Piecewise linear relations

Answer:

this is the answer ................................

Answer:

each parking ticket costs $100 and each traffic violation costs $124.28.

Step-by-step explanation:

To find out the cost of each parking ticket and each traffic violation, we can set up two equations using the information given:

Let x be the cost of each parking ticket.

In the first month, 3 parking tickets cost 3x, and 14 traffic violations cost 14y.

The total cost for the first month is 2030, so we have:

3x + 14y = 2030

In the second month, 11 parking tickets cost 11x, and 11 traffic violations cost 11y.

The total cost for the second month is 2200, so we have:

11x + 11y = 2200

Now that we have two equations, we can use substitution to find the value of x and y.

From the first equation, we can solve for y:

y = (2030 - 3x) / 14

Substituting this expression for y into the second equation:

11x + 11((2030 - 3x) / 14) = 2200

Expanding the expression for y and simplifying the equation:

11x + 2030 - 33x / 14 = 2200

Multiplying both sides by 14:

154x + 28420 = 30800

Solving for x:

x = $100

So each parking ticket costs $100, and each traffic violation costs:

y = (2030 - 3x) / 14 = (2030 - 3 * 100) / 14 = (2030 - 300) / 14 = 1730 / 14 = $124.28

Therefore, each parking ticket costs $100 and each traffic violation costs $124.28.

Answer:

-727.41 dollars

Step-by-step explanation:

To find the cost of each parking ticket and each traffic violation, we can set up a system of two equations. Let's call the cost of a parking ticket "x" and the cost of a traffic violation "y".

For the first month:

3x + 14y = 2030

For the second month:

11x + 11y = 2200

We can solve for x and y using any method, such as substitution or elimination. For this problem, let's use substitution.

First, we'll solve for x in the first equation:

3x + 14y = 2030

3x = 2030 - 14y

x = (2030 - 14y) / 3

Next, we'll substitute this expression for x into the second equation:

11x + 11y = 2200

11((2030 - 14y) / 3) + 11y = 2200

2030 - 14y + 11y = 2200 * 3 / 11

2030 - 3y = 636

-3y = -1394

y = 464.67

Finally, we'll substitute this value of y back into the first equation to find x:

3x + 14y = 2030

3x + 14(464.67) = 2030

3x = 2030 - 6544.68

x = (2030 - 6544.68) / 3

x = -2180.23 / 3

x = -727.41

So each parking ticket costs approximately -727.41 dollars, and each traffic violation costs approximately 464.67 dollars. However, since these values are negative, it means the suspect has received a credit rather than being charged for these fees.

Answer:

a).2x-6-5x-12x. this is answer

Answer:

50 + 5x^2 + 4x.

Step-by-step explanation:

To find the sum of the expressions, we need to simplify each expression first and then add them up.

10 + 3x represents the first expression.

25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.

3x^2 - 5x represents the third expression.

-x^2 + 2x + 15 represents the fourth expression.

Adding all four expressions gives us:

10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15

By combining like terms, we get:

10 + 5x^2 + 4x + 25 + 15

The final simplified sum is:

50 + 5x^2 + 4x.

Answer:

$10576.38

Step-by-step explanation:

To calculate the investment amount required to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money you have after "t" years,

P is the initial investment amount (what you want to find),

r is the interest rate as a decimal,

n is the number of times the interest is compounded per year,

t is the number of years the investment will be compounded for.

In this case,

r = 0.036

n = 12 (because the interest is compounded monthly)

t = 15

So, we can plug in the values into the formula and solve for P:

A = P * (1 + 0.036/12)^(12 * 15)

$23711 = P * (1.003)^(180)

$23711 = P * 2.2375

Dividing both sides by 2.2375:

P = $23711 / 2.2375

P = $10576.38

So, to produce $23711 at an interest rate of 3.6% compounded monthly for 15 years, you would need to invest $10576.38. Rounded to the nearest dollar, this amount is $10576.

Answer:

Second Option  :  21

Step-by-step explanation:

At 1080 ml per day for 7 days, the patient would have to ingest 1080 x 7 = 7,560 ml

Since the can capacity is given in oz we have to convert both values to the same units

1 ml = 0.033814 fl oz

Therefore 7,560 ml ≡ 7,560 ml x 0.033814 fl oz

= 255.634 oz

Since each can holds 12 oz, the number of cans = 255.634/12

= 21.3

From the answer choices, the closest to this value is Second  Option : 21 cans

Answer:

Step-by-step explanation:

x/sin90=17.3/sin53

sin90=1

x=17.3/sin53

x=13.8

Nicholas will earn a commission of

Nicholas will earn a commission of 4% on the total price of the two cars sold to Mr. Sherman.

The total price of the two cars is $33,500 per car, so for two cars, the total price would be

= $33,500 * 2

= $67,000.

Therefore, Nicholas will earn a commission of 4% of $67,000

= $67,000 * 0.04

= $2,680.

hence, Nicholas will earn $2,680 in commission for selling the two cars to Mr. Sherman.

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You can fill in the rest of the table as shown below.

The derivative of a function is a concept from calculus that measures the rate of change of a function at a specific point. It provides information about how the value of the function changes as its input changes.

Use the following differentiation rules to fill the table:

d/dx(f(x)·g(x)) = f(x)·g'(x) + f'(x)·g(x)         (product rule)

d/dx(f(x)/g(x)) = [ g(x)·f'(x) - f(x)·g'(x) ] / [(g(x))²]   (Quotient rule)

d/dx(g(x)/f(x)) = [ f(x)·g'(x) - g(x)·f'(x) ] / [(f(x))²]     (Quotient rule)

x    f(x)   f'(x)   g(x)  g'(x)    d/dx(f(x)·g(x))     d/dx(f(x)/g(x))    d/dx(g(x)/f(x))

0    3       -2    -4     3            17                      -1/16                    1/9

1     2       -1      1      0            -1                         -1                      1/4

2    4        2     3      1            10                       2/9                    -1/8

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Based upon this information, (2) I and III only statements can be proven.

From the given information, we can prove that statement II is true, i.e., BD bisects ABC.

Proof:

Since BD is the perpendicular bisector of ADC, we have AD = CD and ∠ADB = ∠CDB = 90°. Thus, triangles ABD and CBD are congruent (by the hypotenuse-leg congruence criterion), which implies AB = BC and ∠ABD = ∠CBD. Therefore, BD bisects ∠ABC.

However, we cannot prove that statements I or III are true based solely on the given information.

Statement I (BD is a median) would be true if we had additional information that AD = DB = DC, but this is not necessarily true based on the given information.

Statement III (△ABC is isosceles) would be true if we had additional information that AB = BC, but this is not necessarily true based on the given information. In fact, it is only guaranteed that AB = BC if AD = BD = DC, which is not necessarily the case.

Therefore, the correct answer is (2) I and III, only.

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The height of the tree to the nearest hundredth of a meter is 10.77m.

Detailed explanation:

An illustration of identical triangles is shown in the diagram. View the illustration I included with my response to see how triangles can be used to solve this issue.

Because they both share an internal angle, the triangles made by Alyssa and her shadow and the triangle created by the tree and its shadow are examples of comparable triangles.

The ratios of the comparable sides on both sides are proportionate according to the similar triangles theorem.

Therefore, in order to determine the height of the tree, we must make a percentage of the corresponding sides of both triangles. Let x equal the tree's height.

[tex]\frac{BE}{BC} =\frac{DE}{AC}[/tex]

BE = 4.25 meters

DE = 1.65 meters

BC = 27.75 meters

AC = x meters

[tex]\frac{4.25}{27.75} =\frac{1.65}{x}[/tex]

Cross multiply is now used to find x.

4.25x= 1.65(27.75)

x = 10.77

Therefore, the height of the tree is 10.77 meters.

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Complete question:

Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

The area of circle that is needed to be filled with concrete is 509 m².

What is the definition of a circle?

A circle is a kind of ellipse with zero eccentricity and two coinciding foci. The locus of points drawn at equal distances from the centre is also known as a circle. A circle's radius is the distance between its centre and its outer line. A circle's diameter is the line that divides it into two equal halves and is equal to twice its radius.

A circle in the plane has the following equation:

(x-h)^²+ (y-k)² = r²

When the coordinate points are aligned (x, y)

(h, k) is the centre of a circle's coordinate.

r denotes the radius of a circle.

where 2πr is the circumference of the circle

πr²=circle's area

Now,

Given that circumference of the area=80 m

2πr=180

2*22/7*r=80

r=80*7/44

r=140/11 m

then area of the circular pad=πr²

=22/7*140/11*140/11

=2*20*140/11

=5600/11

=509 m²

hence,

              The area of circle that is needed to be filled with concrete is 509 m².        

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Answer:

y = 3x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{1}{3}[/tex] x + 4 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{3} }[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (- 1, - 3 ) into the partial equation

- 3 = 3(- 1) + c = - 3 + c ( add 3 to both sides )

y = 3x + 0 , that is

y = 3x

Answer:

no

Step-by-step explanation:

squares sides are  all equal

rectangle only have 2 side alike

The value of x from the given triangle is approximately 19.10.

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

We can use the Pythagorean theorem to find the value of x. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as follows:

c² = a²+ b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In this problem, c = 25, and we need to find the value of x which is the length of one of the other two sides. Let's call the other side y. Then, we can write the equation as follows:

25² = x² + y²

We are also given that the angle between x and y is 41 degrees. We can use trigonometry to find the value of y. The sine function gives us the ratio of the opposite side to the hypotenuse, so we can write:

sin(41) = y/25

Therefore, y = 25 * sin(41). Now that we have the values of x and y, we can substitute them in the equation derived from the Pythagorean theorem:

25² = x² + (25 * sin(41))²

Solving for x, we get:

x = √(25²- (25 * sin(41))²)

Using a calculator, we get that sin(41) = 0.661437827766148.

Now, we can substitute this value in the equation:

x = √(25² - (25 * sin(41))²)

x = √(25² - (25 * 0.661437827766148)²)

x = √(25² - (16.0359050108801)²)

x = √(625 - 256.132749101278)

x = √(368.867250898722)

x = 19.10

Hence, The value of x is approximately 19.10

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Answer:

270 square units

Step-by-step explanation:

The area of a regular hexagon is given by the equation:

A = (1/2)(a · P)

where a is the hexagon's apothem and P is its perimeter.

1. We can first solve for the hexagon's perimeter by multiplying its side length (given as 15) by 6, since there are 6 sides.

P = 15 · 6 = 90

2. Now, we can plug that perimeter value into the formula for the area of a regular hexagon (above).

A = (1/2)(90 · 6)

A = (1/2)(540)

A = 270 square units

Answer:

It would be C.

Step-by-step explanation:

It would be C.

JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.

Answer:

  6.8 ft

Step-by-step explanation:

You want the height of a tank with a base of 5.5 ft by 4 ft if adding 74.8 ft³ of water fills it halfway.

The volume of a rectangular prism is given by the formula ...

  V = LWH

The filled volume of the tank h feet high is ...

  74.8 ft³ = (5.5 ft)(4 ft)(h/2) . . . . . . the filled height is h/2

  74.8 ft³/(11 ft²) = h ≈ 6.8 ft . . . . . . divide by the coefficient of h

The height of the tank is 6.8 feet.

In this exercise we have to use the knowledge of excel to explain some functions that can be used, as:

In excel cell a division formula can be written as: =(A4+B4+C4+D4+E4)/5

If you track your daily earnings in an Excel spreadsheet, you can use the same spreadsheet to estimate your forecasted earnings for any period of time. You can use Excel's AVERAGE function to find out your average daily income. Multiply your average daily sales by the number of days specified to estimate how much profit you could make over time.

In mathematics, the average of a list of data represents the central value of the set of data. Mathematically defined as the ratio of the sum of all data and the number of items in the list. In statistics, the mean of a particular set of numerical data is also called the mean. For example, the average of 2, 3, 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the center value of 2, 3, and 4. So the meaning of average is to find the average of a group of numbers.

mean = sum of values ​​/ number of values

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Answer: 4(45x^(3)-1)

Step-by-step explanation:

The solution that gives the maximum profit for the linear optimization question is presented as follows;

A maximum profit of $840 can be earned by investing;

$3,000 in stock A

$6,000 in stock B

$7,000 in stock C

Linear programming is a optimization technique that helps in determining the maximizing or minimizing parameters of linear functions.

The parameters in the question, obtained from a similar question obtained online includes;

The amount available to be invested = $16,000

The expected returns for stock A = 4%

The expected return for stock B = 5%

Expected returns for stock C = 6%

Amount to be invested in each stock ≥ $1,000

Amount to be invested in stock C ≤ $7,000

Amount invested in C ≤ 4 × Amount invested in stock A

Amount invested in stock B ≤ 2 × Amount invested in stock A

Let x represent the amount invested in stock A, let y represent the amount invested in stock B therefore;

The amount invested in stock C = 16,000 - x - y

16,000 - x - y ≥ 1000...(1)

16,000 - x - y ≤ 7000...(2)

16,000 - x - y ≤ 4·x...(3)

Therefore, we get;

- y ≥ 1000 - 16,000 = -15000 + x

-y ≥ -15000 + x

16,000 - x - y ≤ 7000

16,000 - x - y ≤ 4·x

-y ≤ 4·x + x = 5·x - 16,000

-y ≤ 5·x - 16,000  

The vertices of the feasible regions on the graph of the inequalities are;

(5,000, 10,000), (3,000, 6,000), (8,000, 1,000), and (14,000, 1,000)

The profit function is;

Profit = 0.04·x + 0.05·y + 0.06·(16000 - x - y)

Plugging in the value of the vertices of the feasible region in the profit function, we get;

Point (5,000, 10,000)

Profit = 0.04 × 5000 + 0.05 × 10000 + 0.06 × (16000 - 5000 - 10000) = 760

Point (3,000, 6,000)

Profit = 0.04 × 3000 + 0.05 × 6000 + 0.06 × (16000 - 3000 - 6000) = 840

Point (8,000, 1,000)

Profit = 0.04 × 8000 + 0.05 × 1000 + 0.06 × (16000 - 8000 - 1000) = 790

(14,000, 1,000)

Profit = 0.04 × 14000 + 0.05 × 1000 + 0.06 × (16000 - 14000 - 1000) = 670

Therefore, the maximum profit of $840 is earned by investing $3,000 in stock A and $6,000 in stock B which indicates that the investment in stock C is $16,000 - $3,000 - $6,000 = $7,000

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There are 2(3/16) cups of shredded cheese on each pizza.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Large pizza = 1(1/4) cups of sauce

Now,

1(3/4) of the sauce = shredded cheese

The amount of shredded cheese.

= 1(3/4) x 1(1/4)

= 7/4 x 5/4

= 35/16

= 2(3/16)

Thus,

The amount of shredded cheese is 2(3/16).

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Answer:

the square root(route?) of four

Step-by-step explanation:

2x2=4, that dot is near two....

The value of the expression represented by |M × N| is 64

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

Using the above as a guide, we have the following:

M = 8 i.e.  {m, a, t, h, e, i, c, s}.

N = 8 i.e. {n, e, v, r, t, h, l, s}.

So, we have

|M × N| = 8 * 8

Evaluate

|M × N| = 64

Hence, the value of |M × N| is 64

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The two sequences have the same number (4) in the same position (third)

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

Using the above as a guide, we have

Sequence 1: 16, 8, 4, 2, 1.....

Sequence 2: 1, 2, 4, 8, 16.....

The number 4 is in the same position for the two sequences

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The interval for which the rocket's height is increasing is 0 to 1 second.

The graph shows the way a toy rocket changes its height once it is launched. In general, it can be seen the height increases for some seconds and then the height decreases.

To calculate the interval let's find out the second or minute at which the rocket loses height.

0 - 1 second (from this moment the rocket loses height)

Based on this, it can be concluded the interval is 0-1 seconds.

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Answer:

[tex] \frac{1}{2} \times 25 \times 10 = 125 [/tex]

[tex] \frac{1}{2} \times breath \times perpedicular \: hight[/tex]

Answer:

x² + 23x + 49

Step-by-step explanation:

area of rectangle = length × width

Area of outer rectangle:

(x + 10) × (2x + 5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

Area of unshaded square:

(x + 1)² = x² + 2x + 1

shaded area = area of outer rectangle - area of square

shaded area = 2x² + 25x + 50 - (x² + 2x + 1) =

= 2x² + 25x + 50 - x² - 2x - 1

= x² + 23x + 49

The ratio that is equivalent to the greatest fraction is B. 8:4.

A ratio is a relative size or value contained in another quantity.  It is computed as the quotient of the smaller and larger values.

Ratios are fractional values, which we can depict as fractions, decimals, or percentages.

Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.

The sum of ratios = 8

5/8 = 0.625

The sum of ratios = 12

8/12 = 0.67

The sum of ratios = 9

2/9 = 0.22

The sum of ratios = 14

9/14 = 0.64

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The amount of protein in Peanut butter is 209.5g.

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the amount of protein in  838g of peanut butter.

Contents of peanut butter: 35%

Carbohydrates - 25%

Protein - 40% Fat

Now 25% of protein in 838g.

25/100×838

0.25×838

209.5 g of protein in peanut butter

Hence, 209.5 g of protein in peanut butter

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