What is the equation of the line that has a slope of -3 and contains a point (-2,3) ?

As per the system of equation, a. 3y = -12x + 6 l y= -4x+ 2 has infinite number of solutions.

The rule to identify the number of solutions to the system of equation is written as,

In the given equation (a1/a2) ≠ (b1/b2), then there will be a unique solution.

Where as If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions.

Finally If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution.

Here we have given that pair of equations to show if the system has no solution, one solution, or infinitely many solutions.

Here we have to take the first equation

a. 3y = -12x + 6 l y= -4x+ 2

Now, we have to write it in the standard form, then we get,

=> 12x + 3y = 6, 4x + y = 2

Here the values of a1 = 12, b1 = 3, c1 = 6 and the values of a2 = 4, b2 = 1 and c2 = 2.

When we take the rule of system of equation we have identified that

=> 12/4 = 3/1 = 6/2

=> 3/1 = 3/1 = 3/1

Therefore, this one has the infinite number of solution.

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Answer:

Direct Variation

y = 3x

y = (2/7)x

y = -0.5x

NOT Direct Variation:

x = -1

y = 4

y = 22x + 7

Step-by-step explanation:

Direct Variations are in the form

y = kx

This is very similar to:

y = mx + b except the b MUST be zero.

Also, direct variations always go through (0,0) that's why b must be 0.

So easy to pick out:

y = 3x

y = (2/7)x and

y = -0.5x are all in the form y = kx and have a y-intercept of zero.

y = 22x + 7 has that extra +7 tacked on to the end of the equation. It does not go through (0,0). It has a b that is 7. So it starts at (0,7). It is not a direct variation.

The other two, x = -1 and y=4 are both not direct variations. Neither starts at (0,0).

x=anumber is a vertical line and y=anumber is a horizontal line. These are not direct variations.

Answer:

  ₹1400

Step-by-step explanation:

You want to know the monthly installment when a refrigerator costing ₹34500 is paid for with ₹6500 down and 24 payments that include 10% simple interest.

The amount remaining after the ₹6500 down payment is ...

  ₹34500 -6500 = ₹28000

The amount to be repaid in installments will be this amount with 2 years' finance charge:

  ₹28000 × (1 +rt) = ₹28000 × (1 +0.10·2) = ₹28000×1.20

  = ₹33600

When that is divided into 24 equal payments, each monthly installment is ...

  ₹33600/24 = ₹1400

Each monthly installment is ₹1400.

For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.

A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.

Z is the number of standard deviations from the mean given by the formula:

z = ( X - μ ) ÷ ( σ )

where

x is the raw score,

μ is the population mean, and

σ is the population standard deviation

A negative value means that the number of standard deviations of an observation is to the left of the mean.

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Answer:

Step-by-step explanation:

42 is an even number so it is divisible by 2

42 divided by 2=21

42 has digits that add up to give 6

If the sum of a number adds up to give 3, 6 or 9 that number is divisible by 3

42 divided by 3=14

Factors of 42 are 21 and 2 and 14 and 3 and 42 and 1

Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.

=) 2*pi*r = 42cm

=) 2*22/7 * r = 42cm

=) r = 42*7 / 2*22

=) r = 147/22 cm

Since Volume of cylinder = pi* r^2*h

= 22/7 * 147/22 * 147/22 * 16 cm^3

= 2245.09 cm^3.

SSS means side side side, SAS means side angle side and AAA means angle angle angle.

There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.

If three sides are given then we will use the SSS postulate

If two sides and one angle is given then we will use the SAS postulate

If three angles are given then we will use the AAA postulate.

Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.

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The Median of 10 and 24 is 17.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The mean and mode are the other two primary trends in addition to the median. The ratio of the total number of observations to the sum of all observations is known as the mean. The value that appears most frequently in the given data collection is called the mode.

Given,

First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median= [tex]\frac{10+24}{2}[/tex]= 34/2= 17

Therefore, The Median of 10 and 24 is 17.

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First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median = 34/2= 17

Therefore, The Median of 10 and 24 is 17.

The situation can be expressed in inequality as: 95x + 0.85y ≤ 500

On solving the maximum amount of miles that can be driven to stay under budget is 253

What is inequality?

If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

For example, x > 3 (x should be greater than 3)

According to the given question:

Total amount to spend is restricted to $500

Let the number of days be x and extra miles covered be y

The car rental company charges $95 per day to rent the car and charges $0.85 per mile.

Therefore the situation van be expressed as:

95x + 0.85y ≤ 500

If the car is rent for 3 days then the maximum amount of miles that can be driven to stay under budget are

95(3) + 0.85y ≤ 500

285 + 0.85y ≤ 500

0.85y ≤ 215

y ≤ 253

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How many pattern block trapezoids would create 2 hexagons?

Answer:

this it's no a math problem

The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.

Here,

The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.

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The number of rides that it would take for the quickpass to be less expensive would be 28 rides.

The monthly quikpass would cost $ 55 and give a person unlimited rides. The single ride on the other hand, would cost $ 2 per ride.

The number of rides till the monthly quikpass is cheaper, can be found by the formula:

= Cost of monthly quikpass / Cost of single rides

= 55 / 2

= 27.5 rides

= 28 rides

In conclusion, if a person takes 28 rides then the monthly quikpass would be less expensive.

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If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.

There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.

For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.

We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.

For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.

However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.

The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.

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The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

12n > 135 + 4.50n

In order to make a profit and solve inequality,

12n - 4.50n > 135

7.5n > 135

n > 18

Thus, it needed to sell more than 18 to make a profit.

Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".

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The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

Let the 3 numbers be x ,x+2 , x+4

The sum of numbers is 45

⟹x+x+2+x+4=45

3x+6=45

3x=39

x=13

Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the inverse of a number a is [tex]\frac{1}{a}[/tex]

then

the inverse of 2 is [tex]\frac{1}{2}[/tex]

Eye color is an example of a discontinuous variation, as the amount of colors is limited and individuals can only have one of these colors.Blood type is another example of a discontinuous variation, as individuals can only have one of the four blood types.

Discontinuous variation refers to characteristics that have only a limited range of values within a population. Eye color is one example of discontinuous variation, as the range of colors is limited and individuals can only have one of these colors. Similarly, blood type is another example of discontinuous variation, as it is determined by the presence or absence of certain antigens in the blood and individuals can only have one of the four blood types. Discontinuous variation is often inherited, determined by the presence or absence of certain genes or alleles. These variations are usually determined by a single gene with two alleles, one of which may be dominant and one of which may be recessive, leading to the limited range of values. Discontinuous variation, then, is an important part of the human population and helps to create the variety and diversity that exists within it.

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If the sum of two numbers is 36 and the larger number is 10 more than smaller number then the larger number is   .

the Sum of two numbers is given to be = 36 ;

also given that " larger number is 10 more than smaller number " ;

let the larger number be = "x" , and

the smaller number be = "y" .

So , according to the question ⇒ x + y = 36 ;

and x = y + 10 , putting x in above eqn.

we get , y + 10 + y = 36

2y + 10 = 36

2y = 36 - 10

2y = 26

y = 26/2 = 13

and x = 13 + 10 = 23 .

Therefore , the larger number is 23 .

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The domain of the function [tex]f(x)=\frac{1}{x}[/tex]  is all real numbers except 0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.

For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].

For this function, the domain is all the values x can take.

Here x cannot take 0 because 1/0 is not defined.

So, the domain of the function is all real values except 0 which can also be written as:

Domain= R-{0}

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Total 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

In the given question, we have to find how many "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

The given word is INQUISITIVE.

The total alphabets in the word INQUISITIVE is 11.

Let us first count the words without U and then insert U wherever applicable.

Now without U we have total 10 alphabets and the alphabet I is repeated by 4 times.

So permutations is 10!/4! = 151,200

Now we need to put U, we can see its 11 alphabets but U should not follow Q so it becomes 10 alphabets.

Hence, Total number of words = 151,200*10

Total number of words = 1,512,000

Hence, 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

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The rate of flow for emptying the tank would be 0.15 liter/minute.

The rate at which the water level in the tank is changing is given by the equation:

ΔV/Δt = flow rate in - flow rate out

where ΔV is the change in the volume of water in the tank, Δt is the time interval over which the change occurs, and flow rate in and flow rate out are the rates at which water flows into and out of the tank, respectively.

In this case, the flow rate is 0.15 liter per minute, and the flow rate out is 0.27 liter per minute. The volume of water in the tank is 4.8 liters.

To determine how long it will take to empty the tank, we can set the volume of water in the tank to 0 and solve for the time interval:

0 = flow rate in - flow rate out

flow rate out = flow rate in

0.27 liter/minute = 0.15 liter/minute

Since the equation is not balanced, we cannot determine the time interval. In order to determine the time interval, we need to have information about both the flow rate in and the flow rate out. Without this information, it is not possible to determine how long it will take to empty the tank.

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The relationship between a parallelogram's area, base, and height:

Area = Base x height

A parallelogram is just a flat shape having four parallel, straight sides that are congruent with one another.

Accordingly, a parallelogram is a closed shape, a flat figure, and a quadrilateral.

Therefore, each parallelogram is:

In such a parallelogram, the length among one side is referred to as the "base," and the length of the perpendicular segment connecting that side to the opposing side is referred to as the "height."

Area = base x height

Thus, a parallelogram's base can be any of its sides. A given parallelogram always has two base-height pairs.

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Yes, the number 16 is a square.

It is the square of the number 4, since 4 x 4 = 16.

A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.

The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.

Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.

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g

=

p

2

−

m

Step-by-step explanation:

3/2 is the quotient when 3/4 is divided by 1/2

When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the  fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.

When we divide one number by another, the result obtained is also known as quotient.

so in order to find the quotient when both fraction is divied

quotient of the division = [tex]\frac{3}{4}[/tex] ÷[tex]\frac{1}{2}[/tex]

=> (3/4) / (1/2)

=> (3/4) * 2

=> 3/2

so quotient of the division = 3/2 or 1.5

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The various output values are displayed on the y-axis and make up the range. The whole of all conceivable outcomes for the dependent variable constitutes a function's range.

The statistical range is the range of values between the highest and lowest for a particular data collection. Another way to represent the range is the difference between the highest and lowest observation. The sample interval is determined by subtracting the largest number from the lowest. For continuous variables, the sample range is a critical measure of variability.

here

A function y = f is an example (x).

The function's range is the range between all of the y values, from least to maximum.

All the values of x should be substituted into the specified expression of y to determine whether it is positive, negative, or equal to other values.

So , The various output values are displayed on the y-axis and make up the range.

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These values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

What is the limit?

A limit in mathematics is the value that a function approaches as its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.

We have,

f(x) = 4xe³ˣ / 1

f(x) = 4xe³ˣ

[tex]\lim_{x \to \infty} f(x) = ?[/tex]l

[tex]\lim_{x \to -\infty} f(x) = ?[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} 4xe^{3x}[/tex]

It is the form -∞ * 0 which is an undetermined form

Write it has a fraction then apply l'Hospital's Rule

[tex]\lim_{x \to -\infty} \frac{4x}{1 / e^{3x} } = \lim_{x \to -\infty} \frac{4}{ -3e^{3x} / e^{6x} }[/tex]

[tex]= \lim_{x \to -\infty} \frac{4}{-3/e^{3x}} } = \lim_{x \to -\infty} \frac{4e^{3x}}{ -3 }[/tex]

[tex]= \frac{4e^{-x}}{ -3 }[/tex]

[tex]= \frac{0}{ -3 } = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} 4xe^{3x}[/tex]

Simply evaluate

[tex]\lim_{x \to \infty} 4xe^{3x} = \infty * \infty = \infty[/tex]

 (∞*∞ is not an undetermined form).

f(x) = 4xe³ˣ

[tex]\lim_{x \to -\infty} f(x) = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hence, these values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

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The best way to find multiple missing numbers in a given integer array with duplicates in Java is to use a hash set and loop.

First, create a HashSet and add all elements from the array to it. Then, loop from 1 to the maximum element of the array and check if each number is present in the HashSet. If the number is not present, it is a missing number. To explain further, a hash set is an efficient data structure for storing unique elements of a collection, and using a loop to check for missing numbers ensures that all numbers from the array are accounted for.

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