Which of the following explains why (x + 3) = (x − 6))
has no solution?

4 shirts ∝ 31

4 = 31k

7 shirts ∝ 54.25

7 = 54.25k

Where k is the constant of proportionality

The constant of proportionality is k = 0.13.

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

We have,

Timberlee buys 4 shirts for $31 and Riley buys 7 shirts for $54.25.

In proportionality terms, we can write as,

4 shirts ∝ 31 _____(1)

7 shirts ∝ 54.25 _____(2)

(1) can be written as,

4 shirts = 31K

7 shirts = 54.24k

Where k is the constant of proportionality.

Now,

The value of k.

From (1)

4 = 31k

k = 4/31

k = 0.13

From (2)

7 = 54.24k

k = 7/54.24

k = 0.13

Thus,

The constant of proportionality is k = 0.13.

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It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are given the first system of equations:

4x + y = 8

x + 3y = 8

thus 4/1 ≠ 1/3 = 1 is consistently independent.

The second system of the equation is;

-4x + 6y = 2

2x - 3y = 1

Therefore, -4/2 = -6/3 = 2 is inconsistent.

The third system of equations is;

5x - 2y = 4

5x - 2y = 6

Thus, 5/5 = -2/-2 ≠ 4/6 is consistent dependent.

Thus, It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

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Based on the mentioned information, each birthday card costs $2.2.

Forming the equation based on the mentioned variables. The equation will be formed as -

Cost of birthday cards × number of cards + cost of thank-you notes × number of notes = total cost

Equation for package a

3x + 2y = 9.60 : Equation 1

Equation for package b

8x + 6y = 26.60 : Equation 2

Multiplying equation 1 with 3

9x + 6y = 28.8 : Equation 4

Now subtracting equation 2 from equation 4

9x + 6y = 28.8

-8x (-)+ 6y = (-) 26.60

The result will be :

x = 2.2

Thus, the cost of birthday card is $2.2

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The value of [tex]\sqrt{13}[/tex] is between 3 and 4 on the number line.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

[tex]\sqrt{13}[/tex] = 3.60

The value 3.6 is going to be between 3 and 4 because it is seen to be more than 3 while the value is also seen to be less than 4.

Hence the solution to the problem is the locations are 3 and 4.

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Yes, r=5 is a solution of inequality r<11.

Given the inequality is r<11

Given the value of r is, r=5

Since 5<11

So yes r=5 is the solution of the inequality r<11.

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Value of tan90 is 1/0 which is undefined

Let AB, BC, AC be the base(adjascent side), side opposite to θ, hypotenuse of a right angled triangle respectively.

Now as per sine, cosine and tangent formulas, we have here:

It is seen from these formulaes that

Now, other formulas for trigonometry ratios are:

The other way of representing trigonometric values formulas are:

Therefore, value of tan90 is undefined.

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The fraction value of tan90° after using trigonometric value is 1/0 that is undefined.

What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan 90°

Tan 90 degrees in radians is written as

=>tan (90° × π/180°)

=> 1/0 = undefined.

Hence the fraction value of tan 90° is 1/0 that is undefined.

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The cost of the hotel for 1 night is $130 using the ratio concept.

If b is not equal to 0, an ordered pair of real numbers a and b, represented as a / b, is a ratio. An equation that balances two ratios is called a proportion. For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 male and 3 girls. The formula a: b or a/b can be used to compare any two values.

However, the percentage formula is represented as a:b::c:d or a:b=cd.

There are three types of proportion. They are:

1) Direct Proportion.

2) Inverse Proportion.

3) Compound Proportion.

4) Continued Proportion

Given,

Cost for four rental nights = $520

The cost for one rental night is given by

x = 520/4

x = $130 per night

Therefore, the cost of the hotel for 1 night is $130.

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Answer:

A

Step-by-step explanation:

36x = 535 - 31

36x = 504

36/36 x = 504/36

x = 14

[tex]{ \green{ \boxed{ \red{ \sf{x = 14}}}}}[/tex]

Step-by-step explanation:

[tex]{ \purple{ \tt{36x + 31 = 535}}}[/tex]

[tex]{ \purple{ \tt36x = 535 - 31}}[/tex]

[tex]{ \purple{ \tt{36x = 504}}}[/tex]

Divide both the sides by 36 then,

[tex]{ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = 14}}}}}[/tex]

The equation which best shows the relationship between Davis' savings, y and the number of months passed, x is; y = 20 + 5x.

It follows from the task content that the equation which represents the relationship between Davis' savings and the number of months passed be determined.

According to the task content;

Davis has $20 in his savings account, and he adds $5 every month.

Therefore, we have;

y = 20 + 5x

This follows from the fact that the amount added after each month is $5.

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Using World problem : work and time,

Himari will take 13 hour and 12 minutes to complete the job alone.

We have given that

Time taken by Even to do a job = 11 hours

let "x hours" be the time taken by humari to do this job alone .

Even'rate to do a job = 1/11 per hour

Himari and Even work together and do the job in 6 hours .

rate at which both are working together and do the job = 1/6 per hour.

Himari' rate to do job = 1/x hours per day

Now , using the formula "together work "

Even'rate + Himari'rate = rate of together work

=> 1/11 + 1/x = 1/6

we solve the above equation and find out the value of x

multiple both sides with 66x we get,

=> 6x + 66 = 11x

=> 5x = 66

=> x = 66/5 = 13 hours and 12 minute

Hence, Himari will take 13 hour and 12 minutes to do job alone .

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Measure of all angles must equal 180 degrees.

Therefore,
(4x+20) + (2x+34) + x = 180

6x + 54 + x = 180

7x + 54 = 180

7x = 126

x = 18

4(18)+20 = 92

Angle A = 92

2(18)+34 = 60
Angle C = 60 degrees

Unknown angle is 18 degrees because the "x" represents the third angle.

Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

The total charge for this job is $12131.04.

Charge per square yard to remove old carpet = $5.99

Charge per square yard to install the new carpet = $4.50

Charge for carpet and pad they selected per square yard = $16.99 and $3.00

Dimension of the living room = 17 1/2 by 20 feet

⇒ 35/2 by 20 feet

Dimension of the hall = 4 by 12 feet

The living room and the hall is in the shape of rectangular.

The formula of the area of the rectangle is

A= length x width

the total area of the living room and the hall is

⇒ (35/2) x 20 + (4 x 12)  

⇒ 398 square feet.

The total cost is

⇒ 5.99 + 4.50 + 16.99 + 3. 00

⇒30.48

Thus, the total charge for this job is

⇒398 x 30.48

⇒$12131.04

Total cost (TC) in that is the overall economic cost of production and is made of variable cost, which varies in step with the amount of a terrific produced and includes inputs together with exertions and raw materials, plus fixed cost, which is unbiased of the quantity of an amazing produced and includes inputs that cannot be various in the brief term including homes and machinery, which include probably sunk prices.

Total cost in economics includes the full possibility price (blessings received from the next-nice alternative) of every issue of production as part of its constant or variable prices.

The additional total cost of one additional unit of manufacturing is known as marginal cost.

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Explanation:

To isolate the Y from y - 3 = 2/5 (x+4), you need to add 3 from both sides to move it to the right side of the equation:

y - 3 = 2/5 (x+4)

+3         +3

y = 2/5 (x+4) + 3

Answer:

add 3 to both sides

or move 3 across the equal sign, which will change its sign from - to +

= y = 2x + 8 / 5 +

60 seconds long will it take for the planes to reach the same altitude.

Given that,

Two planes are being monitored by an air traffic controller. Plane A is initially at an altitude of 3500 feet, while Plane B is initially at a height of 1970 feet. The altitude of Plane A is increasing at a rate of 40.25 feet per second, while Plane B is doing so at a rate of 65.75 feet per second.

We have to find how long will it take for the planes to reach the same altitude.

Let us take x as the number of seconds in time.

We get,

3500+40.25x for Plan A.

1970+65.75x for Plan B.

Take,

3500+40.25x=1970+65.75x

3500-1970=65.75x-40.25x

1530=25.5x

x=1530/25.5

x=60

Therefore, 60 seconds long will it take for the planes to reach the same altitude.

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Answer: You can find a right degree angle of a triangle when it’s a 90 degrees or if you can see it makes like a square.

The equation for S, in terms of t, is S = 18 - 2t

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The initial value is 18 inches,

The rate of change is -1.5 inches per hour,

t is the number of hours.

S = 18 - 2t

Number of Hours after the                      Depth of Snow on Hudson's Lawn

Storm                                                                           (Inches)

0                                                                                        18

1                                                                                          16

2                                                                                         14

3                                                                                         12

Therefore, the equation for S, in terms of t is S = 18 - 2t.

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The different proportional relationship is given by:

Relationship B.

The justification is:

Since graph B has a different constant of proportionality and different equation, it is different than other three graphs.

The definition of a proportional equation is given as follows:

y = kx.

Which means that the output variable y is obtained with the multiplication of the constant of proportionality k and the input variable x.

The constant is obtained as the division of y by x of a point (x,y) different of the origin, as follows:

k = y/x.

Hence, for each relationship, the constant is given as follows:

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x² + (y – 3)² = 36 and x² + (y + 8)² = 36 are equations that represent circles having a diameter of 12 units and a center that lies on the y-axis

Given : x² + (y – 3)² = 36, x² + (y – 5)²= 6, (x – 4)² + y² = 36, (x + 6)² + y² = 144 and x² + (y + 8)² = 36

and x² + (y + 8)² = 36

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

Let's compare the given equations with the standard equation:

x² + (y – 3)² = 36 can be written as:

(x-0)² + (y – 3)² = 6²

This has a center (0, 3), radius r = 6 and diameter = 12 units

x² + (y – 5)²= 6 can be written as:

(x-0)² + (y – 5)² = (√6)²

This has a center (0, 5), radius r = √6 and diameter = 2√6 units

(x – 4)² + y² = 36 can be written as:

(x-4)² + (y – 0)² = 6²

This has a center (4, 0), radius r = 6 and diameter = 12 units

(x + 6)² + y² = 144 can be written as:

(x+6)² + (y – 0)² = 12²

This has a center (6, 0), radius r = 12 and diameter = 24 units

x² + (y + 8)² = 36 can be written as:

(x+0)² + (y + 8)² = 6²

This has a center (0, -8), radius r = 6 and diameter = 12 units

Therefore, the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36

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Answer:

  4x² +4x -20

Step-by-step explanation:

You want the difference between 6x² -5x -12 and 2x² -9x +8.

The difference is found by subtraction. This is the same as adding the opposite.

  (6x² -5x -12) - (2x² -9x +8)

  = 6x² -5x -12  -2x² +9x -8

  = (6 -2)x² +(-5 +9)x +(-12 -8)

  = 4x² +4x -20

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The quadrilateral with the given vertices is a Rhombus , the correct option is (C) .

In the question ,

it is given that ,

the vertices of the quadrilateral are (0,2), (6,0), (0,-2), (-6,0)

let us rename , the coordinates as A(0,2) , B(6,0) , C(0,-2) , D(-6,0) .

the distance between two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

distance between A(0,2) and B(6,0) is

AB = √(6 - 0)² + (0 - 2)²

AB = √(6² + (-2)²)

AB = √(36+4)

AB = √40

distance between B(6,0) and C(0,-2) is

BC = √(0 - 6)² + (-2 - 0)²

BC = √((-6)² + (-2)²)

BC = √(36+4)

BC = √40

distance between C(0,-2) and D(-6,0) is

CD = √(-6 - 0)² + (0 - 2)²

CD = √((-6)² + (-2)²)

CD = √(36+4)

CD = √40

distance between D(-6,0) and A(0,2) is

DA = √(0 -(-6))² + (2 - 0)²

DA = √(6² + 2²)

DA = √(36+4)

DA = √40

we see that the length of all the sides  is √40 ,

all the sides are same in Square and Rhombus ,

But from the graph below, we see that the quadrilateral formed is in the shape of the Rhombus .

Therefore , The quadrilateral with the given vertices is a Rhombus .

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The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

Given that,

We have to find the Find the average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table below.

x           f(x)

1           90

4           87

7           84

10          81

We have to find the slope of the 2 points.

The points are (4,87) and (7,84)

The slope point is rise/run

Rise is y₂-y₁

Run is x₂-x₁

So,

Slope = (84-87)/(7-4)

Slope = (-3)/(3)

Slope = -1

Therefore, The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{4 +5}{6 +6} \implies \cfrac{ 9 }{ 12 } \implies \cfrac{3 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{3 }{ 4 }}(x-\stackrel{x_1}{(-6)}) \implies y +5 = \cfrac{3 }{ 4 } ( x +6) \\\\\\ y+5=\cfrac{3 }{ 4 }x+\cfrac{9}{2}\implies y=\cfrac{3 }{ 4 }x+\cfrac{9}{2}-5\implies {\Large \begin{array}{llll} y=\cfrac{3 }{ 4 }x-\cfrac{1}{2} \end{array}}[/tex]

Answer:

[tex]\displaystyle \boxed{ y=\frac{3}{4}x-\frac{1}{2} }[/tex]

Step-by-step explanation:

      First, we will find the slope. This is done by finding the change in y over the change in x.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }= \frac{4--5}{6--6} =\frac{4+5}{6+6}=\frac{9}{12}=\frac{3}{4}[/tex]

      Next, we will find the equation. We will create a point-slope equation and simplify into slope-intercept form.

y - 4 = [tex]\frac{3}{4}[/tex](x - 6)

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{9}{2}[/tex] + 4

y = [tex]\frac{3}{4}[/tex]x - [tex]\frac{1}{2}[/tex]

Answer: Yes. The answer is -1.

Step-by-step explanation:

2x+3y=4, y=2

Would look like this: 2x+3(2)=4.

1. Multiply 3 x 2 = 6

2) 2x + 6 =4

3) Subtract 6 from both sides

4) Will look like this: 2x = -2

5) -2 / 2 = -1

Answer: -1

Equation: 2x+3(2)=4.

Answer:

x= -1

Step-by-step explanation:

2x + 3y = 4

2x + 3(2) = 4

2x + 6 = 4

2x = 4 - 6

2x = -2

x = -2/2

x = -1

Answer:

Okay, sorry for answering a few minutes late!

Step-by-step explanation:

So, for data in a table to be a function, the input must only have one output.

Short and sweet answer, hope this helps!

The value of the inequality X + 3 < 6 is x < 3.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information given, the inequality will be illustrated thus:

x + 3 < 6

Collect like terms

x < 6 - 3

x < 3

The value is x < 3.

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Answer: Angles 6,2,3 are the same and are all 112 degrees.

Angles 1,4,5,8 are the same and are all 68 degrees.

Step-by-step explanation:

Angles 6,2,3 are all 112 degrees because of diagonal angle rule.

Angles 1,4,5,8 are 180-112=68 degrees because we can use 180 degree angle rule.

Hope this helped, If you have any questions or clarifications, comment below!

Please rate!

Answer:

length: 20m. width: 15m

Step-by-step explanation:

70/2 = 35

35         35

+5          -5

40         30

40/2     30/2

20         15

Answer:

Step-by-step explanation:

y + 8= 2(x-1)

y+8=2x-2

y=2x-10

Slope equals 2