to create any parabola, as it is the most basic form. By manipulating the equation, you can create different shapes and sizes of parabolas. For example, you can add a constant to the equation to move the parabola up and down the y-axis, or you can add a coefficient to the x^2 term to make the parabola wider or narrower. You can also add an x term to the equation to make the parabola move left or right along the x-axis. All of these changes to the parent function will create a different shape of parabola, but the parent function will always remain the same.

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The probability of scoring a total of 9 is 1/6, as there is only one combination of results (1 + 8) that add to 9.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to happen. Probability can be used to make predictions and understand the likelihood of different outcomes. It is an important concept in decision making and risk assessment.

Sample space diagram for the two fair spinners:

Spinner 1 | Spinner 2
 1      |  1
 2      |  2
 3      |  3
 4      |  4

Total
2 |  4  |  6  |  8  |  9  | 10  | 12

The probability of scoring a total of 9 is 1/6, as there is only one combination of results (1 + 8) that add to 9.

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The domain of the given function is f(x) = √(-12 + 4x) is x ≥ 3.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The function is given in the question, as follows;

f(x) = √(-12+4x)

The domain of a square root function is restricted by the condition that the expression inside the square root must be non-negative.

In this case, we need to ensure that -12 + 4x ≥ 0:

-12 + 4x ≥ 0

4x ≥ 12

x ≥ 3

So, the domain of f(x) = √(-12 + 4x) is x ≥ 3.

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1. Simplify each side of the  linear equation by using the inverse operations.

2. Use the addition or subtraction properties of equality to isolate one of the variables.

3. Use the multiplication or division properties of equality to solve for the remaining variable.

1. Simplifying the equation: The first step in solving linear equations in two variables is to simplify each side of the equation by using inverse operations. This means you will use addition or subtraction to get rid of any constants and multiplication or division to get rid of any coefficients.

2. Isolating one of the variables: Once the equation has been simplified, use the addition or subtraction properties of equality to isolate one of the variables. This means you will move the terms with the variable to one side of the equation and the constants to the other side.

3. Solving for the remaining variable: Finally, use the multiplication or division properties of equality to solve for the remaining variable. This means you will divide or multiply both sides of the equation by the coefficient of the remaining variable. Once done, the equation should be solved and you will have the value of the remaining variable.

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The sum of their ages after 3 years will be 46 years.

What is age?

A time frame in a person's life, defined in years from birth, that is frequently characterised by a certain stage or level of mental or physical development and involves the development of legal ability and responsibility is known an age.

Step by step Explaination:

The sum of the ages of the son and father before 5 years was 30 years.

The sum of their ages after 3 years=?

Let us assume that the present age of the son is x years and the father is y years.

So, according to the question

The sum of their ages before 5 years = 30

(x-5)+(y-5) = 30

x+y-10 = 30

x + y = 40

Now, the sum of their age after 3 years will be

(x+3)+(y+3) = x+y+6

substituting the value of x + y

x+y+9 = 40+6= 46 years.

Hence, the sum of their ages after 3 years will be 46 years.

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Answer:

C

Step-by-step explanation:

{(5, 5), (6, −6), (8, 7), (−9, 9)}

Both 0.7% and 17/25 are approximations and if you need more precision you can convert them to decimal form and or use more significant figures.

What is the decimal representation and fraction representation?

A decimal representation of a number is a way of expressing the number in terms of a decimal point and the powers of 10.

A fraction representation of a number is a way of expressing the number as the ratio of two integers, called the numerator and denominator. The numerator represents the number of parts of the whole, and the denominator represents the total number of parts in the whole.

0.7% is a decimal representation of a percentage. It means 0.7 parts per 100. It can also be written as 0.007 as a decimal.

17/25 is a fraction representation. It means 17 parts out of 25. It can also be written as 0.68 as a decimal.

Both 0.7% and 17/25 are approximations and if you need more precision you can convert them to decimal form and or use more significant figures.

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The three characteristics of an absolute value:

1) The absolute value of any number is always non-negative.

2) The domain is all real numbers and  range is all whole numbers.

3) The graph is V shaped, symmetric about the y -axis and makes a right angle at the origin.

As we know that an absolute value of any number is nothing but the distance from zero of that a number is on the number line.

The absolute value of any number is always positive.

i.e., for any number p,

|-p| = p and |+p| = p

From definition of absolue value the domain is all real numbers and  range is all real numbers greater than or equal to zero.

The graph of the absolute value function is V shaped and symmetric about the y -axis.

The graph of absolute value function f(x) = |x| makes a right angle at the origin.

The graph lies completely above the x-axis.

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The area of the hexagons having side 15.5 cm and height 28.5 cm will be 662.625 cm^2.

A hexagon or sexagon is a six-sided polygon or 6-gon that forms the shape of a cube in geometry. The sum of any basic hexagon's interior angles is 720°.

The hexagon has six sides in mathematics; what makes this specific form so fascinating is because it best fills a plane with equal size units and leaves no wasted space. Because of its 120-degree angles, hexagonal packing also reduces the perimeter for a given area.

As we have,

Area of Hexagon = 3/2 x s x h

Where, s = side of hexagons

h = height of hexagons.

So, for determining the value of area of hexagons, we will put the value of (s) and (a) in the above formula.

So, we will get the area of hexagons as:

(3/2) * 15.5 * 28.5 =662.625 cm^2

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Answer:

Step-by-step explanation:

There are not a lotta steps here. U just gotta look at the diagram and find the similarities.

∠D = ∠G because they both have the pointy thing.(acute)

∠A = ∠R because they r both obtuse.

∠S = ∠B (we know that because we have done the previous two already so it makes sense if this were to happen)

∠P = ∠C (same thing)

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The percent of increase in the cost of season tickets is, 10%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Last year, the cost of season tickets was $1,310.

And, This year, the cost is $1,441.

Now, The percent of increase in the cost of season tickets is find as;

⇒ Increase percent = (1441 - 1310) / 1310 × 100

                               = 10%

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The area of the land is 2.31 × 10¹⁰ square meters in scientific notation.

We can represent this area as 2.31 × 10⁴ square kilometres.

The unit square kilometres is more appropriate to represent the area of the forest land in scientific notation.

This question associates to Laws of indices specifically in powers of 10

The given parameters of the rectangular section dimensions of forest land are;

5.5 × 10⁵ m by 4.2 × 10⁴ m

Therefore, the area of the rectangular section of forest land is = 5.5 × 10⁵ m × 4.2 × 10⁴ m = 2.31 × 10¹⁰ m²

1 km² = 1 × 10⁶ m²

∴ 2.31 × 10¹⁰ m² = 2.31 × 10¹⁰/(1 × 10⁶) km² = 2.31 × 10¹⁰ ⁻ ⁶ km² = 2.31 × 10⁴ km²

2.31 × 10¹⁰ m² = 2.31 × 10⁴ km²

--The given question is incomplete, the complete question is

"Drag each label to the correct location Not all labels will be used.

The dimensions of a rectangular section of forest land are 5.5 x 10⁵ meters and 4.2 × 10⁴ meters. Complete the following sentences:

2.31 × 10³ 2.31 × 10⁴ 23.1 × 10⁵ 23.1 × 10⁹ 2.31 × 10¹⁰ 23.1 × 10¹⁰square meters square kilometres

The area of the land is____square meters in scientific notation.

We can represent this area as____ square kilometres in scientific notation.

Hint: square kilometre is equal to 1 × 10⁶ square meters.

The unit____ is more appropriate to represent the area of the forest land in scientific notation."--

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