A 18-foot ladder is leaning against a building. if the bottom of the ladder is sliding along the pavement directly away from the building at 1 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?

Answer:

5

Step-by-step explanation:

3x+2-3x+7+5x

3x-3x+5x+2+7

5x+9

Coefficient is the 5 of the 5x.

Answer:

700

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

A) x(x-1)(x+1)

Step-by-step explanation:

In the second term on the LHS, the denominator \(x^2-1=(x-1)(x+1)\), and \(x-1\) is contained in the first term. Therefore, the least common denominator would be \(x(x-1)(x+1)\).

a, b, and c are collinear points. b is the midpoint of ac .

The coordinate of c is 3. So, the coordinate of point c is 3.

If b is the midpoint of ac, it means that the coordinates of a, b, and c lie on the same line and b is exactly halfway between a and c.

Given that the coordinate of a is -8 and the coordinate of b is -2.5, we can determine the coordinate of c as follows:

The distance from a to b is equal to the distance from b to c. Since b is the midpoint, the distance from a to b is half of the distance from a to c. Mathematically, we can express this relationship as:

|a - b| = |b - c|

Substituting the given coordinates, we have:

|-8 - (-2.5)| = |-2.5 - c|

Simplifying further:

| -8 + 2.5 | = |-2.5 - c|

| -5.5 | = |-2.5 - c|

Since the absolute value of a number is always positive, we can drop the absolute value signs:

5.5 = 2.5 + c

Now we solve for c:

5.5 - 2.5 = c

3 = c

Therefore, the coordinate of c is 3. So, the coordinate of point c is 3.

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Answer:

Step-by-step explanation:

66 times 66  for area is 4356 then 4356 divided by 22 is 217.8 so 218

Answer:

16.703

Step-by-step explanation:

right angle triangle thus we use puthagoras theorem to find the unknown length.

By converse of pythagoras theorem,

c² = a² + b²

c = √a² + b²

where c is the hypothenuse, a and b can be any 2 side of the right angle triangle

so x = √c² - a² = √ 20² - 11² ≈ 16.703 (or u can use calculator to find the long string of decimals and then round off on your own)

The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.

Substituting the values given in the problem, we get:

(x', y') = (4*(-6), 4*(-2))

Simplifying,

(x', y') = (-24, -8)

Therefore,

The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).

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Answer:

x=12

Step-by-step explanation:

Both Angles together have a 180 degrees, set your formula up as

180=(10x-20)+(6x+8)

180=10x+6x-20+8

180+20-8=16x

192=16x

192/16=x

12=x

Answer:

x = 12

Step-by-step explanation:

The two angles form a straight line so they add to 180

10x-20 + 6x+8 = 180

Combine like terms

16x -12 = 180

Add 12 to each side

16x-12+12=180+12

16x = 192

Divide each side by 16

16x/16 =192/16

x = 12

The appropriate test statistic for the test is t = 16/0.037.

The appropriate test statistic for the test is obtained by dividing the estimated slope of the regression line (in this case, 16) by the standard error of the slope (0.037). The test statistic measures how many standard deviations the estimated slope is away from the hypothesized value of 0. By calculating the ratio of 16 divided by 0.037, we obtain the t-value, which is used to assess the significance of the estimated slope in relation to the null hypothesis.

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The reason why both graphs are parallel because they have the same slope but different y-intercept.

Think about it. If both graphs have same slope and same y-intercept. The graph will intercept each others infinitely.

Then if we change the y-intercept into any numbers that aren't the same as another equations for ex.

y = -5x+1 and y = -5x+10

then we will get the parallel graph. Or if you solve the equation, the equation will not be true, thus giving the graph parallel.

But if it is y = -5x+1 and y = -5x+1 which both are the same graph. Then the graph will intercept each others infinitely. Or if we solve the equation, we will get 0 = 0 which makes the equation true for all real numbers.

Therefore, the reason why both graphs are parallel is because that they have the same slope but different y-intercept.

That's all.

Answer:

c

Step-by-step explanation:

The variance of the sample means will be 0.3428.

What is Variance of sample means?

The variance of the sampling distribution of the mean is the population variance divided by the sample size.

Given that;

A uniform continuous distribution has a maximum of 14 and a minimum

of 2.

Samples of size 36 are drawn from the distribution.

Now,

The population variance = 14 - 2

                                      = 12

And, Sample size = 36

Since, The variance of the sample means is defined as;

= Population variance / Sample size

Substitute all the values, we get;

= 12 / 35

= 0.3428

Thus, The variance of the sample means will be 0.3428.

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Answer:

The distance should be 10 I believe

Answer:

D

Step-by-step explanation

y/4 + 12/4 = 28/4

y+12=28

y=16

Answer:

D

Step-by-step explanation:

Answer:

His employer contributes with $4712.53 towards his health insurance on an annual basis.

Step-by-step explanation:

With the information provided, you know that Billy's employer pays 65% of his health insurance premium and you can subtract this from 100% to know the percentage that Billy has to pay:

100%-65%=35%

Also, the information states that Billy has $105.73 withheld from his paychecks twice each month and you can multiply this for 24 to find the total amount that he pays per year and that represents 35%:

$105.73*24=$2537.52

Finally, you can use a rule of three to found the amount that represents 65% which would be what his employer pays given that $2537.52 represent 35%:

2537.52 →  35%

     x       ←  65%

x=(2537.52*65)/35

x=$4712.53

According to this, the answer is that his employer contributes with $4712.53 towards his health insurance on an annual basis.

the answer is 142.24 cm

Answer:

142.24 centimeters tall

Step-by-step explanation:

Can you mark me brainliest

Part A: The monthly payment for the truck is $595.07

Part B: Kevin will spend $63.75 when he fills the truck's 25-gallon tank.

Part C: Kevin's cost per mile is $0.304.

An annuity is a financial product that provides a stream of payments to an individual over a specified period of time. An annuity is typically purchased from an insurance company or financial institution in exchange for a lump sum of money.

An average is a mathematical value that represents a typical or central value within a set of data. There are different types of averages, including the mean, median, and mode.The mean, or arithmetic mean, is the most common type of average, and it is calculated by adding up all of the values in a data set and dividing by the number of values.

Part A:

To calculate the monthly payment for the truck, we can use the formula for the present value of an annuity:

Monthly payment = (PV * r) / (1 - (1 + r)⁽⁻ⁿ⁾)

Where:

PV = Present value of the loan (truck cost - down payment)

r = Interest rate per period (annual rate / 12)

n = Total number of periods (5 years * 12 months per year)

Using this formula, we have:

PV = $35,500 - $4,200 = $31,300

r = 6% / 12 = 0.005

n = 5 years * 12 months per year = 60

Monthly payment = ($31,300 * 0.005) / (1 - (1 + 0.005)⁽⁻⁶⁰⁾) = $595.07

Therefore, the monthly payment for the truck is $595.07.

Part B:

To calculate how much Kevin will spend when he fills the truck's 25-gallon tank, we can multiply the number of gallons by the average gas price:

Cost of filling tank = 25 gallons * $2.55/gallon = $63.75

Therefore, Kevin will spend $63.75 when he fills the truck's 25-gallon tank.

Part C:

To calculate Kevin's cost per mile, we need to first calculate how much he spends on gas per mile.

In one year, Kevin fills up his tank 2 times per month, for a total of 24 times per year. If he drives 7,500 miles in the first year, then he drives an average of 7,500 / 24 = 312.5 miles between fill-ups.

So, Kevin spends $63.75 every 312.5 miles on gas, or $0.204 per mile.

In addition to gas, Kevin spends $750 per year on insurance.

Therefore, Kevin's total cost per mile is:

Cost per mile = (gas cost per mile) + (insurance cost per year / miles driven per year)

Cost per mile = ($0.204) + ($750 / 7,500) = $0.304 per mile

Therefore, Kevin's cost per mile is $0.304.

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Answer:

x=4 so both the answer is 0

Step-by-step explanation:

3x-12=x-4

3x-x=-4+12

2x=8

2x÷2=8÷2

x=4

so

3x-12=4-x

3×4-12=4-4

12-12=4-4

0=0

Answer:

-39/x2+2x-4

Step-by-step explanation:

Answer:

7627.36

Step-by-step explanation:

Correct me if im wrong, Can I please get branliest? :•)

One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.

DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.

In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.

Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.

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Answer:

$6.50 per 1 box

Step-by-step explanation:

$91.00 ÷  14 boxes = $6.50 per 1 box

Check Work:

$6.50 x 14 boxes = $91.00

The Average speed of a world class sprinter, is he runs 100 yards in 10 sec is 36 km/h.

If an athlete can run 100 meters in 10 seconds,  It is said that he cannot run 10 meters in one second. That may also apply to the physical world we live in. But you clearly state that you want to say mathematically whether he ran 10 meters in his 1 second.

If a sprinter runs 100 meters in 10 seconds, then, First, we need to convert meters to kilometers and seconds to hours. 1 meter = 1/1000 kilometers 100 meters = 100/1000 kilometers = 1/10 = 0.1 kilometers 1 second = 1/3600 hours 10 seconds = 10/3600 = 1/360 hours.

Now,
According to the question:

Given that,

Distance covered by sprinkler = 100m

Time taken by sprinkler = 10 seconds

Using the equation of velocity

Distance/ Time = velocity

Now, substituting the values -

= 100/10

= 10

Thus, the velocity is 10m/s

To convert it into m/s in to km/h -

= (10/1000) x 3600

= 36000/1000

= 36

Therefore, The average velocity of sprinkler is 36 km/h

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Answer:

A) 0

Step-by-step explanation:

hope this helps, pls mark brainliest :D

The line integral ∫Cx^2y^2z dz is equal to zero.

We want to evaluate the line integral ∫Cx^2y^2z dz, where the curve C is given by |z| = 2. Since C is a closed curve (it lies on a cylinder with top and bottom at z = 2 and z = -2, respectively), we can use the divergence theorem to convert the line integral into a surface integral.

Applying the divergence theorem, we have:

∫∫S F · dS = ∫∫∫V ∇ · F dV

where F = (x^2y^2, 0, z) and S is the surface of the cylinder.

We can simplify ∇ · F as follows:

∇ · F = ∂/∂x (x^2y^2) + ∂/∂y (0) + ∂/∂z (z) = 2xy^2

Thus, the surface integral becomes:

∫∫S F · dS = ∫∫∫V 2xy^2 dV

We can then use cylindrical coordinates to evaluate the triple integral:

∫∫∫V 2xy^2 dV = ∫0^2π ∫0^2 ∫0^2 (2r^3 sinθ cosθ) dr dz dθ

= 0

Therefore, the line integral ∫Cx^2y^2z dz is equal to zero.

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The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.

2. Within-group variance:

1. Between-group variance.

This is the variance that can be attributed to differences between the group means.

It is calculated by comparing the mean of each group to the overall mean of all the data points.

The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:

This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.

It is calculated by comparing the individual data points in each group to their respective group mean.

The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.

If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.

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Lily, the cheer team's captain, is putting together a performance for a tournament. A routine may be no less than 3 minutes in length and no more than 5 minutes in total. For which the two solutions are the shortest and longest permitted lengths, write an absolute value.

The absolute value for 3 is 3 .

The absolute value for 5 is 5.

The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2

Absolute value is the non-negative value of a real number x, independent of its sign, is its absolute value (or modulus), | x |.

For example, 5 has an absolute value of 5, and -5 has a value of 5. Another way to think about a number's absolute value is as its distance from zero on the real number line. In addition, the distance between two real numbers is the absolute value of their difference.

Given that,

A routine may be no less than 3 minutes in length and no more than 5 minutes in total.

By absolute value equation

we can get 2x−5|+|2x−3|=m

By solving we get 2 m values they are,

m={-8,2}

Here, -8 we can take but the answer will be in decimal soo we take 2.

|2x−5|+|2x−3|=2

We get

\(|4x-8|=2\\|x-2|=1\\|x|=3\\\)

If we take 2x =y

|y−5|+|y−3|=2

\(|2y-8|=2\\|y-4|=1\\|y|=5\)

Therefore,

The absolute value for 3 is 3 .

The absolute value for 5 is 5.

The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2.

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The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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Answer:

-12y^4+6x^4+x^2y^2\

Step-by-step explanation: