In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.

From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.

A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.

The explanation of the translation is given as follows:

According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)

The translation rule for translating point k units up is given as:

(x,y) → (x, y+k).

Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).

Then,

The vertex A' =

A (-1, 2) → (-1 -3, 2+6)

= (-4, 8)

Therefore, the vertex A' is at (-4,8).

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From the translation described, the vertex A' is at the point (-4,8).

A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.

Angles, polygons, and graphs are the most typical places to locate the vertices.

The explanation of the translation will be:

Based on the translation rule for translating a point h units left is follows as

(x, y) → (x-h, k)

The translation rule for point k units up is follows as:

(x,y) → (x, y+k).

Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).

The vertex A' ;

A (-1, 2)

(-1 -3, 2+6)

= (-4, 8)

Therefore, the vertex A' is at the point (-4,8).

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Answer:

D. Negative

Step-by-step explanation:

Always read the graph from left to right

The graph is going down thus it is negative

Answer: Negative.

Step-by-step explanation: The graph of the line falls from left to right which makes it negative.

Answer:

  not similar

Step-by-step explanation:

You want to know if two isosceles triangles are similar, given that one has a base angle of 78°, and the other has an a.pex angle of 16°.

The base angles of the triangle with a.pex angle 16° will be ...

  (180° -16°)/2 = 82° . . . . . . not 78°

Two isosceles triangles will be similar if they have congruent base angles. These triangles do not, so they are not similar.

Answer:

153

Step-by-step explanation:

x+27=180

x=180-27

x=153

Answer:

10

Step-by-step explanation:

I am not absolutely sure but i think that is correct

The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.

What is parallel and perpendicular?

In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.

In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.

We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.

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Answer:

The answer is C

Step-by-step explanation:

If you substitute every x value for 5, you know that every equation can have 5 as an answer but C.

A. 3x+2=4x-3

Isolate the x(s) and combine like terms

3x+2-2=4x-3-2

3x=4x-5

3x-4x=4x-4x-5

-x=-5

-x(-1)=-5(-1)

x=5

Therefore A is a solution

B. (x+2)(x-5)=0

Substitution--Substitute every x for a 5

(7)(0)=0

anything multiplied by 0 will be 0

B. Is a solution because it is true.

C. 4x+2=15

Isolating the x(s) and combine like terms

4x+2-2=15-2

4x=13

4x÷4=13÷4

x=3.25

C is not a solution because x should equal to 5 but in this equation x can only be equal to 3.25. C is wrong.

We know our answer so we don't have to keep solving the rest of the equations.

But I'll just do D

D. 3x-10=x

Isolate the x(s) and combine like terms

3x-x-10=x-x

2x-10=0

2x=10

2x÷2=10÷2

x=5

D is a solution.

The equation relating to A to B is A = 45 + b and the amount is $66.

An equation is used to show the relationship between the variables that are illustrated.

In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.

Let the books be represented as b. The equation will be:.

A = 45 + 1b

A = 45 + b

where A = amount earned.

The amount earned when 21 books are sold will be:

A = 45 + b

A = 45 + 21

A = 66

The amount is $66.

This illustrates the concept of equations.

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Equation (B) "y = 3x + 10" represents the growth of the puppy.

So, the equation that represents the situation:

Then:

For example, Salomon checks the weight for the 6th time then:

So, the equation is correct.

Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.

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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}

Which equation represents the growth of the puppy? Select one:

A. y = x + 3

B. y = 3x + 10

C. y = 10x + 3

D. y = x + 10

The wave length of the gamma ray with a frequency of 1.0 x 10¹⁹ is 3 x 10⁻¹¹

Wave length:

Wavelength refers the distance between two peaks (or troughs) of a wave, and is therefore measured in meters.

The formula for calculating wave length is,

λ = c/v

where,

c = 3.0 × 10⁸, i.e. the speed of light, and

λ = wavelength , and

ν = frequency .

Given,

Here we have the frequency as 1.0 x 10¹⁹.

Now we need to find the wave length of the gamma ray.

Here we know that value of c = 3 x 10⁸

And the value of v = 1.0 x 10¹⁹

Wen we apply the value on the formula then we get,

λ = ( 3 x 10⁸) / ( 1.0 x 10¹⁹)

When we simplify it, then we get,

v = 3 x 10⁻¹¹

Therefore, the wavelength of the gamma ray is 3 x 10⁻¹¹.

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We will have that the expression has the solution of:

Therefore the solution is D. -5.

When we elevate to the power of 3 -5 will be equal to -125.

Applying power rules, the equations that is true when x = 10 but false when x = -10 is given as follows:

x³ = 10000.

The behavior of the exponents of 10 is different for even and for odd exponents, as follows:

In this problem, we have two exponents, as follows:

We want different results for the power when x = 10 and when x = -10, hence the correct option will involve the odd exponent 3.

The third power of 10 is calculated as follows:

10³ = 10 x 10 x 10 = 100 x 10 = 1000.

Hence the equation that is true for x = 10 and false for x = -10 is:

x³ = 10000.

As when x = -10, the result is:

(-10)³ = (-10) x (-10) x (-10) = 100 x (-10) = -1000.

The options are given by the image at the end of the answer.

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The equation

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

The line with that slope and that passes throught (1,6) is:

The following graph shows both equations:

Answer:

The equation of the line is;

Explanation:

Given that the line has a slope of;

And passes through the point;

Applying the point-slope equation of straight line;

substituting the given values and solving;

Therefore, the equation of the line is;

A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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The percentage of the employed population are people older than 40 who do not work in the hospitality industry is B. 17%.

The city's residents work in the hospitality industry = 28%

The residents that are age 40 or younger, and 15% of residents are people age 40 or younger = 55%

Those who work in the hospitality industry that are younger than 40% = 15%

Therefore, those that don't work in the industry will be:

Percentage of 40 or older - Percentage of those working

= (100 - 55%) - 28%

= 45% - 28%

= 17%

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The equation of the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

The given parameters are

Leading coefficient = 1

Zeros =  − 2 , − 4 , 3 , and 3 .

Polynomial equations have their multiplicities to add up to their degree.

This means that the multiplicity of the zeros is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

From the question, the polynomial is to be factored

This means that we represent it as

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

Hence, the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

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Polynomial is an expression consisting of indeterminates and coefficients the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3)

Polynomial is an expression consisting of indeterminates and coefficients, which involves  the operations like addition, subtraction, multiplication, and positive-integer powers of variables

Factors are the numbers which divide the expression or number with a remainder zero.

We need to write the factored form of the polynomial functions with real; coefficients and zeros minus two comma  minus four comma three and 3.

The leading coefficient of the polynomial is 1. Leading coefficient means coefficient of leading term.

Zeros =  − 2 , − 4 , 3 , and 3 .

Let the polynomial is of variable x.

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

(x-(-2))=x+2

(x-(-4))=x+4

(x-3)=x-3

So the factored form is (x+2)(x+4)(x-3)(x-3)

the polynomial is P(x)=(x+2)(x+4)(x-3)(x-3)

Hence the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3).

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The angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

The length of the ladder = 3.8 meter

The length of wall = 2.1 meter

Draw the figure using the measurements

We have to use the trigonometric function

The angle that a ladder make with the ground

sin θ = Opposite side / Hypotenuse

sin θ = 2.1/3.8

θ = 33.54 degrees

The distance from the foot of the ladder from the wall

cos θ = Adjacent side / Hypotenuse

cos 33.54 = Adjacent side / 3.8

Adjacent side = 3.8 × cos 33.54

= 3.16 meters

Hence, the angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

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The fraction 1/ (x- 3/6) can be simplified in its simplest form as  6/(6x -3).

From the question  were given the expression as  1/ (x- 3/6) , which have the numerator as 1 and the denominator as  (x- 3/6) , then

the denominator can be expressed as

(x- 3/6)

which can be  simplified as :

(6x -3)/6

then we can place it back to the normal equation as 1/ (6x -3)/6, since the equation now appear in form of inverse function, Then this can be expressed by simplifying it as  6/(6x -3).

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$128,000 represents 100%

To find how much is 4% we can use the next proportion:

Solving for x:

Her commission is $5,120

After subtraction we can see Stephanie has only 1 pizzas left.

What is subtraction?

The definition of subtraction is subtracting one number or amount from another. It is addition's opposite operation. Subtraction subtracts a number from another to find the difference, whereas addition adds or groups numbers to find the sum. The word "subtract" can also mean to compare two values to determine how many factors account for a value's difference from another. That is the most fundamental concept behind the term "difference" for the solution to a subtraction problem.

We are given that,

Stephanie has 5 pizzas, Also she shared 4 of the pizzas with her friends

Hence she is left with 5-4= 1 pizza
Hence Stephanie has left with 1 pizza

Therefore the correct option is option D)
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Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;

8  -  [tex]1\frac{2}{5}[/tex] = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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The identified acute angles in the diagram are: D. Angle WZY and angle WXY.

An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.

For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.

In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.

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In these linear expressions one is equivalent which is  3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .

An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.

Alternatively pluging; we will see that none of the exponents can be greater than 1.

2x - 3(1.3x - 2.5) = 5.9x + 7.5

2x -3.9x + 7.5 = 5.9 + 7.5

-1.9x + 7.5 ≠  5.9 + 7.5

thus linear expression is not equivalent.

3- 2( - 2.6x + 2.1) = 5.2x - 1.2

3 + 5.2x -  4.2 = 5.2x - 1.2

5.2x - 1.2 = 5.2x - 1.2

thus, linear expression is equivalent.

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Answer: 3, 9, and 9

Step-by-step explanation:

X+3x+3x=217x=21x=33, 9, 9=21

(a) The probability that the next page you read contain zero is 0.8187.

(b) The probability that the next page you read contains  or more typographical errors is 0.0175.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes

The probability that the next page you read contains zero. The expected number of typographical errors on a page of a certain magazine is  

That is, y = 0.2

Let  is a random variable representing the number of typos per page.

Since, we have a large number of letters per page, and the number of errors in one page will be small, we use Poisson distribution. The probability function of the Poisson distribution is defined as,

[tex]P(x = i) = e^-^y\frac{y^i}{i!},..... i = 0, 1, 2, ...[/tex]          ...(1)

Here, y is a parameter.

Find the probability that the next page you read contains zero.

That is, find P(y = 0)

plug y = 0 in equation (1), we get

P(x = 0) = 0.8187

The probability that the next page you read contain zero is 0.8187

Given the question that the probability that the next page you read contains  more typographical errors. The expected number of typographical errors on a page of a certain magazine is 0.2

That is y = 0.2

Let is a random variable representing the number of typos per page.

Find the probability that the next page you read contains more typographical errors.

That is find P(x ≥ 2)

P(x ≥ 2) = 1 - P(x ≤ 1)

= 1 - (P(x = 0) + P(x = 1))

= 1 - 0.982477

= 0.0175

The probability that the next page you read contains  or more typographical errors is 0.0175.

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Answer:

Step-by-step explanation:

13.

m1 is 120 because angle 120 and angle 1 are tranversal angle

So now we know that angles m1 and m2 are vertically opposite angle

Then m2 = 120

m1 = 120

m2 = 120

14.

angle 1 and 105 have the sum of 180 because they are Interior angles on the same side of the transversal

So angle 1 equals 180-105=75

angle 2 and angle 1 are on a line so the sum of the 2 angles are 180

So: 180 - 75 = 105

m1 = 105

m2 = 75