Use the midpoint formula
to select the midpoint of
line segment GR.
G(3,4)
R(5,-2)

Solution

Step1

The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.

Step2

Two pairs angles are equal, hence they are similar

Answer

Are similar by AA

Answer:

27

Step-by-step explanation:

Answer:

-9.6

Step-by-step explanation:

\(2\frac{2}{5} =2.40\\-\frac{1}{4} =-0.25\)

If change them into decimals it looks like that.

Then all you have to do is use standard calculator to find the answer.

\(\frac{2.40 }{-0.25} =-9.6\)

Answer:9 and 3/8  

Step-by-step explanation:

you have to make 2 and 2/5 into an improper fraction then make the -1/4 into a -4/1 then multiply across to make 48/5 then you have to reduce down to 8 and 8/5. but that cant happen so you reduce again and get 9 and 3/8.

To calculate the company's annual holding cost, we need to multiply the annual average inventory by the holding cost per unit.

First, we need to calculate the annual average inventory. The formula for the average inventory is (Q/2), where Q represents the order quantity.

Given:

Annual requirements (Demand) = 7500 units

Ordering cost = BD 12

Order quantity (Q) = 150, 300, 45000 (Assuming these are different order quantities)

Holding cost per unit = BD 0.5

For each order quantity, we can calculate the annual average inventory using the formula (Q/2). Then, we multiply the average inventory by the holding cost per unit.

For order quantity Q = 150:

Average Inventory = Q/2 = 150/2 = 75 units

Holding Cost = Average Inventory * Holding cost per unit = 75 * 0.5 = BD 37.5

For order quantity Q = 300:

Average Inventory = Q/2 = 300/2 = 150 units

Holding Cost = Average Inventory * Holding cost per unit = 150 * 0.5 = BD 75

For order quantity Q = 45000:

Average Inventory = Q/2 = 45000/2 = 22500 units

Holding Cost = Average Inventory * Holding cost per unit = 22500 * 0.5 = BD 11250. Now, we sum up the holding costs for each order quantity:

Annual Holding Cost = BD 37.5 + BD 75 + BD 11250 = BD 11362.5 Therefore, the company's annual holding cost is BD 11362.5.

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Answer:

x = 16

Step-by-step explanation:

Since the numbers are in ascending order, x is the number with the highest value here.

From the arrangement, we can see that the median (the middle number) is the third number which is 9

The mean is the sum of the numbers divided by their count. So we set up the mean and equate to the median

We have this as;

(1 + 9 + 9 + 10 + x)/5 = 9

29 + x = 5(9)

29 + x = 45

x = 45-29

x = 16

Hello,

well I guess the correct answer is D

you can see the correct graph below

for all x<1 this is the line y = 1

and then this is the line defined by y = x

hope this helps

The measure of each of the acute angles of the right triangle is 32° and 58°.

A right triangle is a kind of triangle which has a right angle (90°) and two acute angles (less than 90°).

Let x = measure of one of the acute angles

If the measure of one acute angle of a right triangle is 6 less than twice the measure of the other acute angle, then

measure of the other acute angle = 2x - 6

The sum of all the angles of any triangle is equal to 180°. Hence,

90° + x + 2x - 6 = 180°

Solve for the value of x.

3x = 96

x = 32

Solve for the measure of the other acute angle.

2x - 6 = 2(32) - 6 = 58

Hence, the two angles are 32° and 58°.

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The two different mathematical models derived from the Fibonacci's rabbits problem are the Fibonacci sequence and the matrix multiplication model.

The two different mathematical models that can be derived from the Fibonacci's rabbits problem are:

1. Fibonacci sequence:

Start with the initial values of the rabbit population, typically 0 and 1.

Apply the recursive formula F(n) = F(n-1) + F(n-2) for n ≥ 2, where F(n) represents the nth Fibonacci number.

To find any term in the sequence, calculate the sum of the two preceding numbers.

For example, F(0) = 0, F(1) = 1, F(2) = F(1) + F(0), F(3) = F(2) + F(1), and so on.

Continue this process until you reach the desired term in the sequence.

2. Matrix multiplication model:

Create matrices A, B, and C to represent the rabbit population and transformations.

Matrix A: [F(n), F(n-1)] representing the rabbit population at time n.

Matrix B: [[1, 1], [1, 0]] representing the transformation matrix.

Raise matrix B to the power of (n-1) because the first multiplication is already accounted for with matrix A.

Multiply matrix A with B^(n-1) to obtain matrix C, representing the rabbit population after n time periods.

The value F(n) is the first element of matrix C.

Both models provide different perspectives on the growth of the rabbit population. The Fibonacci sequence emphasizes the iterative nature of the problem, while the matrix multiplication model provides a more direct and efficient approach by leveraging matrix operations. These models can be used to calculate Fibonacci numbers and understand the growth pattern of various populations beyond just rabbits.

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\(\boxed{\sf cos(A+B)=cosAcosB-sinAsinB}\)

Now

\(\\ \sf\longmapsto cos(x+1)\)

\(\\ \sf\longmapsto cosxcos(1)-sinxsin(1)\)

Answer:

100°

Step-by-step explanation:

The sum of any polygon angles add to  ( n-2)(180)   where n is the number of sides ......for a quadrlateral    ( 4-2)(180 ) = 360

60 + 90 + 110 +  x = 360    shows    x = 100 °

Answer:

sin75^°-sin15^°=1/√2

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during set  World War II.

The purpose of Lend-Lease was to provide military aid to countries fighting against the Axis powers during World War II. The program was enacted by the United States in 1941 and allowed the US to provide war materials to its allies without requiring repayment. It was a major factor in the Allied victory, as it allowed the US to supply its allies with much needed war material and resources. The US provided a variety of goods, including food, oil, weapons, and tanks. It also supplied the Soviet Union with millions of tons of military equipment and supplies. Lend-Lease was instrumental in helping the Allies win the war, as it allowed them to gain a huge advantage over the Axis powers by providing essential supplies and resources.

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The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.

You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

Now according to the question,

Possible letter combinations

Choose any letter and make it a repeat letter = 26 ways

But, there are ⁴C₂ = 6 spots available for the identical letters.

And there are (25)×(24) other methods for selecting the other two letters.

The total amount of "words" equals ⁴C₂ × 26 × 25 × 24 = 93600.

Furthermore, because the numerals cannot be repeated = 10 × 9 = 90

So, the total number of choices = 93600 × 90 = 8,424,000

Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.

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Answer:

h = 61.83 feet

Step-by-step explanation:

length of string from Hector to kite = c = 86 feet.

and 4 feet off the ground.

angle A = 42° 15' 30"

req'd:  how high is the kite?

angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')

angle A = 42.26

to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp

Sin(A) = a / c

Sin(42.26) = a / 86

a = Sin(42.26) * 86

a = 57.83 feet

therefore, the height of the kite from the ground = h = 57.83 + 4

h = 61.83 feet

The cube with he greater side length is: cube B.

Volume of a cube = a³

Surface area of a cube = 6a²

Therefore:

Volume of cube A = 125 in.³

125 = a³

√125 = a

a = 5 in.

Side length of Cube A = 5 in.

Surface area of Cube B = 121 in.²

121 = 6a²

√(121/6) = a

√(121/6) = a

10.7 = a

a = 10.7

Side length of cube B = 10.7 in.

Therefore, the cube with he greater side length is: cube B.

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The smallest angle of the right triangle is 27 degrees.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sum of angles in a triangle is 180 degrees.

Therefore, the measure of the smallest angle in the triangle can be found as follows:

90 + 6x + 3 + 2x + 7 = 180

combine like terms

90 + 6x + 3 + 2x + 7 = 180

8x + 100 = 180

subtract 100 from both sides of the equation

8x + 100 = 180

8x = 80

divide both sides by 8

8x / 8 = 80 / 8

x = 10

angle 1 = 6(10) + 3 = 60 + 3 = 63°

angle 2 = 2(10) + 7 = 20 + 7 = 27°

Therefore,

smallest angle of the triangle = 27 degrees.

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Answer:

$66.55 dollars i took the same question

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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The important resonance structures for the given ion must be drawn, showing all lone pairs of electrons, formal charges, double bonds, and electron flow arrows.

Resonance structures are alternative representations of a molecule or ion that differ only in the placement of electrons. They are important in understanding the stability and reactivity of organic compounds. In this case, we are asked to draw the important resonance structures for a specific ion.

To start, we need to identify the ion and its molecular formula. Once we have that information, we can determine the possible resonance structures. Each resonance structure is a valid Lewis structure that obeys the octet rule and maintains the overall charge of the ion.

To draw the resonance structures, we begin by placing the atoms in their correct positions and adding lone pairs of electrons as needed. Next, we identify any double bonds or formal charges present in the original ion.

Using curved arrows, we show the movement of electrons to generate alternative resonance structures. The movement of electrons can involve breaking and forming bonds, as well as the shifting of lone pairs.

By drawing all the important resonance structures, we gain a better understanding of the electron distribution and the stability of the ion. This knowledge is crucial for predicting the reactivity and behavior of the compound.

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The logistic differential equation for these data is \(\frac{dP}{dt}\, =\, 0.0013P(1-\frac{P}{5900})\)

The logistic differential equation is a mathematical model used to describe the growth of a population when there is a limiting factor that affects the growth rate. It is based on the idea that the growth rate of the population decreases as it approaches a maximum capacity or carrying capacity.

The equation is typically written as:

dP/dt = rP(1 - P/K)

where dP/dt is the rate of change of the population over time, P is the population size at any given time, r is the intrinsic growth rate, and K is the carrying capacity.

In the given problem, the carrying capacity is 5900, which means that the population cannot exceed 5900 individuals. The growth rate is given by k = 0.0013 per year. Thus, the logistic differential equation can be written as:

dP/dt = 0.0013P(1 - P/5900)

This equation represents the rate at which the population grows over time, taking into account the limiting factor of the carrying capacity. The solution to this differential equation can be used to predict the population size at any future time, given the initial population size and the growth rate.

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The integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

To evaluate the integral of du/sqrt(a^2 - u^2), we can use a trigonometric substitution. Let's substitute u = asin(theta), where theta is a new variable. Differentiating u with respect to theta gives du = acos(theta)*d(theta).

Now, let's substitute these expressions back into the integral:

∫(du/sqrt(a^2 - u^2)) = ∫((acos(theta)d(theta))/sqrt(a^2 - a^2sin^2(theta)))

Simplifying the expression under the square root:

= ∫((acos(theta)d(theta))/sqrt(a^2(1 - sin^2(theta))))

= ∫((a*cos(theta)d(theta))/(acos(theta)))

= ∫d(theta)

= theta + C

Since we made the substitution u = asin(theta), we need to express the result in terms of u. Using the relationship u = asin(theta), we can find theta = arcsin(u/a). Therefore, the integral becomes:

∫(du/sqrt(a^2 - u^2)) = theta + C = arcsin(u/a) + C

Hence, the integral of du/sqrt(a^2 - u^2) is arcsin(u/a) + C, where a is a constant and C is the constant of integration.

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Answer:

  a) 23.1 million

  b) year 2013

Step-by-step explanation:

Given a population in millions is modeled by A = 23.1e^(0.0152t) for t years after 2000, you want to know the population in year 2000, and the year in which the population is 28.3 million.

When t=0, the exponential factor is 1. The population is given by the coefficient of that factor: 23.1

The population in 2000 was 23.1 millions.

We can solve for t to find the year the population is 28.3 million:

  28.3 = 23.1e^(0.0152t)

  28.3/23.1 = e^(0.0152t) . . . . .divide by 23.1

  ln(28.3/23.1) = 0.0152t . . . . . take natural logs

  t ≈ 13.36

The population will reach 28.3 million in the year 2013.

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Answer:

OK so this may or may not help u ...

this can be taken as the straight line with equation

y = mx + c

here f(x) is taken to be y

the attached pic is the graph of this function

so I think the value of x before it explodes would be 18.875

and x represents the time

and f(x) represents height so we see that the highest possible value of f(x) from the graph is 302

Answer:

10.7 cm

Step-by-step explanation:

A= bh

\(\sqrt{115}\) = 10.7 cm

Answer:

y = 3/4x - 14

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

m = 3/4

The Y-intercept is located at (0, -14)

So, the equation of the line is y = 3/4x - 14

Answer:

37.5%

Step-by-step explanation:

She starts with 12.

She ends up with 7.5 at the end.

7.5/12 = 0.625

1 - 0.625 = 0.375 or 37.5%

The decrease of petrol in Jane's car is 37.5%

Your welcome!

Kayden Kohl

8th Grade

Answer:

-6 because if you minus 14 to 20 you will get -6

Answer:

A. is the answer.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

a fraction is equal to 0 when the numerator is 0

x - 4 = 0

x = 4

The correct answer is x=4.

Step-by-step explanation:

When the numerator is 0, a fraction is equal to 0.

x - 4 = 0

x = 4

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