Find missing side length given two similar triangles

Answer:

Given

Addition property of equality

Division property of equality

Step-by-step explanation:

The first line is given.

Next 2x was added to each side.  The addition property of equality says that for an equation to stay in balance, it you add something to one side of the equation, you have to add that same thing to the other side of the equation.

The same is true for the division property.

The classification and the output rule for each function in this problem is given as follows:

1. Output rule: y = 5x + 11. Classification: Linear.

2. Output rule: y = 2^x. Classification: Exponential.

3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.

A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:

y = mx + b.

In which:

Hence, for the first table, as 5 is added to x when x increases by one, the rule is:

y = f(x) = 5x + 16.

An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:

y = a(b)^x.

In which:

Hence, for the second table, the rule is:

y = 2^x.

For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.

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The order of reasons that best justifies each step of the equation's solution is as follows;

It follows from the task content that the reasons which best justify each step of the solution be identified.

Therefore; Given the equation; -2(x - 5) = 4x; we have;

Ultimately, the reasons which best justifies each of the steps as required are as provided above.

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Answer:  Justification for each step is provided below.

Step-by-step explanation:

Original Equation: -2(x - 5) = 4x

-2x + 10 = 4x  -->  Distributive property - simplify the left side

-2x + 10 + 2x = 4x + 2x  -->  Addition property of Equality - add 2x to both sides

10 = 6x  -->  Simplifying

10/6 = 6x/6   -->   Division Property of Equality - divide each side by 6

5/3 = x   -->  Simplifying

The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​;

(a) exactly​ three = 0.1314

(b) at least​ four = 0.7953

(c) less than eight = 0.93382

The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;

P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)

We are given;

p = 41% = 0.41

n = 12

Thus;

1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is​ exactly​ three;

P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)

P(3) = 0.1314

2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least​ four;

P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

P(x ≥ 4) = 0.7953

3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;

P(X < 8) = 0.93382

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Emi will need to locate the whole in this case because she already has the part and the percentage.

In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.

The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.

The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.

Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.

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The total number of cattle Frank currently owned could be C)350

The problem is asking multiples of 7.

Multiples of 7 come into play after working the the percentage as follows

Frank sold 30%, the percentage left is

= 100% - 30%

= 70%

= 0.7

The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.

= 350 / 0.7

= 500

This means Frank had 500 cattle sold

0.3 * 500 = 150

currently having

= 500 * 0.7 = 350

= 500 - 150 = 350

Remember that a cattle will always be in whole number

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Answer:

82.96-22% = 67.83

Step-by-step explanation:

82.96-22% = 67.83

The pairs of events, A and B, that are disjoint include option A and B.

It should be noted that disjoint events simony means the events that are mutually exclusive as they can't occur at the same time.

For option A, because a person can be either male or female but not both, events A and B are disjoint.

For B, because the person already earns more than $100,000, events A and B are not disjoint.

For C, because the sum of two dice cannot be three when one die is three, events A and B are disjoint.

Therefore, A and C are disjoint.

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Complete question

Which of the following pairs of events, A and B, are disjoint?

(a) A person is selected at random. A is the event "sex of the person selected is male" and B is the event "sex of the person selected is female."

disjoint / not disjoint

(b) A person is selected at random. A is the event "the person selected earns more than $100,000 per year" and B is the event "the person selected earns more than $250,000 per year."

disjoint / not disjoint

(c) A pair of dice are tossed. A is the event "one of the dice is a 3" and B is the event "the sum of the two dice is 3."

disjoint / not disjoint

The solution to the system of equations, in terms of x, considering the augmented matrix, is of:

The augmented matrix of a system of equations is built as follows:

In this problem, there are three columns before the |, the there are three variables given as follows:

x,y and z.

The expression from the first row is:

x -0.05z = 2.

The expression from the second row is:

y + 2z = 1.

The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:

x - 0.05z = 2

0.05z = x - 2.

z = (x - 2)/0.05

z = 20x - 40.

Hence the solution for y is:

y = 1 - 2z

y = 1 - 40x + 80

y = -40x + 81.

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Answer:

  D.  2x -y = 2

Step-by-step explanation:

You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.

The graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...

  x/a +y/b = 1

  x/1 +y/(-2) = 1

Multiplying this equation by 2 gives ...

  2x -y = 2 . . . . the standard form equation for the line

__

Additional comment

The standard form equation can also be developed from the coordinates of points on the line:

  (y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1

  (2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)

  6x -3y = -6 +12

Dividing by 3 gives the standard form equation ...

  2x -y = 2

Answer:

supplementary angles

Step-by-step explanation:

1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given

2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.

3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive

4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality

5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Answer:

Step-by-step explanation:

Given:

2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10

factor it

I used MatLab   roots(x)  to find these so I kinda cheated :P

-2.5,  -2 ,  1

so we know  -2 is a factor and,  then

x+2=0    is a factor

so the "x+2"  answer C)

Answer:

y = 3x + 12

Step-by-step explanation:

y = mx + b  
The m is the slope and the b is the y intercept.

Slope:

Change in y over the change in x.  The ordered pair is written in the form (x,y)

[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3

The slope is 3.

Use the slope of the 3 and the x and y from one of the ordered pairs given.  I am going to use the point (5,3), but either point will work

slope 3

x = 5

y=3  Plug these all in and solve for b

y = mx + b

3 = (3)5 + b

3 = 15 + b  Subtract 15 from both sides

-12 = b

This is the y intercept

y = 3x - 12

Answer:

Slope-intercept form,

→ y = 3x - 12

Step-by-step explanation:

Formula we use,

→ y = mx + b

The value of slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (12 - 3)/(8 - 5)

→ m = 9/3

→ [ m = 3 ]

Then the value of b will be,

→ y = mx + b

→ 12 = (3)8 + b

→ b + 24 = 12

→ b = 12 - 24

→ [ b = -12 ]

Now the slope-intercept form is,

→ y = mx + b

→ [ y = 3x - 12 ]

Hence, the answer is y = 3x - 12.

Answer:

23

Step-by-step explanation:

the numbers from -10 to 10 cancel out, so all that is left is 11+12=23

Answer:

0.150985

Step-by-step explanation:

You add the two decimals together which gives you 120788.

Then, you move the decimal 4 places which is 12.0788.

Then you divide 12.0788 by 2 which gives you 6.0394.

Finally, you divide 6.0394 by 40 which gives you 0.150985.

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

1 ) Cross-multiply...

[tex]\frac{3}{x}[/tex] ÷ [tex]\frac{15}{45}[/tex]

[tex]3[/tex] × [tex]45 = 15[/tex] × [tex]x[/tex]

[tex]135=15x[/tex]

2 ) Flip the equation...

[tex]15x=135[/tex]

3 ) Divide both sides by 15...

[tex]\frac{15x}{15}[/tex] = [tex]\frac{135}{15}[/tex]

[tex]x = 9[/tex]

Hope this helps! :)

Answer:

1024

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

, then

8 × [tex]2^{7}[/tex]

= 2³ × [tex]2^{7}[/tex]

= [tex]2^{(3+7)}[/tex]

= [tex]2^{10}[/tex]

= 1024

Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;

The number of each currency Abigail plans to buy are;

A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.

The amount Abigail Henderson budgeted = $1,360

The per currency exchange rate for country A = $1.30

The per currency exchange rate for country B = $1.60

The number of currency A Abigail wants = 4 × The number of currency B

Which gives; x = 4·y

The equation that represents Abigail's total cost of buying currencies is presented as follows;

1.3·x + 1.6·y = 1,360

Plugging in the value of x gives;

1.3 × (4·y) + 1.6·y = 1,360

6.8·y = 1,360

y = 1,360 ÷ 6.8 = 200

The number of currency of country B, Abigail purchases, y = 200

The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800

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The total cost is $12.74

In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.

1 gallon of milk costs $2.48,

1 gallon of ice-cream costs $1.49

and 1b of strawberry costs $0.58

You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.

So by unitary method total cost would be,

(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74

Therefore, the total cost is $12.74

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The $100 start-up fee and $25 monthly rental gives;

The cost of using the phone for 1 month = $125

The cost of using the phone for 6 months = $250

The cons of using the phone for n months = $(100 + 25·n)

Please find attached the graph of the cellphone plan over a period of two years (24 months)

A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.

The start-up fee of the cell phone plan = $100

The amount charged each month = $25

First part;

The total cost for the start-up fee and monthly rental for 1 month = $100 + $25

The total cost for 1 month = $125

The total cost for 6 months = $100 + 6 × $25 = $250

The total cost for n months = 100 + n × 25 = $(100 + 25·n)

Please find the graph of the total cost to the number of months created with MS Excel

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Answer:

the probability of rolling a 6 is 1/6

Step-by-step explanation:

because there are six possible outcomes and it is a fair die, each outcome must be equally as likely, therefore there is a 1/6 chance of rolling any number.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]

Answer:

19 liters

Step-by-step explanation:

Answer:

Step-by-step explanation:

The required sketch graph of given straight line is shown below in the image.

The general equation of line is written as Y = mx + c where, m is the gradient of straight line, c is the point where the line cut y-axis.

we have, line y = x - 1

So, slope of line is 1 and y-intercept is -1

Thus,required graph of straight line is

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Answer:

D

Step-by-step explanation:

supplementary angles sum to 180° , that is

∠ 1 + ∠ 2 = 180°

67° + ∠ 2 = 180° ( subtract 67° from both sides )

∠ 2 = 113°

3-3(9x²+15x-15x+25)-4(6x²+9x-4x+6)

3-27x²-75-24x²-20-24

3-51x²-119

-116-51x²

The value of x so the the the function has the given value is as follows:

A function relates an input to an output.

In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.

Therefore, let's find the value of x so that the function has the given values.

m(x) = -3/5x - 4;  m(x) = 2

let's find the value of x when  m(x) = 2

2 = - 3/5x - 4

2 + 4 = - 3/5x

6 = - 3/5 x

cross multiply

-3x = 30

x = 30 / - 3

Hence,

x = - 10

w(x) = 5/6x - 3; w(x) = -18

let's find the value of x when  w(x) = -18

- 18 = 5/6x - 3

- 18 + 3 = 5 / 6 x

- 15 = 5 / 6 x

5x = - 90

x = -90 / 5

Hence,

x = - 18

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The person that I agree with is Glenda I don't agree with any of you. I think there must be a different reason for the arrangement.

The periodic table, commonly known as the periodic table of (chemical) elements, is a table that displays the chemical elements in a tabular format.

The chemical elements are ordered from left to right and top to bottom by increasing atomic number, or the number of protons in an atom's nucleus, which generally corresponds to increasing atomic mass.

The elements in the periodic table are organized into rows, called periods, in ascending atomic number order. Vertical columns, referred to as groups, in which the elements have similar qualities.

I agree with Glenda because they're arranged in atomic number.

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The solutions to the financial ratio requirements based on the supplied facts are:

A. Current ratio is 1.125.

B. Acid test is 1.

C. Average days' collection is 26.7 days.

D. Asset turnover is 1.4x.

E. Profit margin on sales is 14.63%.

Financial ratios are ratios that show the relative magnitude of one financial account to another.

Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.

Current Ratio = Current Assets ÷ Current Liabilities

= $18,000 ÷ $16,000

= 1.125

Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities

= ($18,000 - 2,000) ÷ $16,000

= $16,000 ÷ $16,000

= 1

Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days

= $3,000 ÷ $41,000 x 365

= 26.7 days

Asset Turnover = Net Sales ÷ Total Assets

= $41,000 ÷ $29,000

= 1.4x

Profit Margin on Sales = Net Income ÷ Net Sales x 100

= $6,000 ÷ $41,000 x 100

= 14.63%

Current Assets = $18,000

Accounts Receivable = $3,000

Current Liabilities = $16,000

Inventory = $2,000

Net Sales = $41,000

Total Assets = $29,000

Net Income = $6,000

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