Making connections between arithmetic sequences and linear function


Use the graph or the formula to write the equation of the line in a slope intercept form

The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given that a table for showing the relation between length and width of a field;

                Width (w)                                     Length (l)

                       0                                                   50

                     100                                                 150

                     200                                                250

                     300                                                350

We see, that, width is 50 less than the length.

Therefore, the function (w) to represent the length of the field will be =

w = l-50

Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)

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Answer:

-4,-2,2

Step-by-step explanation:

look where line reaches zero

Answer:

[tex]{\huge\pink{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]

[tex] \frac{4}{3} \div 12 \\ = \frac{4}{3} \times \frac{1}{12} \\ = \frac{4}{3 \times 12} \\ = \frac{4}{36} \\ = \frac{1}{9 } \\ = 0.11[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex] \huge\red{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

Answer:

1/9 is the answer

4/3 x 1/12 just multiply but the reciprocal

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

David launches a rock straight up over the edge of a 60-foot cliff and into the ocean. After 4 seconds, the rock reaches a maximum height of 108 feet. Six seconds later, the rock enters the ocean.  . Create a graph to represent the scenario. The graph should include at least the x- and y-intercepts and the vertex. (A complete graph consists of axis labels and appropriate scales, ordered pairs for each identified point, the function, and appropriate domain/range.)  . Write a function to model the scenario.  Part C. Create a table of values to represent the scenario. Be sure to include at least five values. Values should include at least the x- and y-intercepts and the vertex.  Part D. Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)

Step-by-step explanation:

By using scale factor formula we can evaluate the measure of side EF.

When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.

The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.

Therefore,

2/3  =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF

EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]

By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.

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Answer:

y = 9    x= -11

Step-by-step explanation:

opposite angles of a trapezoid are supplementary.

The two angles of  the same base in an isosceles triangle are congruent.

-6x-16 = 50

-6x = 66

x= -11

The supplementary of 50 is 130

3x+16y+19 = 130

-33 +16y +19 = 130

16y = 144

y = 9

The sum of all 4 angles is 360 degrees

In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.  

Diagonal of a rhombus bisects the angles of the rhombus at the vertex.

So as m∠MNL is 120°,

∠MNO = ∠LNO = 120/2 = 60°

The diagonals intersect each other at a 90 degree angle, therefore

m∠MON = 90°

Considering ΔMNO, right angled at O.

cos(∠MNO) = NO/ MN

cos(60) = NO/ 8

NO = 0.5×8 = 4

NP = NO + OP

NP = 2NO

NP = 2×4

NP = 8 in

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Answer:

True

Step-by-step explanation:

A rectangle is a parallelogram with four right angles, opposite sides parallel, opposite sides congruent, opposite angles congruent, consecutive angles are supplementary, and the diagonals bisect each other.

The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.

What is upper and lower bound of a function?

A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.

Given,

 [tex]f(h) = \frac{48-h}{48}[/tex]

where    f(h) = Percentage of battery left

              h = Hours of cell phone use

Lower Bound of parameter h,

h = 0 ( When percentage is 100%)

f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1

Upper bound of parameter h,

h = 48 (When percentage is 0%)

f(h) = [tex]\frac{48-48}{48}[/tex] = 0

Therefore the upper bound of h is 0 and lower bound of h is 1.

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The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].

An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.

[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]

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Answer:

let's take AC as x

AB is half of AC making it ½x

½x+½x+x+x=120

3x=120

[tex] \frac{3x}{3} = \frac{120}{3} [/tex]

x =120÷3

x=40

therefore AC is 40 while AB is 20

Answer:

AB = 20 ft

AC = 40 ft

Step-by-step explanation:

Perimeter of a rectangle = 2(l+b)

Perimeter (given) = 120 ft.

AB = ½ of AC

AC = 2 AB

Let x be the length of AB.

Then, AC = 2x

Now,

2(2x+x) = 120

2×(3x) = 120

6x = 120

x = 120/6 = 20 ft.

2x = 2×20 = 40 ft.

AB = 20 ft.

AC = 40 ft

Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and   Range: (0,∞).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given :  f(x)=[tex]2^{x}[/tex]+1

If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.

The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.

The values of its y-axis remain between 0 and. This is the set of y values, or the range.

However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.

The exponent's addition to 1 moves the function to the left without changing the range.

The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)

 Range: (0,∞)

Therefore , the solution of the given problem of function comes out to be

Domain: (-∞, ∞) and   Range: (0,∞).

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Following is the graph of two given equations.

The mapping of functions of two variables onto a Cartesian coordinate system, which is made up of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate, is done analytically through the use of graphs. The intersection of each axis, which is a real number line, at its zero point is known as the origin.

On solving the two equations,

2x-3y=-6                              ....(1)

7x-3y=9                               .....(2)

Firstly we will find common points by elimination -

The common points are - (3,4)

Then We can find all the values of equation (1)

2x-3y=-6                          

x    0      3    -3

y    2      4     0

7x-3y=9

x    0      3    10

y   -3      4    20.33

The respective graph is attached below

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Answer:

64 sequences of 4 fish are possible.

Answer:

120x - 96y + 32

Step-by-step explanation:

12 (10x + 3 -8y)

We use the distributive property to solve

120x - 96y + 32

One of the most important when writing the order of an equation is always written the number with the variable first; that is why the answer is

120x - 96y + 32

Answer:

5 x 2 x 3.14 = 31.4

Formula of circumference:

radius(half of your diameter or given radius) x pi(3.14 or 22/7 depending on what they tell you to use for pi) x 2(just always there when finding circumference)

Answer:

Circumference : 31.4 cm

Step-by-step explanation:

Circumference = 2× 3.14 × 5 cm

= 10× 3.14 cm

= 31.4 cm

Answer:

his mistake is that he didn't need to remove one even number on the spinner so we just need to take 2/5x1/5equals2/25

Answer:

...

Step-by-step explanation:

since the area of a square is side² then we can just square root the area and find the side

first one to the left would be √16, which would equal 4, which in this case is correct

first one the right is √220 which is about 18.832

bottom left √65 which is about 8.062

bottom left √83 which is about 9.110

Answer:

The answer is C

Step-by-step explanation:

opposite of y-axis.

10L  fuel does Asma's car use per 100 km of highway driving

In this question, we have to use the unitary method

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

What is a unitary in math?

a unitary state. (mathematics, of an algebra) That contains an identity element. (mathematics, linear algebra, mathematical analysis, of a matrix or operator) Whose inverse is equal to its adjoint.

So from the unitary method, we can solve it

12 L of gasoline per 100 km

so for 5/6

12 L * 5/6

= 10 L

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The difference between the population means - 3.4 and -1.84 when calculated is found to be -2.62 years.

The 95% confidence interval for the difference in true mean ages of cars owned by students and faculty is between -3.4 and -1.84 years.

We know that the sample of 138 cars which belongs to the students have an average age of 5.13 years. The standard deviation = 3.45 years.

Then again,

A sample of 111 cars which belongs to the faculty have an average age of 7.75 years.  The standard deviation= 2.08 years.

So the difference between them will be , s - f

= 3.45 - 2.08 = 1. 37

and the mean will be , mean of students - mean of faculty =

-2.62.

This is the point of difference between their means.

The SD is found to be as 0.3961.

and MOE is 0.78

with these details now we will calculate the required intervals,

The lower end is found to be as  -2.62 - 0.78 = -3.4

The upper end is found to be as  -2.62 + 0.78 = -1.84

Therefore, the mean difference between the cars is - 3.4 and -1.84.

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The table representing ratio of peaches in a box should be completed as follows;

Boxes    Peaches

2                 6

3                 9

5                15

6                18

The table representing ratio of strawberries in a box should be completed as follows;

Boxes    Strawberries

2                 6

4                12

5                15

8                24

In order to have a proportional relationship and equivalent ratios that is constant, the variables x for boxes and y for peaches must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 6/2 = 18/6

Constant of proportionality (k) = 3.

When y = 9 peaches, the value of x is given by;

x = y/k

x = 9/3

x = 3 boxes.

When x = 5 boxes, the value of y is given by;

y = kx

y = 3(5)

y = 15 peaches.

Also, we would determine the constant of proportionality (k) based on the given parameters:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/4 = 15/5

Constant of proportionality (k) = 3.

When x = 2 boxes, the value of y is given by;

y = kx

y = 3(2)

y = 6 strawberries.

When x = 8 boxes, the value of y is given by;

y = kx

y = 3(8)

y = 24 strawberries.

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a) The minimum number of dogs that could have a mass of more than 27 kg is 6.

b) The maximum number of dogs that could have a mass of more than 27 kg is 18.

We have a table which shows information about the masses of some dogs.

Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.

But we wants minimum of 12 and 6 is 6 .

so, the minimum number of dogs with mass more than 27 kg is 6.

b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.

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Complete question:

The above table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 27 kg

b) Work out the maximum number of dogs that could have a mass of more than 27 kg

can I explain what statistical mean