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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.

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

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.

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:

Answer:

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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Neptune's distance from the Sun is about 78 times farther than that of Mercury. This result is computed by dividing Neptune's average distance from the Sun by Mercury's average distance from the Sun.

The subject here is to determine how many times Neptune is farther from the Sun than Mercury. We have the average distance from the Sun to Neptune as 4.503 × 109 km and the average distance from the Sun to Mercury as 5.791 × 107 km. To find out how many times Neptune is farther from the Sun than Mercury, we divide the distance of Neptune by the distance of Mercury: (4.503/5.791) x 109-7 which equates to 0.77782 times 102 or 7.7782 × 101. Therefore, Neptune is approximately 78 (7.8 × 101 when rounded to the nearest ten-thousandths) times farther from the Sun than Mercury.

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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.

To know more about percentages follow

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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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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

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

9x+4 +32 = 90

9x+36 = 90

9x=54

x = 54/9 = 6

x = 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.

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