dreamy donuts sells bags of donut holes and donuts by the dozen. Cleo spends $25 to purchase 2 bags of donut holes and 4 dozen donut donuts. Gavin spends $20 to buy 4 bags of donut holes and 3 dozen donuts. Let x be the cost of a donut and y be the cost of a dozen donut holes.

if 5x² +5x+xy=4 then the value of y'(4) is -21/4

A differential equation is an equation that contains one or more functions with its derivatives.

The given expression is  5x² +5x+xy=4

Five times of x square plus five times of x plus x times of y equal to four.

Differentiate with respect to x.

10x+5+y(x)+xy'(x)

if x=4

10(4)+5+y(4)+4y'(4)=0

40+5-24+4y'(4)=0

21+4y'(4)=0

4y'(4)=-21

Divide both sides by 4

y'(4)=-21/4

Hence, if 5x² +5x+xy=4 then the value of y'(4) is -21/4

To learn more on Differentiation click:

https://brainly.com/question/24898810

#SPJ1

The area of the circular section is equal to 3π square meters. (Correct choice: C)

Herein we find the case of a circular section whose area must be found by the following formula:

A = (θ / 360) · π · R²

Where:

If we know that θ = 270° and R = 2 m, then the area of the circular section is:

A = (270 / 360) · π · (2 m)²

A = (3π / 4) · (2 m)²

A = 3π m²

To learn more on circular sections: https://brainly.com/question/13672518

#SPJ1

Answer: To find the principal value of arctan(-1.44) to the nearest minute, we first need to find the value of arctan(-1.44) in radians.

We can use the arctan function in a mathematical software or calculator to find the result. The value of arctan(-1.44) in radians is approximately -0.8623.

Next, we convert the result from radians to minutes, by multiplying the radians by 180/π and then multiplying the result by 60.

-0.8623 * 180/π * 60 = -50.47 minutes

So the principal value of arctan(-1.44) to the nearest minute is approximately -50 minutes.

Step-by-step explanation:

Answer:

p = 1

Step-by-step explanation:

since (p, 2p + 1) is a solution then it makes the equation true.

substitute x = p and y = 2p + 1 into the equation and solve for p

11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side

11p - 4p - 2 = 5

7p - 2 = 5 ( add 2 to both sides )

7p = 7 ( divide both sides by 7 )

p = 1

Answer:

$56.84

Step-by-step explanation:

52.35 + 8.5% + 18% ÷ 4 = $56.84475

The dilated coordinates:

D(-7, 0) → D' (-7/5, 0)

E(-7, -5) → E' (-7/5, -1)

F(-2, -5) → F' (-2/5, -1)

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.

Given:

Coordinates: D(-7, 0), E(-7, -5), F(-2, -5).

The shape is dilated by the scale factor of 1/5.

The dilation rule:

D(-7, 0) → D' (-7/5, 0)

E(-7, -5) → E' (-7/5, -1)

F(-2, -5) → F' (-2/5, -1)

Hence, the dilated coordinates are given above.

To learn more about the dilation in geometry;

https://brainly.com/question/10713409

#SPJ1

The complete question:

Find the dilated coordinates with the scale factor of 1/5,

D(-7, 0), E(-7, -5), F(-2, -5).

Kelly can run 1/2 mile in 3 minutes. 1/6 mile Kelly run in 1 minute if he runs at the same pace the entire time.

The word "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards.

Kelly can run 1/2 mile in 3 minutes so the ratio is 1/2 mile per 3 minutes

= [tex]\frac{\frac{1}{2} }{3}[/tex]

For transforming 3 to 1 we need to divide by 3 because we have to keep the ratio value, we have to divide also the numerator by 3 :

= [tex]\frac{\frac{1}{2} }{3} \times \frac{\frac{1}{3} }{\frac{1}{3}}[/tex]

[tex]= \frac{\frac{1}{2} \times \frac{1}{3} }{3 \times \frac{1}{3} }[/tex]

= 1/6 / 1

= 1/6

Learn more about the Miles here: https://brainly.com/question/29806974

#SPJ1

Answer:

length x width x height divided by 3

The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603

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

Base fee = $85.00

Rate = $2 off

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

R(n) = n(85 - 2n)

Where n is the number of rooms

This means that

n = 9

So, the notation is

R(9)

The value is

R(9) = 9 *(85 - 2 * 9)\

R(9) = 603

Hence, the value is $603

Read more about functions a

https://brainly.com/question/28277110

#SPJ1

The number of bouts that Andrew won during the last would be = 20 bouts.

The number of fencing bouts that Andrew won = 4

The number of bouts he losses every 4 wins = 3 bouts

The total number of bouts he is having this year = 35 bouts.

The number of bouts he won amongst the number that he lost would be calculated as;

= 4+3 = 7

= 4/7 × 35/1

= 4× 5 = 20 bouts.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Therefore, we have proved that the value of the expression

(3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.

In mathematics, addition, multiplication, and division are necessary. They result in the following when combined: An equation, some data, and a mathematical function Values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions can all be found in a declaration of fact. Different phrases and words can be compared and evaluated.

Here,

To prove that the value of the expression doesn't depend on x, we need to show that the x-term disappears when we simplify the expression.

Starting with:

(3/5x² - 0.4cy - 1.5y + 1) - (y² - 2/5xy + 0.6x²)

Distributing the negative sign in the second set of parentheses:

3/5x² - 0.4cy - 1.5y + 1 - y² + 2/5xy - 0.6x²

Rearranging the terms by collecting like terms, we get:

(3/5 - 0.6)x² + (2/5y - 0.4c)y - y²- 1.5y + 1

Simplifying further, we get:

(-0.1)x² + (0.4y - 0.4c)y - (y² + 1.5y - 1)

Notice that there is no x-term in the final expression, which means that the value of the expression doesn't depend on x.

Therefore, we have proved that the value of the expression (3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Answer:

[tex]y=-105x+1300[/tex]

Step-by-step explanation:

Define the variables:

Given information:

Therefore:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Determine if the equation is linear by calculating the slope between each pair of (x, y) points:

[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]

[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]

As the slope is the same, the equation is linear.

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The initial purchase price of the computer was $1,300. So when x = 0, y = 1300.  Therefore, the y-intercept is 1300.  

We have already calculated the slope as -105.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:

[tex]y=-105x+1300[/tex]

The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.

The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.

Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.

For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:

x = 2y + 3

2y = x - 3

y = (x - 3)/2

Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.

Learn more about inverse functions here:
https://brainly.com/question/30350743
#SPJ1

Lourdes will spend an amount of  $1.50 more if she buys only 3-packs of paper.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

If Lourdes buys only 3-packs of paper, she will need to buy 12 / 3 = 4 sets of paper.

At $10.50 per set, this will cost her 4 x $10.50 = $42.

If Lourdes buys only 4-packs of paper, she will need to buy 12 / 4 = 3 sets of paper.

At $13.50 per set, this will cost her 3 x $13.50 = $40.50.

So, Lourdes will spend $42 - $40.50 = $1.50 more if she buys only 3-packs of paper.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ1

Answer:

1) {2,0,-2}

2) {1,-3,1}

3) {1,3,5}

4) {0,1,2}

The function can be used to model the exponential growth or decay that occurs in real-life situations that fit this particular pattern is y = 4(-0.4)ˣ + -4

An exponential function is a mathematical function that has the form

=> y = abˣ,

where a is a constant and b is the base of the exponential.

To start, we will use the first point, (1, -1.6), to write an equation that relates x and y. Let's call the constant a in our exponential function "k". Using the point (1, -1.6), we can write the equation:

=> -1.6 = k * b¹

Next, we will use the second point, (2, -0.64), to write another equation that relates x and y. Using the point (2, -0.64), we can write the equation:

=> -0.64 = k * b²

Now that we have two equations, we can solve for the two unknowns, k and b, by dividing the two equations:

=> (-0.64) / (-1.6) = k * b² / k * b¹

b = (0.64 / -1.6)¹

b = -0.4

With b determined, we can substitute it back into one of the equations and solve for k:

=> -1.6 = k * (-0.4)¹

=> k = -1.6 / (-0.4)

=> k = 4

So our exponential function that passes through the points (1, -1.6) and (2, -0.64) and has a y-intercept of -4 is:

y = 4 * (-0.4)ˣ + -4

To know more about exponential function here.

https://brainly.com/question/2456547

#SPJ4

The value for variable m in equation Z = m + mwg is m = Z - mwg.

What are variables?

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The equation is given as -

Z = m + mwg

To get the value for variable m, subtract mwg from Z and take it to left-hand side.

Z - mwg = m

Reverse the equation and get it in right form -

The equation obtained is -

m = Z - mwg

Therefore, the value is m = Z - mwg .

To learn more about variables from the given link

https://brainly.com/question/82796

#SPJ1

The images of the functions are listed below:

Case 1: f(x) = √(- x) (Correct choice: A)

Case 2: f(x) = √(x - 4) (Correct choice: D)

Case 3: f(x) = √x - 3 (Correct choice: A)

Case 4: f(x) = √(x - 4) - 4 (Correct choice: A)

In this problem we find four cases of functions that must be transformed by rigid transformations. Rigid transformations are transformations applied on functions such that its features are not altered. We should apply, if possible, the following rigid transformations:

Reflection across the y-axis

f(x) → f(- x)

Translation to the right

f(x) → f(x - k), where k > 0

Translation downward

f(x) → f(x) - k, where k > 0

Now we proceed to determine the image of each function:

Case 1

f(x) = √x

Reflection across the y-axis

f(x) = √(- x)

Case 2

Translation 4 units right

f(x) = √(x - 4)

Case 3

Translation 3 units down

f(x) = √x - 3

Case 4

Translation 4 units right and 4 units down

f(x) = √(x - 4) - 4

To learn more on rigid transformations: https://brainly.com/question/28004150

#SPJ1

Using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and sometimes "pc" is also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without boundaries and without a standard measurement.

So, calculate as follows:

5880/100 * 11.5 = 676.2

Now,

5880 - 676.2 = 5,203.8

Now, calculate the percentage as follows:

806.59/5,203.8 * 100

15.5%

Therefore, using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.

Know more about percentages here:

https://brainly.com/question/24304697

#SPJ1

A repeating decimal like 0.2222222.... is a rational number and can be written as the fraction 2/9.

A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100.

A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number that can be written as the fraction 1514013912/5000000

The square root of a perfect square is a rational number and also a whole number.

The square root of a prime number is an irrational number.

The definition of a rational number is one that may be stated as a fraction or as a portion of a whole number. For example -7, 2/3, 3.75 Numbers that cannot be stated as a fraction or ratio of two integers are referred to be irrational numbers. There is no limit to how one might convey them. For example √2, √3, e

Learn more about rational and irrational numbers at: https://brainly.com/question/20400557

#SPJ1

Answer: Caleb bought 15 grams for his mom

Step-by-step explanation:

5/4 is equal to 1.25, so Caleb bought 1.25 x 12 grams.

1.25 x 12 = 15 grams.

Answer:

The domain for the interval of decrease is 3 ≤ x ≤ 5

Mike buys 3 oranges and 1 lemon at the

farmers market. What fraction of his

purchase were oranges?

answer :

3/4

Answer: 3/4

Step-by-step explanation:

there are a total of four purchases and three of them were purchases we can represent this with the fraction 3/4

The most accurate comment about the graph  data is: "China's steel production is increasing while its major competitors' production is declining."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."

This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.

While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.

The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

By the inverse of a number, 0.3⁻¹ = 10/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 0.3⁻¹ = 10/3

Now, We can simplify as;

⇒ 0.3⁻¹

⇒ (3/10)⁻¹

⇒ 10/3

Thus, By the inverse of a number, 0.3⁻¹ = 10/3

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Each person will get 1 [tex]\frac{7}{9}[/tex] cups of ice cream.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that, Brian is splitting 4 quarts of ice cream with members of the team.

Assume the number of members of the team = 9

We have to find how many cups each member gets.

First we have to convert the measurement quarts to cups.

1 quart = 2 pints

1 pint = 2 cups

1 quart = 2 × 2 cups = 4 cups

We have 4 quarts of ice cream.

4 quarts = 4 × 4 = 16 cups

Number of cups each member gets = 16/9 cups = 1 [tex]\frac{7}{9}[/tex] cups

Hence there will be 1 [tex]\frac{7}{9}[/tex] cups for each member.

Learn more about Division here :

https://brainly.com/question/14775006

#SPJ1