Solving Polynomial Equations

25x²-9=0

The width and the length that gives the largest possible areas are 75 meters by 37.5 meters

From the question, we have the following parameters that can be used in our computation:

Number of warehouses = 4

Perimeter of fence = 300 meters

Represent the width with x and the length with y

So, we have the following equations

Area = 4xy

Perimeter = 2(4x + y)

Substitute the known values in the above equation, so, we have the following representation

2(4x + y) = 300

Divide both sides by 2

2x + y = 150

Make y the subject

y = 150 - 2x

Substitute y = 150 - 2x in Area = 4xy

A = 4x(150 - 2x)

This gives

A = 600x - 8x²

Differentiate and set to 0

600 - 16x = 0

So, we have

16x = 600

Divide by 16

x = 37.5

Recall that

y = 150 - 2x

So, we have

y = 150 - 2 x 37.5

Evaluate

y = 75

Hence, the dimensions are 75 meters by 37.5 meters

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Answer:

394,898

Step-by-step explanation:

9.8% = 0.098

0.098x = 38700

Divide both sides by 0.098

x = 38700/0.098

x = 394,897.9591836735

Rounding

x = 394,898

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  a, c, b

Step-by-step explanation:

Collect terms, subtract the constant, divide by the y-coefficient.

(a) 4y + (y - 1) = 29   ⇒   y = 6

(c) (2y + 3) - 4 = 9​   ⇒   y = 5

(b) 4y - y + 1 = 13   ⇒   y = 4 . . . . . this equation is not what you have written

__

Additional comment

The second equation suffers from a typo, so your answer may vary.

Answer:

in order acb  

Step-by-step explanation:

Answer:

y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)

Step-by-step explanation:

Given the quadratic function:

[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]

We can rewrite the function above using perfect square form:

[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]

Finding an inverse, we swap the terms of x and y:

[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]

Square root both sides, solving for y:

[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]

Subtract both sides by 2:

[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]

Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.

Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.

Balance after 8 years is $2,306.86 at an interest rate of 15 % compounded yearly.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

given, Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest

from the general formula of compound interest

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

where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.

Given, P = 700$

r = 15%

t = 8 years

A = 700(1 + 15/100)⁸

A = 2306.86$

Therefore, At a 15% annual compounded interest rate, the remaining balance after 8 years is $2,306.86.

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Explanation:

We have 7 at the center. Going 2 units to the left of center gets us to 7-2 = 5. Going 2 units to the right of center gets us to 7+2 = 9.

Since the mean is 7 and the standard deviation is 2, this tells us that the values 5 and 9 are exactly one standard deviation away from the mean.

Due to the empirical rule (aka 68-95-99.7 rule), we just found that roughly 68% of the population is between 5 and 9.

Half of this is 68/2 = 34%, so this is the percent of values between 7 and 9.

Answer:

10

Step-by-step explanation:

50 students.

20% = 20/100 = 1/5

50*1/5 = 10

There are 10 left-handers.

Step-by-step explanation:

I don't see options but here's the solution

2x²+9x-3=-x²+x

2x²+x²+9x-x-3=0

3x²+8x-3=0

(3x-1)(x+3)=0

Therefore x=⅓ or-3

Answer:

Step-by-step explanation:

Answer:

0 ÷ 3 = 0

Step-by-step explanation:

if x = 0 you put it in where the x is

Answer:

A. 18.5

Step-by-step explanation:

When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]

A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.

A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.

Steps to convert Improper fraction to Mixed Fraction :

So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]

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The  largest amount of money they can borrow is $$276.268.65

The main formula used in this problem is the Present Value of an annuity Formula:

P = R[1-(1+i)⁻ⁿ]/i

Where;

The maximal monthly payment that Bethany and Samuel can afford is $1,500.

The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.

This implies that

R=1,500

t=30

r=%5.1 = 5.1 /100 = 0.051

m=12, because they make the payments monthly

i=r/m=0.051/12=0.00425

n=mt = 12*30=360

That is,

i) they will make 360 monthly payments,

ii) the largest amount of money they can borrow can be found using the formula:

P = R[1-(1+i)⁻ⁿ]/i

Substituting the known values:

P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425

Therefore, $276.268.65 is the largest possible principal for the situation

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Answer:     y = mx + b

Step-by-step explanation:

On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is = 1000

obtained = 500

so, 500/1000X100 = 50%

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The point shown on the graph is

(4, -5, 6)

An ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.

Each axis also has an orientation, and the length of all three axes is equal.

In ordered triplet, the order of the axis is (x, y, z)

z is vertical up positive and down negative

y is horizontal right is positive and left is negative

x is the axis pointing to us which is positive pointing away is negative

Using this information, to trace the point shows that the point marked by a dot is  (4, -5, 6).

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keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

Answer:

ed = 3

lm = 30.6

Step-by-step explanation:

Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.

What is division?

With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".

The bigger amount that is divided into equal halves is called the dividend.

The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.

The value of a digit in a number is determined by its place in the number, or place value.

Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.

Example - 4 ÷ 2 = 2

In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).

Example - 40 ÷ 20 = 2

For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).

Example - 400 ÷ 200 = 2

Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).

Therefore, place value blocks help in division for making it simpler.

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6. Larry's total sales during the pay period is $20,000.

7. Tom should leave $3 (approximate)

What is the meaning of total sales?

Total sales revenue usually referred to as gross sales is the sum of the value of the products and services a company provides to its clients over the course of a given reporting period.

Given that Larry earns $840 per pay period, plus a commission of 8% on his sales.

Assume that Larry sale $x during the last pay period.

The total earn is 840 + 8% of x

= 840 + 0.08x

According to the question:

840 + 0.08x = 2,440.00

Subtract 840 from both sides:

0.08x = 2,440 - 840

0.08x = 1600

Divide both sides by 0.08

x = 1600/0.08

x = 20,000

The sales is $20,000.

7. Given that,  Tom's bill at a local restaurant was $19.47. He leaves 15% of the total bill as a tip.

15% of $19.47

= 15/100 × $19.47

= 2.920

≈ 3 (approximate)

Tom should leave $3.

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Answer:

1/12

Step-by-step explanation:

3/4 - 2/3 = 9/12 - 8/12 = 1/12

Answer:

The answer is 1/12 good luck with the rest

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have [tex]x1[/tex]=2    [tex]x2[/tex]=-11

then quadratic function will be

(x+2) (x+11)

[tex]x^2+2x+11x+22[/tex]

[tex]x^2+13x +22[/tex]

this is our required quadratic equation.

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Complete question is: Write a quadratic function f whose zeros are 2 and -13.

Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.

Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.

Now we have x¹ = 2    x² = -11

then quadratic function will be

(x+2) (x+11)

x² + 2x + 11x + 22

x² + 13x + 22

This is our required quadratic equation.

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The complete question is-

Write a quadratic function f whose zeros are 2 and -13.

Answer:

b. (2,0)

Step-by-step explanation:

To find which ordered pair is a solution, we have to replace then into the equation, and the result has to be an identity, that is, 0 = 0.

Equation:

[tex]y = -5x + 10[/tex]

Option a:

[tex](-15,5)[/tex], so [tex]x = -15, y = 5[/tex]

[tex]y = -5x + 10[/tex]

[tex]5 = -5(-15) + 10[/tex]

[tex]5 = 75 + 10[/tex]

[tex]5 = 85[/tex]

Not an identity, so this ordered pair is not a solution.

Option b:

[tex](2,0)[/tex], so [tex]x = 2, y = 0[/tex]

[tex]y = -5x + 10[/tex]

[tex]0 = -5(2) + 10[/tex]

[tex]0 = -10 + 10[/tex]

[tex]0 = 0[/tex]

Identity, and thus, the correct answer is given by option b.

Answer:

X=14

Step-by-step explanation:

180-58-75=3x+5

3x+5=47

3x=42

X=14

Total Liabilities  + Equity = $220,000.

Total Assets = $220,000.

What is Ratio Analysis and Balance Sheet?

The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.

One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.

Here we are given in the Question,

Assets

Cash = $45,000

Inventory = $41,000

Property = $134,000

Liabilities

Notes  = $55,000

Wages  = $56,000

and

Equity

Stock = $50,000

Investment = $59,000

Total Liabilities  + Equity = ( Notes + wages ) + (stock + Investment)

Total Liabilities  + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)

Total Liabilities  + Equity = $220,000.

Total Assets = Cash + Inventory + Property

Total Assets = $45,000 + $41,000 + $134,000

Total Assets = $220,000

Therefore,

Total Liabilities  + Equity = Total Assets.

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