For what numbers x, -2π ≤ x ≤ 2π, does the graph of y = csc(x) have vertical asymptotes?

For what numbers x, -2π ≤ x ≤ 2π, does the graph of y = cot(x) have vertical asymptotes? ...?

Answer:

E. HH, C. AA

Step-by-step explanation:

Got these from the quiz

The sequence alternates between adding 2 and multiplying by -4. Starting with 6, the sequence progresses by these operations to reach 120. Following this pattern, the next term after 120 is a) 122 by adding 2.

The student has asked to make a conjecture about the next item in the sequence 6, 8, -32, -30, 120. To determine the pattern, let's look at the differences between each pair of numbers.

From 6 to 8, we add 2.

From 8 to -32, we multiply 8 by -4.

From -32 to -30, we add 2.

From -30 to 120, we multiply -30 by -4.

It appears that the sequence alternates between adding 2 and multiplying by -4. Following this pattern, after 120 the next operation should be adding 2.

Therefore, the next number in the sequence would be 120 + 2 = 122. Hence, the answer is option a. 122.

To find the orthocenter of triangle ABC with vertices A(0,6), B(4,6), and C(1,3), one must plot the triangle, calculate the slopes of its sides, find the slopes and equations of the altitudes, and determine their intersection point, which is the orthocenter.

The question involves finding the orthocenter of the triangle ABC with vertices A(0,6), B(4,6), C(1,3). To find the orthocenter, we have to identify the altitudes of the triangle and find their point of intersection. Here are the steps:

Upon completing these steps, the point of intersection is the orthocenter of the triangle ABC.

In the function f(w) 10w+8, the number 10 represents the number of laps Jessica increased her swim by each week.

To find out what the coefficient 10 represents in the linear function f(w) = 10w + 8, we need to understand the structure of the function.

In this function:

- w represents the week of the summer.

- f(w) represents the number of laps Jessica swam in week w.

- The coefficient 10 is multiplied by w, indicating a relationship.

Since the linear function represents the number of laps Jessica swam each week, the coefficient 10 represents the number of laps Jessica increased her swim by each week.

So, the correct answer is: C. The number of laps Jessica increased her swim by each week

Complete question:

The table below represents the total number of laps Jessica swam in the pool this summer:

Week   Laps

1              18

2             28

3             38

4              48

If the linear function representing the number of laps Jessica swam each week is f(w) 10w+8, what does the 10 represent in this function?

The number of laps Jessica swam in total

The week of the summer that Jessica swam

The number of laps Jessica Increased her swim by each week

A The number of laps Jessica swam in week

Answer:

C) 2

Step-by-step explanation:

I took the quiz and got a 100%.

To solve the equation b + c = 10/a for a, isolate a on one side of the equation by multiplying both sides by a, distribute a to both terms inside the parentheses, and then solve for a by dividing both sides by (b + c).

To solve the equation b + c = 10/a for a, we need to isolate a on one side of the equation. We can start by multiplying both sides of the equation by a to get rid of the denominator:

a(b + c) = 10

Next, we can distribute a to both terms inside the parentheses:

ab + ac = 10

Finally, we can solve for a by dividing both sides of the equation by (b + c):

a = 10 / (b + c)

Final answer:

The possible time lengths for the child's nap are 2.5 to 3.5 hours, and for night time sleep are 11.5 to 12.5 hours, as each can vary by up to 30 minutes.

Explanation:

The question asks about the possible time lengths for a child's nap and night time sleep, given that each can vary by 30 minutes. The average nap time is three hours, so the possible nap lengths range from 2.5 hours (3 hours - 30 minutes) to 3.5 hours (3 hours + 30 minutes). Similarly, the average night time sleep is 12 hours, meaning the possible night time sleep lengths range from 11.5 hours (12 hours - 30 minutes) to 12.5 hours (12 hours + 30 minutes).

The child's nap can be from 2.5 to 3.5 hours and night sleep from 11.5 to 12.5 hours, totaling a possible sleep range of 14 to 16 hours per day.

The child's nap time can vary by 30 minutes from the average of 3 hours, meaning the possible lengths for nap time range from 2.5 hours to 3.5 hours. Similarly, the night time sleep also has a variability of 30 minutes from the average of 12 hours, which gives a range of 11.5 hours to 12.5 hours for night time sleep. Therefore, the possible lengths for the child's total sleep time can range from a minimum of 14 hours (2.5 hours nap + 11.5 hours night) to a maximum of 16 hours (3.5 hours nap + 12.5 hours night).

Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.

To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.

To set up the proportion, we have:

We can write the proportion as:

h1/s1 = h2/s2

Substituting the known values into the proportion gives us:

60/10 = x/25

Now we solve for x:

x = (60/10) * 25

x = 6 * 25

x = 150

Therefore, the height of the second building is 150 feet.

Answer:

Option A

Step-by-step explanation:

The equation has x intecepts at -1 and -5.

Hence function would be of the form

a(x+1)(x+5) for some real a.

To find a, let us use y intercept

When x =0 we have y =a(1)(5)

y intercept is given as -30

i.e. 5a = -30

a=-6

So

f(x) = -6(x+1)(x+5)

Option A is the right answer.

Answer:

f(4)=23

Step-by-step explanation:

Plug 4 in to the function

f(4)=4(4)+7

f(4)=16+7

f(4)=23

Final answer: 23

Answer:

Option A

Step-by-step explanation:

Whenever we want to arrange a number of objects or letters or numbers n then we must check whether

i) repitition is allowed

If repitition is allowed then total number of ways = n!

ii) repitition not allowed.

In this case again we have to check whether order matters or not.

If order matters then no of ways nPn.  

Here n =5

We find that nPn = 5!

Thus both are correct.

Hence option A

Answer:

Option D. 2.51 is correct.

Step-by-step explanation:

Magnitude of first earthquake = 8.6

Let intensity of first earthquake be x

[tex]Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)[/tex]

Magnitude of second earthquake = 8.2

Let intensity of second earthquake be y

[tex]Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)[/tex]

Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)

[tex]\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51[/tex]

Hence the required factor is 2.51

Therefore, Option D. 2.51 is correct.

Answer:

2.51

Step-by-step explanation: