11. What is the length of the missing side, x?
40 in.
51°
Your answer
74°
35 in.
74°
X
49 in.
55°

Jamal is correct ( ½+⅓ =⅚), when he says that when adding two unit fractions, the numerator is found by adding the denominators, and the new denominator can be found by multiplying the previous denominators.

A denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

In a fraction, the number above the line is the numerator. For instance, the numerator of the fraction 3/5 is 3. A fraction's numerator displays the number of pieces that make up the whole while the denominator.

Adding 2 unit fractions example ½ and ⅓

By Jamal’s theory, 2+3=5

2*3=6

½+⅓ =⅚

Hence the theory is proved right.

Drawbacks of Jamal’s Shortcut,

It is only for the unit fraction and not for any other type of fractions.

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Answer:

$960

Step-by-step explanation:

Quarterly Dividend Per Share = $0.12

Quarterly Dividend For 2000 shares = 0.12 x 2000 = $240

Since there are 4 quarters in a year, yearly dividend for 2000 shares at $0.12 per share

= $240 x 4 = $960

The correct option B. It is a one-to-one function; for the given graph.

For the given question;

As, in the given graph for the function, for each value of the domain (the value of x), there is only one value of range (y).

Thus, the given graph shows the one-to-one function.

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Answer:

(3,2)

Step-by-step explanation:

since -3 + 9 =6

6 ÷ 2 =3

2 + 2 = 4

4 ÷ 2 = 2

therefore (3,2)

The domain of the graphed function is option (D)

What is the domain of a graphed function?

In mathematics, the domain of a function is the set of inputs that the function accepts. It is also known as dom(f) or dom f, where f is the function.

The domain of the graphed function is option (D) x is all real numbers.

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For given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13

In this question, we have been given two functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x²

We need to find f(x) - g(x)

We need to subtract function g(x) from function f(x)

= f(x) - g(x)

= 3x² - 8 - (5 - 2x - 2x²)

= 3x² - 8 - 5 + 2x + 2x²

= 3x² + 2x² + 2x - 8 - 5

= (3 + 2)x² + 2x - (8 + 5)

= 5x² + 2x - 13

Therefore, for given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13

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Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.

What is Sequence?

A list of numbers or objects in a special order is called sequence.

Given that;

The nth term of a sequence = 3n²

Now,

Let [tex]a_{n}[/tex] be the nth term.

Then, [tex]a_{n} = 3n^{2}[/tex]

Let m be the term which is the first term with a value greater than 1000.

Then, [tex]a_{m} > 1000[/tex]

Substituted the value of [tex]a_{m}[/tex] we get;

3m² > 1000

Divide by 3 we get;

m² > 1000/3

m² > 333.333

Take square root both side;

m > √333.33

m > 18.25

Thus, m = 19

So, 19th term is the first one with a value greater than 1000.

Hence, [tex]a_{19} = 3(19)^2 = 3 * 361 = 1083[/tex]

Thus, Position of 1083 is 19 in the sequence that is the first one with a value greater than 1000.

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If £N is shared between three people in the ratio 2:3:7 The largest share is £540 more than the smallest share. the value of N is 1296.

Let x represent the sharing unit

Hence,

2x :3x :7x

so

7x = 2x + 540

7x - 2x = 540

5x =540

Divide both side by 5x

x = 540/5

x = 108

Sharing unit

2x = 2 ×108

= 216

3x = 3 × 108

= 324

7x = 7 × 108

= 756

Value of N = 216 + 324 +756

Value of N = 1296

Therefore we can conclude that the value of N is 1296.

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The value of the smiley face provided in the question is 908.

The first step is to determine the value of each of the shapes.

The value of the rectangle would be determined first. Using the third given equation, let r represent the value of one rectangle.

(4 x r) + (2 x r) - (3 x r) = 15

4r + 2r - 3r = 15

3r = 15

r = 15 / 3 r

r = 5

The next step is to determine the value of the triangle. The second equation would be used. Let t represent the value of the triangle.

(3 x 5) + (4 x t) = 47

15 + 4t = 47

4t = 47 - 15

4t = 32

t = 32 / 4

t = 8

Finally, the value of the star would be determined. Let the value of the star be represented with s. Using the first equation:

5 + (3 x 8) - s = 17

5 + 24 - s = 17

29 - s = 17

s = 29 - 17

s = 12

Now, the value of the smiley face can be determined:

12 x (8  + 12 - 5) + 8(8 . 12 - 5)

12 x (15) + 8(91)

180 + 728 = 908.

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The sunflower would be 11 inches tall after 6 weeks  and it would be  (5+w) inches tall after w weeks .

In the question ,

it is given that

the height of the sunflower when it was planted = 5 inches

rate of growth of sunflower = 1 inch per week

let y represents the height of the sunflower after x weeks .

So , According to the question , the equation becomes

y = 5 + 1*x

to find the height after 6 weeks , substitute x=6

we get ,

y = 5 + 1(6)

y=5+6

y=11

height after 6 weeks will be 11 inches .

to find the height after w weeks , substitute x=w

we get ,

y = 5 + 1(w)

y=5+w

sunflower will be (5+w) inches tall

Therefore  , the sunflower would be 11 inches tall after 6 weeks  and it would be (5+w) inches tall after w weeks .

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Answer:

2x-y=18

-2x-9y=2

cancel 2x

add equation:

-y+(-9y)=20

-10y=20

y=-20/10

y = -2

input y in any equation:

2x-(-2)=18

2x+2=18

2x=18-2

2x=16

x= 8

Answer:

Step-by-step explanation:

-125/4

-124/4=-31

-31 1/4

Answer:

Explanation:

Given:

We must remember that:

Since the value of cos x is given, we plug in the value into 2cos^2x-1. So,

Therefore, the exact value of cos 2x is 7/8.

The Area of the figure ,composing of a square and four semicircles is 832.7 sq. units

The Length of the side of the square is 18 units which is also the diameter of the semicircle.

So, The Area of square is Length * Length = 18*18 = 324 sq. units

Now, the radius of semicircle = 0.5(diameter)= (0.5)*18 = 9 units

The area of semicircle = half of area of circle = (0.5)3.14(radius)(radius)

The area of one semicircle = (0.5)3.14(9)(9)

The area of one semicircle = 127.17

The Total area of figure consists of 4 semicircles and one square

So, Total area = 4(area of 1 semicircle) + area of square

Total area = 4(127.17) + 324

Total area =  832.68 sq. units

rounding off the total area = 832.7 sq. units

Therefore, the total area of the given figure is 832.7 sq. units.

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The value of the inequality is n > 7. 75

Inequalities are simply defined as mathematical relations that makes an unequal or unbalanced comparison between two elements or numbers and even for known mathematical expressions

They are frequently used in comparing two or more numbers on the number line and this is carried out on the basis of their magnitude or size.

Absolute value can be defined as the value of a number irrespective of its direction from zero on the number line.

The absolute value of a number must take the positive sign.

It is represented with the symbol '| |'

Given the inequality:

-5 + |1 - 8n| > 58

find the absolute value

-5 + 1 + 8n > 58

collect like terms

8n > 58 + 4

8n > 62

Make 'n' the subject of formula by dividing both sides by 8

8n/8 > 62/8

n > 7. 75

Hence, the value is n > 7. 75

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Answer:

The longest side of a quadrilateral with length of consecutive even integers is 26 feet.

The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers.

A quadrilateral is a polygon with 4 sides.

Therefore, the sides are consecutive even numbers.

Hence,

smallest side = x

Therefore, perimeter is the sum of the whole sides of the quadrilateral.

x + x + 2 + x + 4 + x + 6 = 92

4x + 12 = 92

4x = 92 - 12

4x = 80

x = 80 / 4

x = 20

Therefore, the longest side of the quadrilateral is 20 + 6 = 26 ft.

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Brian will have 46.90 miles to his destination after 41 minutes of driving.

In the question ,

it is given that

Brian has 69 miles left to his destination after 15 minutes of driving

let x denotes the driving time ( in minutes)

and y denote the remaining distance ( in miles )

so the point is represented by (15,69)  

and given that

Brian has 58.8 miles to his destination after 27 minutes of driving

so the second point is (27,58.8).

Since the relationship is given to be linear , hence it will represent a line .

the equation of line passing through the two points (15,69) and (27,58.8) is given by

(y-69)=(58.8-69)/(27-15) * (x-15)

y-69 = -10.2/12 * (x-15)

y-69 = -0.85(x-15)

y-69= -0.85x+12.75

y = -0.85x + 81.75

So , the linear relationship between remining distance and driving time is given by y = -0.85x + 81.75 .

to find miles will he have to his destination after 41 minutes of driving

Substituting x=41 we get

y = -0.85(41) + 81.75

y = -34.85 + 81.75

y = 46.90 .

Therefore , Brian will have 46.90 miles to his destination after 41 minutes of driving.

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The probability that washing dishes will take time between 14 and 16 minutes is equal to 25%.

This type of probabilty can be termed a uniform probability in which all the outcomes or results are equally likely.

The lower limit can be represented as a and in this problem is 12 minutes and the upper limit can be considered b and in this problem is 20 minutes.

The equation to find probability, in this case, can be given as:

P ( c ≤ X ≤ d ) = d - c / b - a

Here c = 14 and d = 16 as we have to find the probability that washing dishes will take between 14 and 16 minutes.

Therefore;

P ( 14 ≤ X ≤ 16 ) = 16 - 14 / 20 - 12 = 2 / 8 = 0.25

Converting it into percentage:

0.25 = 0.25 × 100 = 25%

Therefore, the probability that washing dishes will take her between 14 and 16 minutes is calculated to be 25%.

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For both triangles to be proven to be similar to each other by the SAS similarity theorem, it also needs to be shown that: A. angle N ≅ angle Z.

The side-angle-side similarity theorem (SAS) states that two triangles can be proven to be similar to each other if two pairs of corresponding sides of the two triangles are proportional to each other and one pair of corresponding angles of the two triangles are congruent to each other.

In the image given, we know that in both triangles:

XZ/LN = 6/2 = 3

ZY/NM = 9/3 = 3

Therefore:

XZ/LN = ZY/NM = 3

This means that the two triangles have two pairs of corresponding sides that are proportional to each other.

Thus, we also need to show that both triangles have a pair of congruent included angles before we can prove both triangles are similar to each other.

Thus, what needs to be shown is: A. angle N ≅ angle Z.

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Answer:

14.375 or 14 3/8

Step-by-step explanation:

5.75*2.5=answer

Answer 5 3/4

Step by step explanation:

So her speed is 5 3/4 mph.

So you just calculate 5 3/4 x 2.5 and you get 14 3/8

I hope this helps

Answer: x = -21/2

Step-by-step explanation:

2x/2 = -21/2

x = -21/2

Divide both sides by 2.

-21 is not divisible by 2, so -21/2 is improper in simplest form.

The issues are divided into groups according to the four mathematical operations: addition, subtraction, multiplication, and division (suitable for pupils in the second or third grade who have mastered decimal division). Here answer will be $66.

These worksheets on money word problems expose pupils to practical issues and arithmetic applications. The issues are divided into groups according to the four mathematical operations: addition, subtraction, multiplication, and division (suitable for pupils in the second or third grade who have mastered decimal division).

Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative numbers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. However, the set of real values obtained by the operation is its codomain of definition, active codomain, image, or range. The set that contains the values created is referred to as the codomain. For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.

Each month payment= $125

8 months payment= $125*8= 1000

cost of a car= $934

cost to pay all at once= $1000-$934

                                    = $66

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We need to solve the s varibale for the given equation:

Hence, s=32

Command Economies -More Public Property, Smaller Wealth Gap ,Less chance for higher income

Mixed Market Economies- Larger Wealth Gap, Greater chance for

higher income, More private property

Economy: An economy encompasses all of the activities related to the production, consumption, and trade of goods and services in an entity, whether the entity is a nation or a small town. No two economies are identical. Each is formed according to its own resources, culture, laws, history, and geography

Command Economies                            Mixed Market Economies

More Public Property                               Larger Wealth Gap

Smaller Wealth Gap                                 Greater chance for higher income

Less chance for higher income               More private property

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Answer:

in the picture

Step-by-step explanation:

No, the combination lock is not appropriate. This is so as the repetition is  allowed, neither permutation nor the combination rule holds true or valid.

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The answer of the given function is [tex](f-g)(x) = 2x^3+7x^2-7x-3[/tex]. So the answer is C option.

f(x) is a function that can be named to avoid repeatedly writing it out. The function's name is f, and we are providing the variable x to it.

And g(x) also has a similar meaning.  

The given question is a quadratic equation problem.

Given: f(x)= 2x³+7x²-4x-5

And g(x)= 3x-2

To find: (f-g)(x) we have to simply subtract the above to equations

That is [tex](f-g)(x)[/tex] = 2x³+7x²-4x-5-(3x-2)

On opening the brackets we get;

[tex](f-g)(x)[/tex]= [tex]2x^3+7x^2-4x-5-3x+2[/tex]

[tex]= 2x^3+7x^2 -7x - 3[/tex] { here we subtracted and added the like terms together}.

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Step-by-step explanation:

always remember (for your life) : the sum of all angles in a triangle is always 180°.

and the sum of all angles around a single point on one side of a line is also always 180°.

so,

180 = 65 + 51 + angle PSR

angle PSR = 180 - 65 - 51 = 64°

angle PST is the supplementary angle to angle PSR (that means together they have 180°), because of the principle of all angles around a single point (S) on one side of a line (TSR).

so,

180 = angle PST + angle PSR = angle PST + 64

angle PST = 180 - 64 = 116°

Answer:114

Step-by-step explanation:

Answer:

2x² + 12x

Step-by-step explanation:

   Area of rectangle = length * width

Poster 1:

        length = x inches

        widht = (x + 5) inches

Area of poster 1 = x * (x + 5)

                           = x*x + x*5     {Distributive property}

                           = x² + 5x square inches

Poster 2:

      length = x inches

       width = (x + 7) inches

Area of poster  =x *(x+ 7)

                        = x*x + x*7

                        = x² + 7x

Area of wall = area of poster1 + area of poster 2

                    = x²+ 5x + x² + 7x

                    = x² + x² + 5x + 7x    {Combine like terms}

                    = 2x² + 12x

Answer:

[tex]2x^2+12x[/tex]

Step-by-step explanation:

Dimensions of Poster 1:

Dimensions of Poster 2:

The posters can be modeled as rectangles.

[tex]\boxed{\textsf{Area of a rectangle}=\sf length \times width}[/tex]

Therefore, the expressions for the area of each poster are:

[tex]\implies \textsf{Area of Poster 1}=x(x+5)[/tex]

[tex]\implies \textsf{Area of Poster 2}=x(x+7)[/tex]

Therefore, the expression that represents the area of the wall that the posters will cover is the sum of the expressions of the areas of the individual posters:

[tex]\begin{aligned}\textsf{Area of wall posters will cover}&=\textsf{Area of Poster 1}+\textsf{Area of Poster 2}\\& = x(x+5)+x(x+7)\\&=x^2+5x+x^2+7x\\&=x^2+x^2+5x+7x\\&=2x^2+12x\end{aligned}[/tex]