Which theorem or postulate justifies this statement?
/8 = /10
O linear pair postulate
O alternate exterior angles theorem
O vertical angles theorem
O alternate interior angles theorem
O corresponding angles postulate

Answer:

[tex]X=-2\frac{2}{5}[/tex]

Step-by-step explanation:

1/2(x+2)=-1/3(x+3)

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

           +1/3x

5/6x+1=-1

      -1.  -1

5/6x=-2

/5/6.   /5/6

x=-2*6/5

x=-12/5

x= -2 2/5

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

The given error full solution is

5x+5(-2x-12)=130

5x+-10x-60=130

65x=130x=-2.

Correct answer is given as

5x+5(-2x-12)=130.

We solve this question using Bodmas rule. So first we remove the parenthesis.

5x+5(-2x-12)=130

5x+5(-2x)+5(-12)=130

5x-10x-60=130

-5x=130+60

-5x=190

dividing both side by by (-5). We, get

x=190/(-5)

x=-38

Hence, the correct answer is x=-5

Answer:

0.08 divided by 13.56 = 0.00589970501.

Step-by-step explanation:

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Answer: 0.00589970501

Answer: -6

Step-by-step explanation:

Answer:

5 + (1/x)

Step-by-step explanation:

(3x - 4x + 2) - (7x - 10x - 8x)

3x - 4x + 2 - 7x + 10x + 8x

(3x - 4x - 7x + 10x + 8x) = 10x

10x + 2

  10x + 2     10x        2               1

  ---------- = ------- + ------- = 5 + ------

      2x          2x        2x              x

I hope this helps!

Answer:

The probility is 10%

Step-by-step explanation:

We can figure out area of any polygon we majorly follow the two steps first we divide any polygon into the shape of any known geometrical figures or in general integrate it.

A two-dimensional figure, form, or planar lamina's area is a measure of how much space it takes up in the plane. The area is simply the amount of cloth or other material with the specified thickness needed to build a model of the shape or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint. It is the two-dimensional representation of a curve's length or a solid's volume, where length is a one-dimensional concept and volume is a closely related three-dimensional term.

There are a tonne of 2-D shapes all around us, including circles, triangles, squares, rectangles, parallelograms, and trapezoids. You are able to draw.

To figure out area of any polygon we follow the following two ways:

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The rate of change is 21.6 mpg.

The rate of change determines how one variable changes because of another variable. This rate value can be either positive or negative. Considering x as an independent variable and y as a dependent variable, the rate of change for these two variable is given by,

[tex]\text{rate of change}= \frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}[/tex]

From the given value, miles traveled is a dependent variable because it depends on the amount of gas. So the amount of gas is the independent variable.

Therefore, the rate of change is,

[tex]\begin{aligned}\text{rate of change}&=\frac{\Delta y}{\Delta x}\\&=\frac{\mathrm{259.2\;miles}}{1\mathrm{2\;gallons}}\\&=\mathrm{21.6\;mpg}\end{aligned}[/tex]

Therefore, the rate of change is 21.6 miles per gallon.

This formula is also used to calculate gas mileage.

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The complete question is -

Mariam uses 12 gallons of gas to drive 259.2 miles in her car. Find the rate of change.

The measure of the base and the height of the parallelogram are;

Height = 3 ft

Base = 9 ft

The formula for the area of a parallelogram is expressed as;

Area = Base × Height

From the question, we are told that the base of the parallelogram is 6 ft more than the height. Thus;

Base = 6ft + h

If the area of the parallelogram is 27 ft^2​, then the measures of the base and the​ height is calculated as;

27 ft² = ( 6 + h ) × h

27 = 6h + h²

h² + 6h - 27 = 0

h² + 9h - 3h - 27 = 0

h(h + 9) - 3(h + 9) = 0

(h + 9)(h - 3) = 0

h = -9 or 3

We will pick the positive one which is 3 and so;

height = 3ft

Base = 6 + 3

Base = 9ft

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The values of x and y are given by 8 and 9 respectively.

Since the quadrilateral is a parallelogram. So the opposite sides should be equal and parallel.

So,

4x-17 = 2x-1

4x-2x = 17-1

2x = 16

x = 8

Again the angles (3y+5) and (5y-13) are alternating angles with respect to parallel opposite sides of parallelogram and diagonal as transversal. So they are equal.

3y+5 = 5y-13

5y-3y = 13+5

2y = 18

y = 18/2

y = 9

So the values are, x=8 and y=9.

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c. Yes ΔCBA is congruent to ΔCDE because satisfying meaning of definition by congruency.

How to rotate a triangle using a single point as center?

Following these steps will allow you to rotate a triangle around a fixed point: To one of the triangle's vertices, draw a line extending from the fixed point. Draw the rotated line by taking the angle measurement from this line at the fixed point.

a. The triangle is rotated by ∠ACE , the ray CA also rotated by ∠ACE. Thus the image of ray CA lines up with CE.

b. The rotated edge of CA is CE, thus the image of A coincides with E.

c. Rotation by ∠ACE using C as center.

  As figure is rotated from ∠C from ΔCBA

⇒ΔCAB ≅ ΔCED

Thus the definition of congruence as that a triangle will be are other triangle if they are congruent

∠CBA ≅ ∠CDE

AC = CD

AB = DE

Yes ΔCBA is congruent to ΔCDE because satisfying meaning of definition by congruency.

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The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Roman's equation is correct.

What is an equation?

An equation is composed of two expressions joined by an equals sign. The phrases on each side of the equals sign are referred to as the equation's "bottom left" and "top part." The right hemisphere of an equation is frequently considered to be zero. Assuming that this does not limit the generality, it is possible to implement this by subtracting the right-hand side from both sides. The most frequent sort of equation is a polynomial equation, which has two polynomial sides. A scale into which weights are inserted is akin to an equation. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal.

given equations,

Allie's equation is y = 2x - 8

Roman's equation is y = -2x + 8

Roman's equation matches the given graph, so his equation is correct.

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The value of cos 2θ will be;

⇒ cos 2θ = 7/25

What is an expression?

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 sides of triangle are 3 , 5, 4

Now,

Since, In a triangle;

cos 2θ = 2cos²θ - 1   .....(i)

And, cos θ = Base / Hypotenuse

Substitute all the values, we get;

cos θ = Base / Hypotenuse

cos θ = 4 / 5

Substitute above value in equation (i), we get;

cos 2θ = 2cos²θ - 1  

cos 2θ = 2(4/5)² - 1  

cos 2θ = 32/25 - 1

cos 2θ = 7/25

Thus, The value of cos 2θ will be;

⇒ cos 2θ = 7/25

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For every 60 miles traveled 3 gallons of fuel usage is increasing approximately.

Given,

Manuel is using a table to calculate information for an upcoming business trip.

We have to find the number of gallons of fuel he uses increases by approximately for every 60 miles traveled.

Here,

Distance in miles ;- 120, 180, 240, 300, 360

Fuel used in gallons;- 6, 9, 12, 15, 18

Then,

3 gallons of fuel is used

Lets check for this to all;-

That is,

For every 60 miles traveled 3 gallons of fuel usage is increasing approximately.

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The value of the given linear functions are:

5. f(3) = 1

6. f(1) + g(2) = 14

7. g(0) = 11

8. g(2) - f(0) = 22

9. f(-1) - g(3) = 20

10. 2g(-4) = 2

We are given the linear functions:

f(x) = 2x - 5 and

g(x) = |- 3x - 11|

Let us solve one by one:

5. f(3)

Substitute the value of x with 3 in f(x), we will get;

f(3) = 2 * 3 - 5 = 6 - 5 = 1

6. f(1) + g(2)

f(1) = 2 * 1 - 5 = 2 - 5 = -3

g(2) = |- 3 * 2  - 11| = |- 6  - 11| = 17

f(1) + g(2) = -3 + 17 = 14

7. g(0)

g(0) = |- 3 * 0  - 11| = | - 11| = 11

8. g(2) - f(0)

g(2) = |- 3 * 2  - 11| = |- 6  - 11| = 17

f(0) = 2 * 0 - 5 = 0 - 5 = -5

g(2) - f(0) = 17 - (-5) = 22

9. f(-1) - g(3)

f(-1) = 2 * -1 - 5 = -2 - 5 = -7

g(3) = |- 3 * 3  - 11| = |- 9  - 11| = 20

10. 2g(-4)

g(-4) = |- 3 * -4  - 11| = |12  - 11| = 1

2g(-4) = 2 * 1 = 2

Thus, the value of the given linear functions are:

5. f(3) = 1

6. f(1) + g(2) = 14

7. g(0) = 11

8. g(2) - f(0) = 22

9. f(-1) - g(3) = 20

10. 2g(-4) = 2

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The value of fraction [tex]8\frac{9}{20} -5\frac{7}{12}[/tex] = 2.86.

= [tex]8\frac{9}{20} -5\frac{7}{12}[/tex]

it is in the mixed fraction so write it as unmixed.

= 20*8+9 /20 - 12*5+7 / 12

= 160+9 /20 - 60+7 /12

= 169/20 - 67/12

= 8.45 - 67/12

= 12*8.45 - 67 / 12

= 101.4 - 67 / 12

= 34.4/12

= 344/10/12

= 344/10*12

= 344/120

= 2.86

Therefore the value of fraction [tex]8\frac{9}{20} -5\frac{7}{12}[/tex] = 2.86.

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Check the picture below.

Answer:

The answer is 8.

Step-by-step explanation:

Since 48 10s, equals 480, and 6 tens equal 60, we do 480/60 which equals  8.

The total cost of all the 2- liter sodas will be proportional to the number of 2- liter sodas that Sue buys is c = 1.25s

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each.

Let the number of soda be s.

The total cost will be:

c = 1.25 × s

c = 1.25s

The cost is 1.25s.

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Answer:

A = 40 cm^2

Step-by-step explanation:

A = (3+13)/2 * 5

A = 16/2 * 5

A = 8 * 5

A = 40 cm^2

From the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

As given in the question,

Quantity of 60% solution in making 50% solution is = 7 gallons

Let us consider y gallons be the quantity of 35% solution to make 50% solution.

Quantity used to make 50% solution is (7 + y)

Required equation is:

(y × 35%) + (7× 60%) = (7+y) 50%

⇒(35y/100) + (420/100) = (350 + 50y)/100

⇒35y + 420 = 350 + 50y

⇒50y - 35y = 420 -350

⇒15y = 70

⇒y = 4.666..

⇒y = 4.7 gallons ( approximately)

Therefore, from the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.

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20% is .20

multiply .20 to every subtotal to get the tip

$46.42? no its really 44.92

$34.70? yes

$24.86? yes

0.0088 is standard deviation of  blood presure is normally distributed.

What is standard deviation simple terms?

Blood pressure in china

=   P( x> 182.6 )

   =  P( x> 182.6 - 128/23)

 =   P( Z > 2.3739 )

= 0.0088

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Answer:

y= -1x + 4 or y= -x + 4

Step-by-step explanation:

Interpret the coefficient as the percent increase in the dependent variable for every 1% increase in the independent variable.

Log-linear models specify how the cell counts depend on the levels of categorical variables, going beyond simple summary statistics. They simulate the relationships and interactions between categorical variables. For Poisson, Multinomial, and Product-Multinomial sampling, the log-linear model makes sense. Log-linear models specify how the cell counts depend on the levels of categorical variables, going beyond simple summary statistics. They simulate the relationships and interactions between categorical variables. For Poisson, Multinomial, and Product-Multinomial sampling, the log-linear model makes sense.

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First we are supposed to find 30% of 451

30/100×451 = 135.3

So, 451 - 136= 315.7

Therefore I would be left with 315.7

Answer:

$315.70

Step-by-step explanation:

the sum of these is 451 so to find 30 percent we multiply 451 by 30 percent

First turn 30 percent into a decimal by moving the decimal point to places to the left

0.30 and now we multiply

0.3x451

135.30 is 30% of 451 and since someone is taking it we subtract it by 451

451-135.30

315.70 is what you are left with

But if it was tax you would add this to the total amount you are spending

Hopes this helps please mark brainliest

Therefore, the final code would be:values = [ 14, 10, 8, 19, 7.13] print(values[2], values[-2])This code would print the following output:8 19

Indices, also known as exponents or powers, are mathematical symbols that express the repeated multiplication of a number. These numbers show how many times the base number has been multiplied by itself. For example, the index of 2 in the formula 23 is 3, which indicates that 2 is multiplied by itself three times to provide the value 8. Indices are often written as little numbers to the right and above the base number, with the latter enclosed in parentheses or brackets. Indices are often used to indicate the size or quantity of a number in mathematical model, but they may also be used to represent the degree of a polynomial function or the order of a derivative in calculus.

How to solve?

To print the integer at index 2 of the values list, we can use the following code: print(values[2])

To print the integer at index -2 of the values list, we can use the following code: print(values[-2])

Here, the index -2 refers to the second-to-last element in the list, which is the integer 19.

Therefore, the final code would be:

values = [ 14, 10, 8, 19, 7.13]

print(values[2], values[-2])

This code would print the following output:

8 19

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