What is the value of x in the solution for the system of equations 6x−3y=27 and 18−2y=2x ?

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The radius of circle is 41.5.

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Answer:

the face value of the loan is $5,263.16.

Step-by-step explanation:

To determine the face value of the loan, we need to use the formula:

Face Value = Proceeds / (1 - Discount Rate * Time)

where "Time" is the time period of the loan in years.

Since the loan is for 6 months, we need to convert this time to years by dividing it by 12. Therefore, "Time" = 6/12 = 0.5 years.

Now, we can substitute the given values into the formula:

Face Value = 5,000 / (1 - 0.1 * 0.5)

Face Value = 5,000 / (1 - 0.05)

Face Value = 5,000 / 0.95

Face Value = $5,263.16 (rounded to the nearest cent)

Therefore, the face value of the loan is $5,263.16.

Answer:

Step-by-step explanation:

Given: In triangle ABC, AB = AC and D is the midpoint of BC.

To prove:

i) AD is perpendicular to BC.

We can prove this by using the midpoint theorem, which states that a line segment connecting the midpoints of two sides of a triangle is perpendicular to the third side and half as long as the third side.

Since D is the midpoint of BC, we have BD = DC. Thus, the line segment AD connects the midpoints of sides AB and AC of triangle ABC.

By the midpoint theorem, AD is perpendicular to BC and AD = BC / 2.

ii) AD bisects angle BAC

We can prove this by using the fact that if two line segments are perpendicular and one is an altitude of a triangle, then the two line segments divide the triangle into four smaller triangles that are congruent by SAS congruence.

Since AD is perpendicular to BC, we have two right triangles, ABD and ACD. By the Pythagorean theorem, we have AB = AC, which means that ABD and ACD are congruent by SAS congruence.

Since ABD and ACD are congruent, we have angle BAD = angle CAD. Also, since angle BAC is the sum of angles BAD and CAD, we have angle BAC = 2 * angle BAD.

Therefore, by substitution, we have angle BAC = 2 * angle CAD. This means that angle CAD is half of angle BAC, or in other words, AD bisects angle BAC.

Hence, we have proved that in triangle ABC, AD is perpendicular to BC and AD bisects angle BAC.

Answer:

Step-by-step explanation:

we can determine the maximum height using the expression given after finding the value of time at which the object reaches the maximum height. In order to find the time at which the object reaches the maximum height we need to use one of the UAM formulas.

and the compatible UAM formula is: vf=vi+at, we use UAM formula because the object is uniformly accelerating due to gravitational force.

vf=vi+at, at the point where the object reaches the maximum height its velocity will be zero so vf=0 and vi=29.4m/s.

given

a=-9.8m/s^2

vf=0

vi=29.4m/s

t=?

0=29.4-(9.8)t

-29.4= -9.8t

t= 29.4/9.8

t=3 seconds, it takes 3 seconds to reach the maximum height starting from a height of 30m.

h=30+29.4(3)-4.9(3)^2

h=30+88.2-44.1

h=118.2-44.1

h=74.1 m

The numerical value of y in the function y = 8 - 2x when x equals 8 is -8.

A function is simply a relationship that maps one input to one output.

Given the function in the question;

y = 8 - 2x

To determine the value of y, replace all occurrences of x in the function with 8 and simplify.

y = 8 - 2x

Plug in x = 8

y = 8 - 2( 8 )

y = 8 - 16

y = -8

Therefore, the value of y is -8.

Option B) -8 is the correct answer.

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In the triangle  ΔJKL,  the length of side k found using the law of cosines is approximately 1764 inches.

What is meant by the law of cosines?

The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

If ABC is a triangle, then as per the statement of cosine law,  we have:

c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]

where,

c = length of side c

a = length of side a

b = length of side b

γ = angle opposite c

Given a triangle, ΔJKL

The length of side l= 920 inches

The length of side j = 880 inches

∠K = 157°

According to the law of cosines,

k² = l² + j² - 2.l.j . cos K

  = 920² + 880² - 2 * 920 * 880  * cos (157°)

=  846400+ 774400 - (-1490481.46)

= 3111281.46

k = 1763.88 = 1764 inches.

Therefore the length of side k found using the law of cosines is approximately 1764 inches.

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ABCD is a parallelogram.

The proof is given below.

A special form of quadrilateral called a parallelogram has both pairs of opposite sides parallel and equal.

Given:

ABCD is a quadrilateral.

The diagonal of ABCD are AC and BD.

∠1 ≅ ∠2

That means AB = CD. (the sides of opposite angles)

And BE = ED.

and BD bisect AC at E.

That means BE = BD.

To prove ABCD is a paralleogram:

∠AED ≅ ∠BED (opposite angle)

And EC = AE (given)

So, BC = AD.

The sides are equally spaced because the diagonals bisect each other.

So, the opposite sides are parallel.

Therefore, ABCD is a parallelogram.

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The name of the relationship is b. Alternate interior angles.

Alternate interior angles are two angles that are located on opposite sides of a transversal line, but within the same two lines. When two lines are cut by a transversal line, the alternate interior angles are always congruent, meaning that they have the same measure.

In this case, angles ∠1 and ∠4 are alternate interior angles. Alternate interior angles are formed when two parallel lines are cut by a transversal line. When this happens, corresponding angles are formed on the same side of the transversal.

The alternate interior angles are the two angles that are on opposite sides of the transversal. These angles are also congruent, meaning that they have the same measure.

To summarize, alternate interior angles are two angles that are located on opposite sides of a transversal line and within the same two lines. In this case, angles ∠1 and ∠4 are alternate interior angles, meaning that they have the same measure.

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To calculate the mathematical value of 20, you would use the  : 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.

ASL stands for American Sign Language. It is the visual language used by the deaf and hard of hearing communities to communicate. In ASL, the sign for the number 20 is done by holding up both hands with the palms facing out and fingers spread apart. The hands are then moved together in a circular motion with the fingers crossed at the end. This sign is also used to represent the mathematical concept of multiplication. To express the value of 20 in ASL, you would sign the number 20 by making the above mentioned sign, and then sign the word "equals". To calculate the mathematical value of 20, you would use the formula: 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.

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The value of the given expression increases, because as x decreases, 5/x increases

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, what happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number,

We know that, If the denominator of the fraction is decreased, the value of a fraction is increased while the numerator remains unchanged.

Therefore, if the value of x in the given starts decreasing the value of the whole fraction will start increasing.

Hence, the value of the  expression increases, because as x decreases, 5/x increases

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A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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Answer:

the answer should be negative one and one-fourth, negative one -half

Step-by-step explanation:

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15 solids found in the house and their mass are:

15 liquids and volumes of these liquids :

Some typical solid objects that can be found in a typical house would be chairs, tables, televisions, lamps and lampshades and tableware like plates, bowls, and spoons.

As for liquids, there is milk, mustard and ketchup. Then there are the cleaning liquids such as shampoos and hand sanitizers.

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The present value of the payment is: $25,015.42

Now, According to the question;

An annuity is series of equal annual payments or receipts made for a certain number of years.

A delayed annuity is that which the first cash flow occurs at a time later than year one.

A standard annuity is that which the first cash flow occurs a year from now.

An advanced annuity is that which first cash flow  occurs immediately or now.

$5,100 per where the first payment occurs in year 6 and end 20 years from today is an example of a delayed annuity.

Present Value = A ×( 1 - (1+r)^(-n))/r

                       = 5,100 × ( 1 - (1+0.079)^(-11))/0.079

                      = 36,586.01

Present Value = Future Value × (1 + r)^(-n)

Present Value = $ 36,586.01  × (1+0.079)^(-5)

Present value = $25,015.42

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The total cost of the ticket is 125.35 dollars.

A ticket to an all day concert is priced at $115, plus an additional 9% sales tax.

The statements that describes how to find the total cost of the ticket can be represented as follows:

sale tax = 9% of 115

sale tax = 9  / 100 × 115

sale tax = 1035 / 100

sale tax = 10.35 dollars

Therefore,

total cost = 10.35 + 115

total cost = 125.35 dollars

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Answer: 7/80

Step-by-step explanation: This is already the simplest form of this fraction.

Answer: 7/80

Step-by-step explanation:

Answer:

236

Step-by-step explanation:

number of chairs left = total chairs - 7 chairs

total chairs = 9 × 27

= 243

243 - 7

= 236

Answer: 236

Step-by-step explanation:

We have to figure out how many chairs there are in total so you will do 9*27. That is 243. If 7 were removed, you would do 243-7 which is 236. Therefore, there are 236 chairs left.

Answer:

Part A
x + y = 150

Part B
7x + 5y = 850

Part C
Solution is x = 50, y = 100

there are 50 adult tickets and 100 student tickets sold

Step-by-step explanation:

Let x = number of adult tickets and y= number of student tickets

We have the following equation

x + y = 150        (1)   =>total number of tickets

7x + 5y = 850   (2)  > total cost of x adult and y student tickets

Multiply (1) x 5:

5x + 5y = 750    (3)

Subtract (2) - (3)

7x + 5y - (5x + 5y) = 850 - 750

7x - 5x + 5y - 5y = 100
2x = 100

x = 50

y = 150 - 50 = 100

Answer:

The maximum battery life is 27 hours

Step-by-step explanation:

The box plot represents the number of hours of battery life in different cell phones.

We have to find the maximum battery life.

What is box plot?

The box plot is a type of chart often used in explanatory data analysis.

Now,

By figure the maximum life of a battery is 27 hours.

Hence, The maximum battery life is 27 hours.

Answer:

x = 9

Step-by-step explanation:

if three or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally , that is

[tex]\frac{3}{x}[/tex] = [tex]\frac{2.5}{7.5}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )

x = 3 × 3 = 9

Answer:

a

Step-by-step explanation:

The required highest common factor of 25, 75, and 150 is 25.

The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.

To find the HCF of 25, 75, and 150, we can first find the prime factorization of each number and then look for the common factors.

Prime factorization of 25,  25 = 5²

Prime factorization of 75:, 75 =  5² × 3

Prime factorization of 150,  150 = 2 × 3² × 5²

The largest factor that all three numbers have in common is 5², which is 25.

So, the HCF of 25, 75, and 150 is 25.

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The coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis include the following:

P" = (-4, 0).

Q" = (-(3), 1) = (-3, 1).

R" = (1, -2).

In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of triangle P′Q′R′, the coordinates of triangle P′′Q′′R′′ include the following:

(x, y)                               →              (-x, y)

Coordinate P' = (4, 0)   →  Coordinate P" = (-(4), 0) = (-4, 0).

Coordinate Q' = (3, 1)   →  Coordinate Q" = (-(3), 1) = (-3, 1).

Coordinate R' = (-1, -2)   →  Coordinate R" = (-(-1), (-2)) = (1, -2).

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To convert kilometers per hour (kph) to miles per hour (mph), we use the following formula: mph = kph x 0.621371. This is because there are 0.621371 miles in a kilometer.

To calculate the value of 130 kph in mph, we can simply plug the value into the formula: mph = 130 x 0.621371 = 80.78 mph. Therefore, the value of 130 kph in mph is 80.78 mph. To further understand how this conversion works, we can break down the calculation into its basic components. First, we divide 130 by 1. That gives us 130. Then, we multiply 130 by 0.621371, which gives us the result of 80.78. Therefore, the value of 130 kph in mph is 80.78 mph. The above formula and calculation can be used to convert any value from kph to mph. All we need to do is plug the kph value into the formula and we will get the equivalent mph value. It is important to note that the conversion from kph to mph is not exact, as there are slight variations in the exact value of a kilometer. However, this formula provides a good approximation and is accurate enough for most purposes.

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Answer:

Step-by-step explanation:

Ans:n^th=2n-1

we are going to use the formula of arithmetic sequence.

We need to find the first term of the sequence which is 1 and find the difference between any two number.

Then simply multiply the different by (n-1)

Finally add the result with first term which is 1.