Solve for x and y.
2x - (5-x) = 3x + 2(x-7)

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is the condition to be congruent?

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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A quadrilateral has diagonals that are perpendicular but not congruent

is a rhombus.

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

From the properties of a rhombus, we know,

A rhombus has an equal number of sides. In this case, ABCD equals DA.

At an angle of 90° divides each of the diagonals. In this instance, diagonals AC and BD split at a 90° angle.

A rhombus has parallel opposite sides. In this case, AB || CD and AD || BC.

In a rhombus, the opposite angles are equal. ∠A = ∠C, while ∠B = ∠D.

The sum of adjacent angles is 180°.

Diagonals of a rhombus bisect each other at the right angles but they are not congruent.

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Answer:

The expression "5.25x + 1246x" is equivalent to "1771x"

The sampling method used in this case is random sampling and the sample is representative.

A sample is a small proportion of individuals taken from the general population to be studied. For a sample to be representative it is expected that all the individuals represent the population, for example, if the population includes people of different ages the sample should include this too.

The random sample selected is representative because the seats of the students selected are distributed within the class rather than in only one row or line.

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By calculating, The GCF of the given numbers 49 and 28 is 7.

What is Algebraic expression ?

An algebraic expression is an expression that consists of numbers, variables and operators such as addition, subtraction, multiplication and division. These expressions can be used to solve equations and other mathematical problems. Algebraic expressions can also be used to represent relationships between different variables. For example, the expression 4x + 2y can be used to represent the relationship between two variables, x and y.

So lets first find the prime factorization of 28

prime factorization of 28 = 2 × 2 × 7

So lets first find the prime factorization of 49

prime factorization of 49 = 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, The GCF  of the  given numbers 49 and 28 is 7.

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A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.

Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.

Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.

The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.

With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.

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3/2 is a slope of a line perpendicular to the line whose equation of

2x+3y=-3 .

One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.

As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.

If two lines cross at a right angle, they are said to be perpendicular to one another.

A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.

This can be done by rearranging the equation into the slope intercept form.

2x +3y = -3

3y = -2x -3

y = -2/3x - 1

Thus, the slope of the given line is -2/3.

The slope of the perpendicular line is the negative reciprocal of the given line.

Slope of perpendicular line = 3/2

The slope-intercept form was:

(i) The reciprocal of m is 1/m.

(ii) The negative reciprocal of m is -1/m.

Negative reciprocal of -2/3

= -1 ÷ (- 2/3)

= -1 × (-3/2)

= 3/2

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The length of the missing side is 12cm.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. So if we know the lengths of two sides of a right triangle, we can use the theorem to find the length of the third side.

Given:

Base (b) = 16 cm

Hypotenuse (c) = 20 cm

We can use the Pythagorean theorem to find the length of the missing side (a), which is the side opposite the right angle and adjacent to the base.

c^2 = a^2 + b^2

20^2 = a^2 + 16^2

400 = a^2 + 256

144 = a^2

a = 12cm

once we have the length of the missing side, we can use the values of the base and hypotenuse to find the six trigonometric functions:

Therefore, the length of the missing side is 12cm.

The question is incomplete as it does not include the figure. Hence I have attached the figure for a complete understanding of the problem.

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The algebraic expression will be Y=a+9

Where Y=number of cards Angelica has now, a=added movie cards,

what are expressions?

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. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

As given

Angelica buys 3 packets of movie cards and 6 packets of cartoon cards

and and adds these to the 3 packets of movie cards she already has

Now let a=packets of movies she already has

and Y=number of cards Angelica has now

Therefore, The algebraic expression will be

             Y=a+3+6=a+9

            Y=a+9

             Where a=3

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The possible length of the third side of a triangle, say x, with the other two sides are 5 inches and 12 inches. is  

7 ≥ x ≥ 17

The length of the third side is within the range of

The sum of the two ides is the highest possible length of the third side

= 12 inches + 5 inches

= 17 inches

The difference of the two ides is the lowest possible length of the third side

= 12 inches - 5 inches

= 7 inches

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The garden can split into 20 plots.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A community garden has an area of 10 square yards.

The community wants to divide it into plots that each have an area of 1/2 square yard.

The number of community garden,

= 10/(1/2)

= 20

Therefore, the number of required plots is 20.

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If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.

The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.

Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.

Let the given sequence be 2, 9, 22, 45, 82, 137, 214

The differences to a pattern in the sequence be

= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137

= 6, 13, 23, 37, 55, 77

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Answer:

1224 cm²

Step-by-step explanation:

The picture is a rectangle with length 60 cm and width 30 cm.

area of rectangle = length × width

area of picture = 60 cm × 30 cm = 1800 cm²

Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.

area of picture and mat = 72 cm × 42 cm = 3024 cm²

The area of the mat is the difference in area between the picture with mat and the picture without mat.

area of mat = 3024 cm² - 1800 cm² = 1224 cm²

Answer:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

Step-by-step explanation:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

The least positive integer is m=132.

m(m−1)+11=N

It is clear that N must be odd and that can be divisible by the prime 11.

However, the following congruences have no solution as it is easy to prove directly by checking the few possibilities with m(m−1) not divisible by 3,5 and 7 respectively

{m(m-1)+2=0(mod 3)

{m(m-1)+1=0(mod 5)

{m(m-1)+4=0(mod 7)

Thus N=∏ with pi≥11

A necessary condition is that (solving the quadratic in m)

√4N-43=x² and from this, we need that

N≡1,3,7(mod10)

By chance, we find the minimum N=113⋅13 which corresponds to m=132

and that could have been calculated by direct trials but the next solution seems to be far from 132.

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Answer:

n = 4

Step-by-step explanation:

Let's put all of our variables on one side, and all of our non-variable numbers on the other. (I like to do this so that the variable isn't negative. You'll still get the same answer.)

So we can minus 2n on both sides, giving us 7 = n + 3.

Then, let's do our non-variables and subtract 3 from each side. This gives us 4 = n or n = 4.

Therefore, n = 4.

Using complementary angles, the value of x = 10.3

Complementary angles are angles in which the sum add up to 90°.

Since in a right triangle, sin(8x - 9) = cos(x + 6). To solve the problem, we proceed as follows.

sin(8x - 9) = cos(x + 6).

Given that cosФ = sin(90 - Ф), we have that

cos(x + 6) = sin[90 - (x + 6)]

So, susbstituting this into the equation, we have that

sin(8x - 9) = cos(x + 6)

sin(8x - 9) = sin[90 - (x + 6)]

This implies that

8x - 9 = 90 - (x + 6)

8x - 9 = 90 - x - 6

8x - 9 = 84 - x

Adding x to both  sides of the equation, we have

8x + x - 9 = 84 - x + x

9x - 9 = 84 + 0

9x - 9 = 84

Adding 9 to both sides of the equation, we have that

9x - 9 + 9 = 84 + 9

9x + 0 = 93

9x = 93

x = 93/9

x = 10.33

x ≅ 10.3

So, the value of x = 10.3

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Answer:

The length of the longer ladder is 36ft

Step-by-step explanation:

30ft/10ft = 3

12ft x 3 = 36ft

Another way to solve this is by cross multiplying

[tex]\frac{10}{12}[/tex] = [tex]\frac{30}{x}[/tex]

10x = 360

x = 36ft

According to the given information in the question the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2.

Inverse operations, such as subtraction and addition multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The opposite of a number, or "inverse," is what is meant by the phrase. i.e., x - 1 = 1 / x.

Negative correlation and inverse relationships are interchangeable terms. Any two or more variables that consistently move in the opposing directions can be described by both. The outcome of measuring an inverse association will result in a negative sign.

To find the inverse of a function, you first need to switch the x and y variables, and then solve for y.

So, the inverse of y=2x²+3x+5 is x = (y - 5 - 3x)/2

Note that the inverse of a function is only possible if the function is a one-to-one function.

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Answer:

c) cryptography

Step-by-step explanation:

Cryptography is a mechanism used to encrypt and decrypt data.

The correct description of each function term is given as follows:

1. Input: A rule to determine the value of the output.

2. Output: The result of applying a function rule to the value of an input, and is the dependent variable.

3. Domain: the set of allowable inputs.

4. Range: The set of possible outputs.

5. Function: A relation in which each input has only one output.

A function has the notation y = f(x), in which.

Hence the input is applied to the function to obtain the output, and these concepts, along with domain and range, are presented in this problem.

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The grapefruit's volume in cubic centimeters to the nearest tenth is equal to 775.8 cubic centimeters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the grapefruit, the diameter of the sphere is given by;

Diameter of sphere = 11.4 cm

Radius = diameter/2 = 11.4/2 = 5.7 cm.

Substituting the given points into the volume of a sphere formula, we have the following;

Volume of sphere = 4/3 × 3.142 × 5.7³

Volume of sphere = 775.8 cubic centimeters.

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Lines AB, BC, and AC have an equal slope, with a slope value of 2/3.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a line AC that has an x-intercept of "2"

Since,

AB is part of line AC thus the slope of AB will be the same as the slope of line AC and the Slope of line BC.

For the slope of line AB:

Since there is no Additional data given on the problem we will assume that every square is a unit square in the graph

Thus, Coordinates of A = (-5, -2)

Since Point B is the x-intercept of line AB thus its coordinates = (-2, 0)

from the formula of the slope of a line:

m = (y₂ -y₁)/(x₂ - x₁)

Thus, the slope of line AB:

m = (0+2)/-2 +5)

m = 2/3

therefore, the slope of the line AB, BC, and AC are equal and the value of the slope is 2/3.

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The value of the integral is given as follows:

C. -7π/2.

The result of the integral is given by the total area of the figure.

From x = -7 to x = -1, the figure is a semi-circle of radius 3, below the y-axis, hence it's area is given as follows:

A1 = -0.5π x 3²

A1 = -4.5π.

From x = -1 to x = 1, with the line, the figure is a right triangle with sides 2 and 2, hence the area is given as follows:

A2 = 0.5 x 2 x 2

A2 = 2.

From x = 1 to x = 3, the figure is quarter circle with radius 2, hence the area is given as follows:

A3 = 0.25π x 2²

A3 = π.

From x = 3 to x = 4, the figure is a right triangle with sides 1 and 4, below the y-axis, hence the area is given as follows:

A4 = 0.5 x 1 x 4

A4 = -2.

Hence the total area, representing the integral, is given as follows:

A = A1 + A2 + A3 + A4

A = -4.5π + 2 + π - 2

A = -3.5π

A = -7π/2.

(the result of the integral is negative but the area is positive).

Meaning that the correct option is given by option C.

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The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.

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. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x²-4x-2=0

Now, solving the above Quadratic Equation

D= √b² - 4ac

From the given equation

a= 3, b-4, c=-2

Then, D= √(-4)² - 4(3)(-2)

D= √16 +24

D = √40

Now, x= (-b ±D)/ 2a

x= -(-4) ± √40/ (6)

x= 4+ √40/6  or x= 4-√40/6

x = 1.72076 or x=−0.387426

Hence, the value of x is 1.72076 and 0.387426.

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Answer:

C. 25.12 inches

Step-by-step explanation:

radius = 4 inches

circumference = 2πr

circumference = 2 × 3.14 × 4 inches

circumference = 25.12 inches

Answer:c is correct 25.12

Step-by-step explanation:

The single payment that is required to settle both debts is given as follows:

$3,897.9.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which:

For the $2,100 payment in 6 months = 0.5 years, the principal is obtained as follows:

(1 + 0.5 x 0.063) P = 2100

P = 2100/(1 + 0.5 x 0.063)

P = $2,035.88.

For the $1,950 payment in 9 months = 0.75 years, the principal is obtained as follows:

(1 + 0.75 x 0.063) P = 1950

P = 1950/(1 + 0.75 x 0.063)

P = $1,862.02.

Hence the single payment is obtained as follows:

2035.88 + 1862.02 = $3,897.9.

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The weighted average for A,B and C will be 0.333.

What is weighted average?

Weighted average is a mean calculated by giving values in a data set more influence according to some attribute of the data. It is an important section in CAT quantitative aptitude. Weighted average is an average in which each quantity to be averaged is assigned a weight, and these weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Now,

Given weight for A=0.5, B=0.1 and C=0.4

Weighted average=(A+B+C)/3

=(0.5+0.1+0.4)/3

=1/3

Weighted average=0.33

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The dimensions of the poster are given as (x^2 - 6) inches by (x^2 + 12) inches.

The area of the poster is given by the product of these two dimensions:

Area = (x^2 - 6) inches * (x^2 + 12) inches

Area = x^4 - 6x^2 + 12x^2 - 72

Area = x^4 + 6x^2 - 72 inches^2

So, the area of the poster is x^4 + 6x^2 - 72 inches^2.

Using the subtraction operation, the number of flowers with 10 petals that Mrs. Moth picked was 6.

A subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

The subtraction operation involves the minuend, the subtrahend, and the difference.

The minuend is the number or value being subtracted from by the subtrahend.  The result of a subtraction operation is known as the difference.

The total number of picked flowers = 24

The number of flowers with 9 petals = 6

The number of flowers with 8 petals = 7

The number of flowers with 3 petals = 5

The total number of flowers identified = 18 (6 + 7 + 5)

The number of flowers with 10 petals = x

x = 24 - 18

= 6

Thus, 6 flowers had 10 petals out of the 24 Mrs. Moth picked.

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