x2 + y2 − 5px = 0 polar form

The equation is given by 5n + 100n = 210

Peggy has 8 quarters and 2 nickels

Let's call q the number of quarters and n the number of nickels.

If Peggy has four times as many quarters as nickels, we can write the following equation:

q = 4n

Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so

0.25q + 0.05n = 2.10

Because she had $2.10. Now, we can replace the first equation on the second one

0.25(4n) + 0.05n = 2.10

1n + 0.05n = 2.10

Finally, we can multiply both sides by 100, so

100n + 0.05(100)n + 2.10(100)

100n + 5n = 210

Therefore, the equation that can be used to solve the problem is

5n + 100n = 210

Now, we can solve the equation for n

105n = 210

105n/105 = 210/105

n = 2

Then, q is equal to

q = 4n

q = 4(2)

q = 8

It means that Peggy has 8 quarters and 2 nickels.

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complete question is listed below:

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

Which of the following equations could be used to solve the problem?

On+4 n=210

5 n+100 n=210

n+4 n=2.10

5n+100 n=2.10.

Answer:

Step-by-step explanation:

a. The average rate of change in the number of worldwide cell phones can be calculated as:

Average rate of change = (change in number of cell phones) / (change in time)

The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,

Average rate of change = 1.94 billion / 2 years = 0.97 billion/year

So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.

b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:

C(t) - 14.02 = 0.97t

Simplifying, we get:

C(t) = 0.97t + 14.02

So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.

c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).

C(7) = 0.97(7) + 14.02 = 20.83 billion

Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.

Answer: B. 3300

Step-by-step explanation: Answers in the 5000 range would be Expenses, and 2000 would be Liabilities, which are both opposite of capital. "S.E." in accounting typically stands for "Shareholder Equity" or "Stockholder's Equity" and would be one type of capital.

Answer:

C. 13.77 m

Step-by-step explanation:

The sum of the three angles of a triangle is 180°

In the given triangle, two of the angles are 37° and 90°

Third angle = 180 - (37 + 90) = 53°

By the law of sines, ratio of a side to the sine of the opposite angle is the same for all sides and their opposite angles

∴
[tex]\dfrac{a}{\sin 90} = \dfrac{11}{\sin 53}\\\\\sin 90 = 1\\\sin 53 = 0.7986\\\\\rightarrow \dfrac{a}{1} = \dfrac{11}{0.7986}\\\\a = 13.7735\\\\a\approx 13.77\; m[/tex]

Answer:i think the answer is D but it could be C but i know for a fact it is definitely not A or B

Step-by-step explanation:

We require x = 170 televisions to minimize total cost

The minimum of a function is the lowest value of that function.

Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.

To find the minimum value, we differentiate C(x) with respect to x and equate to zero.

So,  C(x) = x² - 195x² + 66000x + 15000

dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx

= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx

= 2x - 195(2)x + 66000 + 0

= 2x - 390x + 66000

= -388x + 66000

Equating to zero, we have

dC(x)/dx = 0

-388x + 66000 = 0

-388x = -66000

x = -66000/-388

x = 170.1

x ≅ 170

So, we require x = 170 televisions to minimize total cost

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The values of x and y are x = 6 and y = 3√5

Triangle 1

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

The right triangle where one of the angles is 45 degree

This is a special triangle such that

Hypotenuse = Legs * √2

So, we have

x = 3√2 * √2

Evaluate

x = 6

Triangle 2

Here, we have:

The right triangle where one of the angles is 60 degrees

So, we have

cos(60) = y/6√5

This gives

y = 6√5 * cos(60)

Evaluate

y = 3√5

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The evaluation of equations by resolving into quadratic equations and factoring are presented as follows;

A quadratic equation is an equation which can be expressed as; f(x) = a·x² + b·x + c, where a, b, and c are real numbers and a ≠ 0.

1. √(30 - x) = x

x = √(30 - x)

x² = 30 - x

x² + x - 30 = 0

Factoring the above quadratic equation, we get;

(x + 6)·(x - 5) = 0

2. x = √(42 - x)

x² = 42 - x

x² + x - 42 = 0

(x + 7)·(x - 6) = 0

3. √(12 - r) = r

Squaring both sides of the equation, we get;

(12 - r) = r²

r² = 12 - r

r² + r - 12 = 0

(r + 4)·(r - 3) = 0

4. m = √(56 - m)

m² = 56 - m

m² + m - 56 = 0

(m + 8)·(m - 7) = 0

5. r = √(-1 - 2·r)

r² = -1 - 2·r

r² + 2·r + 1 = 0

(r + 1)² = 0

6. √(4·n + 8) = n + 3

4·n + 8 = (n + 3)² = n² + 6·n + 9

4·n + 8 = n² + 6·n + 9

n² + 6·n + 9 - (4·n + 8) = 0

n² + 6·n + 9 - 4·n - 8 = 0

n² + 2·n + 1 = 0

(n + 1)² = 0

7. -n + √(6·n + 19) = 2

-n + √(6·n + 19) = 2

√(6·n + 19) = n + 2

(6·n + 19) = (n + 2)² = n² + 4·n + 4

6·n + 19 = n² + 4·n + 4

n² + 4·n + 4 = 6·n + 19

n² + 4·n + 4 - (6·n + 19) = 0

n² - 2·n - 15 = 0

(x - 5)·(x + 3) = 0

8. 4 + √(-3·m + 10) = m

√(-3·m + 10) = m - 4

-3·m + 10 = (m - 4)² = m² - 8·m + 16

-3·m + 10 = m² - 8·m + 16

m² - 8·m + 16 = -3·m + 10

m² - 8·m + 16 + 3·m - 10 = 0

m² - 5·m + 6 = 0

(m - 3)·(m - 2) = 0

9. x - 5 = √(x + 1)

Squaring both sides, we get;

(x - 5)² = (√(x + 1))²

(x - 5)² = x + 1

x² - 10·x + 25 = x + 1

x² - 10·x + 25 - (x + 1) = 0

x² - 10·x + 25 - x - 1 = 0

x² - 11·x + 24 = 0

(x - 8)·(x - 3) = 0

10. n - 7 = √(3·n - 21)

(n -7)² = (3·n - 21)

n² - 14·n + 49 = 3·n - 21

n² - 14·n + 49 - (3·n - 21) = 0

n² - 14·n + 49 - 3·n + 21 = 0

n² - 17·n + 70 = 0

(n - 10)·(n - 7) = 0

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Answer:

x = -3/5

Step-by-step explanation:

Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]

Solve for the variable x by isolating x-term, first move subtract both sides by 3x:

[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]

Subtract both sides by 9:

[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]

Therefore x = - 3/5

Answer:

x = -3/5 (or) x = -0.6

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 8x + 9 = 3x + 6

Then the value of x will be,

→ 8x + 9 = 3x + 6

→ 8x - 3x = 6 - 9

→ 5x = -3

→ x = -3 ÷ 5

→ [ x = -3/5 ]

Hence, the answer is -3/5.

Answer:

347

Step-by-step explanation:

Im not sure if that helps but thats the answer I got.

By using the long division method, The value of expression  8328 ÷ 24 after divide is,

⇒ 8328 ÷ 24

   = 347

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The mathematical expression for divide is,

⇒ 8328 ÷ 24

Now, We can formulate;

We can use the long division method for the expression as;

⇒ 8328 ÷ 24

⇒ 8328 / 24

 24 ) 8328 ( 347

     -  72

       -----

        112

     -   96

        ------

             168

           -  168

            --------

                  0

Therefore, We get the correct answer,

By using the long division method,

The value of expression  8328 ÷ 24  after divide is,

⇒ 8328 ÷ 24

   = 347

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The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.

The length of the rectangle is 0.9 cm.

The width of the rectangle is 0.4 cm.

The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.

The area of the rectangle is:

A = (l)(b)

Substituting the values:

A = (0.9)(0.4)

A = 0.36 sq. cm.

The area of the circle is:

A = πr²

A = (3.14)(0.2)²

A = 0.1256 sq. cm.

The area of the shaded portion is:

Area of shaded portion = area of rectangle - area of circle

Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm

Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.

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Answer:

The answer is (A) 8.1%.

Step-by-step explanation:

The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:

P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11

Using a calculator, we get:

P(4 heads in 11 flips) ≈ 8.1%

Therefore, the answer is (A) 8.1%.

The new account balance at the end of 2 years is $517.

Simple interest

5 yearsUsing this formula I= (P+r×t)

Where: I=Interest=?

P=Principal=$400

r=Interest rate=3.5%

t=Time=5 years

Hence: I= ($400×0.035 x 5) which makes I= $70

2 years

I=Interest=?

P=Principal=$470

r=Interest rate=5%

t=Time=2 years

I=($470+0.05×2) which makes I=$47

New balance:

New balance=$400+$70+$47

New balance=$517

Inconclusion the new account balance at the end of 2 years is $517.

Distance reading at the start of journey = 12468

Distance reading at the end of the journey = 12845

Distance traveled in the journey = 12845 - 12468 = 377 miles

Cost of petrol per mile = 13p

Cost of petrol for the journey = 13 × 377 = 4901p

Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds

Cost of petrol used in the journey is 49.01 pounds

If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

Divide its principal by the risk premium, the time period and other factors to arrive at simple interest. Simple return = principal + interest + hours is the marketing formula. This process makes it easier to calculate interest. The most typical technique to figure out interests is as a portion of the principal sum. He will only pay his half of the 100% interest, for example, if he borrows $100 from a partner and agrees to repay the loan with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must pay the interest. Interest is often set as an annual percentage of the loan total.

given:

FV = 1000(1.06)²⁵

FV =  1000 × 4.2918

FV = 4291.8

If you put $1,000 per year into an account yielding 6% interest that is compounded annually, you will have $4291.8 in the account after 25 years.

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Answer:

Step-by-step explanation:

line a is 5ft

Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

--------------------

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

--------------------

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

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

--------------------

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

The points are as selected on the graph.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:

x    f(x)

-2   -9

0    -9

2    -9

7    -9

9    -9

Check the attached image for the points on the graph

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The values of h is v3 in span fv1; v2g and h is fv1; v2; v3g is 4.

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

We are given that;

v1 and v2 are not scalar multiples to each other

So, they are not linearly dependent

Now,

1(10h -42) -3(-14 +3h) +2 (18-20) =0

10h -9h-4 =0

h = 4

Therefore, by vectors the answer will be 4 so that the vector v3 is in {v1,v2}.

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Answer:

Step-by-step explanation:

If a ball plus a bat costs 1.10 dollars and the price of the bat is 1 dollar more than the ball, what is the cost of the bat?

If we represent the price of the ball as "p", then the price of the bat will be "p + 1", since the problem tells us that the price of the bat is 1 dollar more than the price of the ball.

We also know that the sum of the price of the ball and the bat is 1.10 dollars. We can write this as an equation:

p + (p + 1) = 1.10

Simplifying and solving for p, we get:

2p + 1 = 1.10

2p = 0.10

p = 0.05

Therefore, the price of the ball is 0.05 dollars. To calculate the price of the bat, we can add 1 dollar to the price of the ball:

p + 1 = 0.05 + 1 = 1.05

So, the price of the bat is 1.05 dollars.

Answer:

[tex]A. \;x^2 -7x + 1[/tex]

[tex]B.\;5x^2 + 2x[/tex]

Step-by-step explanation:

Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.

The standard form of polynomial is given by

[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.

The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]

and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)

The number of elements in the complement of the union set of A and B is given as follows:

12.

The universal set is given as follows:

S = {1, 2, 3, ... , 23, 24, 25}.

The union between two sets is composed by the elements that belong to at least one of the sets, hence the union of sets A and B is given as follows:

A U B = {2, 3, 4, 6, 8, 12, 13, 14, 16, 18, 22, 24, 25}.

The number of elements in the union set is of:

13.

The complement of a set is composed by all the elements that belong to the universal set but to not belong to the set. As the union of A and B has 13 elements, and the universal set has 25 elements, the number of elements of the complement is given as follows:

25 - 13 = 12.

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Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.

According to the table:

The total number of Yellow Trains is 450.

The total number of all modes of transportation is 4730.

To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:

percentage = (part/whole) x 100

Substituting the values we have:

percentage = (450/4730) x 100

percentage = 0.095 x 100

percentage = 9.5%

Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.

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The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.

Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.

To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:

Assets                                    2017        2018        Change   % Change

Cash                                     $2,500 $3,900  $1,400  56%

Accounts receivable, net    $35,000 $40,000  $5,000     14%

Inventory                               $85,000 $122,000  $37,000   44%

Other current assets            $3,400      $4,110       $710        21%

Total current assets              $125,900  $170,010   $44,110    35%

PPE, net                                 $180,000  $230,000  $50,000  28%

Other assets                         $15,000    $26,000   $11,000    73%

Total assets                          $320,900   $426,010  $105,110 33%

Interpretation

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Answer:

Step-by-step explanation:

ASQASSA

The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70

To calculate the cost of gasoline for the old truck, we can use the following formula:

Cost of gasoline = Price per gallon × Number of gallons used

Given that

Price per gallon = 3.74

Number of gallons used = 5 gallons

We have

Cost of gasoline = $3.74/gallon × 5 gallons

Evaluate

Cost = $18.70

Hence, the cost is $18.70

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Complete question

An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon

Answer:

x = 3

y = 6

Step-by-step explanation:

2x - y = 0

3x - 2y = -3

-----------

2x-y = 0 ---> 2x = y ---> y = 2x ----> 3x - 2(2x) = -3 ---> 3x - 4x = -3 ---->

-----> -x = -3 ---> x = -3/-1 = 3 -----> x = 3

y = 2x ----> y = 2 (3) ----> y = 6

The proportional equation for the given graph would be y = 2. 5 x

The proportional equation takes the form :

y = mx

Where:

m = slope or the change in y as a result of x

The value of the slope is :

= Change in y / Change in x

= ( 15 - 0 ) / ( 6 - 0 )

= 15 / 6

= 2. 5

The proportional equation is:

y = 2. 5 x

In conclusion, the proportional equation would be y = 2. 5 x .

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The area of the shaded region is 73.5 cm square.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.

We are given the dimension of the shaded region.

Length = 15 cm

Breadth = 7 cm

The area of the trapezium is

Area = 1/2(sum of non parallel sides)height

Area = 1/2 (12 + 9) 7

Area = 1/2 x 21 x 7

Area = 73.5

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Answer:

According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.

Step-by-step explanation:

The equation given is:

y = 20x + 0

where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:

y = 20(20) + 0

y = 400

Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.

The way it can be shown that the equation Ax=b does not have a solution for some choices is A. Row reduce the matrix A to demonstrate that A has a pivot position in every row

A us 2 x 2 matrix, then Ax =b will not have a solution fot some B if rank(A) <2

This implies A does not have pivot position in every row in its reduced row echelon form.

This shows that option A is correct.

The augmented matrix [A b] is

[tex]\left[\begin{array}{ccc}1&4&b1\\3&-12&b2\end{array}\right][/tex]

Perform R2 = R2 +3 R1

[tex]\left[\begin{array}{ccc}-1&4&b1\\0&0&b2 = 3b1\end{array}\right][/tex]

New solutions exist if [tex]b_2 + 3b_i = 0[/tex]

0 = [tex]3b_1 + b_2[/tex]

Thus, the equation Ax = b have the solution if rank(A) = rank([A b])

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