2) Line segment MK has endpoints at (2, 3) and (5, ?4). Segment M'K' is the reflection of MK over the y-axis. Which statement describes the relationship between MK and M'K'? A)M'K' is twice the length of MKB)M'K' is half the length of MK.C)M'K' is the same length as MK.D)More information is needed to determine the relationship

Answer:

-1/6

Step-by-step explanation:

Parallel lines are lines which have the exact same slope but different y-intercepts. This means any line which is parallel and does not cross will have the exact same slope of -1/6.

A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

---------------------------------------------------

[tex]a_1=27;\ a_2=9;\ a_3=3;\ a_4=1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\r=\dfrac{9}{27}=\dfrac{1}{3}\\\\\boxed{a_1=27;\qquad a_n=\dfrac{1}{3}\cdot a_{n-1}}[/tex]

Answer:

2 hours

Step-by-step explanation:

Answer:

during the 7th and the 9th lap

Step-by-step explanation:

I just did it

Answer:

Divide 5.4 by 0.5

Step-by-step explanation:

It's says to find the number of laps she swam. It doesn't ask us to figure out how many laps she could have run with the amount of laps she did.

To find the number of laps Flo swam, divide the total distance Flo swam (5.4 km) by the length of one lap in the pool (0.05 km). This results in 108 laps.

To find out the number of laps Flo swam, we must take the total distance she swam and divide it by the length of one lap in the pool. According to the chart, the length of one lap in a standard-sized pool is 0.05 kilometers. Therefore, the best method would be to divide 5.4 (the total distance Flo swam in kilometers) by 0.05 (the length of one lap in kilometers).

So, we take 5.4/0.05 = 108. This means that Flo swam 108 laps in the pool. Remember, when you want to find how many times a certain distance fits into another, you should utilize division.

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Answer:

(-3,3)

Step-by-step explanation:

3x=36-15y and 11x =-78+15y

We move all x  and y terms to the left hand side of the equation , so that we can apply elimination method

3x=36-15y , Add 15 y on both sides , 3x + 15y = 36

11x =-78+15y, subtract 15y on both sides, 11x -15y = -78

Now we add both equations

3x  + 15y = 36

11x -15y = -78

------------------------

14x  = -42

divide both sides by 14

x= -3

Now Plug in -3 for x in any one of the given equation

3x=36-15y

3(-3) = 36 - 15y

-9 = 36 - 15y

Subtract 36 on both sides

-45 = -15y

Divide both sides by -15

So y= 3

Answer is (-3,3)

The x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]

The graph of the function is given as:

y = cot(3x)

To determine the x-intercept of the graph, we set the graph to 0.

So, we have:

cot(3x) = 0

Take the arccot of both sides

3x = arccot(0)

Evaluate the arccot of 0

[tex]3x = \frac{\pi}2[/tex]

Divide both sides by 3

[tex]x = \frac{\pi}6[/tex]

Hence, the x-intercept of the graph of the function y = cot(3x) is [tex]x = \frac{\pi}6[/tex]

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The x-intercepts of the graph of the function  [tex]\( y = \cot(3x) \)[/tex] occur at points where  y = 0 , which happens when [tex]\( \cot(3x) = 0 \).[/tex]

1. Set [tex]\( y = \cot(3x) \)[/tex] and solve for  x : [tex]\( \cot(3x) = 0 \).[/tex]

2. Since [tex]\( \cot(x) = \frac{1}{\tan(x)} \)[/tex], this equation becomes [tex]\( \frac{1}{\tan(3x)} = 0 \)[/tex].

3. Tangent is zero at multiples of [tex]\( \frac{\pi}{2} \)[/tex], so [tex]\( \tan(3x) \)[/tex] is zero at [tex]\( 3x = \frac{\pi}{2} \)[/tex], [tex]\( 3x = \frac{3\pi}{2} \)[/tex], [tex]\( 3x = \frac{5\pi}{2} \)[/tex], and so on.

4. Solve for [tex]\( x \)[/tex]: [tex]\( x = \frac{\pi}{6} \)[/tex], [tex]\( x = \frac{\pi}{2} \)[/tex], [tex]\( x = \frac{5\pi}{6} \)[/tex], and so on.

5. Each of these values represents an x-intercept on the graph of [tex]\( y = \cot(3x) \)[/tex].

Answer:

10.5

Step-by-step explanation:    if he got the pants on sale the price would be 59.5 becuase 70*15%=10.5 and u would subtract 70-10.5=59.5

70-59.5=10.5

Answer:

$10.5

Step-by-step explanation:

Answer:

13.9%

Step-by-step explanation:

The value of car is modeled as:

[tex]V(t)=21,000(0.861)t[/tex]

Here we can see that, each year Nathan has considered 0.861 of the previous year value or we can say that Nathan has considered 86.1% of the previous year value. So,

[tex]100-86.1=13.9[/tex]

We subtract the percentage value considered from 100 to find out the percentage decrease in the value of the car.

The value of new car is decreasing by 13.9% each year.  

Final answer:

Nathan's car decreases in value by 13.9% each year according to the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]

Explanation:

The value of Nathan's car decreases by a certain percentage each year, which can be determined from the depreciation model [tex]V(t) = 21,000(0.861)^t.[/tex]The model shows that each year, the value is multiplied by 0.861. To find the percent decrease, we subtract this number from 1 and then convert the result into a percentage:

1 - 0.861 = 0.139

0.139  imes 100% = 13.9%

Therefore, the value of Nathan's car decreases by 13.9% each year based on this model.

The student is seeking the solution for a linear equation in the form 'y = mx + b'. From the problem, the equation is 'y = 2x +1' and we have to find the x value (α) for y = 9. The answer is α = 4 when (α, 9) is a solution to our equation.

The subject of this problem is Mathematics, and it specifically deals with linear equations, in the form of y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The equation given in the problem is y = 2x + 1. The student wants to find the value of α such that (α, 9) is a solution to the equation.

To solve this, we substitute 9 for y in the equation and solve for x:

9 = 2x + 1

Subtract 1 from both sides:

8 = 2x

Finally, divide both sides by 2 to solve for x:

x = 4

Thus, the value of α that makes (α, 9) a solution to the equation y = 2x + 1 is α = 4.

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Not A: We can't have [tex]x=0[/tex] because [tex]\log0[/tex] is undefined for a logarithm of any base.

B is true: [tex]\log1=0[/tex] for any base.

Not C: If [tex]x=b^c[/tex], then [tex]\log_bb^c=c[/tex], but [tex]\log_cb^c=c\log_bc[/tex] which only reduces to [tex]c[/tex] if [tex]\log_bc=1[/tex]. This can only happen if [tex]b=c[/tex], however, but we've assumed otherwise.

Not D: The reasoning for C not being correct is enough to rule out this possibility.

Answer:

D

Step-by-step explanation:

Rational functions are functions whose main operation on the variable is a ratio or fraction. This means we find x or the input value in the denominator of the function. Since fractions involve division and division has special circumstances, this reflects on the graph. Because when we divide we cannot divide by 0, any x value which makes the denominator 0 is an asymptote. On the graph, asymptotes are represented by dashed lines where the function doesn't follow.

To find the asymptotes, we set the factors in the denominator to 0 and solve for x. Let's do the each for each options:

a. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.

b. x=0 and x+5=0 so x=-5. This does not match the graph.

c. x=0. This does not match the graph.

d. (x+5)=0 so x=-5 and (x-2)=0 so x=2. This matches our graph.

This means only a and d are options. We will substitute a value to see the behavior of the graph. We pick x=-2. In D, this would give us a positive y. This matches the graph. In A, this would give us a negative y which does not match the graph.

Answer:

In the figure below :

d = 2.08, e = 5, c = 5.42 , a = 22.78°, b = 67.22°

Step-by-step explanation:

Side lengths :

[tex]2\cdot e=10\\ \Rightarrow e=5 feet\\\frac{d}{e}=\frac{5}{12}\\\Rightarrow d=\frac{25}{12}\approx 2.08 feet[/tex]

By pythagoras theorem,

[tex]c^2=d^2+e^2\\c^2=29.33\\c\approx 5.42 feet[/tex]

Now to find angles,

[tex]a+b+90^{\circ}=180^{\circ}\\\Rightarrow a+b=90^{\circ}\\\tan a=\frac{d}{e}\\\Rightarrow \tan a =0.42\\\Rightarrow a=22.78^{\circ}\\\Rightarrow b=67.22^{\circ}[/tex]

The unknown side lengths of the shed's roof are:

Angle measure at the top of the roof: 22.62 degrees

Vertical length of the roof (rise): 4.17 feet

Horizontal length of the roof (run): 5 feet

To determine the unknown angle measures and side lengths of the shed's roof, we can use the given information about the roof pitch and span.

Angle Measures

The roof pitch is 5:12, which means that for every 12 horizontal inches, the roof rises 5 inches. This corresponds to an angle of approximately 22.62 degrees.

Side Lengths

The span of the roof is 10 feet, which represents the horizontal distance from one side of the shed to the other.

Since the roof pitch is 5:12, we can calculate the rise of the roof by dividing the span by 12 and multiplying by 5:

Rise = (10 feet * 12 inches/foot) * (5/12) = 41.667 inches ≈ 4.17 feet

Therefore, the unknown side lengths of the shed's roof are:

Angle measure at the top of the roof: 22.62 degrees

Vertical length of the roof (rise): 4.17 feet

Horizontal length of the roof (run): 5 feet

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Answer:

It goes to zero three times

Step-by-step explanation:

s(t) = e^ cos(x)

To find the velocity, we have to take the derivative of the position

ds/dt =  -sin x e^ cos x dx/dt

Now we need to find when this is equal to 0

0 =  -sin x e^ cos x

Using the zero product property

-sin x=0   e^cos x= 0

sin x = 0

Taking the arcsin of each side

arcsin  sinx= arcsin 0

x = 0 ,pi, 2 pi

e^cos x= 0

Never goes to zero

Answer:

The velocity is equal to 0 for 3 times.

Step-by-step explanation:

Given position function s = ecos(x)

Its velocity function, s' = ds/dt = e(-sinx)dx/dt

Between [0,2π], s'=0, -e(sinx)dx/dt=0

sinx=0

x=0, π, 2π

The velocity is equal to 0 for 3 times.

Answer:

c=8

Step-by-step explanation:

3c/8 = (c+4)/4

We can use cross products to solve

3c          c+4

-----  =   ----------

8             4

 3c*4 = 8 *(c+4)

12c = 8c+32

Subtract 8c from each side

12c-8c = 32

4c = 32

Divide by 4

4c/4 = 32/4

c =8

The solution to the equation 3c/8 = c+4/4 is found by first simplifying the equation to 3c = 4c + 16, then isolating 'c' gives -c = 16, and finally multiplying both sides by '-1' gives the solution, c = -16.

To solve the equation 3c/8 = c+4/4, firstly we'll simplify it, eliminating fractions by multiplication. The equation becomes 3c = 4c + 16.

Next, we rearrange the equation to isolate 'c', by subtracting '4c' from both sides which results in -c = 16.

Finally, to get the value of 'c', we multiply both sides by '-1'. Hence, the solution to the equation is c = -16.

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Answer:

c. between 0&1 and 2&3

Step-by-step explanation:

The roots of the given quadratic functions lie between 0&1 and 2&3 thus option (C) is correct.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given quadratic equation,

f(x) = 2x² - 5x + 1

The value of x will be as,

x = [-(-5) ± √((-5)² - 4 ×2 × 1)]/(2 × 2)

x = (5 ± √17)/4

x = 0.219 and x = 2.28

So, 0 < 0.219 < 1 and 2 < 2.28 < 3.

Hence "The roots of the given quadratic functions lie between 0&1 and 2&3".

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Brad deposits $17 per month. Hence, after 6 months, Brad will have $115 in his account.

The subject of the question is a simple arithmetic problem involving Brad's savings account. The first month, he started with $27. The next month, he had $44 in his savings account, so he adds ($44-$27) = $17 to his account each month. In the third and fourth months, he added the same amount twice, so he had $78 ($44 + $17*2). Hence, after 6 months, he will have $115 in his savings account because for the fifth and sixth months he will add ($17*2 = $34) to his account of $78 from the fourth month.

In simpler terms, we can break down these steps into the following:

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Given the fact that Brad saves an equal amount of $17 each month, after 6 months, his total saved amount will be $129.

The question is about calculating the amount of money Brad will have saved in 6 months, given that he saves an equal amount each month. From the information provided, we can determine that Brad saves $17 each month ($44 - $27 = $17). After two months, we can see that $78 - $44 = $34, which confirms that Brad is indeed saving $17 each month, since $34 / 2 = $17. Now, to find how much Brad will have saved after 6 months, we need to multiply the monthly saving amount by 6 and add that to the initial amount. This gives us: $27 + ($17 * 6) = $27 + $102 = $129.

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kx + c = 9

Subtract C from both sides:

kx = 9-c

Divide both sides by k:

x = (9-c)/k

Answer:

He needs to save $90.75 each month to reach his goal.

Step-by-step explanation:

We have the cost of his vacation that is $1089.

We know that Todd has a year to save the money.

We know that a year in terms of time is twelve months (12 months).

If we want to calculate how much does he need to save each month we need to divide the total cost of his vacation by the amount of months in a year ⇒

[tex]\frac{1089}{12}=90.75[/tex]

We find that Todd needs to save $90.75 per month to reach his goal.

Answer:

The value of x nearest to tenth is, 1.5 units

Step-by-step explanation:

In right angle triangle as shown in figure

by definition of tangent ratio i,e   [tex]\tan \theta = \frac{opposite side}{Adjacent side}[/tex]

[tex]\tan 37^{\circ} = \frac{x}{2.1}[/tex]

[tex]0.7535540501= \frac{x}{2.1}[/tex]

or

[tex]x = 0.7535540501 \times 2.1 = 1.58246351[/tex] units

Therefore, the value of x nearest to tenth is, 1.5 units

Answer:

There is around a 40% chance if I have done my calculations correctly

Answer: 17.19%

Step-by-step explanation:

[tex]P=\dfrac{_{10}C_7 + _{10}C_8 + _{10}C_9 + _{10}C_{10}}{2^{10}}[/tex]

   [tex]= \dfrac{120+45+10+1}{1024}[/tex]

   [tex]= \dfrac{176}{1024}[/tex]

  = 0.171875

  = 17.1875%

Answer:

Can not be determined.

Step-by-step explanation:

We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.

Hence, option C is correct i.e. the limit can not be determined.

The constant of proportionality in the equation 4y = 48x is 12 (option C) after dividing both sides of the equation by 4 to get the equation into the form y = kx, with k representing the constant of proportionality.

The question is asking for the constant of proportionality in the equation 4y = 48x. In an equation of the form "y = kx", "k" is the constant of proportionality. Here, to make this equation look like "y = kx", we need to divide both sides of the equation by 4. Doing this gives us:

y = 12x

So, the constant of proportionality in this equation is 12 which corresponds to option C.

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Divide total full time employees by 20 to find how many groups of 20 there are, then multiply that number by 3 to find total part time employees:

250,000 / 20 = 12,500

12,500 x 3 = 37,500 part time employees.

Answer:

The answer is sin^2 (theta)  cos (theta) .

Step-by-step explanation:

We need to rewrite tan (theta)  as sin (theta) /cos (theta)

tan^2 (theta) = sin^2 (theta)/ cos^2 (theta)

We also need to rewrite sec (theta) as 1/ cos(theta)

sec^3 = 1 / cos^3( theta)

tan^2 (theta)       sin^2 (theta)

------------------ =    ----------------

sec ^3 (theta)      cos ^ 2(theta)

                           ---------------------------

                               1

                             -----------

                                 cos ^3 (theta)

Remember when dividing fractions, we can use, copy dot flip

sin^2 (theta)           cos^3 (theta)    

------------------    *   -------------------

  cos ^ 2(theta)           1

Canceling a cos^2(theta)  from the top and bottom,

sin^2 (theta)           cos (theta)    

------------------    *   -------------------

  1                             1

we are left with

sin^2 (theta)  cos (theta)

The answer is sin^2 (theta)  cos (theta) .

The answer is sin^2

Answer:

I think the answer would be B because volume is length times width times height. Therefore, if you multiply the base which is length time width and the height you will get your answer. Let me know if this helps, if not I can further explain it to you.

Step-by-step explanation:

Each floor is 3.35 feet taller than each floor of the Aon Center

Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Height of Burj l Arab Hotel = 1053 feet

Number of floors = 60

Per floor height = 1053/60 = 17.55 feet

Height of Aon center = 1140 feet

Number of floors = 83

Per floor  height = 1140/83 = 13.73 feet

17.55 - 13.73 = 3.815 feet bigger than the Aon center.

Hence "Each floor of Burj I Arab Hotel is 3.815 feet taller than the height of Aon Center".

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Answer:

$132.90

Step-by-step explanation:

Answer:

$120.86

Step-by-step explanation: