Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?

vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem

Answer:

Quotient = 3x² - 2x + 3

Remainder = 1

Step-by-step explanation:

We have to solve: [tex]\dfrac{3 x^{3} + 4 x^{2} - x + 7}{x + 2}[/tex]

We will use synthetic division to calculate this divisor

First, take the constant term of the divisor with the opposite sign and write it to the left. Write the coefficients of the dividend expression to the right Where there is no coefficient for a specific x term, use 0

Step 1: Write down the first coefficient asis

   |  x³      x²       x¹       x⁰
2  |  3       4        -1        7           ←    Coefficient row
   |
   ---------------------------------

       3                                           ← Result Row

Step 2: Multiply the entry in the left part of the table by the last entry in the result row and add he obtained result to the next coefficient of the dividend, and write down the sum.

    |  x³      x²       x¹       x⁰
-2  |  3       4        -1        7          
     |          -6                                         -6 = -2 x 3
   ---------------------------------

       3     -2                                          -2 = 4 + (-6)

Repeat step 2 until we have finished with all the entries. These are the snapshots of each computation. Current operands are in bold

   |  x³      x²       x¹       x⁰
-2 |  3       4        -1        7          
    |          -6        4                              
   ---------------------------------

       3     -2         3

   |  x³      x²       x¹       x⁰
-2 |  3       4        -1        7          
    |          -6        4      -6                        
   ---------------------------------

       3     -2         3       1

The last entry in the result table shows the remainder of the division

The resultant coefficients are 3, -2, 3, 1

Therefore the answer is
Quotient = 3x² - 2x + 3
Remainder = 1

Answer:

3:12 is equivalent 4:16

Step-by-step explanation:

5:8 = 0.625

3:12 = 0.25

15:32 = 0.48...

and 4:16 is 0.25, equal to 3:12

:]

(Brainliest would help a lot) Tell me if this is incorrect!

The value of the missing number in box A is [tex]1\frac{1}{2}[/tex]

The value of the missing number in box B is [tex]7\frac{1}{4}[/tex]

In order to determine the value of A, subtract [tex]1\frac{1}{4}[/tex] from [tex]2\frac{3}{4}[/tex]. Subtraction is the mathematical operation that is sued to determine the difference between two or more numbers

A =  [tex]2\frac{3}{4}[/tex] -  [tex]1\frac{1}{4}[/tex]

[tex]1\frac{3 - 1}{4}[/tex] = 1 [tex]\frac{2}{4}[/tex] = [tex]1\frac{1}{2}[/tex]

In order to determine the value of B, add [tex]4\frac{1}{2}[/tex] and [tex]2\frac{3}{4}[/tex] together. Addition is the process used to determine the sum of two or more numbers.

B = [tex]4\frac{1}{2}[/tex] + [tex]2\frac{3}{4}[/tex]

[tex]6\frac{2 + 3}{4}[/tex] = [tex]6\frac{5}{4}[/tex] = [tex]7\frac{1}{4}[/tex]

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Based on the given graph and line, the distance between the pair of points is 5

To find the distance between two points on a line or a pair of points, first find the coordinates of the points:

(-1, -2) and (-1, 3)

The distance then be found by applying the formula:

=√((x2 – x1)² + (y2 – y1)²)

Solving for the distance gives:

=√((-1 – (-1))² + (3 – (-2))²)

= 5

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the answer to 130x1000 is

130,000

Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius. The circumference is 471 yards

Do not worry; we have you covered. Simply enter the diameter into this formula, C=[tex]\pi[/tex]d, if you know it. Instead, did you receive the radius? No issue, just use the equation C=2[tex]\pi[/tex]r. For all the information you need on calculating a circle's circumference using its diameter or radius, keep reading. To make things simple, we even provide a circumference calculator.

To determine the circumference using the radius, use the formula C = 2[tex]\pi[/tex]r. The radius of the circle is denoted by "r" in this expression. Again, you can enter the number value of, which is a closer approximation of 3.14, into your calculator.

Any line segment that starts at the circle's center and ends at one of the circle's edges is known as a radius.

You might have noticed that this resembles the formula C = [tex]\pi[/tex]d. This is due to the fact that the diameter can be thought of as 2[tex]\pi[/tex]r because the radius is only half as long as the diameter.

Circumference= 2[tex]\pi[/tex]r

                         = 2*3.14*75 yards

                          = 471 yards

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Answer:

interior = 150° , exterior = 30°

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

since the polygon is regular then each exterior angle is

360° ÷ 12 = 30°

the sum of the exterior angle and interior angle = 180° then

interior angle = 180° - 30° = 150°

The domain and the range for the relations are given as follows:

For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.

For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.

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Answer:

let y represent number of months in a row and

let S represents sum of letters that have been sent in y number of months

This simply means that we can write equation:

14*y = S

For any number of months we express it in equation above and we get total number of letters she wrote.

Answer:

[tex]{ \sf{total = 14n \: \: letters}}[/tex]

The value of x is 67°.

To determine the value of x,

Draw a line parallel to lines l and m passing through the vertex at angle x dividing it into two angles a and b.

∠a  = 35°   (Interior Alternate angles are congruent)

∠b + 148°  = 180°  (Co-Interior angles are supplementary)

⇒ ∠b = 32°

∠x  = ∠a + ∠b

⇒ ∠x  = 35° + 32°

⇒ ∠x = 67°

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For given parabola 2x² - 8y = 0,

the axis of symmetry : y-axis

focus : (0, 1)

directrix : y = -1

In this question, we have been given an equation of parabola 2x² − 8y = 0

We need to graph the parabola and identify the axis of symmetry, focus, and directrix.

2x² - 8y = 0

2x² = 8y

x² = 8y/2

x² = 4y

The graph of the parabola  x² = 4y is as shown below.

From this graph, the vertex is (0, 0)

We know that, for a parabola of the form x² = 4ay, the focus is (0, a) and directrix is y = -a

For the parabola  x² = 4y, a = 1

So, the focus is (0, 1) and the directrix is y = -1

And the axis of symmetry for the parabola x² = 4y is the y-axis.

Therefore, for given parabola 2x² - 8y = 0,

the axis of symmetry : y-axis

focus : (0, 1)

directrix : y = -1

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Answer:

105

Step-by-step explanation:

Work out the difference between the highest value and the lowest value in

the list:  -55, 45, -30, 25, -90

The lowest value will be the largest negative number in the list: -90

The highest value will be the largest positive number in the list: 45

the difference between -90 and 45:

-90 - 45 = 105

Answer:

the answer for n is 5

Step-by-step explanation:

2 + n = 7

n = 7-2

n = 5

Answer:

Sarah=x

Lea=3x-4

Rachel=1/2x-3

Amanda=2x+1

Sum=46

x+3x-4+1/2x-3+2x+1=46

6.5x-6=46

6.5x=52

x=52/6.5x

x=8

input x in each sister's age:

Sarah= 8 years

Lea = 3(8)-4=20 years

Rachel = 1/2(8)-3=1 year

Amanda = 2(8)+1=17years

Step-by-step explanation:

Answer:

Step-by-step explanation:  : f(x) = 4x² + 3x – 7f(-2) = 4(-2)²+3(2)-7f(-2) =16+6-7 =32-7 = 25.

Answer:

1: x

A variable is a letter in an equation that represents an unknown value or a value that can change.

2: 2

A coefficient for a variable is the leading number in front of the variable. It tells you how many times the variable happens

3: 2x

A term is a multiplication or division statement separated by a +/- sign.

Hope that helps

Jacob will need 7 months to spend all the money.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob had $180 in his savings account at the beginning of summer vacation. over the next 12 weeks, he mowed lawns in his neighborhood earning $145 and spending $55 each week. he deposited all of his weekly profits into his savings account each week. when summer vacation is over, he plans to spend $180 per month.

The number of months will be calculated as:-

Total money in the account = 180 + 12(145-55)

Total money in the account = $1260

Total months = 1260 / 180

Total months = 7 months

Therefore, Jacob will need 7 months to spend all the money.

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Using a proportional relationship, we have that:

A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

From the table in this problem, the constant is given as follows:

k = 240/5 = 48/1 = 48.

Hence the relationship is:

y = 48x.

Then:

For 300 pencils, the number of boxes is given by:

48x = 300

x = 300/48

x = 6.25.

There are not decimal parts of a box, a complete box is needed, hence 7 boxes are needed, meaning that 6 boxes are not enough for 300 pencils.

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After losing 4 Kg ,the weight of Artur is 14 Kg .

In the question ,

it is given that ,

the ratio of weight of Max : Artur is 5 : 9 .

So the weights of Max and Artur before dieting is 5x and 9x .

Now Artur goes on dieting and lose 4 Kg weight and

the ratio of weight of Max and Artur becomes 5:7  .

and the weights of Max and Artur after dieting is  5x and 7x .

Present weight of Artur = 7x .

As we can see that the change in Artur weight is 9x - 7x = 2x

According to the question

2x = 4

x = 2

hence Artur now weighs 7*(2) = 14 Kg

Therefore , after losing, 4 Kg the weight of Artur is 14 Kg .

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The slope and equation of line with the coordinates (5,6) and (3,4) are 1 and y = x + 1 respectively.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point A(5,6)

Point B(3,4)

Slope m = ?

To determine the slope, plug the given coordinates into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 4 - 6 )/( 3 - 5 )

Slope m = ( -2 )/( -2 )

Slope m = ( -1 )/( -1 )

Slope m = 1/1

Slope m = 1

Next, use the the formula for the equation of line to determine the y-intercept 'b'.

y = mx + b

Plug in slope m = 1 and point (5,6)

6 = 1(5) + b

6 = 5 + b

b = 6 - 5

b = 1

Now that we have both the slope m ( 1 ) and y-intercept b ( 1 ), plug these values into y = mx + b to find the linear equation.

y = mx + b

y = 1x + 1

y = x + 1

Therefore, the slope is 1 and equation of line is y = x + 1.

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Answer:

he will receive $2.51

Step-by-step explanation:

Answer:

the coordinate of point P is (14/5, -1)

Step-by-step explanation:

The length of the edge of the box is 6 cm.

Here, we are given that the volume of a box is 216 cm cube.

Here, we assume that the box is a cube and not a cuboid since only then we will be able to find the edge of the box.

The volume of a cube is given by the formula-

Volume = side × side × side

Let the side of the given cube be x.

Then we can form the following equation-

[tex]x^{3}[/tex] = 216

x = (216)^1/3

we can find the 216 is the cube of 6. Thus,

x = 6

Hence, the length of the edge of the box comes out to be 6 cm.

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By solving a simple linear equation, we will get that:

36° = m∠AOB

We can write a simple linear equation here, we know that:

m∠AOC = 108°

And we also know that:

m∠AOC = 3*m∠AOB

If we replace the first equation into the second one, then we will have the linear equation:

108° = 3*m∠AOB

And we want to solve this for m∠AOB, to do so, we just need to divid both sides by 3, we will get:

108°/3 = m∠AOB

36° = m∠AOB

We conclude that the measure of angle ∠AOB is 36°

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Answer:

1.  3 and -5

2.  7

Step-by-step explanation:

The zeros of functions are the x-values when y = 0, i.e the point(s) at which the line crosses the x-axis.

To find the zeros of the given functions, set the function to zero and solve for x.

Given function:

[tex]y=5(x-3)(x+5)[/tex]

Set the function to zero:

[tex]\implies 5(x-3)(x+5)=0[/tex]

[tex]\implies \dfrac{5(x-3)(x+5)}{5}=\dfrac{0}{5}\\[/tex]

[tex]\implies (x-3)(x+5)=0[/tex]

Using the Zero Product Property, set each factor equal to zero and solve for x:

[tex]\implies (x-3)=0 \implies x=3[/tex]

[tex]\implies (x+5)=0 \implies x=-5[/tex]

Therefore, the zeros of the function are 3 and -5.

Given function:

[tex]y=(x-7)^2[/tex]

Set the function to zero and solve for x

[tex]\implies (x-7)^2=0[/tex]

[tex]\implies \sqrt{(x-7)^2}=\sqrt{0}[/tex]

[tex]\implies x-7=0[/tex]

[tex]\implies x=7[/tex]

Therefore, the zero of the function is 7 (with multiplicity 2).

The integer in the solution set of 5/6m - 4 < 1/3m + 5 that would make it false is 20

The set is given as

S:{−18, 2, 15, 20}

The inequality expression is given as

five sixths m minus four is less than one third m plus 5

Rewrite the inequality expression properly

So, we have

5/6m - 4 < 1/3m + 5

Subtract 1/3m from both sides of the inequality expression

So, we have

1/2m - 4 < 5

Add 4 to both sides of the inequality expression

So, we have

1/2m < 9

Divide both sides of the inequality expression hy 1/2

So, we have

m < 18

This means that the integers in the solution set are integers that are less than 18

These integers are −18, 2, 15

All other integers would make the inequality false

Hence, the solution is 20

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The solution to the equation is f = 75.

The initial charge or setup cost is represented by the intercept or f.

Given equation: 270 = f + 6.50(30)

We must identify the equation's solution and explain what it represents in this situation.

The equation above is written in the form of a slope-intercept function where 6.50 is the gradient or slope of the function and 30 equals the number of shirts. The total cost of printing is 270.

The equation 270 = f + 6.50(30) can be solved as follows:

270 = f + 6.50(30)

⇒ f = 270 - 195 = 75

Therefore, the initial charge or setup cost is represented by the intercept or f. As a result, the setup fee is 65.

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The following results of the quadratic equation are summarized below:

Vertex: (h, k) = (3, 1)

Axis of symmetry: x = 3

Min/Max value: f(3) = 1 (Maximum)

y-Intercept: - 8

x-Intercepts: (2, 0), (4, 0)

Domain: All real numbers.

Range: y ≤ 1.

Sketch of the graph: Please see image.

Standard form: f(x) = x² - 6 · x + 8

Rigid transformations: Horizontal translation / Reflection about x-axis / Vertical translation

In this problem we have a quadratic equation in standard form, whose definition is shown below:

f(x) - h = C · (x - h)²        (1)

Where:

Now we proceed to determine each of the required features:

Vertex

The quadratic equation has a vertex at point (3, 1).

Axis of symmetry

The axis of symmetry of the parabola is x = 3.

Min/Max value

For as the vertex constant is a negative number, then the vertex represents a maximum. Then, we evaluate the function at x = 3:

f(3) = 1

y-Intercept

The y-intercept is the value of the quadratic equation evaluated at x = 0.

f(0) = - (0 - 3)² + 1

f(0) = - 9 + 1

f(0) = - 8

x-Intercepts

The x-intercepts are the values of x such that f(x) = 0, all these can be found by using algebra properties:

- (x - 3)² + 1 = 0

- (x² - 6 · x + 9) + 1 = 0

- x² + 6 · x - 9 + 1 = 0

x² - 6 · x + 8 = 0

(x - 2) · (x - 4) = 0

Then, the x-intercepts of the parabola are (2, 0) and (4, 0).

Domain

The domain of all quadratic equations are all real numbers.

Range

Since the vertex constant is negative, the range of the quadratic equation is the subset of all real numbers equal or less than the y-value of the vertex.

Sketch of the graph

Please check the image attached below to see the graph.

Standard form

The standard form of the quadratic equation is:

f(x) = x² - 6 · x + 8

Rigid transformations done

Let be g(x) = x², it is transformed into f(x) = - (x - 3)² + 1 by using the following rigid transformations:

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Answer:

the 66th term is 1095