This is timed. Please Help me.
Which is the function g(x) for a restricted domain? g(x) = Negative RootIndex 3 StartRoot x minus 4 EndRoot; x greater-than-or-equal-to –4 g(x) = Negative RootIndex 3 StartRoot x 4 EndRoot + 4; x greater-than-or-equal-to 0 g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4 g(x) = Negative RootIndex 3 StartRoot x EndRoot minus 4; x greater-than-or-equal-to 0

Answer:

rows, columns

Step-by-step explanation:

Two dimensional array can be viewed as rows and columns.

It is viewed as matrix or grid as well therefore we can conclude that it can be viewed in terms of rows and columns.

The correct option is the first one, A two-dimensional array can be viewed as rows and columns.

A two-dimensional array is a data structure that stores elements in a grid-like format with rows and columns. It can be visualized as a table or matrix.

In this context, "rows" refer to the horizontal dimension of the array. Each row consists of a series of elements that are stored sequentially from left to right. The number of rows in the array represents the height or the total count of rows.

"Columns" refer to the vertical dimension of the array. Each column consists of a series of elements that are stored sequentially from top to bottom. The number of columns in the array represents the width or the total count of columns.

By organizing data in rows and columns, a two-dimensional array allows for efficient storage and retrieval of elements. The elements within the array can be accessed by specifying both the row and column indices.

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Answer:Sam has 29 movies.

Sam has 11 TV shows.

Step-by-step explanation:

Let x represent the number of movies that Sam has.

Let y represent the number of TV shows that Sam has.

Sam has a total of 40 dvds, movies and tv shows. This means that

x + y = 40 - - - - - - - - - - -1

The number of movies is 4 less then 3 times the number of tv shows. This means that

x = 3y - 4 - - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

3y - 4 + y = 40

4y - 4 = 40

4y = 40 + 4 = 44

y = 44/4 = 11

x = 3y - 4 = 3 × 11 - 4

x = 33 - 4

x = 29

By creating a system of equations from the given problem, m + t = 40 and m = 3t - 4, and solving it through substitution, it was determined that Sam has 29 movies and 11 TV shows in his DVD collection.

To solve the given problem, we need to use a system of linear equations. The two variables we need to find are the number of movies (m) and the number of TV shows (t).

According to the problem, the total number of DVDs, which includes both movies and TV shows, is 40. This can be written as an equation: m + t = 40. Additionally, we are told that the number of movies is 4 less than three times the number of TV shows. This gives us a second equation: m = 3t - 4.

Now we have the following system of equations:

We can solve this system by substitution. First, substitute the second equation into the first equation:

Now that we have found the number of TV shows (t), we can calculate the number of movies (m):

Therefore, Sam has 29 movies and 11 TV shows in his collection of 40 DVDs.

Answer:

A. 1 only.

Step-by-step explanation:

Answer:

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

By definition an outlier is a point "that diverges from an overall pattern in a sample". The residual for this outiler is usually high and when we have presence of outliers our model probably would be not significant since the tendency is not satisfied.        

By definition and influential point is a point that has "a large effect on the slope of a regression line fitting the data:. And usually represent values that are too high or low respect to the others.

Solution to the problem

For this case we assume that we have a high positive correlation between college student's age and the GPA.

So we assume that [tex] 0.7 \leq r \leq 1[/tex]

And We see that after introduce the value of 44 for the age the correlation disappears, that means decrease significantly.

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.

Answer: an equation that represents the total costs of the gym membership based on the number of months is

y = 25x + 50

Step-by-step explanation:

Let x represent the number of months that Frank makes use of the gym at LA fitness in order to get better in shape.

Let y represent the total cost of using the gym for x months.

He has to pay a one-time enrollment fee of $50 and then membership costs $25 per month. This means that the total cist for x month would be

y = 25x + 50

Answer: The length x =17.64ft

Step-by-step explanation:

Looking at the diagram,to find x,we ues adj/hyp = cos 25°

16/x=cos25°

Cross multiply

X=16/cos25°

X=17.64ft

Answer:

17 feet 8 in

Step-by-step explanation:

im doing it in class imao

Answer:

The answer to your question is he sold 47 adult tickets and 37 children tickets.

Step-by-step explanation:

Data

Adult ticket = a = $105

Children ticket = c = $60

Total number of tickets = 84

Total money earn = $7155

Equations

                              a + c      = 84     ------------ (I)

                        105a + 60c = 7155 -------------(II)

Multiply equation I by -60

                           -60a  - 60c = -5040

                          105a   + 60c = 7155

Simplify

                          45a               = 2115

                                           a = 2115 / 45

                                           a = 47 tickets

Substitute a in equation I

                          47 + c = 84

                                  c = 84 - 47

                                  c = 37 tickets

You can form linear equations from the given description then use that system to derive the solution.

The amount of each type of tickets sold are:

Children tickets sold = 37

Adult tickets sold = 47

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let the amount of adult tickets sold be "a"

Let the amount of children tickets sold be "c"

Since the total amount of tickets sold is given as 84

Thus,

Total tickets = children tickets + adult tickets

84 = c + a

a + c = 84

since 1 adult ticket costs $105,

thus, "a" adult tickets cost [tex]105 \times a = 105a \text{\:\:(Written in short)}[/tex] (in dollars)

Similarly,

since 1 children ticket costs $60

"c" children tickets cost [tex]60c[/tex] (in dollars)

Since the price obtained by selling those tickets is $7155

thus,

total amount earned = amount earned by children tickets + amount earned by adult tickets

$7155 = $60c + $105a

Thus, we got the system of equations as:

[tex]a + c = 84\\105a + 60c = 7155[/tex]

Multiplying first equation with -105 to make a's coefficient equal and opposite to make the addition of them eliminate "a":

[tex]-105a -105c = -105 \times 84\\105a + 60c = 7155\\\\\text{Addding both equations}\\\\-45c = 7155 - 8820 = -1665\\\\c = \dfrac{1665}{45} = 37[/tex]

Putting this value in first equation, we get:

[tex]a + c = 84\\a + 37 = 84\\a = 84 - 37 = 47[/tex]

Thus,

The amount of each type of tickets sold are:

Children tickets sold = 37

Adult tickets sold = 47

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Answer:

203 feet.

Step-by-step explanation:

Please find the attachment.

Let h represent the height of the building.

We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.    

We know that tangent relates opposite side of a right triangle to its adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

Upon substituting our given values in above formula, we will get:

[tex]\text{tan}(35^{\circ})=\frac{h}{290}[/tex]

[tex]290*\text{tan}(35^{\circ})=\frac{h}{290}*290[/tex]

[tex]290*0.70020753821=h[/tex]

[tex]h=290*0.70020753821[/tex]

[tex]h=203.0601860809[/tex]

[tex]h\approx 203[/tex]

Therefore, the building is approximately 203 feet high.

Answer:

a) P(8) = 0.1395

b) P(at most three) = 0.0423684

c) P(X > 8) = 0.41

Step-by-step explanation:

Data provided in the question:

Mean, μ = 8

Now,

Probability that the number of oil tankers on any given day is

a) exactly eight

using Poisson distribution

we have

P(x) = [tex]\frac{\mu^xe^{-\mu}}{x!}[/tex]

for x = 8

P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex]

or

P(8) = [tex]\frac{16777216\times e^{-8}}{40320}[/tex]

or

P(8) = 0.1395

b)  at most three

i.e P(0) + P(1) + P(2) + P(3)

thus,

P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354

P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683

P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073

P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862

⇒ P(at most three) = 0.0003354 + 0.002683 + 0.01073 + 0.02862

= 0.0423684

c) more than eight.

P(X > 8) = 1 - P(X ≤ 8)

Now,

P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354

P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683

P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073

P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862

P(4) = [tex]\frac{8^4e^{-8}}{4!}[/tex] = 0.05725

P(5) = [tex]\frac{8^5e^{-8}}{5!}[/tex] = 0.091603

P(6) = [tex]\frac{8^6e^{-8}}{6!}[/tex] = 0.1221

P(7) = [tex]\frac{8^7e^{-8}}{7!}[/tex] = 0.13958

P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex] = 0.13758

Thus,

P(X > 8) = 1 - [ 0.0003354 + 0.002683 + 0.01073 + 0.02862 + 0.05725 + 0.091603 + 0.1221 + 0.13958 + 0.13758 ]

P(X > 8) = 1 - 0.5904814

or

P(X > 8) = 0.41

Final answer:

Explains the probability of different scenarios for the number of oil tankers at a port city per day.(a) The probability of exactly eight oil tankers is 0, as it matches the mean.

(b) The probability of at most three tankers is 0.1724.

(c) The probability of more than eight tankers is 0.

Explanation:

Oil Tankers Probability:

(a) The probability of exactly eight oil tankers is 0, as it matches the mean.

(b) The probability of at most three tankers is 0.1724.

(c) The probability of more than eight tankers is 0.

Answer:

32.40

Step-by-step explanation:

81 x 40% =48.60

81. -48.60 = 32.40

Answer:the college bookstore paid

$57.86 for the book.

Step-by-step explanation:

Let x represent the price that the college bookstore paid the publisher to get the book.

The college bookstore marks up the price by 40%. It means that the value of the mark up would be .40/100 × x = 0.4 × x = 0.4x

Therefore, the selling price of the book at the college bookstore would be

x + 0.4x = 1.4x

If the selling price of a book is $ 81.00, it means that

1.4x = 81

x = 81/1.4 = $57.86

Answer: a. 28ft/s. b. 40.08ft/s. c. 42.4ft/s. d. 43.68ft/s. e. - 20ft/s

Step-by-step explanation: Since your displacement was given that is (y) , we just have to differentiate y with respect to time t. That is the first derivative only.

I have worked it out and here is the attachment.

Final answer:

To find the average velocity during different time periods, we can calculate the changes in height and time. By substituting the given values of t into the height equation, we can determine the heights at different times. We can then calculate the average velocities by taking the change in height divided by the change in time. Additionally, to estimate the instantaneous velocity when t = 2, we can differentiate the height equation and substitute t = 2 into the derivative.

Explanation:

To find the average velocity for a given time period, we need to calculate the change in height and the change in time. Using the equation y = 44t - 16t^2, we can substitute the values of t = 2 and t = 2.5 to find the heights at these times. Then, we can find the average velocities.

(a) For the time period of 0.5 seconds starting at t = 2, we calculate the heights at t = 2 and t = 2.5: y(2) = 44(2) - 16(2^2) = 36 ft and y(2.5) = 44(2.5) - 16(2.5^2) = 35 ft. The average velocity is the change in height divided by the change in time: (35 - 36) ft / 0.5 s = -2 ft/s.

(b) For the time period of 0.1 second starting at t = 2, we calculate the heights at t = 2 and t = 2.1: y(2) = 36 ft and y(2.1) = 44(2.1) - 16(2.1^2) = 37.644 ft. The average velocity is the change in height divided by the change in time: (37.644 - 36) ft / 0.1 s = 16.44 ft/s.

(c) For the time period of 0.05 second starting at t = 2, we calculate the heights at t = 2 and t = 2.05: y(2) = 36 ft and y(2.05) = 44(2.05) - 16(2.05^2) = 37.079 ft. The average velocity is the change in height divided by the change in time: (37.079 - 36) ft / 0.05 s = 21.58 ft/s.

(d) For the time period of 0.01 second starting at t = 2, we calculate the heights at t = 2 and t = 2.01: y(2) = 36 ft and y(2.01) = 44(2.01) - 16(2.01^2) = 36.764 ft. The average velocity is the change in height divided by the change in time: (36.764 - 36) ft / 0.01 s = 76.4 ft/s.

(e) To estimate the instantaneous velocity when t = 2, we can calculate the derivative of the height function. The derivative of y(t) = 44t - 16t^2 with respect to t is dy/dt = 44 - 32t. Substituting t = 2 into this equation, we get dy/dt = 44 - 32(2) = -20 ft/s.

Answer:

Miss Silver stein can serve for 12 guests with amount of cake that she has bought.

Step-by-step explanation:

Given:

Number of cakes she bought = 3

Amount of cakes given to each guest = [tex]\frac{1}{4}[/tex]

We need to find the number of guest cakes can be served.

Solution:

Now we can say that;

the number of guest can have the cake to can be calculated by dividing the  Number of cakes she bought from Amount of cakes given to each guest

framing in equation form we get;

Number of guest can have cake = [tex]\frac{3}{\frac{1}{4}} = 3\times\frac{4}{1} =12[/tex]

Hence Miss Silver stein can serve for 12 guests with amount of cake that she has bought.

To know how much of Hillary's payments are deductible as alimony in 2019, we first need to figure out how old her son was when Hillary got divorced in 2016.

Given that Hillary has to pay until her son turns 18 and this occurs 7 years after the divorce, this means that her son was 18 - 7 = 11 years old in 2016.

Therefore, he will be turning 18 in 2025 (2016 + 9 years).

In 2019, which is 3 years after 2016, her son would be 11 + 3 = 14 years old. As her son has not yet reached 18 years old, Hillary is still making $200 payments per month in 2019.

Given there are 12 months in a year, the total amount of alimony payments that Hillary made in the year 2019 is 12 * $200 = $2400.

So, the amount of her 2019 payments that are deductible as alimony is $2400.

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Answer:

Life hack in this answer!

Step-by-step explanation:

The correct table is the second one, or the table on the bottom right. (Picture included).

Life hack --> To find the relative percentage/frequency of something, all you have to do is take the frequency you are trying to find, and divide it with the total.

Example: You are trying to find the frequency of REGULAR MALE jeans. What is its frequency? To find, all you have to do is divide 120 from 28. Like this:

28 = male regular jeans

120 = total

28 ÷ 120 = ?

28 ÷ 120 = 0.23333333...

Final answer: 0.23

In this scenario, we must round. But remember that you might not always need or have to round.

And, as predicted, the answer of 0.23 is in the second table under REGULAR MALE jeans.

If you have any questions, let me know!

I hope this helps!

- sincerelynini

Answer:

i am 70% sure its a

Step-by-step explanation:

Answer:

3/80

Step-by-step explanation:

If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots

1/5 * 1/4 = 1/20

Luke keeps 3/4 of those so that's

3/4 * 1/20 = 3/80

Answer:

TOTAL ACCELERATION =10.229m/s²

Step-by-step explanation:

total acceleration = [tex]\sqrt{centripetal accleration^{2} +tagential acceleration^{2} }[/tex]

since tangential speed is constant , tangential acceleration =0

Thus total acceleration = centripetal acceleration.

centripetal acceleration = v²/r

v=82.6m/s  , r= 667m

centripetal acceleration = 82.6²/667

centripetal acceleration = 10.229m/s²

TOTAL ACCELERATION =10.229m/s²

Final answer:

The magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m is 10.20 m/s², which is the centripetal acceleration.

Explanation:

The question asks to find the magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m. In circular motion, the total acceleration is the centripetal acceleration, since the tangential speed (speed along the arc of the circle) is constant and there is no tangential acceleration. The formula for centripetal acceleration (ac) is ac = v2 / r, where v is the tangential speed and r is the radius of the circular path.

Using the given values:

ac = (82.6 m/s)2 / 667 m = 10.20 m/s2

Therefore, the magnitude of the centripetal acceleration of the race car is 10.20 m/s2.

Answer:

a) [tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]

[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]

b) [tex] M -\frac{h}{k}>0 [/tex]

Let's say that [tex] a=M -\frac{h}{k}>0[/tex]

If we multiply the woule equation by k we got:

[tex] kM -h >0[/tex]

So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]

c) If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]

And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]

And if that hhapens then the population will tend to 0 for any initial condition established/

Step-by-step explanation:

For this case we have the following logistic equation [tex] \frac{dx}{dt}= kx (M-x)[/tex]

Part a

We want to modify our harvesting for this case, so we harvest hx per unit of time for some [tex] h>0[/tex]

So then the model with harvesting who is proportional is given by:

[tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]

And we can write like this:

[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]

Part b

For this case we assume that [tex] kM>h[/tex]and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0

[tex] M -\frac{h}{k}>0 [/tex]

Let's say that [tex] a=M -\frac{h}{k}>0[/tex]

If we multiply the woule equation by k we got:

[tex] kM -h >0[/tex]

So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]

Part c

If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]

And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]

And if that hhapens then the population will tend to 0 for any initial condition established/

The constant of the expression 15-8y is 15

Constants are values that are not attached to any variable. For example:

Now given the expression 15 - 8y

First, we can re-arrange to have:

-8y + 15

From the expression, we can see that 15 is not attached to any variable. Hence the constant of the expression is 15

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Answer: the weight of Jon's pet is

(3v - 25) pounds

Step-by-step explanation:

The weight of Jon's dog is v pounds.

His cat weighs 21 pounds less than his dog. It means that the weight of his cat would be

(v - 21) pounds

His bunny weighs 3 pounds less than his cat. It means that the weight of his bunny would be

(v - 21) - 3 = (v - 24) pounds

Therefore, the weight of Jon's pets would be the sum of the weight of his dog, his cat and his bunny. It becomes

v + v - 21 + v - 24 = (3v - 25) pounds.

Final answer:

Jon's pets' total weight is calculated by adding the weight of the dog (v pounds), cat (v - 21 pounds), and bunny (v - 24 pounds), which results in 3v - 45 pounds.

Explanation:

To find the weight of Jon's pets, we start with the known weight of the dog and calculate the other animals' weights based on the given relationships. Jon's dog weighs ( v ) pounds. His cat weights 21 pounds less than his dog, so the cat weighs v - 21 pounds. The bunny weighs 3 pounds less than the cat, which means the bunny weighs (v - 21) - 3 pounds or v - 24 pounds.

Therefore, to find the total weight of Jon's pets, we add the weights of the dog, cat, and bunny together:

Dog's weight: v pounds

Cat's weight: v - 21 pounds

Bunny's weight: v - 24 pounds

The total weight is v + (v - 21) + (v - 24), which simplifies to 3v - 45 pounds.

Answer: 0.8413

Step-by-step explanation:

Given : The scores on a test have a normal distribution with mean 24 and standard deviation 4.

i.e. [tex]\mu= 24[/tex]  and [tex]\sigma= 4[/tex]

Let x denotes the scores on the test.

Then, the probability that a student score less than 28 will be :-

[tex]P(x<28)=P(\dfrac{x-\mu}{\sigma}<\dfrac{28-24}{4})\\\\=P(z<1)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=0.8413 \ \ [\text{By z-table}][/tex]

Hence, the the proportion of scores less than 28 is 0.8413 .

Answer:

{3, 5}.

Step-by-step explanation:

y = x^2 - 8x + 15

(x - 5)(x - 3) = 0

x - 5 = 0 or x - 3 = 0

So the roots are {3, 5}.

Answer: 68 child tickets were sold

Step-by-step explanation:

Let x represent the number of child tickets that were sold that day.

Let y represent the number of adult tickets that were sold that day.

A total of 124 tickets were sold on Tuesday. This means that

x + y = 124

At the city Museum child admission is $5.70 and adult admission is $9.80. The total sales from tickets was $936. This means that

5.7x + 9.8y = 936 - - - - - - - - -1

Substituting x = 124 - y into equation 1, it becomes

5.7(124 - y) + 9.8y = 936

706.8 - 5.7y + 9.8y = 936

- 5.7y + 9.8y = 936 - 706.8

4.1y = 229.2

y = 229.2/4.1

y = 55.9

y = 56

x = 124 - y = 124 - 56

x = 68

Answer: he earned $344 in all.

Step-by-step explanation:

When he does work outdoors he earns $12 an hour. This means that if he works outdoors for x hours, he would earn $12x

When he works indoors he earns $8 an hour. This means that if he works indoors for y hours, he would earn $8y.

Last month he worked 18 hours outdoors. This means that the total amount that he earned working outdoors is

12 × 18 = $216

He worked 16 hours indoors. This means that the total amount that he earned working indoors is

8 × 16 = $128

Total amount that he earned is

216 + 128 = $344

Answer:

The answer to your question is below

Step-by-step explanation:

1.-                           y = 2x - 64

                            x - 2y = 14

Substitution

                            x - 2(2x - 64) = 14

Simplification

                            x - 4x + 128 = 14

                             x - 4x = 14 - 128

                            -3x = - 114

                               x = 114/3

                               x = 38

                             y = 2(38) - 64

                             y = 76 - 64

                             y = 12

Solution (38, 12)

2.-                            y = x - 6

                               3x + 2y = 8

Substitution

                               3x + 2(x - 6) = 8

Simplification

                              3x + 2x - 12 = 8

                              5x = 8 + 12

                              5x = 20

                              x = 20 / 5

                            x = 4

                             y = 4 - 6

                             y = -2

Solution (4 , -2)

3.-                           x - y = 12

                            27 + 3y = 2x

                            x = 12 + y

                            27 + 3y = 2(12 + y)

                            27 + 3y = 24 + 2y

                            3y - 2y = 24 - 27

                                     y = -3

                             x = 12 - 3

                             x = 9

Solution y = -3

4.-                          y = 2x + 14

                           -4x - y = 4

                            -4x - (2x + 14) = 4

                            -4x - 2x - 14 = 4

                            -6x = 4 + 14

                            -6x = 18

                                x = 18/-6

                                x = -3

                            y = 2(-3) + 14

                            y = -6 + 14

                           y = 8

Solution   y = 8

Answer:

There is no solution.

Step-by-step explanation:

Answer: the distance from the bottom of the ladder to the base of the building is 12 feet.

Step-by-step explanation:

The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.

The length of the ladder represents the hypotenuse of the right angle triangle.

The distance from the ground to the point where the ladder touches the wall of the building represents the opposite side

Therefore, to determine the distance from the bottom of the ladder to the base of the building, x, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

37² = 35² + x²

1369 = x² + 1225

x² = 1369 - 1225 = 144

x = √144 = 12 feet

Final answer:

To find the distance from the bottom of the ladder to the base of the building, use the Pythagorean theorem with the given ladder height and building contact point. Calculate the distance as 12 feet.

Explanation:

A window-washer is climbing a ladder leaning against a building. In this scenario, the ladder is 37 feet long and touches the building 35 feet above the ground. To find the distance from the bottom of the ladder to the base of the building, we can use the Pythagorean theorem.

By applying the Pythagorean theorem: a² + b² = c², where a and b are the distances from the bottom of the ladder to the building and from the base to the building, respectively, and c is the length of the ladder, we can calculate the distance to be 12 feet.

Therefore, the distance from the bottom of the ladder to the base of the building is 12 feet.

Answer:

  all real numbers except 2 and 4

Step-by-step explanation:

The exceptions in the domain are the values that make the denominator zero. For a denominator of x² -6x +8 = (x -4)(x -2), the values that make it zero are x=4 and x=2.

The domain is all real numbers except 2 and 4.

Answer:

Option D is correct.

The domain of the function f(x) is all real numbers except 2 and 4.

Step-by-step explanation:

f(x) = (x+1)/(x²-6x+8)

The domain of a function expresses the region of values of x, where the function exists.

And logically, a function exists where ever f(x) has a finite value. That is, the only point where A function does not exist is when f(x) gives infinity.

For a rational function, the point where a function doesn't exist is when the denominator of the rational function is equal to 0. Because (numerator/0) --> ∞

So, the denominator in this question is

x²-6x+8

The function doesn't exist when

x²-6x+8 = 0

So, we solve the quadratic equation that ensues to get the values of x where the function doesn't exist.

x²-6x+8 = 0

x² - 4x - 2x + 8 = 0

x(x-4) - 2(x-4) = 0

(x-2)(x-4) = 0

(x-2) = 0 or (x-4) = 0

x = 2 or x = 4

This means that the function doesnt exist at x = 2 and x = 4

Indicating further that the function exists everywhere except at x = 2 and x = 4.

Hence, from the definition of domain given above, it is clear that the domain of the given function is all real numbers except 2 and 4.

Hope this Helps!!!

Answer:

The answer to your question is  r = 3

Step-by-step explanation:

                               2r  - 15 = - 9r + 18

Process

1.- Add 9r in both sides

                              2r + 9r - 15 = - 9r + 18 + 9r

2.- Simplify

                                    11r -15 = 18

3.- Add 15 to both sides

                                   11r - 15 + 15 = 18 + 15

4.- Simplify

                                   11r = 33

5.- Divide both sides by 11

                                   11/11 r = 33/11

6.- Simplify and result

                                   r = 3

Answer:

what ur insta?

Step-by-step explanation:

Answer:

The answer to your question is AC = 14

Step-by-step explanation:

To solve this problem, we must use trigonometric functions.

And we must look for a trigonometric function that relates the opposite side and the hypotenuse.

This trigonometric function is the sine

   [tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]

solve for Opposite side = AC

  AC = hypotenuse x sin α

- Substitution

  AC = 25 x sin 34

- Simplification

  AC = 25 x 0.56

- Result

  AC = 14

Answer: 0.60 gallon

Step-by-step explanation:

There are 12pounds in a standard US gallon.

12pounds= 1 gallon

5.2 pounds=?

5.2/12 × 1 gallon

0.624 gallon

Rounding to the nearest tenth =0.60