A 13-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down the wall when the bottom is 5 feet from the wall? The ladder is sliding down the wall at a rate of ___
(Type an integer or a simplified fraction.)

Explicación paso a paso:

Dado

an = n + 3

bn = 5n-1

a) an-bn = n + 3- (5n-1)

= n + 3-5n + 1

= n-5n + 3 + 1

= -4n + 4

an-bn = 4-4n

b) an + 3bn = (n + 3) +3 (5n-1)

= n + 3 + 3 (5n) +3 (-1)

= n + 3 + 15n-3

= n + 15n + 3-3

= 16n + 0

= 16n

an + 3bn = 16n

3) Dado a1 = 1, a2 = 1

an = an-1 + an-2

Debemos escribir los primeros ocho términos de la secuencia.

a3 = a3-1 + a3-2

a3 = a2 + a1

a3 = 1 + 1

a3 = 2

a4 = a3 + a2

a4 = 2 + 1

a4 = 3

a5 = a4 + a3

a5 = 3 + 2

a5 = 5

a6 = a5 + a4

a6 = 5 + 3

a6 = 8

a7 = a6-a5

a7 = 8 + 5

a7 = 13

a8 = a7 + a6

a8 = 13 + 8

a8 = 21

Por tanto, los primeros ocho términos de la secuencia son 1, 1, 2, 3, 5, 8, 13 y 21

If the takt time for a process is 150 ​seconds, what is the demand for the​ process. The demand is 24 units per hour.

Calculating the demand for a process with a takt time of 150 seconds is relatively simple. To begin, we need to convert the takt time from seconds to hours. This can be done by dividing the takt time by 3,600 (the number of seconds in an hour).

The calculation is as follows:

150 seconds / 3,600 seconds = 0.041666667 hours

Next, we need to calculate the demand for the process by dividing 1 hour by the takt time (in hours). The calculation is as follows:

1 hour / 0.041666667 hours = 24 units per hour

Therefore, the demand for the process is 24 units per hour.

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Answer:

y=8,y=0

that's the answer I got tho

Answer:

heart shaped candle

Step-by-step explanation:

the flower shaped candle has more wax so the first one.

Hope this helps :D

Answer:

Cards C and E

Step-by-step explanation:

Remember that irrational numbers cannot be written as a fraction of two integers:

Is 10 irrational? No, because 10 can be written as a fraction (ex. 10/1, 20/2, etc.)

Is 6/5 irrational? No, because it is a fraction.

Is π irrational? Yes, because it can't be written as a fraction as its digits continue infinitely without repetition.

Is 11/4 irrational? No, because it is a fraction.

Is 8.25635... irrational? Yes, because the ellipsis shows the digits continue infinitely without repetition, otherwise there would be a bar over the digits to show repetition

Is -7 irrational? No, because it can be written as a fraction (ex. -7/1, -14/2, etc.)

Is 6.31(bar) irrational? No, because the bar shows that the digits 3 and 1 repeat.

Therefore, only cards C and E are irrational.

The cards that represent irrational numbers are C (π) and possibly E (8.25635), as π is a well-known irrational number and E is a decimal with multiple digits. The other options represent rational numbers.\

The cards that show irrational numbers are:

C. π (pi) - π is an irrational number representing the ratio of a circle's circumference to its diameter.

E. 8.25635 - This number is not known to be irrational based on the given information, but as it is a decimal with multiple digits, it could potentially be irrational.

The other options, A, B, D, F, and G, represent rational numbers, either whole numbers or fractions, and are not considered irrational.

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The main answer is that the probability equal to P(A) + P(B) - P(A and B) is equal to P(A or B).

To explain further, let's break down the given information. We have two events: A represents the event "the student is in the Music Club," and B represents the event "the student is in the Science Club." We are asked to find the probability that is equal to P(A) + P(B) - P(A and B).

P(A) represents the probability of selecting a student who is in the Music Club, P(B) represents the probability of selecting a student who is in the Science Club, and P(A and B) represents the probability of selecting a student who is a member of both the Music Club and the Science Club.

The expression P(A) + P(B) - P(A and B) is a commonly used formula for finding the probability of the union of two events. It accounts for the possibility of double-counting students who are members of both clubs.

In this case, P(A or B) represents the probability of selecting a student who is either in the Music Club or the Science Club (or both). Therefore, P(A or B) is equal to P(A) + P(B) - P(A and B).

Hence, the probability that is equal to P(A) + P(B) - P(A and B) is equal to P(A or B).

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The segment FG is reflected by the rule (x, y) → (-x, y). Hence, option C is the correct answer.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century. In geometry, object transformations constitute the foundation for the majority of proofs. Transformations allow us to change any image in a coordinate plane. The rules of transformations can be utilised to better understand the images used in video games.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

FG has points at F(-6, -3) and G(-3, 6), and F'(6, -3) and G'(3, 6).

It is reflected by the rule (x, y) → (-x, y).

Hence, option C is the correct answer.

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The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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Answer:

slope:1/2

y intercept:-1/2

equation of the line: y=1/2x-1/2

Step-by-step explanation:

choose two points from the line( I chose (3,1) and (-1,-1)) and then using y1-y2/x1-x2, do 1 - -1/3 - -1 which is 2/4 simplified to 1/2. the slope is 1/2.

now to find the y intercept, you just have to plug in the numbers from one of the sets of points you chose and your slope using y = mx +b(I will be using the point (-1,-1)). equational look like this: -1=1/2•-1+b

since b is the y intercept, solve for b and you get b= -1/2.

so nowsince you know the slope and the y intercept you just plug it in to the equation

y = mx + b and you get y=1/2x-1/2.

the probabilities for each event are Red ball: 1/5, White ball: 7/20, Yellow ball: 9/20 by using formula of  probability =possible outcome /total outcomes

To find the probability of a given event, we need to determine the number of successful outcomes and divide that by the total number of possible outcomes.

In this case, the event we want to find the probability for is not specified, so I will provide the probabilities for each color:

1. Probability of drawing a red ball:

Number of successful outcomes: 4 red balls
Total number of outcomes: 4 red + 7 white + 9 yellow = 20 balls

Probability of drawing a red ball = (Number of red balls) / (Total number of balls) = 4/20 = 1/5

2. Probability of drawing a white ball:

Number of successful outcomes: 7 white balls

Probability of drawing a white ball = (Number of white balls) / (Total number of balls) = 7/20

3. Probability of drawing a yellow ball:

Number of successful outcomes: 9 yellow balls

Probability of drawing a yellow ball = (Number of yellow balls) / (Total number of balls) = 9/20

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Answer:

1, 4, 8, 10

16, 64, 96, 160

Hope it helps u

Thank You

Please mark as brainliest

Answer:

top row is 4 and 10 bottom is 96 and 128

Step-by-step explanation:

goo

Step-by-step explanation:

a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7.

Answer:

8.7x - 4.6

Step-by-step explanation:

4.8x - 4.6 + 3.9x

Group like terms

4.8x + 3.9x - 4.6

Add similar elements: 4.8x + 3.9x = 8.7x

Then you get your answer:

8.7x - 4.6

The given equation of the circle is:

\($$x^2 + y^2 + 8x - 10y - 12 = 0$$\)

a)The center of the circle is \($(-4, 5)$\)  and the radius is \($3$\).

b)The y-intercepts of the circle are \($(0, 5+\sqrt{37})$ and $(0, 5-\sqrt{37})$.\)

a) Center and radius of the circle by completing the square:

Let's first group the \($x$\) terms and \($y$\) terms separately:

\($$x^2 + 8x + y^2 - 10y = 12$$\)

Next, we add and subtract a constant term to complete the square for both x and y terms.

The constant term should be equal to the square of half the coefficient of x and y respectively:

\($$x^2 + 8x + 16 - 16 + y^2 - 10y + 25 - 25 = 12$$\)

\($$\implies (x+4)^2 + (y-5)^2 = 9$$\)

Thus, the center of the circle is \($(-4, 5)$\)  and the radius is \($3$\).

b) X and Y intercepts if they exist:

We get the x-intercepts by setting y = 0 in the equation of the circle:

\($$x^2 + 8x - 12 = 0$$\)

\($$\implies (x+2)(x+6) = 0$$\)

Thus, the x-intercepts of the circle are \($(-2, 0)$ and $(-6, 0)$\).

Similarly, we get the y-intercepts by setting x = 0 in the equation of the circle:

\($$y^2 - 10y - 12 = 0$$\)

Using the quadratic formula, we get:

\($$y = \frac{10 \pm \sqrt{100 + 48}}{2} = \frac{10 \pm 2\sqrt{37}}{2} = 5 \pm \sqrt{37}$$\)

Thus, the y-intercepts of the circle are \($(0, 5+\sqrt{37})$ and $(0, 5-\sqrt{37})$.\)

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Answer:

9

Step-by-step explanation:

I need to write 20 characters

164

Step-by-step explanation:

The solution is,  a coat cost on sale =  $164.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

At a sale, coats were sold for 82% of their original price.

If the coats originally cost $200 each,

so, a coat cost on sale = $200* 82%

                                     =$164

Hence, The solution is,  a coat cost on sale =  $164.

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The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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Answer:

Step-by-step explanation:

first one : 67/100 = .67 per sq feet

Second one: 130/200 = .65 per sq feet

Third one 240/400 = .6 per sq feet

Fourth one: 504/800 .63 per sq feet

so C is the best deal (C.

400 square feet of carpet for $240)

The time spent by Gretchen is 12 minutes and the time spent by Henrik is 14 minutes. Thus, Gretchen will arrive sooner by 2 minutes

From the given information, we are to determine who will arrive sooner between Gretchen and Henrik.

To do this, we will determine the time spent by both of them.

From the given information,

Gretchen lives 2.4 miles away

and

He bikes at a constant rate of 12 miles per hour

From the formula,

Rate = Distance/Time

Time = Distance/Rate

Time = 2.4/12

Time = 0.2 hour

Time = 0.2 × 60 minutes

Time = 12 minutes

For Henrik

He lives 8.4 miles away

and

He drives at a constant rate of 36 miles per hour

From the formula,

Time = Distance / Rate

Time = 8.4 / 36

Time = 7/30 hour

Time = 7/30 × 60 minutes

Time = 14 minutes

Hence,

Gretchen will arrive sooner by 14 minutes - 12 minutes = 2 minutes

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Answer:

5

Step-by-step explanation:

The angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

Example 1:

Find the angle between the lines with equations y = 2x + 3 and y = -3x + 1.

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines.

The slope-intercept form of a line is y = mx + b, where m is the slope.

Comparing the given equations, we can see that the slopes of the lines are m1 = 2 and m2 = -3.

Using the angle between two lines formula, the angle θ between the lines is given by the equation:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values, we have:

tan(θ) = |(-3 - 2) / (1 + (2)(-3))|

= |-5 / (1 - 6)|

= |-5 / -5|

= 1

To find the angle θ, we take the inverse tangent (arctan) of 1:

θ = arctan(1)

θ ≈ 45°

Therefore, the angle between the lines y = 2x + 3 and y = -3x + 1 is approximately 45 degrees.

Example 2:

Determine the angle between the lines with equations 3x - 4y = 7 and 2x + 5y = 3.

Solution:

First, we need to rewrite the given equations in slope-intercept form (y = mx + b).

The first equation: 3x - 4y = 7

Rewriting it: 4y = 3x - 7

Dividing by 4: y = (3/4)x - 7/4

The second equation: 2x + 5y = 3

Rewriting it: 5y = -2x + 3

Dividing by 5: y = (-2/5)x + 3/5

Comparing the equations, we can determine the slopes:

m1 = 3/4 and m2 = -2/5

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |((-2/5) - (3/4)) / (1 + (3/4)(-2/5))|

= |((-8/20) - (15/20)) / (1 + (-6/20))|

= |(-23/20) / (14/20)|

= |-23/14|

To find the angle θ, we take the inverse tangent (arctan) of -23/14:

θ = arctan(-23/14)

θ ≈ -58.44°

Therefore, the angle between the lines 3x - 4y = 7 and 2x + 5y = 3 is approximately -58.44 degrees.

Example 3:

Find the angle between the lines passing through the points (2, 5) and (4, -3), and (1, -2) and (3, 4).

Solution:

To find the angle between the lines, we need to determine the slopes of the two lines using the given points.

For the first line passing through (2, 5) and (4, -3):

m1 = (y2 - y1) / (x2 - x1)

= (-3 - 5) / (4 - 2)

= -8 / 2

= -4

For the second line passing through (1, -2) and (3, 4):

m2 = (y2 - y1) / (x2 - x1)

= (4 - (-2)) / (3 - 1)

= 6 / 2

= 3

Using the angle between two lines formula:

tan(θ) = |(m2 - m1) / (1 + m1m2)|

Substituting the values:

tan(θ) = |(3 - (-4)) / (1 + (-4)(3))|

= |(3 + 4) / (1 - 12)|

= |7 / (-11)|

= -7/11

To find the angle θ, we take the inverse tangent (arctan) of -7/11:

θ = arctan(-7/11)

θ ≈ -32.7°

Therefore, the angle between the lines passing through (2, 5) and (4, -3), and (1, -2) and (3, 4) is approximately -32.7 degrees.

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Answer: $7.58/2=$3.79

Step-by-step explanation:

Answer: 250 metre

Step-by-step explanation:

The radius of the semi circle will be:

Radius r = diameter/ 2

Where diameter = 140

r = 140/2 = 70m

The radius is also equal to the width of the diameter.

Find the quarter of the circumference of a circle.

Circumference of a circle = 2πr

Substitute for r in the formula

Circumference = 2 × 22/7 × 70

Circumference = 44 × 10 = 440 m

Divide the circumference by 4

440/4 = 110 m

The perimeter P of the shaded region will be

P = 110 + 70 + 70

Perimeter = 250 m

Therefore, the perimeter of the shaded region is 250 m

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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To determine whether a function f: z × z → z is onto, we must first understand the definition of an onto function. An onto function is a function that maps every element in its domain to an element in its range. This means that for every element y in the range of f, there exists an element x in the domain of f such that f(x) = y.

For a) f(m,n)=2m−n, we can see that the domain of f is all pairs (m,n) of integers, while the range of f is all integers. To check if this is an onto function, we will take an arbitrary element y in the range and find the corresponding element x in the domain. Let y = 4. Then, we can solve for x by plugging in 4 for y and solving for m and n. We get m = 3 and n = 1, and so we have f(3,1) = 4. Thus, this function is onto.

For b) f(m,n)=m2−n2, we can see that the domain of f is again all pairs (m,n) of integers, while the range of f is all non-negative integers. To check if this is an onto function, we will take an arbitrary element y in the range and find the corresponding element x in the domain. Let y = 9. Then, we can solve for x by plugging in 9 for y and solving for m and n. We get m = 3 and n = 2, and so we have f(3,2) = 9. Thus, this function is also onto.

For c) f(m,n)=mn1, we can see that the domain of f is again all pairs (m,n) of integers, while the range of f is all integers. To check if this is an onto function, we will take an arbitrary element y in the range and find the corresponding element x in the domain. Let y = 5. Then, we can solve for x by plugging in 5 for y and solving for m and n. We get m = 5 and n = 1, and so we have f(5,1) = 5. Thus, this function is also onto.

For d) f(m,n)=|m|−|n|, we can see that the domain of f is again all pairs (m,n) of integers, while the range of f is all integers. To check if this is an onto function, we will take an arbitrary element y in the range and find the corresponding element x in the domain. Let y = 3. Then, we can solve for x by plugging in 3 for y and solving for m and n. We get m = 3 and n = 0, and so we have f(3,0) = 3. Thus, this function is also onto.

For e) f(m,n)=m2 −4, we can see that the domain of f is again all pairs (m,n) of integers, while the range of f is all non-negative integers. To check if this is an onto function, we will take an arbitrary element y in the range and find the corresponding element x in the domain. Let y = 4. Then, we can solve for x by plugging in 4 for y and solving for m and n. We get m = 2 and n = 0, and so we have f(2,0) = 4. Thus, this function is also onto.

In conclusion, all of the given functions are onto functions.

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According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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Answer:

\(x^{2} +4x+4\)

Step-by-step explanation:

Assuming f(x)=\(x^{2}\) and g(x)=x+2, fog(x)=f(g(x))

f(g(x))=\((g(x))^{2}\)=\((x+2)^{2}\)=\(x^{2} +4x+4\)