solve for x: 3(x + 1) = −2(x − 1) + 6.

The solution is

a) The equation of line that has infinitely many solutions is y = ( -3/4 )x + 4

b) The equation of line passing through the point ( 0,1 ) is y = ( -3/4 )x + 1

c) The equation of line passing through (0,2) is y = ( -1/4 )x + 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 0,4 )

Let the second point be Q ( 4 ,1 )

Now , the slope of the line passing through the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 4 ) / ( 4 - 0 )

Slope m = -3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = ( -3/4 ) ( x - 0 )

y = ( -3/4 )x + 4

b)

The equation which passes through the point R ( 0 ,1  ) is given by

Substituting the values in the equation , we get

y - 1 = ( -3/4 ) ( x - 0 )

On simplifying the equation , we get

y = ( -3/4 )x + 1

c)

Now , the equation of line passing through the point ( 0 ,2 ) and has a solution at ( 4 , 1 ) is

Slope m = ( 1 - 2 ) / 4 - 0 )

Slope m = -1/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 2 = ( -1/4 ) ( x - 0 )

y = ( -1/4 )x + 2

Hence , the equations are solved

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The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x - 10) + (3x - 6)

Simplify the expression, then we have

⇒ (x - 10) + (3x - 6)

⇒ x - 10 + 3x - 6

⇒ 4x - 16

The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

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Answer:

3.2 hours

Step-by-step explanation:

You know that it takes him 1 hour to go 17 kilometers so you can divide 54.4 by 17 to get the hours.

Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

Therefore , the solution of the given problem of equation comes out to be 12 pennies.

A equation is a method that links two statements and signifies equivalence with the equals sign (=). In algebra, a scientific assertion that confirms the equivalency of two schemas is referred to as an equation. For instance, the answer obd + 6 = 12 has an equal sign between the elements ptdc + 6 and 12, respectively. There is a mathematical formula that describes the relationship between two phrases on either side of a letter. Frequently, the symbol and the single variable are the same. For example, 4x – 4 = 0.

Here,

Solving once per variable is the key to this issue.

Let x equal quarters and y equal dimes.

So, x + y = 20

Now, we'll build an equation using the coin values and total quantity of cash. (Decimals have been omitted for clarity.) 25x + 10y = 320

In terms of y, let's restate the original equation: y = 20 - x

In the second equation, we will now substitute this for y. 25x + 10(20-x) = 320

Calculate the value of x: 25x + 200 – 10x = 320.

15x = 120

8 quads times x

In light of this, y = 20 - 8 = 12 pennies.

Therefore , the solution of the given problem of equation comes out to be 12 pennies.

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Answer:

d.) y > 41

Step-by-step explanation:

33 < y - 8

41 < y

The graph A represents the same unit rate of 2/5.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Georgia is reading at a rate of 2 pages everything 5 minutes

We have to find the graph below shows the same unite rate

slope of 2/5.

Graph A increasing 5 units in x axis when it increasing one unit on y axis so we take number of pages on X axis and time on y axis then the given condition satisfies.

Hence, the graph A represents the same unit rate of 2/5.

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She will make $ 10130 more per year as an accountant than a public relations expert by frequency .

Frequencies are arranged into visual displays known as frequency distributions in order to make the information more understandable. Absolute or relative frequencies, such as ratios or percentages, can be shown in a frequency distribution. A frequency distribution can be shown using a graph or a frequency table. In a frequency distribution, the precise number of observations and the percentage of observations falling inside each range may both be shown. The distribution in the latter case is known as a relative frequency distribution. An observation's frequency is the frequency with which it appears in the data. For example, the frequency of the number 9 in the following list of integers is 5. (because it occurs 5 times). 1,

given

$58,020 Public Relations Specialist

$68,150 for an accountant

How much more will she make working as an accountant compared to a public accountant? $68,150 - $58,020, or $ 10130.

She will make $ 10130 more per year as an accountant than a public relations expert.

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2,5,4,6,1,7,3 is the correct order to construct a square.

So looking at the 7 available steps, only the step "Construct horizontal PQ" is possible since that's just a matter of drawing a straight line and labeling the endpoints P and Q. In any case, here are the 7 steps in order. The number in parenthesis after the 1st number is the original scrambled order of that step.  

1. Construct horizontal PQ

2. Construct a circle with point P as the center and a circle with point Q as the center, each circle having a radius PQ

3. Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S

4. Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T

5. Construct a circle with point T as the center with a radius TQ

6. Label the point of intersection of circles T and RS closest to point R, point U, and the point of intersection of circles T and RS closest to point S, point V.

7. Construct PU, UQ, QV, and VP to complete square PUQV.

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A circle has a circumference of 91.688 millimeters. The above statement indicates that the circle's radius is 14.6 millimeters.

The radius of a circle or other curvy geometric object pertains to its length. It is the boundaries across another two-dimensional circular surface measured linearly in one dimension. The length of something like a circle's contour is referred to as its circumference, while the length of a form with straight sides is referred to as its perimeter.

Circumference of a circle = 91.688 millimeters

π = 3.14

Radius = ?

Therefore, cicumference of a circle = 2 * π * r

91.688 = 2 * 3.14 * r

r = 91.688/6.28

r = 14.6 millimeters.

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27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

The unit technique is a strategy for addressing issues that entails first figuring out the price of a specific unit, then multiplication that value to figure out the needed value. Simply put, the unit method is employed to derive a single unit value from a multiple that is supplied. For example, 40 pens could cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, abstract algebra, mathematical analysis, or mathematical skills of matrices or operators.

given

6 logs in 4 hours

18hrs= ?x

then you multiply and cross.

so,18x6= 4x

4x/4=108/4

x=27 logs

27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

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Answer:y=-4, x=-1

Step-by-step explanation:

The value of "x" in the algebraic equation

3(-3x - 8) = 3(-6x + 3) which makes it true is equal to 11/3 and option C is correct.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

We shall evaluate for the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) as follows:

-9x - 24 = -18x + 9 {expand the bracket}

18x - 9x = 24 + 9 {collect like terms}

9x = 33

x = 33/9 {divide through by 9}

x = 11/3

Therefore, 11/3 is the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) that makes it true.

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Answer:

Step-by-step explanation:

Answer:

The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.

Factoring the equation:

x²+12x+43=(x+7)(x+6)=0

x+7=0 or x+6=0

x=-7 and x=-6

Therefore, the solutions for the equation are x=-7 and x=-6.

Alternatively, you can use the quadratic formula:

x = (-b± √(b²-4ac))/2a

Where a=1, b=12, c=43

x = (-12± √(12²-4143))/2*1

x = (-12± √(144-172))/2

x = (-12± √(-28))/2

x = (-12± i*√28)/2

x = (-12+ i2√7)/2 or x = (-12- i2√7)/2

These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)

A system of linear equations in two variables can have a unique solution, infinitely many solutions, or no solution.

There are three types of solutions to a system of linear equations in two variables:

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Answer

15/28

Step-by-step explanation:

total no. of students in the class = 15+13

=28

no. of boys = 15

p(boy) =15/28

The slope of y = -9 is 0.

In mathematics, the slope of a line is a number that describes both the direction and the steepness of the line. It is commonly denoted by the letter "m".

The slope is defined as the ratio of the "rise" (change in the y-coordinate) to the "run" (change in the x-coordinate) between any two distinct points on the line. It is also known as the gradient of the line.

A line with a positive slope goes up as it goes to the right, while a line with a negative slope goes down as it goes to the right. A line with a slope of zero is horizontal, and a line with undefined slope is vertical.

The equation y = -9  is a horizontal line, hence, the slope is 0.

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The line of best fit to represent the given data would be y = 13.5x + 10.

What is the best-fit line in statistics?

A best-fit line, also known as a line of best fit, is a straight line that is used to model the relationship between two variables in a set of data.

A line of best fit is a straight line that is the best approximation of the data points. To find a line of best fit, you can use the method of least squares, which involves minimizing the sum of the squared differences between the data points and the line.

Given the data (x,y) = {(0,10), (1,12), (2,15), (3,20), (4,30)}, the slope of the line can be calculated using the formula:

slope = (NΣ(xy) - Σx * Σy) / (NΣ(x^2) - (Σx)^2)

Where N is the number of data points.

Plugging in the data:

slope = (5*(10+24+30+60+120) - (0+1+2+3+4)(10+12+15+20+30)) / (5(0+1+4+9+16) - (0+1+2+3+4)^2)

slope = 270/20 = 13.5

y-intercept can be calculated using the formula:

y-intercept = (Σy - slopeΣx)/N

y-intercept = (10+12+15+20+30 - 13.5(0+1+2+3+4))/5

y-intercept = 10

So, the equation of the line of best fit would be:

y = 13.5x + 10

This equation represents a line with a slope of 13.5 and a y-intercept of 10. This line of best fit can be used to make predictions about the ticket price for a given number of years since 1980.

Hence, the line of best fit to represent the given data would be y = 13.5x + 10.

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The equation that represent how many gallon of water are left in the tub after it ha drained for x minute is A(n) = -8x + 300.

In the given question, we have to write and equation that represent how many gallon of water are left in the tub after it ha drained for x minute.

From the given question, a hot tub that hold 300 gallon of water.

Hot tub drain at a rate of 8 gallon per minute.

So the slope will be = -8 , the negative sign is there because the water is leaving the tub.

Let the amount of water left in the tub at time n minutes is A(n) gallons.

The initial value of A(n) is 300 gallons.

Thus when n = 0, the value A(n) will be 300.

So, we can write the relation as

A(n) = -8n + 300

We need to find the amount left after x minute. So n = x

Now the equation is A(n) = -8x + 300.

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Answer: Let one of the number be X and the other no will be x +18, this is as per given sum.

By sum,

Step-by-step explanation: x + x + 18 = 128

or, 2 x = 128 - 18 = 110

Therefore x = 55 & the other no will be 55 + 18 = 73

Hence, 55 & 73 are the two numbers.

You need to show what you have problem with and then I could help you.

The measure of arc GH is 102°.

What is inscribed angle?

In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.

Given:

The measure of inscribed angle ∠FHG is 39°.

We have to find the measure of arc GH.

Since,

FG = 2*m ∠FHG

FG = 2(39°)

FG = 78°

Let FH = 180°

⇒ GH = FH = FG

   GH = 180° - 78°

   GH = 102°

Hence, the measure of arc GH is 102°.

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First twenty prime numbers among the set of prime numbers are as follow :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

As given in the question,

Prime numbers are defined as the numbers which has only two factors one and the number itself.

Prime number does not exactly get divided by any other integer by leaving remainder equals to zero.

Prime numbers present in the number between 1 to 100 are equal to :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

As prime numbers are already written in ascending order.

First twenty prime numbers are as follow :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Therefore, the first twenty prime numbers are given by :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

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The total amount owed to the lender equals $2,330.

In our calculate, we are using a simple interest because it is only an interest charge that borrowers pay lenders for a loan. It is calculated by using the principal only and does not include compounding interest.

Data

Loan = $2000.00

Interest rate = 5.5%

Time = 3 years

The total amount owed:

= Loan + Interest.

To get our Interest, we will use "S.I. = PRT/100"

= 2000.00 * 5.5% * 3

= $330

Hence, the total amount owed equals to

= $2,000 + $330

= $2,330.

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The remainder when the function f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 is 49. Therefore f(2) = 49

An equation is used to show the relationship between numbers and variables.

Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division.

The remainder theorem states that when a polynomial f(x) is divided by (x - a), it gives a remainder equal to f(a).

Given that f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 with a remainder of 49

Applying the remainder theorem to the above polynomial:

x - 2 = 0

x = 2

Hence:

f(2) = 49

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The domain of the composite function is the intersection of the domain of f(x) and G(x). D f(x) intersection D g(x) The range of the function is now restricted by the domain of the composite function.

Therefore, the range is found by evaluating the function at the points in the domain of f(x).

You find the domain of the function by finding all numbers that can't go into the equation. Usually all that prevents this is whether or not it contains a fraction with x on the bottom or a x under a square root .

The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the graph. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.

The given function f(x) = –37 is a horizontal line which goes from negative infinity to positive infinity.

In this case, the domain can be any number since there is no limit on what the x value can be.

So, the domain of the given function f(x) = –37 will be all real numbers.

And, the range will always be y = –37 because no matter what x value will equal, y will always be equal to –37 in the function of f(x) = –37.

So, the range of the given function f(x) = –37 will be y = –37.

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The values are calculated using the basic properties as follows.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Trigonometric functions are also called as Circular functions.

Given sin θ = [tex]\frac{3}{7}[/tex] and cot θ = [tex]\frac{2\sqrt{10} }{3}[/tex]

In order to solve this, you need to know some of the basic trigonometric properties.

1. cot θ = 1 / tan θ

tan θ = sin θ / cos θ

So, cot θ = cos θ / sin θ

[tex]\frac{2\sqrt{10} }{3}[/tex] = cos θ /  [tex]\frac{3}{7}[/tex]

cos θ =  [tex]\frac{2\sqrt{10} }{3}[/tex] ×  [tex]\frac{3}{7}[/tex]

cos θ = [tex]\frac{2\sqrt{10} }{7}[/tex]

2. tan θ = 1 / cot θ

tan θ = 1 / [[tex]\frac{2\sqrt{10} }{3}[/tex]]

tan θ = [tex]\frac{3}{2\sqrt{10} }[/tex]

3. sec θ = 1 / cos θ

sec θ = 1 / [[tex]\frac{2\sqrt{10} }{7}[/tex]]

sec θ = [tex]\frac{7}{2\sqrt{10} }[/tex]

4. csc θ = 1 / sin θ

csc θ = 1 / [[tex]\frac{3}{7}[/tex]]

csc θ = [tex]\frac{7}{3}[/tex]

Hence the values of the trigonometric functions are calculated.

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