In right triangle abc, altitude cd with length h is drawn to its hypotenuse. we also know ad = 12 and db = 3.

There are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

A number system is defined as a system of writing to express numbers.

The factorial 4! is 24

Factorial value of 3!=6

Factorial value 2!=2

Factorial value 1!=1

4! x 3! x 2! x 1! =24×6×2×1=288

288 can be written as a product 2 and 144 which are perfect squares.

So 2 and 144 are the divisors of 4! x 3! x 2! x 1!

Hence, there are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

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Answer:

x = - √2/2

Step-by-step explanation:

We know that x = rcosθ and y = rsinθ. The unit circle always have radius of 1 unit. Therefore, r = 1 as defined. Hence:

x = cosθ, y = sinθ

x = cosθ, θ = arcsin(y)

x = cos{arcsin(-√2/2)}

Find the measurement or θ that makes sinθ = -√2/2 and that is π + π/4 = 5π/4.

x = cos(5π/4)

And cos(5π/4) = - √2/2 as well. Hence, x = - √2/2.

Answer:

(6, 5 )

Step-by-step explanation:

3x + 2y = 28 → (1)

5x - 3y = 15 → (2)

multiplying (1) by 3 and (2) by 2 and adding the result will eliminate y

9x + 6y = 84 → (3)

10x - 6y = 30 → (4)

add (3) and (4) term by term to eliminate y

19x + 0 = 114

19x = 114 ( divide both sides by 19 )

x = 6

substitute x = 6 into either of the 2 equations and solve for y

substituting into (1)

3(6) + 2y = 28

18 + 2y = 28 ( subtract 18 from both sides )

2y = 10 ( divide both sides by 2 )

y = 5

solution is (6, 5 )

The explicit formula for an arithmetic sequence whose common difference is 8 and the first term is -2 is

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

The sequence is given by the formula

nth term = a + (n - 1) * d

where a = first term

n = the term

d = common difference

In the problem, d = -2 and a = 8, because of this we have

= a + (n - 1) * d

= 8 + (n - 1) * -2

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Answer:

Step-by-step explanation:

7

The solution is Option B.

Number of seats for the students is given by the equation A = 231 seats

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of seats for the students be A

Now , the equation will be

The total number of buses = 3 buses

The total number of seats on each buses = 80 seats

So , the total number of seats = number of buses x number of seats on each buses

Substituting the values in the equation , we get

The total number of seats = 80 x 3

The total number of seats = 240 seats

Now , the teachers has 3 seats each on 3 buses

So , the number of seats for teachers = 3 x 3 = 9 seats

And , the remaining number of seats = total number of seats of students

The total number of seats for students A = total number of seats - number of seats for teachers

Substituting the values in the equation , we get

The total number of seats for students A = 240 - 9

The total number of seats for students A = 231 seats

Therefore , the value of A is 231 seats

Hence , the number of seats for students is 231 seats

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Answer:

the answer is A

[tex]x + 7 > 3[/tex]

To determine if three measures can make a triangle, use the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.

for example

side 1 = 6

side 2 = 8

side 3 = 10

6 + 8 = 14 > 10,

therefore the three sides can make a triangle.

1. Gather the three measures of the triangle.

2. Add the two smallest side lengths together.

3. Compare the sum of the two smallest sides to the longest side.

4. If the sum of the two smallest sides is greater than the longest side, then the three measures can make a triangle.

5. If the sum of the two smallest sides is not greater than the longest side, then the three measures cannot make a triangle.

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The meaning of adjoining  is nearby or next to.

The terms neighboring, adjoining, contiguous, and juxtaposed denote close closeness. Adjacent may or may not indicate touch, but it always implies the lack of something like in between. A home with a garage attached. Adjoining means meeting and touching at some point or line. Two nearby dwellings are an example of adjacent. People on our block are typically considered our neighbors.

In the English language, “adjacent to” means “next to.” For two angles to be adjacent, they must meet the following three conditions: 1. The two angles must share (or have the same) side. 2. They must share a vertex (i.e. a common starting point for the sides).

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PS is the length of either segment multiplied by two ,PS is 38.

A line connecting the vertex with the middle of the other side forms the median angle. As a result, we may state that PR = QS for the provided.

By equating PR and QS, we can determine X's value.

PR = QS

5x-11 = 2x+7

Combine related terms to get 5x-2x = 7+11; divide both sides by 3 to get the x value; and last, multiply the result by 2 to get x = 6.

Find the value of PR and QS, and we'll demonstrate that two are equal as a result.

Correct: 5(6)-11 = 2(6)+7 19 = 19.

PS is the length of either segment multiplied by two, or simply the product of PR and QS.

PS = 19 x 2 = 19 + 19 = 38 (D) (D)

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When adding multi-digit numbers, it's a good idea to employ the commutative property. However, counting up becomes simpler if pupils are aware that they can change the order of the addends and begin adding with the larger number FIRST.

According to the commutative property of addition, the sum is unaffected by changes in the order of the numbers being added. The commutative property of addition can be defined as the fact that adding two integers in any sequence results in the same result. Here, a and b may be fractions, decimals, whole numbers, or even integers.

For instance, 1+2=2+1 and 2x3=3x2.

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1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.

To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.

To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.

Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.

2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.

To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player

3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

The reciprocal of the fraction 2/3 is 3/2

4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.

Let's call the cost of a silver ticket x.

The cost of a gold ticket is x + 8.

We know that Patrick spent 10x + 10(x+8) = $140

We can simplify that: 10x + 10x + 80 = 140

Then we have 20x + 80 = 140

Then we have 20x = 60

And x = 3

Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11

5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.

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The function which can which can define the number of flowers in the arrangement is f(x) = 64 + 18x. The domain is found to be [ 0 , 5 ] and the range is [ 64 , 154 ].

Let the number of flowers which is to be calculated be x,

now we know that she already have 64 flowers and that each arrangement will have 18 flowers.

Therefore, the number of flowers can be given by the function , f(x) = 64 + 18x.

Now , we know that the maximum number of flowers which she can buy externally is 5 , which means the domain becomes  [0,5] .

To find the range we will put the value of domain in the given function.

when x = 0 ,

f(0) = 64

when x = 5,

f(5) = 154

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As per the given equation the height of the cliff is 196.225 feet.

We know that the distance an object falls varies directly as the square of the time it is in motion, meaning that the distance is proportional to the square of the time. If we let d be the distance fallen and t be the time, we can write this relationship as [tex]d = kt^2[/tex] for some constant of proportionality k.

We also know that when an object falls for 3 seconds, it falls 144.9 feet. We can use this information to find the value of k:

[tex]144.9 = k(3^2)[/tex]

k = 16.1

Now that we know the value of k, we can use it to find the distance fallen when the time is 3.5 seconds:

[tex]d = kt^2\\d = 16.1(3.5^2)\\d = 16.1(12.25)\\d = 196.225[/tex]

So, the height of the cliff is 196.225 feet.

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The student is testing each soil's permeability, and soil X is more permeable than soil Y. The correct option is A.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.

Porosity can be defined as the quality of the material having pores or holes. The permeability can be defined as the state or quality of a material that allows liquids or gases to pass through it.

The soil which does not hold much water can be considered of high porosity and high permeability. As it is only possible if the soil has a large number of pores and it is not in compact form.  

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The manager should expect the defective nails of 350-pound delivery to contain 23.3 pounds .

The defect rate is a measurement of the proportion of production units that are flawed or useless relative to a certain number of units. Businesses use this assessment to assess the quality of their products and how they affect their bottom line. Although lower rates are desired, no industry has a set acceptable fault rate. Therefore, businesses must choose their goal defect rate.

Defect rate is crucial because it enables firms to calculate the proportion of output units that fail quality checks. This assists the firms in identifying any issues with quality control or manufacturing and estimating the cost of each fault. To estimate the profitability of a product, businesses can also compare failure rates among comparable or dissimilar products.

In ever 4.5 pounds of nail defective nails are = 0.3 pounds

In ever 1 pounds of nail defective nails are = 0.3/4.5 pounds

In ever 350 pounds of nail defective nails are = (0.3/4.5)*350 pounds

⇒ the defective nails in 350 pounds of nails= 105/4.5

⇒ the defective nails in 350 pounds of nails= 23.3 pounds

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A)There are 88 trader sell only one fruit.

B) There are 46  trader sell only two fruit.

Since there are three sets, use the formula

n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)

A represents apple traders = 40

O represents orange traders = 46

M represents mangoes traders = 50

A∪O∪M = total traders = 100

A∩O = 14

O∩M = ?

A∩M = 15

A∩O∩M = 10

B) Substitute values into the formula

100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10

100 = 146 - 29 - O∩M

100 = 117 - O∩M

Make O∩M subject of formula

O∩M = 100 -117

O∩M = 17 traders

Now,

n(A∩O) -n(O∩M) - n(A∩M)

= 14 + 17 + 15

= 46

Therefore, the number of traders that sells two fruits  are 46.

A) oranges n(O)

= 46-(4+10+ x)

= 32

Again,

mangoes n(M).

= 50-(5+10+x)

= 35

Now,

apple n(A)

= 40-(4+10+5)

= 21

Now, adding all of them we get:

n(o) + n(M) + n(A) = 32 + 35 + 21

                            = 88

Therefore, 88 trader sells only two fruit

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The Slope of log - log graph  represents the power of the relationship, and a straight line which indicates that there exists a definite power relationship .

What is Logarithm ?

The Logarithm is defined as  power to which a number must be raised to get some other number .

A log-log plot is the plot in which  both the x-axis  and y-axis use a log scale.

The plot of  logarithms of variables helps in extracting  the information about the power relationship. The case of  freely falling object is  used to illustrate a log - log plot.

A plot of the logarithm of freefall distance as a function of logarithm of time gives  a straight line of slope 2.

Therefore , The slope of log-log plot gives the power of relationship, and a straight line indicating that a definite power relationship exists.

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Answer:

no sign (not positive or negative)

Step-by-step explanation:

The value of the expression

4.3 ⋅ (-3.2) ⋅ 0

is 0, as the value of any number multiplied by zero is 0.

The number zero is neither positive or negative; hence there is no sign.

Answer: 10.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

The solution of the set of equations: 6x - 2y = 8; 3x + 7y = 68  is (4,8)

The problem can be solved using elimination - substitution method.

Set of equations:

6x - 2y = 8   .... (equation 1)

3x + 7y = 68 ..... (equation 2)

Divide equation 1 by 2

3x - y = 4   ..... (equation 3)

Eliminate x by substracting equation 3 from equation 2:

3x + 7y = 68

3x   - y  = 4    _

      8y = 64

         y = 64/8

        y = 8

Substitute y = 8 into equation 3:

3x - 8 = 4

3x = 12

x = 12/3

x = 4

Hence, the solution is (4,8)

Your question is incomplete, but most probably your question was:

What is the solution for the following set of equations 6x - 2y = 8; 3x + 7y = 68 ?

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If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then there will be a total of 345 dragons in this year.

The percentage increase in the number of dragons in Westeros rose = 15%

The total number of dragons in Westeros rose in previous year = 300

So, for calculating the total number of dragons in Westeros rose in this year we will first find the value of 15% of 300 and then add it to 300.

So, finding the value of 15% of 300

As we know, for removing the percentage sign we will divide the given number by 100

So, the value of 15% of 100 = (15/100)*300 = 45

So, the value of the total number of dragons in Westeros rose in this year will be 300+45 = 345

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The correct question may be like:

If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then what will be a total of dragons in this year?

The degree of the polynomial  [tex]2yA^2yA^32y^8[/tex] is 15

A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a degree of 6.

This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.

As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]

The total sum of power is: 1+2+1+3+8=15

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On solving the provided question, we can say that the mean that 6 tests including the last test brian took.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

(91n + 98) / (n + 1)  =  92

    91n + 98  =  92(n + 1)

 91n + 98  =  92n + 92

 98  =  n + 92

6  =  n

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False. Using the unit rate of cost per pound, 5 pounds of apples cost $6.00.

Cost per pound = $12.00 / 8 pounds = $1.50

5 pounds of apples cost = 5 pounds x $1.50 = $7.50

The unit rate of cost per pound can be calculated by dividing the total cost of 8 pounds of apples by the total number of pounds. In this case, the unit rate of cost per pound is $1.50. This means that for every pound of apples, the cost is $1.50. To calculate the cost of 5 pounds of apples, we need to multiply the unit rate of cost per pound by the number of pounds. In this case, 5 pounds of apples cost $7.50, which is calculated by multiplying $1.50 by 5. Therefore, the statement that using the unit rate of cost per pound, 5 pounds of apples cost $7.50 is false.

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Answer:

50x - 200y = 75

3x + y = -5

Step-by-step explanation:

Standard form of a line

Ax + By = C

0.5x +-2y -0.75  Multiply through by 100

50x - 200 - 75 = 0  Add 75 to both sides

50x - 200y = 75

y = -3x - 5  Add 3x to both sides

3x + y = -5

Scale factor required to map the first line segment onto second line segment is 3/9=0.33

The scale factor is the ratio of the length of the image to the length of the pre-image.

In this case, we're looking for the  that would map the first line segment (length 9cm) onto the second line segment (length 3cm).

To find the scale factor, we can divide the length of the image by the length of the pre-image:

scale factor = length of image / length of pre-image

In this case:

[tex]ScaleFactor=\frac{Length Of Image}{Length Of Pre-image}[/tex]

[tex]scale factor = 3cm / 9cm = 1/3=0.033[/tex]

So the scale factor to map the first line segment onto the second line segment is 1/3.

It means the 1st line is 3 times longer than the second one.

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Point p is further from 0 than point q, and to the left of point q.

The correct option is D.

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

Points p and q are negative integers plotted on a number line.

And |p| > |q|.

That means,

The absolute value of p is greater than the absolute value of q.

|p| and |q| are the positive integers.

So, p < q.

So, the q is closer to zero.

And p is left to point q.

Therefore, the q is closer to zero and p is left to point q.

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2) y+ 3÷y is the equation that is not a polynomial. Using addition, subtraction, multiplication, and division of numbers .

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).

given

An algebraic mathematical equation known as a polynomial might have two components. coefficients and parameters

You can combine the solutions to these algebraic equations to achieve the result.

It follows the general formula as follows:

a + a1 + a+ …

2)y+ 3y is the equation that deviates from the formula above.

So, 2)y+ 3y is the equation that is not a polynomial.

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10.  This system has one solution with coordinates (1, -2)

11. This system has one solution with coordinates (0,-3)

12. This system has one solution with coordinates(-1, -2)

13. This system has no solution.

14. This system has no solution.

16.   This system has one solution with coordinates (0,-4)

According to question:-

10. y = x - 3 ------- 1

y = -5x + 3 ------- 2

substitute 1 in 2,

x - 3 = -5x + 3

x = 1

y = 1 - 3 = -2

y = -2

The co-ordinates is (1,-2)

11. y = -3

substitute in y = x-3

-3 = x - 3

x = 0

The co-ordinates is (0,-3)

12. y = 4x + 2 --------- 1

y = -2x - 4 ------------2

Substitute 1 in 2,

4x + 2 = -2x - 4

6x = -6

x = -1

substitute x = -1 in 2

y = -2

The co-ordinates is (-1, -2)

13. y = x - 6 -----1

y = x+ 2 -------2

It has no solution, so there is no co-ordinates.

14. x + y = 4

3x + 3y = 12

It has no solution, so there is no co-ordinates.

16. 2x + 3y = 12 ------1

2x - y = 4 --------2

from 2 we rewrite the equation as y = 2x-4

Sub in eq 1

2x + 3(2x-4) = 12

2x + 6x - 12 = 12

8x = 24

x = 3

y = 2

The co-ordinates is (3,2)

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