Perform the indicated operation. 2 1/6 – 5 2/3

A. -7 1/2

B. -3 1/3

C. -3 1/2

D. 3 1/6

To ascertain points of discontinuity, evaluate where functions are undefined or have limits that do not exist, often due to division by zero or undefined behavior in their basic components. For example, f(x) = 1/ sin x is discontinuous where sin x equals zero.

To find out where a function is discontinuous, we must examine points where the function is not defined or its limit does not exist. For a function defined by building blocks of continuous functions, it will generally remain continuous except at points where it involves division by zero or at points where its simpler components are not continuous.

For example, the function f(x) = 1/ sin x can be seen as the composition of the functions g(x) = 1/x and h(x) = sin x. We know that for a sine function, namely h(x), it is continuous everywhere, but the function g(x) is discontinuous at 0. Hence, f(x) will be discontinuous at points where sin x = 0, which occur at integer multiples of π.

More generally, to check continuity, ask yourself these questions about the function:

If you answer 'no' to any of these, the function might be discontinuous at some points, and hence, it would also be nondifferentiable at those points.

9x+4 +32 = 90

9x+36 = 90

9x=54

x = 54/9 = 6

x = 6

Final answer:

The supplement of an angle measuring 74 degrees and 51 minutes is 105 degrees and 9 minutes. This is calculated by subtracting the given angle from 180 degrees, and borrowing if necessary when subtracting minutes.

Explanation:

To find the supplement of an angle whose measure is 74 degrees and 51 minutes, we need to subtract this angle from 180 degrees. One degree has 60 minutes, so if the subtraction of minutes goes below zero, we need to borrow 1 degree (which is equivalent to 60 minutes).

Step-by-Step Solution

Start with 180 degrees 0 minutes.

Subtract the given angle, which is 74 degrees 51 minutes, from 180 degrees 0 minutes.

If the minutes part of the subtraction is negative, borrow 60 minutes from the degrees.

By subtracting the given angle from 180 degrees, we have: 180° 0' - 74° 51' = 105 degrees and 9 minutes (because we borrow one degree to make up 60 minutes).

So, the supplement of the angle is 105 degrees and 9 minutes.

To find the range of a function in a graph, observe the y-values the function reaches, from the lowest to the highest. The range given in interval notation represents these y-values. Without the actual graph, an exact answer can't be given in this case.

Without a given graph, we cannot discern the correct answer. However, we can still explain how to determine the range of a function given its graph. Starting from the far left of the graph and moving to the far right, the range of the function is the set of all y-values the function takes on. For example, in interval notation, [-4, 8] means the graph starts at least as low as -4 on the y-axis and goes up to at least 8 (including these endpoints). (-4, 3)∪(3, 8) implies that the graph starts at least as low as -4 and goes up to just before 3, and then there is a jump or hole at y = 3, then continues to go up to 8. Without the graph, we cannot determine the exactly right choice from the options provided.

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Answer:

10/40

Step-by-step explanation:

There are 10 red marbles out of a total of 40 marbles.

10 red marbles + 30 blue marbles = 40 total marbles.

If you are required to reduce fractions, then it would be 1/4

The cost of the video game system is $144 and the cost of the games is $432.

Determining the costs of the video game system and the games:

Let the cost of the video game system be x, and the cost of the games be 3x since the games cost 3 times as much as the system.

The total cost is $576, so we can set up the following equation:

x + 3x = 576

Combining like terms:

4x = 576

Solving for x:

x = 576/4

​

x = 144

Now, we find the cost of the games:

The cost of the system is x = 144 dollars.

The cost of the games is 3x = 3 × 144 = 432 dollars.

Answer:

It is 30 exactly um. yes or no

The relationship between parallel lines is that they have the same slope. The equation of the line that is parallel to [tex]2x = 1 - 3y[/tex] and passes through (9,4) is [tex]y=\frac 23x -2[/tex]

Given that:

[tex]2x = 1 - 3y[/tex]

First, we make y the subject

[tex]2x - 1 = 3y[/tex]

Divide both sides by 3

[tex]y = \frac 23x - \frac 13[/tex]

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where:

[tex]m \to slope[/tex]

So, by comparison:

[tex]m = \frac 23[/tex]

Parallel lines have the same slope.

So the slope of the line that passes through (9,4) is [tex]m = \frac 23[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where:

[tex]m = \frac 23[/tex]

[tex](x_1,y_1) = (9,4)[/tex]

So, the equation becomes:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = \frac 23(x - 9) + 4[/tex]

Expand

[tex]y = \frac 23x - 2 \times 3+ 4[/tex]

[tex]y=\frac 23x - 6 + 4[/tex]

[tex]y=\frac 23x -2[/tex]

Hence, the equation of the line that is parallel to [tex]2x = 1 - 3y[/tex] and passes through (9,4) is [tex]y=\frac 23x -2[/tex]

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Answer:

  D)  3.250×10^4 days

Step-by-step explanation:

You know there are 24 hours in a day, so the number of hours must be divided by the hours per day to find the number of days:

  (7.8×10⁵ h)/(2.4×10¹ h/da) = (7.8/2.4)×10⁵⁻¹ da = 3.250×10⁴ da

Answer:

PLEASE HELP!!!

What is 7.8×105 hours in days?

A)1.872×10^4 ​ days

B)3.250×10^6 ​​ days

C)1.872×10^8 ​​ days

D)3.250×10^4 days

Step-by-step explanation:

width = w

 length = w+8

perimieter = 256 feet

formla for perimeter is p=2L+2w

so you have: 256 =2(w+8) +2w =

256 = 2w+16 +2w

256= 4w+16

240=4w

w=240/4 = 60

 width is 60 feet

length = 60+8 = 68 feet

The approximate percent increase in Tanya’s swim club is 20%. Option A is correct.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

Given that Tanya’s swim club increased its $29 membership fee by $6 a year.

Tanya's increased fee is,

Fee = 29 + 6 = $35

Percentage increase = 32 / 29 = 1.20 or 20% increase

Therefore, the approximate percent increase in Tanya’s swim club is 20%. Option A is correct.

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Final answer:

The midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle, parallel to the third side and half its length.

Explanation:

In geometry, the midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle. By definition, this segment is parallel to the third side of the triangle, and its length is half that of the third side. When we think about a triangle, we must consider it as a three-sided figure on a plane, with three angles adding up to 180 degrees. Within this triangle, the midsegment represents a special relationship between its sides and angles.

An example of a midsegment would be if you have a triangle ABC with points D and E being the midpoints of AB and AC, respectively. The midsegment DE would connect these midpoints and have properties that relate to side BC, the side of the triangle to which it is parallel.

The concept of the midsegment is useful in various geometric proofs and problems because it establishes proportional relationships within the triangle. It aids in solving problems by applying these inherent ratios and proportions.

A conditional statement establishes a condition between two statements - if the first is true, the second is also true. In the provided examples, 'When I save money, I have enough money to cover emergencies' is a conditional statement. It suggests that saving money leads to having enough for emergencies, a classic 'if-then' setup.

In the context of logic and reasoning, a conditional statement is an if-then statement. It is a type of logical statement that establishes a condition between two statements, such that if the first statement (the 'if' part) is true, then the second statement (the 'then' part) is also true.

Out of the examples provided in the question, 'When I save money, I have enough money to cover emergencies' is a conditional statement. This is because it suggests a condition where the act of saving money results in having enough money for emergencies. If the action (saving money) is true, then the result (having money for emergencies) is also true.

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This problem is a combination problem since it did not indicate that there is a specified order of songs to be played. The type of combination problem is without repetition. Thus the working equation would be n!/r!(n-r)! wherein n is the total number of songs to choose from and r is the number of songs you can choose at a given time. The answer would be 125970. 

Answer: 125970

Step-by-step explanation:

The number of combinations of n things taken r at a time is given by :-

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Similarly , the  number of combinations of 20 songs taken 8 at a time is given by :-

[tex]^{20}C_8=\dfrac{20!}{8!(20-8)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15\times14\times13\times12!}{8\times7\times6\times5\times4\times3\times2\timews12!}\\\\=125970[/tex]

Hence, the number of different playlists are possible= 125970

Answer:

The solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is [tex]\(y = 7 - 2x\).[/tex]

Explanation:

To solve the equation [tex]\(2x + y = 7\)[/tex] for [tex]\(y\)[/tex], we isolate [tex]\(y\)[/tex] by moving [tex]\(2x\)[/tex] to the other side of the equation. Subtracting [tex]\(2x\)[/tex] from both sides gives [tex]\(y = 7 - 2x\).[/tex]This expression represents [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex], indicating that [tex]\(y\)[/tex] is equal to [tex]\(7\)[/tex]minus twice the value of [tex]\(x\)[/tex]. Thus, for any given value of [tex]\(x\)[/tex], we can find the corresponding value of [tex]\(y\)[/tex] using this equation.

To solve the system of equations [tex]\(2x + y = 7\) for \(y\)[/tex], you can follow these steps:

1. Subtract [tex]\(2x\)[/tex] from both sides of the equation:

[tex]\[y = 7 - 2x\][/tex]

So, the solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is [tex]\(y = 7 - 2x\).[/tex]

To identify a segment congruent to segment AB based on the scenarios provided, one should look for shared lengths or properties of geometric figures that indicate congruence such as equal markings or vector properties.

The question appears to be discussing congruent segments within geometrical diagrams, likely in the context of triangles or vectors. In geometric terms, congruent segments are segments that have the same length. From the information provided, several scenarios involving congruent segments are described. For example, when two triangles within different mediums share a segment, such as AB', or when judgment is required to determine congruence, as in Asch's conformity study.

In order to determine which segment is congruent to segment AB without the accompanying diagram, one would need to look for indications of shared lengths, parallel lines, or properties of similar triangles or figures. Typically, one would look for notation such as 'equals' marks on the segments or use the properties of the specific geometric shapes given (like the properties of triangles or the rules pertaining to vectors) to identify congruent segments.

In the diagram, segment AB is congruent to the segment on the surface AB' which is shared by both the triangle ABB' and AA'B'.

In the given diagram, segment AB is congruent to the segment on the surface AB', which is shared by both the triangle ABB' inside medium 1 and the triangle AA'B' inside medium 2. This is because the angles

Answer:

D. $991.19

Step-by-step explanation:

He starts with $1,234.56 in his account. He has to pay for plumbing supplies, so he writes a check for $115.12 and we have to subtract that amount from his account.

Now he has $1,234.56 - $115.12 = $1,119.44

After that, he has to pay a loan so he writes a check for $225.00.

Now he has $1,119.44 - $225.00 = $894.44

Finally, he deposits $96.75 in his account, so we have to add that amount to the amount he had before.

That's $894.44 + $96.75 = $991.19

5^-3 = 0.008

2^2 = 4

5^6 = 15625

0.008*4*15625 = 500

2^3 = 8

5^2 = 25

25*8 = 200

500/200 = 5/2 = 2 1/2