Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program?​

The value of the x is 11.

What are vertically opposite angles?

Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles. In this instance, the word vertical refers to the vertex as opposed to direction.

We have given,

Two opposite angles:

(6x + 1)°, and 67°

So, We need to determine the value of x.

We know that the property of opposites angles, which the opposite angles are equal to each other.

So, (6x + 1)° = 67°

By calculating further:

6x + 1 = 67

6x = 67 - 1

6x = 66

x = 66/6

x = 11

Hence, the value of the x is 11.

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If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.

What is a digit?

In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.

The first equation is as given t + u = 9

Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.

The second equation is t = (1/2)u => u = 2t

When we replace this in first equation we get -

t + 2t = 9  

3t = 9  

t = 9/3

t = 3

When we replace it again in the equation -

u = 2 t

= 2 · 3

= 6

The requested number is 36.

Therefore, the number is 36 and the second equation is t=u/2.

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Answer:fx

Step-by-step explanation:

Answer: y=2x-15

Step-by-step explanation:

Answer:

y=1/2x + 15

Since,her original flight plan time is X and hence the flight will reach 2 times faster the X becomes X/2 and the additional time 15 minutes which has already been delayed.So,she will arrive her destination in(1/2X+15)min from 4:00 p.m.

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Answer:

Step-by-step explanation:

1 radian is equal to 180^0/Pi

[tex]55=55*\frac{180}{\pi y} \\=54.97787[/tex]

Solving the example, hope it will help you with better understanding.

Given system:

We need to eliminate one of the variables c or d. Let us eliminate d.

We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.

Demonstrating how it works:

2c + 3d = 12, we leave it as is

5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39

Now add up the two equations:

Now we can find the value of d:

Our solution is:

Answer: |-1|

Step-by-step explanation:

So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)

Step-by-step explanation:

10x + 17 + 8X - 31 + 6x - 8 = 180

Use this equation and solve this equation and you will find the answer

Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The data set is,

⇒ -1, 0, 3 ,4, -3, -1

Now, We know that;

The mode is the value that appears the most often in the data set.

Here, In the data set - 1 is most often number.

So, The mode of data set = - 1

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Answer:

x = 5/19

Step-by-step explanation:

For left side, apply logarithm division property:

[tex] \displaystyle{ \ln a - \ln b= \ln \left( \dfrac{a}{b} \right)}[/tex]

Hence:

[tex] \displaystyle{ \ln \left( \dfrac{x}{4x - 1} \right) = \ln 5}[/tex]

Since both sides have same ln, we can cancel ln both sides:

[tex] \displaystyle{ \dfrac{x}{4x - 1} = 5}[/tex]

Solve the equation for x:

[tex] \displaystyle{x = 5(4x - 1)} \\ \\ \displaystyle{x = 20x - 5} \\ \\ \displaystyle{5 = 20x - x} \\ \\ \displaystyle{5 = 19x} \\ \\ \displaystyle{x = \dfrac{5}{19}}[/tex]

Therefore, x = 5/19

Answer:

b < -30

Step-by-step explanation:

27 > B + 57   Subtract 57 from both sides

27 - 57 > b +57 - 57

-30 > b

or

b < -30

The tangent ratio of F by using the rule from trigonometry is 4/3

Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.

The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;

Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.

Therefore, the tangent ratio for F is:

tan θ = 8/6

This can be reduced to 4/3

Therefore, we can conclude that the tangent ratio of F is 4/3.

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The number of items must be made for the average cost to fall to $5 wil be; 900.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

We are given that function = 40x +700 represents the average cost (in dollars) of making items.

Then the item made for function average cost to fall to $5.

= 40x + 700

= 40(5) + 700

= 200 + 700

= 900

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Answer:

ST = 10

Step-by-step explanation:

Δ RSQ and Δ RTP are similar by the AA postulate , then

the ratios of corresponding sides are in proportion , that is

[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )

[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

RT = 3 × 5 = 15

Then

ST = RT - RS = 15 - 5 = 10

The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's solve for x:

3(4x - 10) = 2(3x - 30)

First, we can simplify both sides by distributing the coefficients:

12x - 30 = 6x - 60

Next, we'll move all the x terms to one side of the equation and the constants to the other side:

12x - 6x = -60 + 30

Simplifying further:

6x = -30

Finally, we can solve for x by dividing both sides by 6:

x = -5

Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

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The value of x in the following parallelogram is 15

You should recall that a parallelogram is a quadrilateral whose opposite sides are equal and parallel

The given sides are

This means that

X + 10 = 2x -5

Collecting like terms we have

x-2x = -5-10

-x = -15

Dividing by -

We have x= 15

Therefore x is 15 in the parallelogram.

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Answer: 3/1. 6/2. 9/3. 12/4. 15/5. 18/6. 21/7. 24/8. 27/9 and many more

Step-by-step explanation:

The values of ∠4 and  ∠3 are 116 degrees and 64 degrees respectively.

Given ,

What are supplementary angles ?

The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .

Angles 3 and 4 are supplementary.

The measure of angle 3 is

thirty-five more than one-fourth the measure of angle 4.

So,

∠3 + ∠4 = 180 degrees.

∠3 = 180-∠4 - equation 1

∠3 = 35 + (1/4 ) ∠4 - equation2

As equation 1 and 2 are equal

hence,

180-∠4 = 35 + (1/4) ∠4

180-35 = ∠4 +  (1/4) ∠4

145 =  ((1/4)+1) ∠4

145 = (5/4) ∠4

∠4 = 145 * 4 / 5

∠4 = 29*4

∠4 = 116

∠3  = 180-116

∠3 = 64

Hence the values of  ∠4 and  ∠3 are 116 degrees and 64 degrees respectively.

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Answer: 225°

Step-by-step explanation:

The correct option is D)

Refer Figure

Given:

ABCD  is a square

ABP  is an equilateral triangle

AB=BP=BC  (△ABP is equilateral and AB and BC belong to a square, hence all are equal)

∠ABC=∠ABP+∠PBC=60°+∠PBC

90°−60°=∠PBC

∠PBC=30°

In △BPC

BP=BC

∠BPC=∠BCP= 2

180−∠PBC

​ ( angles opposite to equal sides of a triangle are equal)

∠APC=∠APB+∠BPC=(60+75)°=135°

Hence, Reflex ∠APC=(360−135)°=225°

Answer:

[tex]y=\frac{3}{4}x-\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]m_{\parallel}=\frac{3}{4} \\ \\ y-1=\frac{3}{4}(x+6) \\ \\ y-1=\frac{3}{4}x-\frac{9}{2} \\ \\ y=\frac{3}{4}x-\frac{7}{2}[/tex]

When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) . The line segment's exact midway is where the midpoint is located.

The term "midpoint" describes a point along a line that connects two points. The midway is situated between the two reference locations, which are the line's ends. The line connecting these two places is split into two equally sized sections by the middle. A point that splits a line segment into two equal halves is known as the midway. In other words, the line segment's exact midway is where the midpoint is located. It is demonstrably true that the middle of a number line has the same value as the average of any two matching places on the line.

given

midpoint of AB is equal to (x2 - x1) / 2 (3 + 1) / 2 = 2.

the midpoint of AB is 1

the midpoint of AB is (y2 - y1)/2

= (1+1)/2.

= ( 2 ,1 )

When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) .

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Answer:

The volume of wood in a tree varies directly with the height and the square of the length of the tree. This means that if we increase the height of the tree, the volume of wood in the tree will also increase, and if we increase the length of the tree, the volume of wood will increase by the square of that increase.

This relationship can be expressed mathematically as:

V = khl^2

Where V is the volume of wood in the tree, h is the height of the tree, l is the length of the tree, and k is a constant of proportionality.

This relationship is based on the assumption that the cross-sectional area of the tree remains constant, and that the volume of wood in the tree is directly proportional to the height and the square of the length of the tree.

Answer:

Below

Step-by-step explanation:

A)  Juan reads at   57 pages /hr

B)  Juan reads 9 pages more per hour (57-48) than Lexi

       in 7 hours this will be   7 hr * 9 p/hr = 63 pages

The equation for a is   a=2A-b

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here:  A=1/2(a+b)

                     a=2A-b

Hence, the equation for a is   a=2A-b

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In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.

What is permutation?

An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.

We want to choose 7 objects without replacement from 11 distinct objects

So, since the order of the choices is relevant, we will use permutation.

Therefore,

⇒nPr = n! ÷ (n - r)!

⇒11P7 = 11! ÷ (11 - 7)!

⇒11P7 = 11! / 4!

⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)

⇒11P7 = 1663200 ways

Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.

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A vertical line in geometry is one that crosses the page from top to bottom.

A vertical line in geometry is one that crosses the page from top to bottom. Its cousin is the horizontal line that spans the page from left to right. A horizontal line and a vertical line are perpendicular.

Businesses utilize segmentation as a marketing strategy to focus on a certain market segment or type of customer. While vertical segmentation sharpens your marketing emphasis to target customers in a smaller demographic, horizontal segmentation entails offering a product to a broad range of consumers.

A horizontal object is one that is perpendicular to the horizon. Due to the fact that vertical is the polar opposite of horizontal, anything that forms a 90° (right angle) with either the horizontal or the horizon is referred to as vertical. This means that the horizontal line is one that crosses from left to right. Mathematical applications of the horizontal and vertical.

Therefore, the correct answer is option C. (5.-4) and (-2, 3).

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The yards of thread that will take to make an entire sock will be 3 3/4 yards.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, 2 1/2 yards of thread to make 4 /6

of a sock.

The yards of thread that will take to make an entire sock will be:

= 2 1/2 ÷ 4 / 6

= 5 / 2 × 6/4

= 30 / 8

= 15 / 4

= 3 3/4 yards.

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The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

(-x^4+7x^3+2x+3)/ (x-3)

=-x² + 4x² + 12x + 38 + 117/(x - 3)

Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

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The shadow of the tree at the same time of day was 113.29 foot long.

Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).

In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.

We know that

1 feet = 12 inches

So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet

Now, lets find the shadow of tree

5[tex]\frac{2}{3}[/tex]/2 = 321/x

x = 113[tex]\frac{5}{11}[/tex]

x = 113.29

Thus, the tree's shadow at the same time of day was 113.29 foot long

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