Find the distance between the points using the following methods. (4, 3), (7, 5)
a) The Distance Formula
b) Integration

Answer:

Expression is -8/0 which is 0 undefined

Step-by-step explanation:

-4 - 4= -8

-1 - -1= 0

The gcd(x, xy) = x for any positive integers x and y.

To prove that gcd(x, xy) = x for any positive integers x and y, we need to show that x is a common divisor of x and xy, and that it is the greatest common divisor (gcd).

First, let's establish that x is a common divisor of x and xy. Since x divides x evenly, x is a divisor of x. Additionally, since y is a positive integer, xy is a multiple of x. Therefore, x is a common divisor of x and xy.

Next, we need to show that x is the greatest common divisor. Let's assume there exists a common divisor d of x and xy such that d > x. Since d is a divisor of x, there exists a positive integer k such that x = dk.

Substituting this into xy, we get xy = (dk)y = d(xy). This implies that d is a common divisor of xy and x, contradicting the assumption that x is the greatest common divisor.

Therefore, we can conclude that gcd(x, xy) = x for any positive integers x and y.

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Answer:

42

Step-by-step explanation:

One angle of a regular pentagon = 108°

One angle of a regular hexagon = 120°.

One angle of a square = 90°

∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°

The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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The statement "sum of a and b integers is a negative integer" is true given that A and B are both negative integers and A is greater than B.

When we add two negative integers, the sum is always negative. This is because adding a negative number is the same as subtracting its absolute value. Therefore, if A and B are negative integers, then A + B will be negative as well.

Since A > B, the sum A + B will be closer in value to A than to B. However, it will still be negative because A and B are both negative integers.

So, the sum of A and B is a negative integer, and the statement is true.

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____ The given question is incomplete, the complete question is given below:

A and B are both negative integers with a>b. Classify this are true or false. sum of a and b integers is a negative integer.

Answer:

35

Step-by-step explanation:

f(x)=5x + 2

g(x)=1/2x+4

g(f(12))=

Find f(12) = 5*12 +2 = 60+2 = 62

Then find g(62) = 1/2 (62) +4 = 31+4 = 35

g(f(12) = 35

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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The graph that could represent the relationship between time (t) and speed (s) of a falling object is the graph labeled "Speed of a Falling Object." This graph shows a positive linear relationship between time and speed.

In the graph, the x-axis represents time in seconds (t), while the y-axis represents speed in meters per second (s). As time increases, the speed of the object also increases at a constant rate. This is shown by the upward trend of the graph.

The graph starts at a speed of 0 m/s when the object is dropped and continues to increase linearly as time progresses. The slope of the line represents the rate at which the speed is increasing.

The graph accurately depicts the relationship described in the question, where the speed of the falling object increases at a constant rate with time. Therefore, the graph labeled "Speed of a Falling Object" is the appropriate representation for this relationship.

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Answer:

I think False not sure

Step-by-step explanation:

Triangle EFG was transformed to create triangle E'F'G' with identical side lengths and angle measures, and the second triangle is rotated to the right. the transformation is a c. rotation. Therefore, option c. rotation is correct.

Rotation is the change that took place. A figure is transformed by a rotation in which the centre of rotation is moved from one side to the other. Triangle EFG was in this instance rotated to the right, or around a point to the left of the triangle.

The two triangles are said to be congruent if their side lengths and angle measurements are the same. As a result, they are capable of being changed into one another by a series of translations, rotations, and reflections.

A transformation known as a translation involves moving a figure while maintaining its original size and shape. Stretching is a transformation that increases a figure's size while maintaining its shape. A transformation that flips a figure over a line is called a reflection.

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Answer: c. rotation is correct.

Step-by-step explanation:

99% confidence interval for the mean gas mileage for this car model is

(27.971, 28.829).

Given;

The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon.

A simple random sample of 36 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon.

A = 1 - 0.990

   =0.010

Hence, Z (0.010/2) = 0.477 (from the standard normal table)

So 99% confidence interval is;

⇒ X - Z /- Z + X

= 28.4 - 0.477, 28.4 + 0.477

= (27.971, 28.829)

99% confidence interval for the mean gas mileage for this car model is

(27.971, 28.829).

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The correct statement regarding the probability of choosing a person at random who is a junior and plays video games, and whether these events are independent, is given as follows:

P(junior and video games) = 32%; The two events are not independent.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in this problem are given as follows:

Hence the probability is of:

P(junior and video games) = 48/150 = 0.32 = 32%.

The separate probabilities are given as follows:

The multiplication of these probabilities is of:

0.66 x 0.4 = 0.264.

Which is different of 0.32, hence these events are not independent.

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Answer: x=-0.792

Step-by-step explanation:

For this problem, you want to get like terms onto one side, then solve for x.

\(\frac{1}{25}=5x+4\)

\(-\frac{99}{25} =5x\)

x=-0.792

He walks 5/6 of a mile each day.

Multiply the distance each day by the number of days:

5/6 x 5

When multiplying a fraction by a whole number, multiply the numerator ( top number) by the whole number and leave the denominator ( bottom number as is)

5/6 x 5 = (5 x5)/6 = 25/6 now rewrite as a proper fraction:

25/6 = 4 1/6 total miles.

Answer:

4 1/6 miles over the course of 5 days

Step-by-step explanation:

The given expression is ∫∫(1-x^2)(62-y^2)^2 dxdy over the region R = {(x,y) | x^2 + y^2 ≤ 1}.

To evaluate this expression, we can use polar coordinates since the region R is a circle of radius 1 centered at the origin. So, we can write x = rcosθ and y = rsinθ, and the limits of integration become 0 to 2π for θ and 0 to 1 for r. Substituting these values, we get the integral expression as ∫0^2π ∫0^1 (1-r^2cos^2θ)(62-r^2sin^2θ)^2 rdrdθ.

Next, we can simplify the integrand by expanding the square of (62-r^2sin^2θ) and using trigonometric identities. This simplification leads to the expression ∫0^2π ∫0^1 (3844r^2 - 124r^4 + r^6)cos^2θsin^4θ rdrdθ.

Integrating this expression with respect to r and θ, we get the final result as 205π/128. Therefore, the value of the given expression is 205π/128.

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Answer:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces.

Step-by-step explanation:

theory lang po sa asking napagaralan

Answer:

24

Step-by-step explanation:

Perimeter of rectangle = 2 (4x + 2x)

288= 2* 6x

288 = 12x

x = 288/12

x = 24

2(2x+4x)=288

12x=288

x=24

The areas of the composite figures are, respectively:

Case A: A = 104 m²

Case B: A = 174 m²

Case C: A = 321.461 cm²

Case D: A = 20 m²

In this problem we need to determine four case of composite figures, the area of each composite figure is the result of adding or subtracting the areas of different figures. The area formulas to be used below are introduced below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Quarter of a circle

A = 0.25π · r²

Where:

Finally we determine the area of the composite figures:

Case A

A = (10 m) · (8 m) + 0.5 · (8 m) · (6 m)

A = 80 m² + 24 m²

A = 104 m²

Case B

A = (12 m)² + 0.5 · (12 m) · √[(13 m)² - (12 m)²]

A = 174 m²

Case C

A = (20 cm)² - 0.25π · (10 cm)²

A = 321.461 cm²

Case D

A = (4 m) · (6 m) - 0.5 · (4 m) · (2 m)

A = 24 m² - 4 m²

A = 20 m²

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The equal monthly payments for a car costs $22,000 with a down payment of $4,000 based on each scenario are:

Let's discuss each scenario we have.

5. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 48 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment. Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.01)−48)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−48)/0.01x

=18000/28.95x

≈621.92

Hence the amount of each equal monthly payment is approximately $621.92.

6. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 60 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by: 18000=x(1−(1+0.01)−60)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−60)/0.01x

=18000/35.643x

≈505.01

Hence the amount of each payment is approximately $505.01.

7. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 72 equal monthly installments.

The interest rate is 12% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 12% / 12 = 1% = 0.01

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.01)−72)/0.01

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.01)−72)/0.01x

=18000/46.869x

≈383.63

Hence the amount of each payment is approximately $383.63.

8. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.

The amount of the down payment is $4,000.

The total cost of the car is $22,000.

Hence the balance is:

Balance = Total cost of the car − Down payment

Balance = $22,000 − $4,000 = $18,000

Now we can calculate the amount of each payment.

The payment is to be made in 48 equal monthly installments.

The interest rate is 18% per year.

We need to convert this into the monthly interest rate by dividing by 12.

Hence:

Monthly interest rate = 18% / 12 = 1.5% = 0.015

Let x be the amount of each monthly payment.

Then the equation that represents the above conditions is given by:

18000=x(1−(1+0.015)−48)/0.015

Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:

18000=x(1−(1+0.015)−48)/0.015x

=18000/25.525x

≈704.26

Hence the amount of each payment is approximately $704.26.

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Answer:

1568 in^3

Step-by-step explanation:

Answer:

Volume = 1,568

Step-by-step explanation:

V = Bh

B = 17.5 x 14 = 245

h = 6.4

245 x 6.4 = 1,568

The easier way:

17.5 x 14 x 6.4 = 1,568

Let me know if this helps!

Answer:

One pair of socks is $370.

Step-by-step explanation:

Sean bought three pairs of the same socks and a shoe polish for $1450. If the

polish cost $340, how much is the cost of one pair of socks.

6x - 340 = 1450

6x = 1450 -340

6x = 1110

2x = 1110 / 3

2x = 370

The amount of caffeine C in a pregnant woman's body t hours after consuming is 94 × \(0.944^t\)

"Consuming" refers to the act of ingesting or taking in a substance, usually food or drink, into one's body. In the context of the problem given, consuming refers specifically to the act of drinking or ingesting a 16-oz. cup of iced tea that contains a certain amount of caffeine.

The amount of caffeine C in a pregnant woman's body t hours after consuming a 16-oz. cup of iced tea can be calculated using the formula:

C = Co × \((1 - 0.056)^{t}\)

where Co is the initial amount of caffeine consumed (in milligrams) and t is the time elapsed (in hours).

In this case, Co = 94 mg (the amount of caffeine in the 16-oz. cup of iced tea). Therefore, the amount of caffeine in a pregnant woman's body t hours after consuming the iced tea is:

C = 94 × \((1 - 0.056)^t\)

Simplifying the expression, we get:

C = 94 × \(0.944^t\)

So, for example, if 2 hours have elapsed since the woman consumed the iced tea, the amount of caffeine in her body would be:

C = 94 × 0.944² = 82.6 mg

Therefore, The amount of caffeine C in a pregnant woman's body t hours after consuming is 94 × \(0.944^t\)

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Answer:

x = 14

Step-by-step explanation:

The different types of angle relationships:

Based off of these three angle relationships we can identify the two angles as supplementary angles as the two angles shown form a line therefore we know the sum of those two angles is 180 degrees. Knowing this we can create an equation.

Creating an equation:

We know that the two angles are supplementary angles and we also know that supplementary angles add up to 180 degrees. So the sum of the two expressions represented by the two given angles must equal 180.

In other words 9x - 14 + 5x - 2 = 180

Solving for x

Know that we have created an equation we can solve for x algebraically.

9x - 14 + 5x - 2 = 180

==> combine like terms

14x - 16 = 180

==> add 16 to both sides

14x = 196

==> divide both sides by 14

x = 14

And we are done!

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

\( \textbf{Let's solve for x } \)~

\( \textsf{As we can see, the sum of measures of the} \)\( \textsf{ marked two Angles is equal to 180° } \)

\( \texttt{[ by linear pair property ]} \)

\(\qquad \sf  \dashrightarrow \:9x - 14 + 5x - 2 = 180\)

\(\qquad \sf  \dashrightarrow \:9x + 5x - 14 - 2 = 180\)

\(\qquad \sf  \dashrightarrow \:14x - 16 = 180\)

\(\qquad \sf  \dashrightarrow \:14x = 180 + 16\)

\(\qquad \sf  \dashrightarrow \:14x = 196\)

\(\qquad \sf  \dashrightarrow \:x = 196 \div 14\)

\(\qquad \sf  \dashrightarrow \:x = 14\)

\( \texttt{Therefore, the value of x is 14} \)

I Hope you understood the whole procedure ~

Answer: x=-1 and y=0 .

Step-by-step explanation:

The given linear equations:

\(10y + 9x = -9\ ...(i)\\\\10y + 5x= -5\ ...(ii)\)

Subtract (ii) from (i) , we get

\(10y+9x-(10y+5x)=-9-(-5)\\\\\Rightarrow\ 10y+9x-10y-5x=-9+5\\\\\Rightarrow\ 4x=-4\\\\\Rightarrow\ x=-1\)

Put value of x in (i), we get

\(10y+9(-1)=-9\\\\\Rightarrow\ 10y-9=-9\\\\\Rightarrow\ 10y=-9+9=0\\\\\Rightarrow\ y=0\)

Hence, x=-1 and y=0 .

a. f(x) approaches 0 as x increases without bound.

b. f(x) approaches 0 as x decreases without bound.

c. f(x) approaches 0 as x approaches 0.

d. The value of f(x) will depend on the specific constant value of x.

What is Dominant term?

Dominant term refers to the term in a mathematical expression or equation that has the highest degree or the greatest influence on the behavior of the overall expression. In the context of analyzing the behavior of a function, identifying the dominant term allows us to understand the primary factor driving the behavior of the function as the input approaches certain values, such as infinity or zero.

To determine the corresponding behavior of the function f(x) = (8x)/[(x^3)(x-8)] for different behaviors of x, let's analyze each case:

a. When x increases without bound (approaching positive or negative infinity), we can observe the behavior of f(x) by examining the dominant terms in the denominator. In this case, the term x^3 is the dominant term. As x approaches infinity, the denominator becomes larger and larger, causing f(x) to approach zero. Therefore, f(x) approaches 0 as x increases without bound.

b. Similarly, when x decreases without bound (approaching negative or positive infinity), the term x^3 is still the dominant term in the denominator. As x approaches negative or positive infinity, the denominator becomes larger and larger, making f(x) approach zero. Hence, f(x) also approaches 0 as x decreases without bound.

c. When x approaches 0, we again consider the dominant terms in the denominator. Both x^3 and (x-8) become very small as x approaches 0. In this case, the numerator 8x is relatively small compared to the denominator, causing f(x) to approach 0 as x approaches 0.

d. When x remains constant, the value of f(x) depends on the specific constant value of x. Plugging in the constant value of x into the given function will yield the corresponding value of f(x).

In summary:

a. f(x) approaches 0 as x increases without bound.

b. f(x) approaches 0 as x decreases without bound.

c. f(x) approaches 0 as x approaches 0.

d. The value of f(x) will depend on the specific constant value of x.

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Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

k=75

Step-by-step explanation:

\(\frac{k}{5}\)+8=23

(subtract 8 from both sides of the equation)

\(\frac{k}{5}\)+8-8 = 23-8

(simplify)

\(\frac{k}{5}\) = 15

(multiple all terms by the same value to eliminate fractional denominators)

5. \(\frac{k}{5}\) = 5.15

(cancel multiplied terms that are in the denominator, multiply the numbers)

k=75

Answer:

C.$150

Step-by-step explanation:

The sales man told her that he would sell it to he for ⅓ of the marked price.

Given:

Marked Price= $450

⅓

Required:

⅓ of the marked price or $450

Formula:

⅓*$450

Solution:

⅓ of $450

⅓*$450

$450/3

$150

Hope this help ;) ❤❤❤

Answer:

A.180

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\left(\frac{130}{360} \right)(\pi)(18^{2}) \approx \boxed{367.6}\)

When a 4 is rolled on the die, the player is awarded 17 points.

When a 4.5 is rolled on the die, the player is awarded 19 points.

When a 9 is rolled on the die, the player is awarded 37 points.

Given the function that represents certain number of points is awarded to a player upon rolling a six sided die according to the function.

f(x) = 4x + 1

If the number of die rolled is 4, hence;

f(4) = 4(4) + 1

f(4) = 16 + 1

f(4) = 17

This shows that when a 4 is rolled on the die, the player is awarded 17 points.

If the number of die rolled is 4.5, hence;

f(4.5) = 4(4.5) + 1

f(4.5) = 18 + 1

f(4.5) = 19

This shows that when a 4.5 is rolled on the die, the player is awarded 19 points.

If the number of die rolled is 4, hence;

f(9) = 4(9) + 1

f(9) = 36 + 1

f(9) = 37

This shows that when a 9 is rolled on the die, the player is awarded 37 points.

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