Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-3y=18

The angle between lines 2x 3y =- Z is 90°

We will simplify the given equation of lines in the standard form of x/a=y/b=z/c

where a, b and c are the direction ratios of the line.

We will calculate the angle between these lines using the formula:

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

we are given two lines as 2x = 3y = – z and 6x = -y = -4z

We can write them in standard form xa=yb=zc

as:

For 2x = 3y = – z ⇒x/1/2=y/1/3=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₁= 1/2

b₁=1/3

c₁ = -1

For 6x = -y = -4z ⇒x/1/6=y−1=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₂= 1/6, b₂= -1, c₂= −1/4

Now, putting these values of a₁, a₂, b₁, b₂, c₁, and c₂

in the equation of cosα, we get

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

[tex]cos\alpha =\frac{\frac{1}{2} *\frac{1}{6} +\frac{1}{3} *(-1)+(-1)\frac{(-1)}{4} }{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{3} +\frac{1}{4} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{12} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

cosα=0°

cos⁻¹(cosα)=cos⁻¹(0)

α=90°

Therefore, the angle between the lines 2x = 3y = – z and 6x = -y = -4z is 90°

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Yes, the given set  A={x:x²=4 and 3x=9(0)}  is an empty set.

Given the set:

A={x:x²=4 and 3x=9(0)}

Consider the equation:

x²=4

Solve for x:

x²=4⇒x=±2

Consider the other equation:

3x = 9

Solve for x:

3x = 9⇒x = 3

Because the square of the set element should be 4, the element should be 2 or -2, but 2 or -2 multiplied by 3 gets 6 or -6, which is not equal to 9. As a result, no element exists that can meet both conditions.

The value of ‘x’ is not same in both cases, so this is a null set.

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Answer:

m = 5

Step-by-step explanation:

-12 + 3m=m - 2

3m = m + 10

2m = 10

m = 5

Let's check

-12 + 3(5) = 5 - 2

-12 + 15 = 3

3 = 3

So, m = 5 is the correct answer.

The amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is C: $4184.

How to calculate difference?

The difference is a mathematical operation used to find the amount by which one number is greater or smaller than another number. It is calculated by subtracting the smaller number from the larger number. The difference can be represented by the symbol "-" or the word "minus"

The dollar amount that could be on line 10 if $4184 is on line 11 and the taxpayer will neither receive a refund nor owe the IRS is $4184.

Line 10 on the 1040EZ form is for the "Total payments and credits" which is the sum of all payments made throughout the year, including any tax payments, estimated tax payments, and any credits the taxpayer is entitled to.

Line 11 is for the "Amount you owe" which is the difference between the total tax liability (calculated on the form) and the total payments and credits.

If the taxpayer will neither receive a refund nor owe the IRS, it means that the total payments and credits are equal to the total tax liability.

Hence, the amount on line 10 (total payments and credits) must be equal to the amount on line 11 (amount you owe) which is $4184.

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Answer:

Yes. Since 8 - 11 is -3, -3= -3

Step-by-step explanation:

-3=8-b

-3=8-11

-3=-3

Answer:

Look Below ↓↓↓

Step-by-step explanation:

Let's solve it and see if it is:-

[tex]\bf -3=8-b[/tex]

Simplify both sides of the equation:-

[tex]\bf -3=8-b[/tex]

[tex]\bf -3=8+-b[/tex]

[tex]\bf -3=-b+8[/tex]

Flip the equation:-

[tex]\bf -b+8=-3[/tex]

Subtract 8 from both sides:-

[tex]\bf -b+8-8=-3-8[/tex]

[tex]\bf -b=-11[/tex]

Divide both sides by -1:-

[tex]\bf \cfrac{-b}{-1}=\cfrac{-11}{-1}[/tex]

[tex]\bf b=11[/tex]

Therefore, yes b = 11!!

_____________________

Hope this helps!

Have a great day!

Answer:

18, 19, 20

Step-by-step explanation:

Let the integers be x - 1, x, x + 1.

x - 1 + x + x + 1 = 57

3x = 57

x = 19

x - 1 = 18

x = 19

x + 1 = 20

Answer: 18 , 19 , 20

Step-by-step explanation:

18+19+20=57

The total length of the two boards is 9 inches.

An inch can be defined as a unit of length in the customary system of measurement. Length in inches is either represented by in or ''. For instance, 5 inches can be written as 16 in or 16''. of a foot.

as given, a carpenter has a board that is three and one fourth inches long

i.e. the carpenter has a board that is 3.25 inches long.

and a second board to the end that is five and three fourth inches long

i.e. another board that is 5.75 inches long.

When joined together, the total length of the two boards is 3.25 inches + 5.75 inches = 9 inches.

Therefore, the total length of the two boards is 9 inches.

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Answer:

C

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = G (10, 1 ) and (x₂, y₂ ) = H (3, 5 ) , then

midpoint = ( [tex]\frac{10+3}{2}[/tex] , [tex]\frac{1+5}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = ( [tex]\frac{13}{2}[/tex] , 3 )

Question 1: The value of the dependent variable given a value of the independent is 11.54 (thousands of people)

Question 2: The value of the independent variable given a value of the dependent is 1998 (5 years after 2000)

Real-life application problem: The population of a city is growing at a rate modeled by the equation y = log(5x + 10) + 8, where y is the population in thousands and x is the number of years since the year 2000.

To determine the key properties of the function and sketch its graph:

The function is a combination of a logarithmic and an exponential function.

The domain of the function is all real numbers (since the logarithm function is defined for all positive numbers)

The range of the function is all real numbers greater than or equal to 8 (since the minimum value of the function is 8)

The graph of the function will be a smooth, continuous curve that starts at the point (0,8) and increases without bound as x increases.

Question 1: Determine the value of the population (y) given a value of x = 5 (number of years since 2000)

Solution:

y = log(5x + 10) + 8

y = log(5(5) + 10) + 8

y = log(25 + 10) + 8

y = log(35) + 8

y = 3.54 + 8

y = 11.54 (thousands of people)

Question 2: Determine the value of x (number of years since 2000) given a population of y = 12 (thousands of people)

Solution:

y = log(5x + 10) + 8

12 = log(5x + 10) + 8

4 = log(5x + 10)

5x + 10 = 10^4

5x = 9990

x = 1998 (5 years after 2000)

Note that this is not a realistic scenario, as the population of a city cannot be negative except in the case of extinction.

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For seven hours of landscaping, Company B would be less expensive than Company A.

An equation is defined as any pair of expressions that both contain the equal sign.

Because of this, Company charges $35 per hour and a $250 equipment fee, compared to Company B's $25 per hour and $300 equipment fee.

For t hours of landscaping, Company A will bill the following:

A = 35t + 250 (1) (1)

In a similar vein, Company B bills the following sum for t hours of landscaping:

B = 25t + 300 (2) (2)

Solve equation (1) now with t = 7:

A = 35 (7) + 250

A = 245 + 250

A = 495

So, for 7 hours of landscaping, business A would bill $495.

Similarly, when equation (2) is resolved for t = 7,

B = 25(7) + 300

B = 175 + 30

B = 475

So, for 7 hours of gardening, business B would bill $475.

Therefore, for seven hours of landscaping, Company B would be less expensive than Company A.

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Answer:

A. (x - 3)² + (y + 2)² = 16

Step-by-step explanation:

The formula for a circle plotted on the Cartesian coordinate system is:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

where [tex](a,b)[/tex] is the center of the circle, and [tex]r[/tex] is the length of the circle's radius.

Since the center of the circle in this problem is (3, -2), we know that the left side of the equation should be:

[tex](x - 3)^2 + (y - (-2))^2[/tex]

which can be simplified to:

[tex](x - 3)^2 + (y + 2)^2[/tex]

The radius of the circle is given as 4, so we know that the right side of the equation is:

[tex]4^2[/tex], which is the same as [tex]16[/tex].

Finally, to answer this question, we can put the two sides of the equation together to get:

[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]

First and fourth options are in dilation  that is an enlargement  as k>1 for enlargement in the expression  (kx, ky).

Dilation is the enlarging or shrinking of a fine element( a point on a match grid, polygon, line member) using a specific scale factor. Dilation is one of the five major metamorphoses ingeometry.When a dilation in the match aeroplane has the origin as the center of dilation, you can find points on the dilated image by multiplying the x- and y- equals of the original figure by the scale factor. For scale factor k, the algebraic representation of the dilation is( x, y) →( kx, ky)

The introductory formula to find the scale factor of a ballooned figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

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The complete question is :

Which of the following algebraic rules that represent a dilation that is an enlargement?

1  (1 1/3 x, 1 1/3y)

2 - (1/2 x, 1/2y)

3 - ( 0.1 x, 0.1 y)

4  (3 1/10 x, 3 1/10y)

The volume of each of the 3 samples is given as follows:

The density is given by the division of the mass by the volume, hence:

Density = Mass/Volume

The equation can be solved for the volume as follows:

Volume = Mass/Density.

The density of ice is given as follows:

0.9 g/ cm³.

Hence the volume of each sample is given as follows:

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To write a system of linear inequalities represented by the graph solution boundary line dashed for > and < and solid for ≤ and ≥ is used.

These steps will be used to graphically solve a set of linear inequalities:

1. Find y's inequality solution.

2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.

a. Draw the line as a dashed line if the inequality symbol is missing an equals sign ( or >).

b. Draw the line as a solid line if the inequality sign contains an equals sign (or ).

3. Darken the area when the inequality is satisfied.

4. For every disparity, repeat steps 1 through -3.

5. The region where all of the inequalities intersect will be the solution set.

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The rise and run of the line may be determined using two of its points, and the slope can be calculated.

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The correct matches are: A. Slope = 1.56, B. Slope = 0.86, C. Slope = 3

D. Slope = -5.61, E. Slope = -0.44  

Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.

Here are the correct matches of each pair of points to the slope of the line that joins them:

A. (9, 10) and (7.2) - Slope = (10 - 7.2)/(9 - 7.2) = 2.8/1.8 = 1.56

B. (-8,-11) and (-1,-5) - Slope = (-5 - (-11))/(-1 - (-8)) = 6/7 = 0.86

C. (5,-6) and (2,3) - Slope = (3 - (-6))/(2 - 5) = 9/3 = 3

D. (6.3) and (5,-1) - Slope = (-1 - 6.3)/(5 - 6.3) = -7.3/1.3 = -5.61

E. (4,7) and (6.2) - Slope = (6.2 - 7)/(4 - 6.2) = -0.8/1.8 = -0.44

So, the correct matches are:

A. Slope = 1.56

B. Slope = 0.86

C. Slope = 3

D. Slope = -5.61

E. Slope = -0.44      

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A linear equation in two variables is an equation that can be written in the form of:

ax + by = c,

where a, b, and c are constants, and x and y are variables.

Linear equations in two variables are also called a system of linear equations in two variables. In this type of equation, the variables are related linearly, meaning that the highest power of the variables is 1. This is in contrast to non-linear equations, which have variables with powers greater than 1.

For example,

2x + 3y = 6 is a linear equation in two variables.

4x - 6y = 10 is also a linear equation in two variables.

A system of linear equations in two variables can have one unique solution, infinitely many solutions, or no solution. The solution of the system can be found by different methods such as graphing, substitution, elimination, matrix method, and numerical methods, as mentioned in the previous answers.

Linear equations in two variables are used to model many real-world situations such as in finance, physics, economics, and many more. The study of linear equations in two variables is a fundamental part of algebra and is a stepping stone to more advanced mathematical concepts.

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The line of reflection is also known as the axis of symmetry. Then the correct option is C.

Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The reflection does not change the shape and size of the geometry. But flipped the image.

From the graph, if it is rotated by 72°. Then the figure will remain the same. And the line of reflection is also known as the axis of symmetry.

Thus, the correct option is C.

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Answer:

option 3 = 20w^5

Step-by-step explanation:

attached the solution, hope that helps ....

The required arcs that are shorter than the semi circle are  DA,DB,DC,AC,AB .

Minor arc: an arc that is less than a semicircle. A minor arc is named by using only the two endpoints of the arc.

Given here: Arcs of a circle.

An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. And a semicircle subtends and angle of 180 at the center of the circle.

Thus all the arcs that measure less than 180 are shorter than the semi circle

∴DA,DB,DC,AC,AB are the arcs that measure less than 180 at the center of the circle.

Hence, The required arcs are DA,DB,DC,AC,AB .

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Answer:

$10.57

Step-by-step explanation:

$12.90

-  18%

----------

$10.57

Answer:

[tex]\textsf{1)} \quad 4.1875[/tex]

[tex]\textsf{2)} \quad \dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

The area between a curve and the x-axis can be found using definite integration.  The definite integral of f(x) with respect to x between the limits x = a and x = b:

[tex]\displaystyle \int^b_a \text{f}(x)\; \text{d}x=\left[\text{g}(x)\right]^b_a=\text{g}(b)-\text{g}(a)[/tex]

where a is the lower limit and b is the upper limit.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}\left(+\text{C}\right)$\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\dfrac{1}{4}x^3+\dfrac{1}{6}x+1[/tex]

From inspection of the given graph:

Therefore:

[tex]\begin{aligned}\displaystyle\int^2_{-1}\left(\dfrac{1}{4}x^3+\dfrac{1}{6}x+1\right)\;\text{d}x&=\left[\dfrac{1}{4\cdot4}x^{3+1}+\dfrac{1}{6\cdot 2}x^{1+1}+x\right]^2_{-1}\\\\&=\left[\dfrac{1}{16}x^4+\dfrac{1}{12}x^2+x\right]^2_{-1}\\\\&=\left(\dfrac{1}{16}(2)^{4}+\dfrac{1}{12}(2)^2+(2) \right)-\left(\dfrac{1}{16}(-1)^4+\dfrac{1}{12}(-1)^2+(-1)\right)\\\\&=\left(1+\dfrac{1}{3}+2\right)-\left(\dfrac{1}{16}+\dfrac{1}{12}-1\right)\\\\&=\dfrac{10}{3}+\dfrac{41}{48}\\\\&=\dfrac{67}{16}\\\\&=4.1875\end{aligned}[/tex]

[tex]\begin{aligned}\displaystyle \displaystyle \int (x^2+1)(2x-3)\; \text{d}x&=\displaystyle \int \left(2x^3-3x^2+2x-3\right)\; \text{d}x\\\\&=\dfrac{2}{4}x^{3+1}-\dfrac{3}{3}x^{2+1}+\dfrac{2}{2}x^{1+1}-3x+\text{C}\\\\&=\dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}\end{aligned}[/tex]

The symmetry of a quadratic function is a vertical line that is x = − b/2a.

Quadratic function is defined as the function of the form f(x) = ax² + bx + c, where a, b and c are real numbers with a = 0 and it has the domain of a quadratic function is (−∞,∞).

Here we have given that we need to find the symmetry of a quadratic function.

As we all know that When a quadratic function is graphed in the coordinate plane, then the resulting parabola and corresponding axis of symmetry are vertical.

Here we have also know that in order to find the symmetry we have to  replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

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A solution set in of a linear equation system mathematics  to the set of values correctly solve such system which inputted into a system of equations correctly .

The main steps to follow  calculating solution sets for a  linear equations of system

first step is to Convert the  system into a matrix equation

secondly Rewrite  matrix equation into  an augmented matrix

next step is Computing the reduced echelon form of the augmented matrix by use of Gaussian elimination processes

after that The reduced echelon form of the matrix will provide the values for the unknown variables,

using these solutions to writing down the parametric vector equation form that contain the complete set of solutions for the system.

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The percent salinity of the resulting mixture is given as follows:

2.63%.

The percent salinity of the resulting mixture is obtained applying the proportions in the context of the problem.

The proportions are obtained applying the weighed mean, as follows:

0 x 1000 + 0.035 x 3000 = 105 gallons of salt.

Considering that the total mixture is of 1000 + 3000 = 4000 gallons, the percentage of salt in the resulting mixture is given as follows:

105/4000 x 100% = 2.63%.

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The rule of parallel lines: they never intersect each other.

We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.

Parallel lines are always equidistant from each other.

Also, the parallel lines are coplanar.

Mathematically, the parallel lines are represented by the symbol, ‘||‘.

If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.

Two lines parallel to a third line are parallel

As we know, the slopes of parallel lines are equal.

Let us assume that m₁ be the slope of line l₁ and m₂ be the slope of line l₂.

If line l₁ and l₂ are parallel to each other then m₁ = m₂

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The curve's y-intercept is 4, and its slope is 2.

To depict the curve, we will make use of the idea of slope and intercept in linear equations.

A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.

When y = 2x - 4 is put into comparison with the generic form, we get

The curve has a slope of 2 and a y-intercept of -4.

Picking two points on the line y = 2x – 4 will make it easier for us to plot the graph.

Since the supplied line's y-intercept is 4, the line y = 2x - 4 must pass through (0, -4).

Put y = 0

0 = 2x - 4

x = 2

Line passes through (2,0).

Draw a line passing through (0,4) and (2,0) and we get the graph.

Correct question :

How do you graph y = 2x - 4 on a graph?

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Answer:

Step-by-step explanation:

the degree of a polynomial is determined by the biggest exponent. For example, in this equation: 6x^4+3x^3+3x^2+2x+1, you can see that the biggest exponent is the 4, so it would be a polynomial of the 4th degree.

Answer:

max : 2, min : -2

Step-by-step explanation:

this question is kinda hard and brain-intensive but i think i am right

Answer:

max : 2, min : -2

Step-by-step explanation:

max : 2, min : -2

According to the solving the probability  of the spinner and the dice

A.  = 1 / 2.

B.  = 1/6.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.

for the spinner

total number of division = 4

the pink colored  sections = 2

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 2 / 4.

Probability = 1 / 2.

for the Dice

total number of division = 6

the pink colored  sections = 1

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 1/6.

Probability = 1/6.

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