Find the measure of angle x in the figure below:



1)

35°

2)

48°

3)

69°

4)

78°

The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.

In coordinate geometry, every point is denoted by definite coordinates since every point is situated at a fixed distance from the origin point (0,0). Any two points on a coordinate space are situated at a constant distance since their coordinates are fixed with respect to the origin. A line segment has two endpoints, and the coordinates of the endpoints help to determine the length of the line segment. Let us suppose (x1,y1) and (x2,y2) are the two points on a coordinate space then the distance between these two points is given by the distance formula as per the below:

            [tex]d = \sqrt{(x1 - x2)^2 + (y1 -y2)^2}[/tex]

given points are (3 ,7) and (15 ,16).

(x1,y1) = (3,7) and (x2,y2) = (15,16)

We know that two points on a plane have a constant distance in between them, and the distance formula gives the distance between these two points.

                  d =[tex]\sqrt{(x1 - x2)^2 + (y1 - y2)^2}[/tex]

              ∴  d = √(3 - 15)^2 + (7 - 16)^2

              ∴  d = 15 unit.

The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.

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y = -(5/3)x + 4 is slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

rewrite the equation of the given line in to slope-intercept form by solving for y

 3y + 5x = 6    

    3y = -5x + 6               (subtract 5x from both sides)

       y = -(5/3)x + 2           (divide both sides by 3)

Our line is parallel to this line, so it has the same slope, and a

y-intercept of 4, so we have...

 y = -(5/3)x + 4  

the equation ofa line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = 1 and c = 3, hence

y = x + 3 ← is the equation of the line  

*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept

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-6.48 > -6.5

5.983 < 5.99

3.09 > 3.01

Hope it helps

Answer:

A=6a2=6×(5)2=6×25=150cm2.

Step-by-step explanation:

Answer:

6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?

7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?

8. How many TENS must be added to 7 000 to make it 70 000.

Step-by-step explanation:

It was 5:50 p.m. when Camilla and Megan left the mall.

Add 1 hour and 25 minutes to 12:55 p.m. to determine the time when Camilla and Megan finished shopping for clothes:

12:55 p.m. + 1 hour and 25 minutes = 2:20 p.m.

Add 55 minutes to 2:20 p.m. to determine the time when Camilla and Megan finished eating at the food court:

2:20 p.m. + 55 minutes = 3:15 p.m.

Add 2 hours and 35 minutes to 3:15 p.m. to determine the time when Camilla and Megan left the mall:

3:15 p.m. + 2 hours and 35 minutes = 5:50 p.m.

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Types of expressions in math:

The types of expressions in math listed above are all valid and commonly used expressions in mathematics. Algebraic expressions are used to represent equations, while trigonometric, logarithmic, exponential, factorial, polynomial and rational expressions are used to represent different types of functions.

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The terms of expression 4x² - 3xy are

(a) 4x² and -3xy

(b) 4x² and 3xy

(c) 4x² and -xy

(d) x² and xy

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4 x + y, the two terms are 4 x and y. It is to be noted here that terms add up to form the expression.

Terms: a2,6a,and 9.

Variables: a2,a

Constants:9

Factors: a,a are the factors of term 1,-6 and a are the factors of term 2,and 9 is the factor of term 3.

Coefficients:1 is the coefficient of a2,-6 is the coefficient of a,and 9 is the coefficient of the constant term

Operators:- and+

Given, the expression is 4x² - 3xy.

We have to find the terms of the expression.

The terms are the numbers or the variables added together.

Each term in an algebraic expression is separated by a + sign or - sign.

Therefore, the terms in the given expression are 4x² and -3xy.

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Among the given equation, AX - BY = K is the example of a literal equation.

What is literal equation?

A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. The letter "L" stands for the rectangle's one side's length.

Given equations are:

A. AX - BY = K: is a literal equation as per definition.

B. 5X + 9Y: is not an equation.

C. 4 + 12= 4^2: it is not an equation.

D.8 - 2x = 14: it is not an equation. It is a linear equation with variable 'x'.

Hence, among the given equation, AX - BY = K is the example of a literal equation.

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333 integers,  there are 333 integers between 1 and 1,000 which are divisible by 3.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here

add all the numbers,

1 + 2+ 3 + 4+ 5 = 15

and 15/3 = 5

so it is divisible by 3

not by 9

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There are three types of discontinuity.

If a function f(x) is not continuous at a point 'a' in its domain D, it is said to be discontinuous at that location. A point of discontinuity of the function is thus referred to as point "a."

Any of the following scenarios might cause the discontinuity:

Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.

Discontinuity of the Second Type: If a function f(x) at x = a has neither a left-hand limit nor a right-hand limit, it is said to have discontinuity of the second kind.

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Discontinuity of the First Type: If the right hand of the function exists but is not equal to f, then the function f(x) is said to have a discontinuity of the first kind from the right at x = a. (a). The Left-Hand Limit and the Right-Hand Limit both exist in Jump Discontinuity and are finite, but they are not equivalent to one another.

The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2

The graph of function g is having a point of inflection at x=-2 and  x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.

A function is basically a relation between two sets having a domain , range and a co-domain.

We can represent functions graphically by plotting their equations and putting the value of co- ordinates.

A graph consists of four quadrants two positive and two negative. It helps to visualize data in a clear manner and helps to present data more efficiently.

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By using multiplication and subtraction, it can be calculated that-

Austin has to pay $9 for 3 pounds of chicken

Austin has to pay $(10.50 [tex]\times[/tex] p- 1.50)  for p pounds of chicken

What is subtraction and multiplication?
To find how big or small one number is from the other, then the operation used is called subtraction of numbers

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers

Here, subtraction and multiplication is used

Cost of one pound of chicken = $3.50

Cost of three pounds of chicken = $3.50 [tex]\times[/tex] 3 = $10.50

He has a coupon for $1.50 off the final amount.

Amount of money Austin has to pay for 3 pounds of chicken =

$(10.50 - 1.50) = $9

Amount of money Austin has to pay for p pounds of chicken =

$(10.50 [tex]\times[/tex] p- 1.50)

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Having seven sides, a heptagon is a polygon.It is also occasionally referred to as a septagon.

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After reviewing the generated schedule on Wednesday, you notice your Pharmacy Technician, Abigail Gibson, isn't being scheduled at all during the week. The option that will cause this is B. Availability is not entered

Pharmacy technicians check inventory and fill prescriptions. Pharmacy assistants assist pharmacists in dispensing prescription drugs to patients or medical professionals. Hospitals and retail pharmacies are where they primarily work.

In order to assist and support patients and guarantee they receive the best care, pharmacists collaborate with pharmacy technicians, who are medical professionals.

In addition to primary care, educational, military, or veterinary practices, pharmacy technicians can work in community (retail) pharmacies, hospital pharmacies, pharmaceutical production or sales in the pharmaceutical industry, prisons, and community (retail) pharmacies.

Based on the information illustrated, the correct option is B.

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You can extrapolate the volume formula to get the missing length of a pyramid with a rectangular base.

Determine the volume of a pyramid with a rectangular base using this formula.

Thus, using your algebraic skills, determine the formula again for missing length of a pyramid with a rectangular base.

L = V / (H x W) / 3.

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Answer:

k = -0.25

Step-by-step explanation:

If z varies jointly, that means z = k * x * y

putting in the numbers it gives us,

6 = k * (3) * (-8)

6 = k * (-24)

k = -(1/4) = -0.25

Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct

What is triangle?

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,

The triangles ABC and XYZ are similar by SAS similarity, as,

AC = XZ = 5,

AB = YZ = 13

∠ ACB = ∠ XZY

When you translate and then rotate triangle ABC, you will get triangle XYZ.

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The required value of the C in the algebraic measure of the angles is 61.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here,
The property of the triangle states that the sum of the remote interior angles is equal to the exterior angle,
So, adding c - 18 and c -15 will be equal to c +28
c - 18 + c - 15 = c + 28
c = 28 + 33
c = 61

Thus, the required value of the C in the algebraic measure of the angles is 61.

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Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. Examples include Piaget’s stages of cognitive development and Erikson’s psychosocial stages.

Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. This theory suggests that development does not occur in an orderly, linear fashion, but instead involves abrupt changes in which an individual moves from one distinct stage to the next. Examples of discontinuity theory include Piaget’s stages of cognitive development and Erikson’s psychosocial stages, which are made up of distinct stages of development that an individual must progress through before reaching the next stage. According to discontinuity theory, development is not a gradual, continuous process, but rather is made up of distinct stages with abrupt changes in between. This theory has been useful in helping to explain the development of various aspects of an individual, such as cognitive, social, and emotional development.

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The answer choice which represents a combination of ticket and snacks Edward may purchase is; 7 tickets and 8 snacks.

The given word problem can be expressed as a system of equations as follows;

Let x = number of tickets and

Let y = number of snacks;

Therefore; the system of equations is;

x + y = 15.............(I)

7.50x + 3.75y = 85

The second equation can be expressed as follows;

2x + y = 68 / 3.........(II)

Therefore, by subtracting equation 1 from we have that;

x = 68/3 - 15

x = 7.667 tickets.

And y = 15 - 7.667

y = 7.333 snacks.

On this note, the best combination of tickets and snacks he can get is; 7 tickets and 8 snacks.

By checking; 7 tickets cost; $52.5 and 8 snacks cost; $30. Total = $52.5 + $30 = $82.5.

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Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

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The domain of a function as described by the question, can be found by solving a given function for x such that the values of  x satisfy the equation. And the vertical asymptotes  can be found by solving for x values which make the equation go towards positive or negative infinity.

A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. To put it another way, an asymptote is a line that a curve travels towards as it approaches infinity.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set x.

As asked by the question, the domain of a function can be found by solving the equation f(x) = y for values of x such that the values of x give out a single value y. Similarly, the vertical asymptotes can be found from a rational function [tex]\frac{p(x)}{q(x)}[/tex] by equating the denominator q(x) to 0 and solving for x.  i.e q(x) = 0.

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Answer: 8.9 units

Step-by-step explanation:

We can use the distance formula for a 2d plane:

distance = √[tex](x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]

Plugging in our values for x1, y1, x2, and y2:

x1 = -7

y1 = 0

x2 = -3

y2 = 8

√[tex](-3 - -7)^2 + (8 - 0)^2[/tex]

= √[tex](4)^2 + (8)^2[/tex]

= √[tex]16 + 64[/tex]

= √[tex]80[/tex]

= [tex]8.944271921[/tex]

= 8.9 rounded to the 10th

Answer:

The answer for the problem on the left is 70

The answer to the problem on the right is 120

Step-by-step explanation:

Left Problem:

The sum of the interior angles is 360

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

Now we just need to find x.  

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

540 -50 - 130 - 120 = 240

The x's have the same value so 2402 is 120 .

Each x is 120

The answer to the problem on the left is 70 and the answer to the problem on the right is 120.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, angles and relative position.

Left Problem:

The sum of the interior angles is 360.

(n -2)180 is one formula to find the sum of the interior angles of a polygon.  n stands for the number of sides

(4-2)180

2(180

360

We know three of the angles we subtract them from 360 to find the missing angle

360-60-110-120 = 70

Right Problem:

We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180.  A straight line has an angle measurement of 180.

180-60 = 120

180 - 50 = 130

The sum of the interior angles is

(n-2) 180

(5-2)180

3(180) = 540    Subtract what we know

2x =  540 -50 - 130 - 120 = 240

x = 240 / 2 = 120

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Answer:

One of them must be a mirror image of the other

Step-by-step explanation:

Two shapes are congruent if one is a mirror shape of the other or if both have the same size.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.

The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

Here show an example for better understanding:

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

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The factors are (x + 1)(x + 2)(x + 10)

The process of breaking down an entity—for instance, a number, a matrix, or a polynomial—into a product of another entity—or factors—that, when multiplied together, yield the original number, matrix, or other entity is referred to as factorization or factoring.

Given Equation x³ + 13x² + 32x + 20

so The value of x³ + 13x² + 32x + 20 is

x³ + x² + 12x² + 12x + 20x + 20

=x² (x+1) + 12x (x+1) + 20(x+1)

=(x + 1)(x² + 12x + 20)

=(x + 1)(x² + 10x + 2x + 20)

=(x + 1)[x(x + 10) + 2(x + 10)]

=(x + 1)(x + 2)(x + 10)

Hence the factors are (x + 1)(x + 2)(x + 10).

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The correct question is

Factorize x³ + 13x² + 32x + 20

In the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.

The Latin word "angulus," which means "corner," is the source of the English term "angle."

The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

So, according to the given figure, the angle opposite to side LM in triangle LMN is ∠n.

Therefore, in the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.

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