A rectangle's length is 5.1 more than 2 times its width. Its perimeter is 165.6. Write and solve a system of equations to find the dimensions of the rectangle.

Type the area of the rectangle, rounded to the nearest tenth.

Step-by-step explanation:

a polynomial of degree 4 must have 4 zeroes.

when we know these zeroes, we can define the polynomial by the factors defining these zeroes.

after all, a multiplication of several factors can only be zero, if at least one of the factors is zero.

we have 3 zeroes at x = -1. and 1 zero at x = 0.

so,

f(x) = (x + 1)(x + 1)(x + 1)x

you see ? this will only be zero, if x = -1 or x = 0. and -1 is built in as zero 3 times.

let's do the multiplications :

(x + 1)(x + 1) = x² + 2x + 1

(x + 1)x = x² + x

(x² + 2x + 1)(x² + x) = x⁴ + x³ + 2x³ + 2x² + x² + x =

= x⁴ + 3x³ + 3x² + x

f(x) = 1x⁴ + 3x³ + 3x² + 1x

Answer:

1,000 x 550.343978 = 550343.978

The expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f, so option A is correct.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

The total no of french fries = 68,

The no of friends = f,

The no of french fries given to each friend = 13

The equation according to the question is given as,

The french fries left = The total no of french fries - The no of french fries given to each friend × The no of friends

Substitute the values,

The french fries left = 68 - 13 × f

Therefore, the expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f.

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The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:

The function for this problem is defined as follows:

y = 1.5x² + 4x - 2.

Hence the numeric values of the coefficients are listed as follows:

a = 1.5, b = 4, c = -2.

Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:

The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).

The x-coordinate of the vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate of the vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

The problem asks for the graph of the following function:

y = 1.5x² + 4x - 2.

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Answer: 100 is the ancer m

Step-by-step explanation: my man

Jay, because each point is fraction 1 over 8 unit from 0.

What is absolute length?

For instance, the absolute value of 12:

Absolute value is the length from which the number is from 0 in this they are adding two so it would mean that they are both 1/8 away from 0.

Hence, Jay, because each point is fraction 1 over 8 unit from 0.

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The waterskier has a final speed of approximately 25.350 feet per second.

In this question we need to determine the final speed of the waterskier, that is, the final speed of the waterskier when she leaves the ramp. This can be done by means of the principle of energy conservation, where the total energy is the result of combining translational kinetic energy (K), in pounds-feet per second, related to the speed of the waterskier, and gravitational potential energy (U), in pounds-feet per second.

The equation that represents the situation is described below:

K = U + K'

0.5 · m · v² = m · g · h + 0.5 · m · v'²

0.5 · v² = g · h + 0.5 · v'²

v'² = v² - 2 · g · h

Where:

If we know that v = 30 ft / s, g = 32.174 ft / s² and h = 4 ft, then the final speed of the waterskier is:

v' = √[(30 ft / s)² - 2 · (32.174 ft / s²) · (4 ft)]

v' ≈ 25.350 ft / s

The final speed of the waterskier is approximately 25.350 feet per second.

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Answer: 351.25

Step-by-step explanation:

unless there is more to the question that I am not seeing that is the answer.

The cost of the gas in dollars per gallon would be = $5.3 per gallon.

Liters can be converted to gallon as 1 liter = 0.264 gallon.

On the first day, the cost of gasoline = 1.28 euro per liter

On the first day, the worth of £1 = $ 1.09

Which means, if £1 = $1.09

£ 1.28 = $x

Make $x the subject of formula;

$x = 1.28 × 1.09/1

$x = $1.40

Which means that on the first day, the cost of gasoline in dollars = $1.40

To convert liters to gallon;

1 liter = 0.264 gallon

If $1.40 = 0.264 gallon

$x = 1 gallon

make $x the subject of formula;

$x = 1×$1.40/0.264

$x = 5.3

Therefore, the cost of gasoline in dollar per euro = $5.3 per gallon.

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The simplified form of the expression is -24√35

Expression

Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the expression -6√7.4√5

Now, we have to simplify the expression.

While we looking into the given expression, we have identified that the expression is in the form of multiplication,

So, the first step in solving the expression is to group the similar element,

So, the grouped form of the expression is,

=> (-6 x 4).(√7 x √5)

Now, we have to perform the multiplication on it, then we get,

=> -24√35

Therefore, the simplified form of the expression is -24√35

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The amount of money Samantha would have in the account 18 years after her initial investment is $2406.61

The principal amount = $1000

The interest rate = 5%

Time period = 18 years

The interest is compounded annually

The compound interest

A = [tex]P(1+\frac{r}{n})^{nt}[/tex]

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

n is the number of times the interest applied

A = [tex]1000(1+0.05)^{18}[/tex]

A = 1000 × 2.40661

Multiply the terms

A = $2406.61

Hence, the amount of money Samantha would have in the account 18 years after her initial investment is $2406.61

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According to the concept of quadratic equation, the minimum cost for the x ray machine is $17, 484

Quadratic equation:

Basically, the polynomial equation with highest degree of two is called a quadratic equation.

The general equation is given by ax² + bx + c = 0, where a ≠ 0.

Given,

A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684.

Here we need to find the minimum unit cost.

Here we know that the standard form of a quadratic is given by:

=> ax² + bx + c

From this function, we have to calculate the value of x as,

=> x = -b/ 2a

While we compare the standard form with the given function,

=> C (x)=0.5x²-320x+68,684.

Then we get the value of

=> a = 0.5

=> b = -320

=> c = 68,684

So, the value of x is calculated as,

=> x = -(-320) / 2(0.5)

=> x = 320 / 1

=> x = 1

Now, we have to plug this value into original function would give us the minimum (unit cost):

=> C(320) = 0.5(320)²- 320 (320) + 68,684.

=> C(320) = 0.5(102400) - 102400 + 68, 684

=> C(320) = 51200 - 102400 + 68684

=> C(320) = 17, 484

Therefore, the minimum unit cost is $17, 484

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Answer:

  $1544.40

Step-by-step explanation:

You want to know the amount of interest cost subsidized by the Department of Education during the 4.5-year non-payment period on an $8000 subsidized federal loan at 4.29%.

The interest accrued on the loan amount is found by the simple interest formula:

  I = Prt

The principal is $8000, the rate is 4.29%, and the time period is the non-payment period, 4.5 years. The interest is ...

  I = $8000·0.0429·4.5 = $1544.40

The DoE will subsidize $1544.40 in interest during the non-payment period.

__

Additional comment

For the purpose of this problem, the 10-year period of the loan is irrelevant, as we're only concerned with the 4.5 year period before repayment starts. Because the loan is subsidized, that interest is never "capitalized" and is not due to be repaid by the borrower.

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Answer:

Mai made 7 batches of pink paint.

Mai used 49 cups of white paint.

Step-by-step explanation:

Part 1. Every 2 cups of red paint are 1 batch of pink paint. This means to find the number of batches of pink paint Mai made, we need to divide 14/2. 14/2 = 7. This means she made 7 batches of pink paint.

Part 2. For every 2 cups of red paint, there are 7 cups of white paint.

For every 1 cup of red paint, there are 3.5 cups of white paint.

This means that we need to multiply 14 x 3.5.

14 x 3.5 = 49.

This means she used 49 cups of white paint.

Answer:

-1027.4

Step-by-step explanation:

that is the answer i got from my calculations. I hope this is right

Answer: The sum is 55/28.

Alternate Answer: 1 27/28

Step-by-step explanation:

In this equation, the common denominator between the three fractions would be twenty eight.

5/7 converts to 20/28

1/2 converts to 14/28

3/4 converts to 21/28

After adding all the new fractions together, you get 55/28.

The value of the consecutive numbers are 7 and 8.

Consecutive integers simply means the numbers that follow each others. It should be noted that such numbers have the same difference between them.

From the information given, we want to find two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.

Let the numbers be x and x+1.

Therefore, 6x + (x + 1)² = 106

6x + x² + 2x + 1 = 106

Collect like terms

x² + 8x + 1 - 106

x² + 8x - 105

x² + 15x - 7x - 105

x(x + 15) - 7(x - 15) = 0

Therefore x - 7 = 0

x = 0 + 7

x = 7

Therefore x + 1

= 7 + 1

= 8

The numbers are 7 and 8.

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The depreciation for the first year is $28,800.

If the equipment is sold for $8,860 at the end of year 2, the loss on the sale is $-14,180.

Depreciation is the method used in expensing the cost of an asset. The double declining method is an exponential method that is used to expense the cost of an asset.

Depreciation expense using the double declining method = Depreciation factor x cost of the asset

Depreciation factor for the double declining method = 2 x (1/useful life)

Depreciation expense in year 1 = (2 / 10) x $36,000 = $7,200

Book value at the beginning of year 2 = cost of the asset - depreciation in year 1

$36,000 - $7,200 = $28,800

Depreciation in year 2 = (2/10) x  $28,800 = $5,760

Book value at the end of year 2 = book value at the end of year 1 - depreciation in year 2

$28,800 - $5,760 = $23,040

Loss = sales price - cost price

Loss = $8,860 - $23,040 = $-14,180

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Answer:

heyyy

Step-by-step explanation:

The program to illustrate the information will be:

This function gets the value of the property from the user,

# calculates the tax, then displays the value of the tax

def show_tax():

# getting the value of the property from the user

property_value = float(input("Enter the property value: "))

# calculating the tax

property_tax = property_value * 0.0065

# displaying the value of the tax

print("Property tax: $ {0:.2f}".format(property_tax))

This program will receive the lot number from the user, while the lot number does not equal 0, then it gets the value of the property from the user, calculates the tax, then displays the value of the tax

The main() function will receive the lot number from the user,

# while the lot number does not equal 0,

# call the show_tax() function then ask for the next lot number.

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Answer: 4000

Step-by-step explanation: x by 1000

The transactions of Egert's Company are entered in the general journal as follows:

Date      Account Titles          Debit       Credit

Mar. 1 Cash                         $159,00

Office Equipment              $22,300

Common stock                                   $181,300

Mar. 2 Prepaid Rent           $1,200

Cash                                                      $1,200

Mar. 3 Office equipment $3,300

Office supplies                 $1,580

Accounts Payable                              $4,880

Mar. 6 Cash                     $4,300

Service Revenue                               $4,300

Mar. 9 Accounts Receivable $7,800

Service Revenue                              $7,800

Mar. 12 Accounts Payable $4,800

Cash                                                 $4,800

Mar. 19 Prepaid Insurance $5,300

Cash                                                 $5,300

Mar. 22 Cash                     $4,700

Accounts Receivable                     $4,700

Mar. 25 Accounts Receivable $4,200

Service Revenue                          $4,200

Mar. 29 Dividends          $5,400

Cash                                             $5,400

Mar. 30 Office supplies    $900

Accounts Payable                         $900

Mar. 31 Utility expenses  $800

Cash                                               $800

The general journal is the first accounting record of a business transaction.

The general journal identifies the accounts involved in each transaction, specifying which will be debited or credited in the general ledger.

Mar. 1 Cash $159,00 Office Equipment $22,300 Common stock $181,300

Mar. 2 Prepaid Rent $1,200 Cash $1,200

Mar. 3 Office equipment $3,300 Office supplies $1,580 Accounts Payable $4,880

Mar. 6 Cash $4,300 Service Revenue $4,300

Mar. 9 Accounts Receivable $7,800 Service Revenue $7,800

Mar. 12 Accounts Payable $4,800 Cash $4,800

Mar. 19 Prepaid Insurance $5,300 Cash $5,300

Mar. 22 Cash $4,700 Accounts Receivable $4,700

Mar. 25 Accounts Receivable $4,200 Service Revenue $4,200

Mar. 29 Dividends $5,400 Cash $5,400

Mar. 30 Office supplies $900 Accounts Payable $900

Mar. 31 Utility expenses $800 Cash $800

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1 Egert invested $159,00 cash along with $22,300 in office equipment in the company in exchange for common stock. 2 The company prepaid $1,200 cash for six months' rent for an office. The company's policy is to record prepaid expenses in balance sheet accounts. 3 The company made credit purchases of office equipment for $3,300 and office supplies for $1,580. Payment is due within 10 days. 6 The company completed services for a client and immediately received $4,300 cash. 9 The company completed a 7,800 project for a client, who must pay within 30 days. Mar. 12 The company paid $4,800 cash to settle the account payable created on March 3. Mar. 19 The company paid $5,300 cash for the premium on a 12-month insurance policy. The company's policy is to record prepaid expenses in balance sheet accounts. Mar. 22 The company received $4,700 cash as partial payment for the work completed on March 9. Mar. 25 The company completed work for another client for $4,200 on credit. Mar. 29 The company paid $5,400 cash in dividends. Mar. 30 The company purchased $900 of additional office supplies on credit. Mar. 31 The company paid $800 cash for this month's utility bill.

Enter the transactions in the general journal.

Answer: the probability that it will not rain is 70% (you might need to do 7/10)

the odds in favor of the rain occuring is 30% (again, you might need to do 3/10)

Step-by-step explanation:

since the probability that it will rain is 3/10, there is only 7/10 left, so it is more likely to not rain than to rain.

Since it will rain 3/10 times, it is 30% for the second problem

Give me brainliest please!

Answer: 111/250

Step-by-step explanation:

Step 1: Write down the percent divided by 100 like this:

44.4% = 44.4/100

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,

44.4/100 = (44.4 x 10)/(100 x 10) = 444/1000.

Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(444,1000) = 4. So,

The equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

According to the question,

We have the following information:

Point through which line is passing = (1/3,4)

Slope of the line = 0

We know that the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

We have x' = 1/3 and y' = 4.

y-4 = 0(x-1/3)

y-4 = 0

Adding 4 on both sides of the equation:

y = 4

Hence, the equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

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If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

Suppose the selling price of a towel is x, according to the given condition,

5 = x - 15% of x

5=x-0.15x

5=0.85 x

x=5/0.85

x=5.88

Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.

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The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]

We have,

The product of 500,000 multiplied by 100.

= 500,000 x 100

= 50,000,000

This can be written as:

= 5 x [tex]10^7[/tex]

Therefore,

The simplified form of the expression 500,000 multiplied by 100 equals 50,000,000 or 5 x [tex]10^7.[/tex]

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Answer:

ok i got you its two;)

Step-by-step explanation:

Answer:

[tex]x^2+2x+1[/tex]

Step-by-step explanation:

Note that [tex](a+b)^2=a^2+2ab+b^2[/tex].

Let [tex]a=x[/tex] and [tex]b=1[/tex].

[tex](x+1)^2=x^2+2(x)(1)+1^2=x^2+2x+1[/tex]