This is a variation of problem 10 on page 141 of our textbook. You may want to solve this problem only after you solve the next one, which is the general version of this one. On the other hand, you also may want to solve this one first, and when solving the general one compare your evolving solution against your results in this problem.
A child is flying a kite. If the kite is 105 feet above the child's hand level and the wind is blowing it on a horizontal course at 6 feet per second, the child is paying out cord at _____________ feet per second when 165 feet of cord are out. Assume that the cord remains straight from hand to kite. (If you have ever flown a kite you know that this is an unrealistic assumption.)
For a solution of this problem (after the set closes) see the next problem.

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

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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

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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.

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Answer:

x^5y

Step-by-step explanation:

To find the greatest common factor (GCF) of 35x^5y and 42x^5y^3, we need to find the largest expression that divides into both of these polynomials.

The common factor in both of these polynomials is x^5y, which is the GCF. So, the GCF of 35x^5y and 42x^5y^3 is x^5y.

Teo is 10.5 years old and Richard is 25.5 years old.

Represent Teo's age with x.

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

Richard = x + 15

Their combined age is 36

So, we have the following representation

x + (x + 15) = 36

Evaluate the like terms

2x + 15 = 36

2x = 21

x = 10.5

Recall that

Richard = x + 15

So, we have

Richard = 10.5 + 15

Richard = 25.5

So Teo is 10.5 years old

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Answer:

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

Answer:

10a²/7

Step-by-step explanation:

25a/7×2a/5

50a²/35

10a²/7

Answer:

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The probability values

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

n = 14

p = 2/14

The probability P(x =1) can be calculated as

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

In this case, we have

P(x = 1) = C(14, 1) * (2/14)^1 * (1 - (2/14))^(13

Evaluate

P(x = 1) = 0.2696

The probability P(x >= 1) can be calculated as

P(x) = 1 - P(0)

In this case, we have

P(x >= 1) = 1 - [C(14, 0) * (2/14)^0 * (1 - (2/14))^(14)]

Evaluate

P(x >= 1) = 0.8845

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Answer: To find the inverse of the function f(x), we need to switch the roles of x and y, so that x becomes the dependent variable and y becomes the independent variable. Then, we need to solve for x in terms of y.

Let y = √x - 5, then x = y^2 + 5.

To find f^-1(2), we need to substitute 2 for y in the equation x = y^2 + 5:

x = 2^2 + 5 = 9

So f^-1(2) = 9.

This means that the inverse of f(x) at 2 is 9. In other words, if f(x) = 2, then x = 9.

Step-by-step explanation:

The area of the circle representing the population of California is 689.5 units

What is area of the circle?

Area of the circle is is them measure of size of circle. The area of circle is given by pi* r^2. where r is the radius of the circle which is equal to half the diameter. and pi is a mathematical constant. its value is 3.14.

We are given that the radius representing a circle for ohio is 8

Area of circle = 3.14 * (8^2)

Area of circle = 200.96

Now the area of the circle representing the population of California

given by,

= (39800000*200.96)/11600000

= 689.5

Hence the area of the circle representing population of California is 689.5

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Answer:

length x width x height divided by 3

The range of the quadratic function is {y |0 ≤ y < 9}

The range of a function is the set of output values of the graph. In other words mean the range of a function is the set of y values of the graph.

Given,

Parabola opens from

Closed circle point = (-2, 4) , then decreases

y ≤ 4

vertex = (0,0)

at vertex y = 0

then increases to

Open circle point = (3, 9)

y < 9.

It can be concluded,

value of y is such that 0 ≤ y < 9.

Range = {y | 0 ≤ y < 9}

Hence, the range of the function is {y | 0 ≤ y < 9}

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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.

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Answer:

Step-by-step explanation:

1+1=2 your welcome

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

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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.

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The complete question:

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

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

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

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Answer:

-40

Step-by-step explanation:

100-40+10-100-20+20-(+10)

=60+10-100-20+20-10

=70-100-20+20-10

=-30-20+20-10

=-50+20-10

=-30-10

=-40

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.

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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

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The total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km. Thus Option d is correct

The total length of 3km, 464m, 8km, 550m and 900m in kilometre

As we know that 1000m = 1 km, now

= 3000 + 464 + 8000 + 550 + 900

= 12914 m

= 12.914 km

Thus, the total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km

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The intersection points are (6, 6) and (-6, -6).

What is Intersection points?

The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.

The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.

6 sin(Ф) = 6 cos(Ф)

Dividing both sides by 6 and rearranging terms, we get:

tan(Ф) = 1

This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].

Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.

Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).

Therefore, the intersection points are (6, 6) and (-6, -6).

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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.

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

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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.

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Answer:

$56.84

Step-by-step explanation:

52.35 + 8.5% + 18% ÷ 4 = $56.84475