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Looking at this proof of the Pythagorean Theorem, which statement would be true?

Answer:

That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.

_

Average of given n numbers X1,X2,.........,Xn is x= £xi/n

Let the my number be x

Given:- The average of 3,15,x is 40

£xi/n =40

3+15+x/3=40

Multiplying 3 both side

18+x=120

x=120-18

x=102

Hence, my number is 102

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 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 plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]

because they have same slope(rate of change )

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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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answer step by step:

hope this helps

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

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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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:

Answer:

Non-linear

Step-by-step explanation:

Because the line is not straight.

We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.

To find the area of a rectangle, use the formula given below:

Area of a rectangle = (length)(width).

Given the parameters:

To show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:

(x + 3)(x + 2) = 9

Apply the distributive property of equality

x(x + 2) + 3(x + 2) = 9

x² + 2x + 3x + 6 = 9

Combine like terms:

x² + 5x + 6 = 9

Add -6 to both sides of the equation

x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]

x² + 5x = 3

Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.

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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

The solution for the expression x² = 12 will be x = ±2√3.

The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,

√x² = √12

x = √(2×2×3)

x = ±2√3

We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,

Thus, the value of x is ±2√3.

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Answer:

Greater.

Step-by-step explanation:

The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.

Thus, the domain for f(x) is all real numbers greater than or equal to 2.

Answer:

The domain for f(x) is all real numbers greater than or equal to 2.

Step-by-step explanation:

Given function:

[tex]f(x)=2x^2+5 \sqrt{x-2}[/tex]

The domain of a function is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken:

[tex]\implies x-2\geq 0[/tex]

Therefore:

[tex]\implies x-2+2\geq 0+2[/tex]

[tex]\implies x\geq 2[/tex]

Therefore, the domain of the given function is greater than or equal to 2.

Answer:

True???

Step-by-step explanation:

Is this a true or false question?

P+12=even number

Examples...

12+12=24

16+12=28

66+12=78

Answer:

YES

Step-by-step explanation:

even + even = even

always and forever

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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The order of the rotational pentagon is 6.

The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.

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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 the first applicant with advanced training in programming is found on the third interview is  0.0469

Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so

Geometric distribution is: (1-75%)

                                        =0.75

The density function of geometric distribution is,

[tex]P(X=x)=p(1-p)^{x-1}[/tex], for all x = 1,2,3,....

Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:

P(X=3) =[tex]0.75(1-0.75)^{3-1}[/tex]

          =[tex]0.75(1-0.75)^{2}[/tex]

          =0.75×0.0625

          =0.0469

Hence, the required probability is 0.0469

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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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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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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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Answer:

Answer:

Below in bold.

Step-by-step explanation:

10% = 0.10 as a decimal fraction.

After t years:

Amount = 6000(1 + 0.10)^t

Answer:

(3,2)

Step-by-step explanation:

since -3 + 9 =6

6 ÷ 2 =3

2 + 2 = 4

4 ÷ 2 = 2

therefore (3,2)