Which method of reasoning reaches a general conclusion on the basis of a number of observations that form a pattern?

deductive reasoning
inductive reasoning
complementary reasoning
supplementary reasoning

For the table, y = 25x.
When x = 12, y = 25*12 = 300

For the graph, y = 30x
When x = 12, y = 30*12 = 360

When x = 12, the value of y on the graph is 60 more than its value in the table.

Answer:

The correct option is C. The value of y be on the graph than is 60 more than the y value in the table when x = 12.

Step-by-step explanation:

If a line passing through two points then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given table it is clear that the line passing thought the points (4,100) and (5,125).

[tex]y-100=\frac{125-100}{5-4}(x-4)[/tex]

[tex]y-100=25(x-4)[/tex]

[tex]y-100=25x-100[/tex]

[tex]y=25x[/tex]

The value of this function at x=12 is

[tex]y=25(12)=300[/tex]

From the given table it is clear that the line passing thought the points (0,0) and (2,60).

[tex]y-0=\frac{60-0}{2-0}(x-0)[/tex]

[tex]y=30x[/tex]

The value of this function at x=12 is

[tex]y=30(12)=360[/tex]

The difference between y value in the graph and in the table at x=12 is

[tex]360-300=60[/tex]

The value of y be on the graph than is 60 more than the y value in the table when x = 12. Therefore the correct option is C.

Answer: D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.

Step-by-step explanation:

Let 'r' represents the number of roast beef sandwiches it provides and 't' represents the number of tuna sandwiches.

Then, the total number of roast beef sandwiches and tuna sandwiches is equal to the number of employees :

[tex]r+t=20[/tex]....................(1)

Also, the cost of each roast beef sandwich and cost of each tuna sandwich is same as $5.

If company wants to use the entire budget of $150, then we have another equation :-

[tex]5r+5t=150\\\5(r+t)=150[/tex]

If we divide 5 on both sides we get

[tex]r+t=30[/tex].............................(2)

When we compare equation (1) and (2) we get 20=30 but it is not possible therefore the system has no solution.

Therefore, the correct statement is "The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150."

Solving a system of equations to help a company plan revenue and production constraints.

The system of equations:

20b + 30h = 275 (total revenue equation)

8b + 9h = 53 (total boxes equation)

By solving these equations simultaneously, the company can determine the number of cow bells and air horns to produce to make $275 while satisfying the box constraint.

Answer:

No solution

Step-by-step explanation:

[tex]2x-7=y[/tex]

[tex]y=2x+3[/tex]

To solve the system of equations, we use substitution method

Lets substitute the second equation y=2x+3 for y in the first equation and solve for x

[tex]2x-7=2x+3[/tex]

Lets solve for x

subtract 2x on both sides

[tex]2x-2x-7=2x-2x+3[/tex]

[tex]-7=+3[/tex] is false

So, no solution for this system of equations

Answer:

Property's actual area  = 6400 m²

Step-by-step explanation:

Scale = 1 : 500

Side on map = 16 cm

Side of property = scale x side on map = 16 x 500 = 8000 cm

Area of property = 8000 x 8000 = 64000000 cm²

Area of property = 6.4 x 10⁷ cm² = 6.4 x 10³ m²

Property's actual area  = 6400 m²

1st number can be 0-9 = 10 numbers

2nd number can be 0-9 = 10 numbers

3rd number can be 0-9 = 10 numbers

10 * 10 * 10 = 1000 combinations

Answer:

The correct answer is [tex]y = \frac{10}{9}(x+3)^2+2[/tex]

Step-by-step explanation:

The correct answer to the question is not provided in the options listed below.

In order to find the equation of the quadratic function that you're looking for, you should identify the two points the parabola passes through: the vertex (that is point (-3,2)) and the y-intercept (the point (0,12)).

As we are given the vertex of the quadratic function, we can use the completed square form:  [tex]y=a(x-h)^2+k[/tex], where h and k are, respectively, the x and y coordinates of the vertex.

As (-3,2) is the vertex, we have:

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

Now, as the graph passes through the point (0,12), we can replace x=0 and y=12 in the formula above in order to find the value of a. Then, we make a the subject of the equation:

[tex]12=a(0+3)^2+2[/tex]

[tex]12=9a+2[/tex]

[tex] 10=9a[/tex]

[tex] \frac{10}{9}=a[/tex]

So, the equation of the parabola is [tex]y=\frac{10}{9}(x+3)^2+2[/tex].

Answer:

1.6

Step-by-step explanation:

In this case, to flip any of the points to map up accurately to the other points, we would have to do a transformation of reflection about the y-axis. The reason behind this is that out of other transformation process, we can only achieve the image of triangle ∆A’B’C’ through reflection.

Dilation will not work since it only changes the size of the object. The shape and position will not affected.

A translation will not work because although the shape can move, it still needs to flip to achieve triangle ∆A’B’C’.

A rotation will also not work because when you rotate it, the shape will still not map over the new one.

Therefore the only answer to this question would be to reflect triangle ∆ABC about the y-axis.

The student is trying to find the 4th term in a mathematical sequence where the first term is 13 and the rule for each term is to add 5. Thus, the 4th term of this sequence is 28.

The student is asking about a mathematical sequence where the first term is 13 and the term to rule is 'take away -5', or in other words, add 5 (since subtracting a negative number is the same as addition). So, to find the nth term of this sequence, you subtract (or add in this case) -5 to the first term, and continue in the sequent term.

Using these rules, here are the first four terms of the sequence: 1st term - 13. 2nd term [tex]- 13 + 5 = 18[/tex]. 3rd term [tex]- 18 + 5 = 23[/tex]. 4th term[tex]- 23 + 5 = 28.[/tex]

So, the 4th term in this sequence is 28.

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divide 21 3/4 by 1 1/3 = 16 5/16

 she can make 16 dresses

To convert 0.36 repeating into a fraction, we get [tex]\frac{4}{11}[/tex].

To convert the repeating decimal 0.36 repeating (written as 0.363636...) into a fraction, follow these steps:

⇒ 100x = 36.363636...

⇒ 100x - x = 36.363636... - 0.363636...

⇒ 99x = 36

⇒ x = [tex]\frac{36}{99}[/tex]

⇒ x = ([tex]\frac{36}{99}[/tex]) / ([tex]\frac{99}{9}[/tex]) = [tex]\frac{4}{11}[/tex]

Therefore, the fraction equivalent of 0.36 repeating is [tex]\frac{4}{11}[/tex].

Answer:

the answer is -10

you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights

T(x)={a if x <_ 2, b if x > 2}

 if it's 2 nights or less use option a, a = 75x

 if its longer than 2 days use option b, b= 50x + 50

Answer:

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}

Step-by-step explanation:

A hotel chain charges $75 per night for first two nights.

If the number of nights of the stay are x then charges for x nights

= 75x where x ≤ 2

If the stay is for than 2 nights then charges for x nights

= Charges for two first 2 nights(@$75 per night) + charges for other than initial 2 nights (@$50 per night)

= (75×2) + 50x where x > 2

Therefore total cost of the hotel if represented by t then the function will be

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}

Hello : let  A(-1,3)    B(4,-2)
the slope is :   (YB - YA)/(XB -XA)
(-2-3)/(4+1)  = -1
an equation is : y=ax+b     a is a slope

y = -x +b

the line through point  B(4,-2) :  -2 = -1(4)+b
b = 2 
the equation is : y =-x+2

Answer:

3552

Step-by-step explanation:

Hence, the volume of pyramid is:

3x^2 cm^3

We know that a volume(V) of a oblique square pyramid with height 'h' and base area A is given by the help of formula:

[tex]V=\dfrac{1}{3}\times (Ah)[/tex]

Now, according to the ques we have:

The base edge of an oblique square pyramid is represented as x cm.

The height is 9 cm.

Hence, the base area (A) is calculated as:

[tex]A=x^2[/tex]

( Since the base is in the shape of a square and we know that the area of square with side length s is given as:

[tex]Area=s^2[/tex] )

So, the volume of the pyramid is calculated as:

[tex]V=\dfrac{1}{3}\times (x^2\times 9)\\\\V=3x^2 \ cm^3[/tex]

Hence, the volume of pyramid is:

3x^2 cm^3

A pyramid is a solid shape with several triangles and a base. The volume of the pyramid in terms of x is 3x^2 cm3

The volume(V) of an oblique square pyramid with height 'h' and base area A is expressed according to the formula:

V = Bh/3

B is the base area = x * x = x^2

h is the height = 9cm

Substitute

V = x^2*9/3

V = 3x^2cubic cm

Hence the volume of the pyramid in terms of x is 3x^2 cm3

Learn more on volume of pyramid here: https://brainly.com/question/218706

Answer: 4

Step-by-step explanation:

Answer: The correct option is 4, i.e., translation.

Explanation:

It is given that the triangle DEF is congruent to GHJ by the SSS theorem.

From the given figure it is noticed that the triangle DEF and GHI are isosceles triangle.

Reason for correct option:

In transition the side and angles of the shape are not effected and the figure transfers from one place to another place without making any other change.

Since the both triangle are congruent and the position of all sides and angles are same, therefore option 4 is correct.

Reason for incorrect option:

In dilation the size of the figure is either stretched or compressed according to the scale factor k. But in the given figure the size of both triangles are same it means option A is incorrect.

In reflection the distance of all the point in preimage and all the image are same from the central line. Any central line does not exist in given figure. SO, the option B is incorrect.

In rotation the side length and angles are not affected but the position are not same, therefore the option C is incorrect.

Answer: Translation

Step-by-step explanation:

Given: Triangle DEF is congruent to GHJ by the SSS theorem.

From the given picture two sides of both triangles are equal therefore, the triangle DEF and GHI are isosceles triangle.

We know that a transition is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance that maps produces images.

Since the both triangle are congruent and just position of triangle GHJ is shifted to the right and down.

Therefore, the  transition is rigid transformation which is required to map DEF onto GHJ