Two triangles are similar. First triangle has sides of length 6, 8, and 14. The shortest
side of the other has length 12.
a) What is the scale factor going from first to the second triangle?
b) Determine the length of the longest side of the second triangle.

[tex]\huge\text{Hey there!}[/tex]

[tex]\text{If John is currently 9 years old and we’re trying to figure out how old he will be}\\\text{in 20 years.}[/tex]

[tex]\text{Let us label your equation to:}[/tex]

[tex]\text{9 - a = 20 OR BETTER YET a - 9 = 20; your “a”-value will be labeled as}\\\text{John future age.}[/tex]

[tex]\textsf{Equation:}[/tex]

[tex]\mathsf{a - 9 = 20}[/tex]

[tex]\textsf{ADD 9 to BOTH SIDES}[/tex]

[tex]\mathsf{a - 9 + 9 = 20 + 9}[/tex]

[tex]\textsf{SIMPLIFY IT}[/tex]

[tex]\mathsf{a = 20 + 9}[/tex]

[tex]\mathsf{a = 29}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{John\ will \ be \ \boxed{\mathsf{29}} \ years \ old}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

It should be noted that 6.208 x 10^9 and 9.7 x 10^4 expressed in scientific notation will be 0.64 × 10^5.

It should be noted that quotient simply means that we've to divide the numbers that are given.

This will be 6.208 x 10^9 and 9.7 x 10^4 expressed in scientific notation will be:

=(6.208 × 20^9) / (9.7 ×10^4)

= 0.64 × 10^5

The value is 0.64 × 10^5.

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Answer: 5541 pages

Step-by-step explanation:

2489+3052= 5541 pgs

The simplified value of the given expression is  -11 - 2x.

BODMAS stands for Brackets of Division, Multiplication, Addition and Subtraction.

Here, we are given an expression as follows-

(3 * -8) + (2x+5) - (4x-8)​

According to the rules of BODMAS, brackets must be solved first. Hence, we simplify the terms in brackets first as given below-

(-24) + (2x + 5) - (4x - 8)

Opening up the brackets we get-

-24 + 2x + 5 - 4x + 8

= -24 + 5 + 8 + 2x - 4x

= -24 + 13 -2x

= -11 - 2x

Thus, the simplified value of the given expression is  -11 - 2x.

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Answer: answer should be;

x^2+9x+13

Step-by-step explanation:

hey there;

f {x} - g {x}

=2x^2 + 7 - x^2+9x-6

=2x^2-x^2+9x+ 7-6

=x^2+9x+13

So, this is the following answer. You may mistook the question or the question itself is wrong.

Hope it helps!

Answer:

119

Step-by-step explanation:

76,108,116,122,127,135

if you cross them out you are left with 116 and 122, when you have 2 numbers you add them together then divide by 2 so that would give 119

hope this works :)

[tex] \frac{108 + 127}{2?} = 117.5[/tex]

4x

5+4/2=5 imput x since you cant forget your variable

The amount that Tristan would earn in 5 years is  $657.30.

When an amount is compounded monthly, it means that both the amount invested and the interest that has already accrued increases in value every month or 12 times in a year.

The first step is to determine the future value of the investment.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

$2000 x (1.00475)^(12 x 5)

$2000 x (1.00475)^60

= $2,657.30

Amount he would earn = $2,657.30 - $2,000 = $657.30

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Oscar bought 8.73 meters of fence board to build the fence.

The metric system and the International Systems of Units both use the metre (m), also spelt as meter, as the basic unit of length (SI). In the British Imperial and American Customary systems, it is equivalent to roughly 39.37 inches.

A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets.

Oscar purchases three boards that measure 2.91 meters long each to build a fence.

Let say the length of one board be x = 2.91 meters.

Then the total length of fence board Oscar purchases is:

= 3x = 3 × 2.91 meters = 8.73 meters

Hence Oscar purchased 8.73 meters of fence board.

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a. Organizing the transaction data in accounts under an accounting equation for each year is as follows.

Accounting Equation: Assets = Liabilities + Equity

Year 1:

        Cash        Accounts      =     Liabilities     + Equity

                       Receivable

1)                           $31,130                                  $31,130  Service Revenue

2)     $24,904      (24,904)

3)                                 (311)                                      (311)  Bad Debts Expense

Bal. $24,904         $5,915                                $30,819

Year 2:

        Cash        Accounts      =     Liabilities     + Equity

                       Receivable

Bal. $24,904       $6,226                                 $30,819 Retained Earnings

1)                               (233) +233

2)                       $36,329                                $36,329  Service Revenue

3)     $32,151        (32,151)

4)                             (285)                                     (285) Bad Debts Expense

Bal. $57,055      $9,808                               $66,863  

b. Determining the following amounts is as follows:

                                                                             Year 1            Year 2

1. Net income                                                    $30,819       $36,044

2. Net cash flow from operating activities       24,904           32,151

3. Balance of accounts receivable at the end  6,226             10,171

4. Net realizable value of accounts receivable 5,915            9,808

Year 1:

1) Accounts Receivable $31,130 Service Revenue $31,130

2) Cash $24,904 Accounts Receivable $24,904

3) Bad Debts Expense $311 Allowance for Uncollectible Accounts $311

Year 2:

1) Allowance for Uncollectible Accounts $233 Accounts Receivable $233

2) Accounts Receivable $36,329 Service Revenue $36,329

3)  Cash $32,151 Accounts Receivable $32,151

4)  Bad Debts Expense $285 Allowance for Uncollectible Accounts $285

Net income for Year 2 = $36,044 ($36,329 - $285)

Year 1:

Net income                    $30,819

Non-cash expense                311

Accts receivable              (6,226)

Cash from operations $24,904

Year 2:

Net income                    $36,044

Non-cash expense                 52 ($285 - $233)

Accts receivable              (3,945)

Cash from operations  $32,151

Year 1:

Account Titles            Debit      Credit

1) Service Revenue $31,130

2) Cash                                  $24,904

Ending balance                      $6,226

Net Realizable Accounts Receivable = $5,915 ($6,226 - $311)

Year 2:

Account Titles            Debit      Credit

Beginning balance   $6,226

1) Allowance for Uncollectibles $233

2) Service Revenue 36,329

3)  Cash                                    32,151

Ending balance                      $10,171

Net Realizable Accounts Receivable = $9,808 ($10,171- $363)

Account Titles            Debit      Credit

Bad Debts Expense                   $311

Accounts Receivable $233

Bad Debts Expense                  285

Balance                      $363

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Required a. Organize the transaction data in accounts under an accounting equation for each year.

b. Determine the following amounts:

1. Net income for years 1 and 2.

2. Net cash flow from operating activities for Years 1 and 2.

3. Balance of accounts receivable at the end of Years 1 and 2.

4. Net realizable value of accounts receivable at the end of years 1 and 2.

Answer:

Answer is 1+- √2

Step-by-step explanation:

[tex] \frac{ - ( - 4) + - \sqrt{ {4}^{2} - 2 \times( - 8) } }{2(2)} [/tex]

[tex] \frac{4 + - \sqrt{32} }{4} [/tex]

[tex]1 + - \sqrt{2} [/tex]

To plot the graph of equation 3(2x + 2) - (x − 4) < 18, we need to simplify the equation of inequality first which can be simplified as

3(2x + 2) - (x − 4) < 18

6x +  6 -x+ 4 < 18

5x + 10 < 18

5x <18 - 10

5x < 8

x < 8/5

x < 1.6

So,  we need to plot the line graph of the equation of  inequality x < 1.6 which is attached to the solution where Blue is marked or plotted in the graph, and also note that at 1.6 there is a hollow circular mark which resents the inequality

Correct question is plot the graph of equation 3(2x + 2) - (x − 4) < 18

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The answer is -2x² + 14X

The first step is to open the bracket by multiplying both values in the bracket by -2x

-2x(x-7)

= -2x² + 14x

Hence the solution to the expression is -2x² + 14x

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Given the distance covered and the time elapsed, Ryashkina's average walking rate is approximately 3.97 meters per second.

Rate or speed is expressed as distance walked or traveled per unit time.

R = s/t

Given the data in the question;

First convert 41 minutes to seconds.

⇒ 41min = ( 41 × 60 )s = 2460sec

Now, Elapsed time t = 2460s + 56.23s = 2516.23 second

Next, we determine the rate.

R = s / t

R = 10000m / 2516.23 s

R = 3.97m/s

Given the distance covered and the time elapsed, Ryashkina's average walking rate is approximately 3.97 meters per second.

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Carmen's total earning will be 10x when 10% earning is assumed to be x.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Let x be the earning of Carmen's that is equals to 10% of total earning.

Then total earning that is 100% will be equals to the multiplication 10% and x both with 10 :

10%( total earning of Carmen's ) = x

100%( total earning of Carmen's ) = 10x

Therefore, Carmen's total earning will be 10x when 10% earning is assumed to be x.

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Answer: The probability that a student chosen at random has a cat and a dog is; P(cat and dog) = 9/25.

Step-by-step explanation:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

The information above are drawn in a Venn diagram in the attached image.

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

Therefore, the number of students who own a cat and a dog is 9.

The probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Answer:

median:11

mode:11

mean:11.143

range:

Step-by-step explanation:

median is the middle number so you first arrange the numbers in an ascending order after rounding off each number. Then you're gonna cancel one number from the left and one from the right until they remain two numbers then you add them and divide by 2 to get 11

I'm not sure about mode coz it's the most repeated number

mean is where you add all numbers and divide them by the total amount of numbers.

I tried!

Answer:

find the value of 8x³-y³

Answer:

3.9  It would be between the numbers 3 and 4 on a number line, but closer to 4

Step-by-step explanation:

If you put this in your calculator hit the square root button and then the number 15, your calculator will spit out 3.87298334621 then round this to the nearest tenths place.  Look at the digit 7 to decide to round up for down.  This number would be closer to 3.9 than 3.8

Answer: C, B, D, A

Step-by-step explanation:

[tex]\ln(xy)=\ln x+\ln y\\\\\ln(x/y)=\ln x-\ln y\\\\\frac{\ln y}{\ln x}=\log_{x} y\\\\\ln (x^y)=y \ln x[/tex]

These are all standard logarithm rules.

Answer:

a) 2

b) left to right

Step-by-step explanation:

a) slope= (y2 -y1)/(x2-x1)

(-13-(-21))/(-6-(-10))

8/4

2

b) left to right

The rate that the cars should be rented to produce the maximum income is: 41 Dollars/Day, Maximum income 7615.

Let y represent the  income

Let  x  represent the increase in rental price after increasing the rental price is 40+x.

Let 190-5x represent the number of cars rental after a rental price increase

Income expression

y=(190-5x) (40+x)

Let differentiate y with respect to x and set y' =0 to determine the maximum income

Hence,

y=(190-5x) (40+x)

=(190) (40) + 190 (x) -5x(40) -5x-(x)

=7600 +190x-200x-5x²

y= -5x² +10x+7600

Differentiate with respect to x

y'=d/dx ( -5x² +10x+7600)

y'=-10x+10x

set y'=0

-10x+10=0

10x=10

x=10/10

x=1

Maximum Rate =40+x

=40+1

=41 Dollars/Day

Maximum Income is

y= ( -5x² +10x+7600)

=(−5(1)²+10(1)+7600)

=−5(1)+10+7600

=5+10+7600

=7615

Therefore the rate that the cars should be rented to produce the maximum income is: 41 Dollars/Day, Maximum income 7615.

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Answer: 3.5

Step-by-step explanation:

To find the length of the missing leg, we need to use the Pythagorean Theorem (a^2 + b^2 = c^2 where c is the hypotenuse)

1) Plug in numbers

2^2 + b^2 = 4^2

2) Square

4 + b^2 = 16

3) Flip Equation and Subtract

16 - 4 = b^2

16 - 4 = 12

4) Square Root of 12

The square root of 12 is ~3.46, so you need to round to the nearest tenth, which is 3.5

Answer:

-18

Step-by-step explanation:

-10 + |-4| - |-12|       Since there are the | |, then any negative number inside would become a positive as it will become its absolute value, which for -4, would be 4, because it is 4 spots away from the 0 on a number line and vice versa.

-10 + 4 - 12   Answering from left to right,

-10 + 4, if you would rather make it so they are both equal, you change the + to the opposite which would be - and change the 4 back to a negative because that is what it would be if you changed the equation to be subtraction instead to be easier as they would both be negatives now, so you would subtract -10 - -4 and get -6.

-6 - 12. Again, switch the - to the opposite, which is +, and then make 12 the opposite that it was before so they both share the same symbol, making it

-6 + -12, which would be -18.

answer as by using mid point formula and then after equating the corresponding co ordinates we get the answer -7 and -3

It should be noted that the area of the shaded figure based on the information will be 9600 m².

It should be noted that the area of a rectangle is calculated by multiplying the length by the width that's given.

It should be noted that this shape can be used

to form two rectangles and the areas will be added together.

Therefore, it should be noted that the area of the rectangle will be:

= (60 × 60) + (100 × 60)

= 3600 + 6000

= 9600 m²

In conclusion, it should be noted that the area of the shaded figure based on the information will be 9600 m².

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Answer:

Pick any x coordinate to substitute for x, whatever answer you get is your Y coordinate

Step-by-step explanation:

Example

x=3

(3/2)*(3) + 2 = 6.5

So my coordinates end up being (3,6.5)

5x-16=5+4x

    +16+5

   5x=21+4x

  -4x       -4x

     x= 21

Step-by-step explanation:

Run the Ingleby marathon for free if  A ≥ £900

Given data

a. Joe raise more than £400 and run the Ingleby marathon for free

Run the Ingleby marathon for free if A> £400

b. Joe raise at least £900 and run the Ingleby marathon for free

Run the Ingleby marathon for free if __________

The first part of the statement gives the clue and it rewritten as

a. Raise more than £400 and run the Ingleby marathon for free

Run the Ingleby marathon for free if A> £400

more than £400 is represented as A> £400

The statement means amount greater that £400 and it is written mathematically as A> £400

The second statement is done as follows:

b. Joe raise at least £900 and run the Ingleby marathon for free

Run the Ingleby marathon for free if __________

In this case Joe runs the marathon if the amount is of the that is at least £900, which implies amount of 900 and above or simply put: amount of 900 or more than 900 .

This represented mathematically as: A ≥ £900

Hence we say Run the Ingleby marathon for free if  A ≥ £900

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Complete question

The complete question is attached