8÷955 Dividing by one digit divisors

The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

The Following is the determination of the quadratic equation's solution;

2x² + 12x - 3 = 0

2x² + 12x = 3

multiply across by two

x² + 6x = ³/₂

Add the two sides of the equation after squarely multiplying the coefficient of x by half.

(x + 3)² = ³/₂ + 3²  + 6x + 9 =

9 + ³/₂ (x² + 6x + 9)

= 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

The complete question is : Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.

2(x2 + 6x + 9) = 3 + 18

2(x2 + 6x) = –3

2(x2 + =6x) = 3

x + 3 = 21/2

2(x2 + 6x + 9) = –3 + 9

(x + 3)2 = 6/2

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Answer:

x ≤ -3 or x ≥ 3

Step-by-step explanation:

Answer:

To solve this inequality, you can start by isolating the absolute value term on one side of the inequality. To do this, you can subtract 9x from both sides, which gives you:

|9x| - 9x ≥ 27 - 9x

|9x| - 9x ≥ -9x

Next, you can apply the properties of absolute values to simplify the expression. The absolute value of a number is always positive, so the absolute value of any expression will be equal to the expression itself if it is positive, and equal to the negative of the expression if it is negative.

Since the inequality is "greater than or equal to," you need to consider both cases.

If 9x is positive:

9x - 9x ≥ -9x

0 ≥ -9x

x ≤ 0

If 9x is negative:

-9x - 9x ≥ -9x

-18x ≥ -9x

-9x ≥ 0

x ≤ 0

In both cases, the solution is x ≤ 0. This means that any value of x that is less than or equal to 0 will satisfy the inequality.

To write this solution in interval notation, you can use the notation [0,∞) to represent all values of x that are greater than or equal to 0. Alternatively, you can use the notation (-∞,0] to represent all values of x that are less than or equal to 0.

Step-by-step explanation:

If all the letters have the same frequency then they have may or may not be  equal codes.

What is Huffman encoding?

A lossless data compression algorithm is Huffman coding. Input characters are given variable-length codes, the lengths of which are determined by the frequency of the matching characters.

The variable-length codes (bit sequences) assigned to input characters are Prefix Codes, which indicates that no other character will have a code that is the prefix of the code assigned to that character. This is how Huffman Coding ensures that the produced bitstream cannot contain any ambiguities during decoding.

Let's use a counter example to better grasp prefix codes. Assume that the four characters a, b, c, and d have the variable length codes 00, 01, 0 and 1, respectively. Because the code assigned to c is the prefix of the codes assigned to a and b, this coding causes uncertainty. If the bit stream being compressed is 0001, the decompressed output might be "cccd," "ccb," "acd," or "ab."

In huffman coding, if two nodes have the same frequency, they are considered to be identical for compression reasons, therefore you can select either one and gain an equal amount of compression.

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The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

Suppose that we have a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

In which:

The function in this problem is defined as follows:

f(x,y) = xe^(3xy).

Applying the product rule, the partial derivative relative to x is given as follows:

fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).

Applying the chain rule, the partial derivative relative to y is given as follows:

fy(x,y) = 3x²e^(3xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

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Answer: 22.5 and 67.5

Step-by-step explanation:

A complementary angle means that two angles add up to 90°

If one angle is 3 times the other,

let x be the value of the other angle.

The bigger angle would be 3x.

Therefore,

3x+x=90°

4x=90°

x=22.5

22.5 is the measure of the smaller angle

and 22.5x3=67.5 would be the other (larger) angle.

Answer:

22.5 degrees and 67.5 degrees

Step-by-step explanation:

3x + x = 90

4x=90

x=90/4

x=22.5

other angle is 3x which is 67.5

No, the injection and surjection do not have to come from the same function for there to exist a bijection between the two sets.

A bijection is a mathematical function that establishes a one-to-one correspondence between two sets, known as the domain and codomain. This means that for every element in the domain, there is exactly one element in the codomain, and vice versa. A bijection is both an injection and a surjection, meaning that it is both injective and surjective. Injective means that each element in the domain is mapped to a unique element in the codomain, while surjective means that every element in the codomain is mapped to at least one element in the domain. Therefore, a bijection establishes a perfect match between the two sets, where each element of one set is paired up with a unique element of the other set.

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The triangle should have 4.35 metres of wire, which means the square should have 6.978 meters

Let "x" is the cutting distance from one end of the wire.

Then, area of square would be ,

 Area =  (x/4)²

The side of equilateral triangle would be,

 L=(10-x)/3

height would be (10-x)/3*√(3)/2

=> (10-x)√(3)/6

So, the area of triangle is

Area of triangle= ((10-x)/3)² ×√(3)/4

=> (10-x)² ×√(3)/36

So, the total area is ,

A = (x/4) + (10 - x)²/36√3

Differentiating Area w.r.t x

dA/dx=x/8-2 ×√(3)/36(10-x)

=> x/8+20× √(3)/36-2 × √(3)/36x

Putting the expression equal to 0,

x/8+20× √(3)/36-2 × √(3)/36x = 0

=> x(1/8+ √(3)/18

=> 10√(3)/18

x*0.22122 = 0.96225  

 x=4.35

Substituting the value of x

This corresponds to minimum area which is:

 A(4.35)=(4.35/4)^2+(10-4.35)^2 × √(3)/36=1.183+1.536

=> 2.719m²

Thus , the minimum area is 2.71 square meters when x=4.35 m. As a result, the wire should be cut such that the dimension of the square is formed by the piece having a length of 4.35 m, and the equilateral triangle is formed by the piece having a length 5.65 m.

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A ∝ 1/M

A = K/M

A is the acceleration and M is the mass of the object.

The object's acceleration for an object of mass 13 kg is 4 m/s²

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass.

This means,

A ∝ 1/M

A is the acceleration and M is the mass of the object.

Now,

A = K/M

26 = K / 2

K = 26 x 2

k = 52

Now,

M = 13

A = K/M

A = 52/13

A = 4 m/s²

Thus,

The object's acceleration for an object of mass 13 kg is 4 m/s²

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On solving the provided question, we got to know that - distance she covered from her starting position is 2731 miles

If two things are equal, an equation declares it. A "=" equals sign will appear in the format: 7 + 2 = 10 − 1 What is on the left (7 + 2) equals what is on the right (10 1), according to that equation. The statement "this equals that" is analogous to an equation.

The flight's first leg is 1020 miles long and lasts (1.5 hours) at 680 mph. We'll refer to this as our triangle's side B.

The second leg of the journey is 1360 miles (2 hours x 680 mph) long. We'll refer to this as the triangle's side C.

The law of cosines allows us to determine the triangle's side a's length.A is a 170° angle between the two sides whose lengths we are aware of. (180° - 10° = 170°).

[tex]a^2 = b^2 + c^2 - (2)*(a)*(b)*cos(A)[/tex]

[tex]a^2 = (1020 miles)^2 + (1360 miles)^2 - (2)*(1020 miles)(1360 miles)*cos(170)\\ a^2 = 1040400 miles^2 + 1849600 miles^2 - (2774400 miles2)*cos(170)\\ cos(170) = -0.9848\\ a^2 = 2890000 miles^2 + 2732251 miles^2 = 5622250.6 miles^2\\ a = (5622250.6 miles^2)^{\frac{1}{2} } = 2371 miles[/tex]

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Balloon's altitude = 43.7ft as

change in altitude/500 = tan 5°  

change in altitude = .0875*500

                              =43.7ft

Answer:Antonio drove 24 miles west

Step-by-step explanation: 50-26=24

Answer:

Given, x²+y²+4X −2y= −1

⇒x²+4x+y²=−1

⇒(x²+4x+4)+(y² −2y+1) =−1+4+1

⇒(x+2)²+(y−1) = 2²

Clearly, = (−2,1)

Radius = 2

The radius of the circle is 2. Therefore, A) is the answer

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Given the equation of the circle as x² + y² + 4x - 2y = -1

Factorize the equation using the completing square:

x² + y² + 4x - 2y = -1

x² + 4x + (2)²  + y² - 2y + (-1)² = -1 + (2)² + (-1)²

(x+2)² + (y-1)² = -1 + 4 + 1

(x+2)² + (y-1)² = 4

(x+2)² + (y-1)² = 2²

Comparing this equation with (x-a)² + (y-b)² = r²:

r = 2

Thus, the radius of the circle is 2

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The system of equations representing the charges for plans A and B include the following:

y = 0.2x - 50

y = 0.3x - 105

A graph of the system of equations for plans A and B are shown in the image attached below.

In order to write the system of equations representing the charges, we would have to calculate the slope of the line based on the data points described above for each plans.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (66 - 50)/(580 - 500)

Slope, m = 16/80

Slope, m = 0.2

At point (500, 50), a linear equation for plan A can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the point-slope form formula, we have;

y - 50 = 0.2(x - 500)

y - 50 = 0.2x - 100

y = 0.2x - 100 + 50

y = 0.2x - 50.

For plan B, the slope is as follows;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (69 - 45)/(580 - 500)

Slope, m = 24/80

Slope, m = 0.3

At point (500, 45), a linear equation for plan B can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 45 = 0.3(x - 500)

y - 45 = 0.3x - 150

y = 0.3x - 150 + 45

y = 0.3x - 105.

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Complete Question:

Three cell phone plans, A, B, and C, each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500. These tables show the monthly charges for plans A and B when different numbers of messages are sent. Plan A Cell Phone Charges

Phone plans A and B each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500.

Plan A charges $50 monthly for 500 text messages and $66 monthly for 580 text messages.

Plan B charges $45 monthly for 500 text messages and $69 monthly for 580 text messages.

Letting x represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B. Then graph the equations for plans A and B on the same coordinate grid.

Answer:

solve for N cause that is the only variable

Step-by-step explanation:

The equation of the line in slope-intercept form is y = 0.5x + 1

From the question, we have the following parameters that can be used in our computation:

Points = (0, 1) and (-4, -1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = slope

This means that

c = 1

So, we have the following representation

y = mx + 1

At (-4, -1), we have

-1 = -4m + 1

This gives

-4m = -2

Divide by -4

m = 0.5

So, we have

y = 0.5x + 1

Hence, the equation  is y = 0.5x + 1

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Answer:

630

Step-by-step explanation:

35% of 1800 = 0.35 × 1800 = 630

The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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That's so the 4th 1 option is correct organizing their data into a frequency distribution and the 2nd option C.

Frequency distributions are visual displays that organise and present frequency counts so that the information can be interpreted more easily. Frequency distributions can show absolute frequencies or relative frequencies, such as proportions or percentages. It is easier to identify patterns of our data set by looking at a graph of the frequency distribution. So here is both the points which are given in the caution. So the first point option is correct organizing the data into a frequency distribution can make patterns within the data more evident And the 2nd point option C. is correct. It is easier to identify patterns of our data set by looking at a graph of the frequency distribution.

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Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

What is extrapolation?

A statistical technique called extrapolation aims to understand the unknown data from the known data. It uses historical data to attempt to predict future data. For instance, using the current population size and growth rate to project the size of a population in a few years.

Predicting hypothetical values outside of a specific data set is the goal of extrapolation.

Contrary to interpolation, which typically focuses on estimating past values, extrapolation is used to predict unknown future values due to its predictive nature.

Hence, extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

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Answer:

The last one on the right

Step-by-step explanation:

The others are 2 equations in x and y, while the last is one equation in x  only and another in y only

The solution is Option D.

The system of equations 3 = y + 1 and x = -6 are equations is one variable

What is Linear Equation in 2 variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

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 equation be represented as A

Now , the value of A is

a)

Let the system of equations be

y = 3x - 1   be equation (1)

y = 3x + 1   be equation (2)

Now , the equations are linear equations in 2 variables

b)

Let the system of equations be

-2x + y = 2   be equation (1)

-4x + 2y = 4   be equation (2)

Now , the equations are linear equations in 2 variables

c)

Let the system of equations be

y - 1 = 2 ( x + 4 )   be equation (1)

y + 3 = -5 ( x + 1 )   be equation (2)

Now , the equations are linear equations in 2 variables

d)

Let the system of equations be

3 = y + 1   be equation (1)

y = 2

x = -6   be equation (2)

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution

So , the equation is linear equation is one variable

Hence , the equations y = 2 and x = -6 are equations in one variable

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The variables x and y show a positive correlation

From the question, we have the following parameters that can be used in our computation:

Next, we plot the graphs of the points using a graphing calculator

See attachment for the graph

From the graph, we can see that the points are approximately linear

And the points show a linear pattern with a positive slope

This means that the correlation is positive

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As per the given dice, the probability of the total being equal to 8 is 1/9 or 11.11%.

Probability:

In statistics, probability refers the possibility of the particular event.

Given,

Here we need to find the probability of the total (when you sum up the dice) being equal to 8.

In order to calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8.

Hence both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6).

So, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.

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The value of a for which v is a linear combination is given as follows:

a = -8.

How to obtain the value of a?

A vector generated by adding two or more vectors (with various orientations) and multiplying by scalar values is known as a linear combination of two or more vectors.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

-x = -1.

2x - y = 4.

5x + 4y - 3z = -6.

-x + 3y - z = a.

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

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Answer:

y+3 = -7/3(x-3)

y = -7/3x + 4

Answer:

as per the question the nth term is 7,9,13,21,37,69.

Step-by-step explanation:

By looking at the consecutive numbers We can understand, the difference of consecutive terms of given series: 7, 9, 13, 21, 37,… forms a G.P.: 2, 4, 8, 16, 32, …. And more.

So when we subtract the first term from the second term we get:

9−7=2 and after doing the same for the following numbers we get: -

13−9=4

21−13=8

37−21=16

Let the nth term be x,

x−37=32 and now solve this equation to get the nth term∴x=32+37

=69

hence the next term is 69

The completed statement obtained using the proportional relationship between the recipes and the number of bags of snack mix made are presented as follows;'

A proportional relationship is one in which the output variable is a constant multiple of the input variable.

The possible recipe to make 6 bags of snacks obtained froma similar question is presented as follows;

3 cups of granola

1 cup of raisins

1.5 cup of almonds

0.5 cup of cranberries

0.75 cup of chocolate chips

The evaluation of the possible statements in the question that requires completion using proportional relationships of the recipe, are presented as follows;

1. To make 18 bags of snack mix, Sherry needs ___ cups of almonds

18 = 3 × 6

Therefore, the amount ingredients required to make 18 bags of the snack mix is 3 times the amount of ingredients in the recipe, which indicates;

The number of cups of almonds Sherry needs = 3 × 1.5 = 4.5

2. Sherry needs 6 cups of granola to make ___ bags of the snacks

The number of granola required for 6 bags = 3 cups

6 = 2 × 3

The number of bags of the snack mix 6 cups of granola can make is twice the number made by 3 cups, of granola or 2 × 6 = 12 bags of snack mix.

3. If Sherry uses 1 cup of cranberries, she will need to use ___ cups of resins

The number of cups of cranberries in the recipe = 0.5 cups

Number of cups of resins in the recipe = 1 cup of resin

Therefore, 1 cup of resin is required for 0.5 cups of cranberries

2 × 1 = 2 cups of resins will be required for 2 × 0.5 = 1 cup of cranberries

4. The recipe will make ___ bags of snack mix if Sherry  uses only 1 cup of granola

3 cups of granola are required for 6 bags of snack mix

Therefore; 3/3 = 1 cup of granola will be required for 6/3 = 2 bags of the snack mix

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The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.

The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.

Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.

Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.

N (# of periods) = 12 months

I/Y (Interest per year) = 11.99%

PV (Present Value) = $6,299.59

PMT (Periodic Payment) = $-350

Results:

FV = $3,009.15

Sum of all periodic payments = $3,850 ($350 x 11)

Total Interest = $559.57

The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)

The total amount paid in full in the first month = $6,299.59

Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)

Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.

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We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When are given an x and y equation that is [tex]y=x+\frac{1}{5} x[/tex] , and the further discussion can be defined as follows:

We must now imagine a condition that can be represented by the above equation.

Let's calculate the place money in piggy bank over two weeks in a row.

In the first week, I deposit a [tex]\frac{1}{5}[/tex]  of a particular amount of money, and the next week, I deposit a quarter of such previous week's investment.

We must now determine the entire amount of money that I have deposited.

We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

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