Which postulate proves the two
triangles are congruent?
A. SAS
B. HL
C. SSA
D. ASA

Answer:

140

Step-by-step explanation:

arc AB = 140 because is inscribed by a central angle so the arc and the angle are equal

Answer: ab=14.7

Step-by-step explanation:

a) The vector (9,0,9) is a linear combination of the given vectors.

b) The vectors (0,3,-1,2), (1,2,1, -2) and (3,0,5, -10) in R+ are linearly independent.

[0 1 3 | 0]

[3 2 0 | 0]

[0 2 8 | 0]

[0 -4 -16 | 0]

R2 -> R2 - 3R1

a) To determine whether the vector (9,0,9) is a linear combination of the vectors (1,1,0), (1,0,1), (2,1,1) and (0,1,-1), we need to find coefficients c1, c2, c3 and c4 such that:

c1(1,1,0) + c2(1,0,1) + c3(2,1,1) + c4(0,1,-1) = (9,0,9)

This can be written as a system of linear equations:

c1 + c2 + 2c3 = 9

c1 + c3 + c4 = 0

c2 + c3 - c4 = 9

We can solve this system using row reduction:

[1 1 2 | 9]

[1 0 1 | 0]

[0 1 -1 | 9]

R2 -> R2 - R1

R3 -> R3 - 2R1

[1 1 2 | 9]

[0 -1 -1 | -9]

[0 -1 -5 | -18]

R3 -> R3 - R2

[1 1 2 | 9]

[0 -1 -1 | -9]

[0 0 -4 | -9]

R2 -> -R2

R3 -> -(1/4)R3

[1 1 2 | 9]

[0 1 1 | 9]

[0 0 1 | 9/4]

R1 -> R1 - 2R3

R2 -> R2 + R3

[1 1 0 | 9/2]

[0 1 0 | 45/4]

[0 0 1 | 9/4]

We can see that the system has a unique solution, which is c1 = 9/2, c2 = 45/4, c3 = 0, and c4 = -9/4.

b) To determine whether the vectors (0,3,-1,2), (1,2,1,-2), and (3,0,5,-10) in \(R^4\) are linearly independent, we need to check whether the equation:

c1(0,3,-1,2) + c2(1,2,1,-2) + c3(3,0,5,-10) = (0,0,0,0)

has only the trivial solution c1 = c2 = c3 = 0.

This can be written as a system of linear equations:

c2 + 3c3 = 0

3c1 + 2c2 = 0

-c1 + c2 + 5c3 = 0

2c1 - 2c2 - 10c3 = 0

We can solve this system using row reduction:

[0 1 3 | 0]

[3 2 0 | 0]

[-1 1 5 | 0]

[2 -2 -10 | 0]

R1 -> -R1

R3 -> R3 - R1

R4 -> R4 - R1

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Answer:

Solution given:

∆ ABE is similar to ∆ ACD

since their side will be proportional

AB/AC=AE/AD

AB/(AB+BC)=AE/(AE+ED)

63/(63+7)=(7x-40)/(7x-40+18)

9/10=(7x-40)/(7x-22)

doing crisscrossed multiplication

9(7x-22)=10(7x-40)

63x-198=70x-400

400-198=70x-63x

202=7x

x=202/7 or 28.85units.

Answer:

\(x=28\frac{6}{7}\)

\(x \approx 28.857\)

Step-by-step explanation:

It is given that lines (BE) and (CD) are parallel, thus (<AEB) and (EDC) are congruent by alternate interior angles theorem. Moreover, (<A) is shared between the two triangles, therefore it is also congruent. Hence, triangles (ABE) and (ACD) are similar by (angle-angle) similarity.

Side (AD) is composed of segments (AE) and (ED), therefore one can find the total measure of segment (AD):

AD = AE + ED

AD = 7x - 40 + 18

AD = 7x - 22

Side (AC) is made of segments (AB) and (BC), thus one can find the total length of the side (AC) by adding these two segments:

AC = AB + BC

AC = 63 + 7

AC = 70

When two triangles are similar, the ratios of the sides are equal. Therefore, one can make the following statement:

\(\frac{AE}{AD}=\frac{AB}{AC}\)

Substitute,

\(\frac{7x-40}{7x-22}=\frac{63}{70}\)

Cross products,

\(70(7x-40)=63(7x-22)\)

Distribute,

\(490x-2800=441x-1386\)

Inverse operations,

\(490x-2800=441x-1386\)

\(49x-2800=-1386\)

\(49x=1414\)

\(x=28\frac{6}{7}\)

9514 1404 393

Answer:

  A.  x^3 − 9x^2 + 14^x + 24

Step-by-step explanation:

(x − 4)(x^2 − 5x − 6) = x(x^2 − 5x − 6) -4(x^2 − 5x − 6)

  = x^3 -5x^2 -6x -4x^2 +20x +24

  = x^3 +x^2(-5-4) +x(-6+20) +24

  = x^3 − 9x^2 + 14x + 24 . . . . matches the first choice

Answer:

The other person is right it is "x^3 − 9x^2 + 14x + 24"

Step-by-step explanation:

They showed their work so i felt like u could just look at theirs!!!

Xoxo

Answer:

The numbers for which the given property hold true are 12 and -7

Step-by-step explanation:

Let the number be \(x\).

As per the given statement:

Square of the number (\(x^{2}\)) is 84 more than five times of the number (\(5x+84\)).

Writing in the equation form:

\(x^{2} =5x+84\)

To find:

All the numbers for which above equation holds true.

Solution:

\(x^{2} =5x+84\)

Let us solve the above equation by rearranging the terms and then let us find the roots of the equation.

It is a quadratic equation(i.e. maximum power of \(x\) is 2) so it will have 2 solutions  i.e. 2 values of \(x\) for which the above equation will hold true.

\(x^{2} -5x-84=0\)

Let us factorize the equation.

\(\Rightarrow x^{2} -12x+7x-84=0\\\Rightarrow x(x -12)+7(x-12)=0\\\Rightarrow (x+7)(x-12)=0\\\Rightarrow \bold{x=12, -7 }\)

So, the numbers for which the given property hold true are 12 and -7.

Answer:

the answer is B thats wat equals to g(x)

Answer:

2x or h(x)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1=1 therefore x can not be 1

Answer:

1

Step-by-step explanation:

Since the question is asking what makes the statement x>1 true, we can determine that 1.2, 4, and 8 all fit because these numbers are all greater than 1 and, if we plug them in for x, it makes the expression correct. The statement is not asking if x is greater than OR EQUAL to 1, only if it is greater than. Since 1 is NOT greater than 1, that is the answer.

Answer:

5 pounds

Step-by-step explanation:

54.89 - 49.75 = 5.14

Then once that was rounded is turned to 5 pounds

Answer:  5.14 pounds, A

Step-by-step explanation:

54.89 - 49.75 = 5.14 pounds

For square a of perimeter 24 cm and square b has an area equal to one-fourth the area of the square a, the perimeter of square b is 12 cm.

Given that a square has a perimeter of 24 cm. And another square b has an area equal to one-fourth of the area of square a. To find the perimeter of square b, we need to find the length of the side of square b using the area of square

Area of the square a = side² of the square a
The perimeter of the square a = 4 × side of the square a

Given that, Perimeter of square a = 24 cm⇒ 4 × side of square a = 24 cm⇒ side of square a = 24 / 4 cm⇒ side of square a = 6 cm.

Area of square b = 1/4 × Area of square a = 1/4 × side² of square a= 1/4 × 6² cm²= 9 cm²

Side of square b = √9 cm = 3 cm
Perimeter of square b = 4 × 3 cm = 12 cm

Therefore, the perimeter of square b is 12 cm.

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Answer:

false, because cos(x) has no definite answer, and equations aren't identities

Step-by-step explanation:

Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!

THIS IS THE COMPLETE QUESTION BELOW

Problem number 26 of the Rhind Papyrus says:

Find a quantity such that when it is added to ¼ of itself the result is 15.

The modern day equation that models this problem is x +

¼x = 15. What is the solution to the equation?

A) x = 10

B) x = 12

C) x = 15

D) x = 30

Answer:

The quantity is X= 12

The solution is 12+ ¼(12)= 15

Step by step Explanation

Problem number 26 states " "

The question above can be represented as this,

x + ¼x = 15

Here we want to find the value of x in such a way that when that value is substitute in the expresion we have 15 as our answer,But here we can perform some manipulation, by saying

4/4x + ¼x = 15 ..............eqn(1)

Even with this we can still get the above expression by saying

4/4x= x which means we're still correct.

Then the expresion eqn(1) can simplified as

5/4x = 15

If we multiply both sides by 4/5 we have

=(5/4x)×(4/5)

= 15×(4/5)

= (15/1)×(4/5)

X= 60/5

X = 12

The quantity is X= 12 and the solution is

12+ ¼(12)= 15

Answer:

b

Step-by-step explanation:

To calculate the income Alice will receive in her first year of retirement, we need to consider her pension fund, the state pension, and the annuity rates.

Given: Alice's salary: £55,000

Her contributions to the pension scheme: 8% of salary

Employer contributions and tax relief: 4% of salary

Retirement age: 66

State pension: £9,000 per year

First, let's calculate Alice's pension fund. She has been in the scheme from age 35 to 66, which is a total of 31 years. During this period, she has made contributions of 8% of her salary, topped up by 4% from the employer and tax relief. So, her annual contributions are (8% + 4%) of £55,000 = £5,500.

Her total pension fund would be £5,500 x 31 = £170,500.

Next, let's consider the annuity rates. Annuity rates determine the income that can be purchased with the pension fund. The rates vary based on factors such as age, gender, and prevailing market conditions.

Using the annuity rates, Alice can calculate the income she will receive from her pension fund. Let's assume the annuity rate is 5% per year. So, the income from her pension fund would be £170,500 x 5% = £8,525.

Finally, we add the state pension to calculate Alice's total income in her first year of retirement:

Total income = Pension fund income + State pension

Total income = £8,525 + £9,000 = £17,525.

Therefore, Alice will receive £17,525 as her income in the first year of retirement.

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The profit function if the cost and revenue is given  P(x) = -0.01x² + 3.2x - 150.

To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).

The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

Substituting the given expressions for R(x) and C(x), we have:

P(x) = (9x - 0.01x²) - (150 + 5.8x)

Simplifying this expression, we get:

P(x) = 9x - 0.01x² - 150 - 5.8x

Combining like terms, we have:

P(x) = -0.01x² + 3.2x - 150

Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.

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Answer:

1) \(3x^{2}\)-19x-14

2) x=0, x=3

Step-by-step explanation:

1) (3x+2)(x-7)

Distribute the 3x to both x and -7, as well as the 2 to both x and - 7.

\(3x^{2}\) - 21x + 2x -14

Combine like terms

\(3x^{2}\) - 19x - 14

2)

In order to find the factors of x, set the expression equal to 0.

\(3x^{2}\) - 9x = 0

Factor out the highest common multiple (3x)

3x(x-3) = 0

In order for x to satisfy the equality, you must either have a 0 in the parenthesis -> (x-3)=0 -> x =3

Or 3x = 0 -> x = 0

Hope this helps!

Answer: Is a plane figure with at least 3 straight sides and angles, and typically five or more sides.

Step-by-step explanation:

A) The expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) For 50 ft, Area = 3000 \(\rm ft^2\), For 100 ft , area = \(\rm 12000\ ft^2\) and For 150 ft, area = 26000 \(\rm ft^2\)

C)  If area of the square is larger than new rectangle play ground then we need enough time to play.

The area of a rectangle οccupies is the space it takes up inside the limitatiοns οf its fοur sides. The dimensiοns οf a rectangle determine its area. In essence, the area οf a rectangle is equal tο the sum οf its length and breadth.

Let us take side length οf the square = x

Adding 50 feet fοr οne side then , length οf rectangle = x+50 feet.

Nοw decreasing 20 feet fοr οther side then, width οf rectangle = x- 20 feet.

A) Now area of the rectangle is ,

A = length*width

=> A = (x+50)(x-20)

=> A = \(x^2-20x+50x-1000\)

=> A = \(x^2+30x-1000\)

Then , the expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) If side length x= 50 ft then

Area = \(50^2+30\times50-1000 = 2500+1500-1000 = 3000 ft^2\)

If side length x = 100 ft then

Area = \(100^2+30\times100-1000 = 10000+3000-1000 = 12000 ft^2\)

If side length = 150 ft then

Area = \(150^2+30\times150-1000= 22500+4500-1000= 26000 ft^2\).

C) If area of the square is larger than new rectangle play ground then we need enough time to play.

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The matching sets for the given orbitals are as follows:

A. 3, 2, -1

C. 5, 1, -1

G. 4, 0, -1

H. 3, 2, 3

In quantum mechanics, each electron in an atom is described by a set of quantum numbers that provide information about its energy level, orbital shape, and orientation. The quantum numbers include the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml).

For the given orbitals, we need to match the orbital names with the sets of quantum numbers. Let's go through each option:

A. The quantum numbers 3, 2, -1 correspond to the orbital name 3dxy. The principal quantum number (n) is 3, the azimuthal quantum number (l) is 2, and the magnetic quantum number (ml) is -1. This describes a d orbital in the xy plane.

C. The quantum numbers 5, 1, -1 correspond to the orbital name 5py. The principal quantum number (n) is 5, the azimuthal quantum number (l) is 1, and the magnetic quantum number (ml) is -1. This describes a p orbital oriented along the y-axis.

G. The quantum numbers 4, 0, -1 correspond to the orbital name 4pz. The principal quantum number (n) is 4, the azimuthal quantum number (l) is 0, and the magnetic quantum number (ml) is -1. This describes a p orbital oriented along the z-axis.

H. The quantum numbers 3, 2, 3 correspond to the orbital name 3dxyz. The principal quantum number (n) is 3, the azimuthal quantum number (l) is 2, and the magnetic quantum number (ml) is 3. This describes a d orbital with complex orientation in space.

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The rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

To find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form, the rectangular coordinates of the above points are given below:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

The rectangular coordinates of the point(s) of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ) can be found by converting the polar equations to rectangular form and solving for the x and y coordinates.

To convert the polar equations to rectangular form, we can use the relationships x = rcos(θ) and y = rsin(θ). Substituting these expressions into the given polar equations, we get:

For the equation r = 2sin(2θ):

x = 2sin(2θ)cos(θ)

y = 2sin(2θ)sin(θ)

For the equation r = 2sin(θ):

x = 2sin(θ)cos(θ)

y = 2sin^2(θ)

To find the points of intersection, we need to set the x and y coordinates of both equations equal to each other and solve for θ. However, solving this system of equations algebraically can be complex due to the trigonometric functions involved.

Graphing the polar curves and visually inspecting the points of intersection may provide a more intuitive approach to finding the rectangular coordinates. By plotting both polar curves on a graph, the points where the curves intersect can be determined by their shared coordinates.

In summary, to find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.

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The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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The corollary states that for every positive real number ε, there exists a positive integer n such that

The corollary of the Archimedean principle states that for any positive real number ε, there exists a positive integer n such that ε is greater than the reciprocal of n, i.e., ε > 1/n. In other words, there exists a positive integer n such that the fraction 1/n is smaller than any given positive real number ε.

To prove this corollary, we can assume that ε is a positive real number. By the Archimedean principle, there exists a positive integer m such that m > ε. Now, consider the positive integer n = ⌈1/ε⌉ + 1, where ⌈x⌉ denotes the ceiling function, rounding up x to the nearest integer.

We have:

1/ε < 1/(⌈1/ε⌉ + 1) ≤ 1/(1/ε) = ε.

Therefore, we can conclude that for any positive real number ε, there exists a positive integer n = ⌈1/ε⌉ + 1 such that ε > 1/n.

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A symmetrical distribution of exam scores in a college course indicates that the student's scores are evenly distributed across the entire range of scores. This suggests that about an equal number of students had relatively high and relatively low scores.

Correct answer will be b) About an equal number of students had relatively high and relatively low scores.

And that there is no single group that overwhelmingly outperformed or underperformed the others. Furthermore, it indicates that there were a substantial number of students who achieved high scores, as well as a substantial number who achieved low scores.

This type of even distribution of scores is often seen when students are equally prepared, and when the exam is designed to be neither too difficult nor too simple.

In conclusion, a symmetrical distribution of exam scores suggests that the students were similarly prepared and that the exam was appropriately challenging.

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Therefore , the solution of the given problem of probability comes out to be the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

Any considerations technique's main objective is to determine the likelihood event that a claim is true or that a particular incident will happen. Any number from 0 to 1, where 0 traditionally represents a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

Given: 86 Latin CDs were lent out, 16 were rock CDs, 45 were hip-hop CDs, and 126 were reggae CDs.

=> CDs loaned out in total: 86 + 16 + 45 + 126 = 273

=> 126 reggae CDs were lent out.

Number of reggae CDs loaned out relative to the total number of CDs loaned out, experimental likelihood of lending a reggae CD

=> A reggae CD's experimental chance of being lent out  = 126/273.

We may calculate the experimental probability's approximation using a calculator as follows:

=> A reggae CD will be lent out with an experimental probability of 0.4615.

Therefore, the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

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Answer:

126/273

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

468/9 = 52

52 x 3 = 156

156 x 3 = 468

True, a data warehouse allows users to specify certain dimensions or characteristics.

In a data warehouse, dimensions represent the different aspects or characteristics by which data can be categorized or analyzed. These dimensions can include various attributes or variables that provide context and organize the data.

Users of a data warehouse can specify these dimensions based on their analytical needs and the nature of the data being stored.

For example, in a sales data warehouse, common dimensions may include product, customer, time, and location.

By specifying these dimensions, users can slice and dice the data based on different criteria and gain insights from various perspectives.

By defining dimensions, users can navigate through the data warehouse and perform multidimensional analysis using tools such as OLAP (Online Analytical Processing).

Dimensions provide a structure for organizing and querying data in a way that facilitates analysis and reporting.

In summary, a data warehouse allows users to specify dimensions or characteristics that help organize and analyze the data stored in the warehouse. These dimensions provide a framework for users to navigate and explore the data from different perspectives.

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So the amount of gain that can be deferred under the installment sale method is $424,879.16.

Percent is a way of expressing a number as a fraction of 100. The word "percent" means "per hundred" in Latin. When a number is expressed as a percentage, it is usually accompanied by the "%" symbol. Percentages are commonly used in many areas of everyday life, such as finance, taxes, and statistics. They are often used to express changes or differences, such as percentage increases or decreases in prices or quantities, or the percentage of people who hold a certain opinion or belong to a certain group.

Here,

To calculate the gain that can be deferred under the installment sale method, we need to first calculate the total gain on the sale. The total gain is equal to the selling price minus the adjusted basis of the property, which is the cost minus the accumulated depreciation.

Selling price = $99,800 cash + $998,000 note = $1,097,800

Adjusted basis = $798,400 - $479,040 = $319,360

Total gain = $1,097,800 - $319,360 = $778,440

To calculate the gain that can be deferred, we need to determine the gross profit percentage. The gross profit percentage is equal to the total gain divided by the selling price:

Gross profit percentage = Total gain / Selling price = $778,440 / $1,097,800 ≈ 0.7097 or 70.97%

Now we can calculate the amount of gain that can be deferred using the formula:

Gain deferred = Gross profit percentage × Payments received

Since the note is due in two years, Skylar will receive half of the payments in 2022 and the other half in 2023. Therefore, the payments received in 2022 are:

$99,800 + ($998,000 / 2) = $598,800

Substituting into the formula, we get:

Gain deferred = 0.7097 × $598,800 = $424,879.16

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Answer:

1/8

Step-by-step explanation:

1/4 of a painting in 2 weeks would be 1/8 painting for 1 week

Answer:

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

The correct statement that describes how the slope relates to the height of the water in the pool is:

The height of the water increases 2 inches per minute.

The slope of the line represents the rate of change of the height of the water with respect to time. In this case, since the slope is 2, it indicates that for every minute that passes, the height of the water in the pool increases by 2 inches.