the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length is

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

The solution for the linear system will be , x(t) = 4 c₁e^t +  4 c₂e^t and

y(t) = -c₂e^t + c₂(1 - t)e^t .

The solution is given by ,

matrix | x y | = c₁ .v . e^λt  + c₂( w + v.t ) e^λt

Given that the matrix has repeated eigenvalue with eigenvector  generalized  vectors ,

λ = 1 with eigenvector v = [ 4 , -1 ] and  generalized  vectors w =[ 0,1 ].

then the solution will be,

c₁ [ 4 , 1 ] e^t +  c₂[ 0 , 1] + [ 4 , -1 ] )e^t

therefore,

x(t) = 4 c₁e^t +  4 c₂e^t

y(t) = -c₂e^t + c₂(1 - t)e^t

Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.

Matrix multiplication, for example, depicts the combination of linear maps.

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The distance between the two towers and the building is 50 ft.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that The height of a tower is 55 ft and the height of a building is 25 ft. If the angle of elevation from the top of the building to the top of the tower is 30.9°.

The distance will be calculated as,

Distance = 30 / tan(30.9)

Distance = 50 ft

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Answer:

116 / 45

Step-by-step explanation:

To add fractions with unlike denominators, we need to find their common denominator.

One way to do this is by finding the least common multiple (LCM) of the denominators.

The LCM of 3, 5, 9 and 15 is 45.

We then convert each fraction so that its denominator is 45:

1/3 = 15/45

3/5 = 27/45

7/9 = 35/45

13/15 = 39/45

Now we can add the fractions:

15/45 + 27/45 + 35/45 + 39/45

To simplify, we can add the numerators and keep the common denominator:

(15 + 27 + 35 + 39) / 45

Which gives us:

116 / 45

Therefore, the sum of the fractions 1/3 + 3/5 + 7/9 + 13/15 is, 116 / 45.

Answer:

24 \(m^{3}\)

Step-by-step explanation:

Volume=l*b*h

as tank is half full so height of water will be 4m

and Voulme will be,

V=3*2*4=24 \(m^{3}\)

while capacity of tank is,

V=3*2*8=48  \(m^{3}\)

The volume of water in the tank, when it is half full, is 24 cubic meters.

Volume in mathematics and physics refers to how much three-dimensional space is occupied by a substance or an object. It is a measurement of the overall volume of space contained inside a three-dimensional object's limits.

The volume of the rectangular tank is given by the formula:

V = l x b x h

where l is the length, b is the breadth, and h is the height of the tank.

Substituting the given values, we get:

V = 3m x 2m x 8m = 48 cubic meters

If the tank is half full, then the volume of water in the tank is:

Vw = (1/2) * V = (1/2) x 48 = 24 cubic meters

Therefore, the volume of water in the tank when it is half full is 24 cubic meters.

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Answer:

This System has no solutions.

Answer:

448 is the answer

Step-by-step explanation:

If u need complete solution do let me know

Answer:

448 yd^2.

Step-by-step explanation:

The surface area consists of 3 rectangles and 2 congruent triangles

= 12*11 + 2 * 10*11 + 2 * 1/2 * 12*8

= 132 + 220 + 96

= 448 yd^2.

Answer:

Where is the question?

Step-by-step explanation:

Answer:

Statement: Triangle ACD is congruent to Triangle BCD

Reason: SSA (Side, Side, Angle)

Answer:

Either A or B, try B first

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The Y int is 1000 and the vertex is 200 it is the only graph whose vertex is at 200 and the y int on 1000

The statement that explains how mental math can be used to find how much farther Josh rode than Claire is that to round 11.4 to 11. Round 6.8 to 7. Then subtract 7 from 11 to get 4. Josh rode 4 miles farther than Claire. That is option A.

The use of metal maths is simply the calculation of a given mathematical problem without the use of an aid such as electronic devices.

The number of miles covered by Josh = 11.4 miles

The number of miles covered by Claire = 6.8 miles

To use mental maths, the values are rounded up to the nearest whole number and the difference between the two are gotten.

That is;

11.4 = 11

6.8 = 7

Therefore the difference in the distance between the two individuals = 11-7 = 4 miles.

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Answer:

58/33 or 1.75

Step-by-step explanation:

The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:

a+b>c

a+c>b

b+c>a

In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:

9+13>15 (true)

9+15>13 (true)

13+15>9 (true)

Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.

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Answer:

21134 bacteria

Step-by-step explanation:

The given parametrs can be interpreted as:

\(y = 8(2.4)^t\)

Required

Find y when t = 9

Substitute \(t = 9\)

So:

\(y = 8(2.4)^9\)

\(y = 8 * 2.4^9\)

\(y = 8 * 2641.81\)

\(y = 21134.48\)

\(y = 21134\) --- approximated

Hence, there are 21134 bacteria

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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Answer: Choice D

(0,-4) (4,0) and (-1,-5)

===========================================================

Explanation:

Plug in x = -4

y = x-4

y = -4-4

y = -8

The point (-4,-8) is on the line instead of (-4,0). This rules out choice A and choice B.

Now plug in x = 1

y = x-4

y = 1-4

y = -3

We get (1,-3) instead of (1,5). So we can rule out choice C.

The answer must be choice D.

The graph is below.

Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

If a person can make 20 badges in one hour using a machine then the time taken by the 10 people to make 300 badges would be 1.5 hours.

What is inverse proportion?

When one quantity increases, the other decreases. This is known as inverse proportion. The speed-time relationship is an example of inverse proportionality. As the speed increases, the journey time decreases, so the time for a journey can be calculated by dividing the distance by the speed.

In the given question, A person can make 20 badges in one hour.

means, 1 person makes 20 badges in 1 hour.

then 1 person can make 300 badges in = \(\frac{300}{20} =15\) hr

So 10 people can make 300 badges in

                                                                  \(=\frac{15}{10}\\=1.5 hr\)

Hence, the time taken by the 10 people to make 300 badges would be 1.5 hours.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.

On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

this question is related to probability.

mutually exclusive

Mutually exclusive events are those events that do not occur at the same time.

For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.

probability

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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The period of the function is 4π, and the amplitude is 2.

Given data ,

Let the function be represented as f ( x ) = y

Now , the value of f ( x ) is

y = 2sin ( 1/2 )x

To find the period and amplitude of the function y = 2sin((1/2)x), we can use the standard form of a sine function: y = Asin(Bx).

In this case, the amplitude (A) is 2.

The amplitude represents the maximum displacement from the midpoint of the sinusoidal function.

To find the period, we can use the formula:

Period = (2π) / |B|.

B = 1/2.

Period = (2π) / |1/2|

P = (2π) / (1/2) = 2π * 2/1 = 4π

Hence , the period of the function is 4π, and the amplitude is 2.

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This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.

By Pythagoras theoram,

\( {p}^{2} + {b}^{2} = {h}^{2} \)

where p is the perpendicular, b is the base and h is the hypotenuse.

Plugging the values,

\( {9}^{2} + {11}^{2} = {h}^{2} \)

Then,

\(h = \sqrt{ {9}^{2} + {11}^{2} } \)

\(h = 14.12(approx.)\)

The x of the right angled ∆ = 14.12

Answer:

the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding

Answer:

\(y=-6+\frac{2x}{5}\)

Answer:

this simplified would be 2x+5y+15

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

7 > x  means what numbers are less than 7

A  and C are not correct because 7 = 7 is not less than 7

B is correct because 7 > -2, and 7 > 0

D is not correct because 8, 10, 20 are more than 7

Please refer to the attached Image for the Answer

Need photo of the segment.

Answer is 2/36 or 5.55...%

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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