4. The chart below represents the kinematics of a freely falling body.
Time
(seconds t)
Total Distance
meters d (t)
1
5
2
20
45
80
125
3
4
5
a. Is the relationship between time and distance an arithmetic sequence?
Explain.
b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s². Show, in terms of n, the distance a falling body covers in t = n seconds of movement.

Answer: 2x+y=5

Step-by-step explanation:

The standard form of a linear equation is

ax+by=c

Move all terms containing variables to the left side of the equation.

2x+y=5

Answer:

2x + y = 5

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y=-2x+5[/tex]

To write the given equation in standard form, collect the terms with variables on one side of the equation, ensuring the term in x is positive.

Add 2x to both sides:

[tex]\implies y+2x=-2x+5+2x[/tex]

[tex]\implies y+2x=5[/tex]

[tex]\implies 2x+y=5[/tex]

For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:

A less than sign, such as a, denotes that an is greater than b.

Given inequality is:

|2x+7|+9 >18.

First we have to rearrange all the variables to the left side of the given equation:

Then,

|2x+7|>18-9

|2x+7|>9

2x+7>9 or 2x+7< -9

S0, x>1 or x< -8

Therefore, x< -8 or x>1

Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

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Answer:

27.3

Step-by-step explanation:

21 times 1.3 = 27.3 = original price

She paid 70% of the regular price of $30.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,

Percentage = 21 / 30

Percentage = 0.7 x 100

Percentage = 70%

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The value of measure of ''angle f'' in the figure will be 46°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In the figure,

The value of angle a and e are;

⇒ a = 115°

⇒ e = 69°

Now,

Since, There are two parallel lines shown in figure.

Hence, We know by the definition of alternate angles of parallel lines,

⇒ ∠a = ∠f + ∠e

Here, We have to given that;

The angles are,

⇒ a = 115°

⇒ e = 69°

So, We get by substitute the value of angle a and e;

⇒ ∠a = ∠f + ∠e

⇒ 115° = ∠f + 69°

Subtract 69° both side, we get;

⇒ ∠f = 115° - 69°

⇒ ∠f = 46°

Thus, The value of measure of angle f;

⇒ ∠f = 46°

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Answer:D

beacuse it is correct  just trust me i have done this class and its correct

Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

The cartesian coordinates of the given polar coordinates are

(A) (2, π); (X, Y) = (-2, 0)

(B) (6, -2π/3); (X, Y) = (-3, -3√3)

The cartesian coordinates for the polar coordinates are calculated by the formulae,

x = rcosθ, and y = rsinθ

Where the polar coordinates are (r, θ).

The cartesian coordinates for the given polar coordinates are as follows:

(A) (r, θ) = (2, π)

Then,

x = r cosθ = 2 cos(π) = 2(-1) = -2

y =r sinθ = 2 sin(π) = 2(0) = 0

Therefore, the cartesian coordiantes are (X, Y) = (-2, 0).

(B) (r, θ) = (6, -2π/3)

Then,

x = r cosθ = 6 cos(-2π/3) = 6(-1/2) = -3

y =r sinθ = 6 sin(-2π/3) = 6(-√3/2) = -3√3

Therefore, the cartesian coordinates are (X, Y) = (-3, -3√3)

The plot for the given polar coordinates on a polar grid is shown below:

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The inequality that is used to find the domain of the function would be B x - 3 ≥ 0

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The given function is f(x) = √x - 3

Here we have to find the inequality that is used to find the domain of the function.

Therefore, the function (x - 3) must be greater than or equal to 0

That is;

x - 3 ≥ 0

We will use the above inequality to find the domain of the function.

When we solve the above inequality, we get the domain of the function then;

x - 3≥0

Now add 3 on both sides, we get;

x - 3 + 3 ≥ 0 + 3

x ≥ 3

Therefore,  the answer is x - 3 ≥ 0

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Answer:

-4

Step-by-step explanation:

Take two points and plug into the distance formula  [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]

We will use (-2, 17) for ([tex]x_{1} , y_{1}[/tex]) and (-1, 13) for ([tex]x_{2} , y_{2}[/tex])

[tex]\frac{13- 17}{-1- -2}[/tex] = [tex]\frac{-4}{1} = -4[/tex]

The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.

In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.

Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.

And we need to find the statement is true or not.

According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.

Here we have counts for two categorical or nominal variables.

So, there is no large value comparision take palce.

Therefore, the statement is false.

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Answer:

m angle B = 27.54 degree

m angle C = 60.85 degree

Step-by-step explanation:

angle A is 90º so the other two angles must sum to 90º

2x+5x-8=90

7x-6=90

7x=96

x=13.77

therefore,

m angle B = 27.54 degree

m angle C = 60.85 degree

The required angles  ∠TBS and ∠TCV are 48° and 22° respectively.

A right-angled triangle is a kind of triangle that has one of its points equivalent to 90 degrees. The other two points summarize to 90 degrees. The sides that incorporate the right point are opposite and the foundation of the triangle. The third side is known as the hypotenuse, which is the longest side of each of the three sides

∠TBV = 24°

∠VBS = 24°

So, ∠TBS = (24° ) = 48°

And,

∠SAU = 92°,

So,

∠VAU = 46°

In ΔTAC

∠TAC + ∠TCA = 90°

∠TCA = 90° - 46° = 44°

This angle is bisect by CV

Then,

∠TCV = 44/2 = 22°

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∠TBS = 48°

SV = 17

∠TCV = 20°

What is a angle bisector?

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

As given in question:

AV , BV and CV are the angle bisector of ΔABC

UV = 17, BV = 18

∠SAU =92° and ∠TBV = 24°

Now,

∠TBV = ∠SBV = 24° ( BV is angle bisector)

So, ∠TBS = ∠TBV + ∠SBV

      ∠TBS = 24° + 24° = 48°

SV = UV = 17 (V is the incenter of ΔABC.)

∠SAU + ∠TBS + ∠TCU = 180° (Sum of angles of a triangle)

92° + 48° + ∠TCU = 180°

∠TCU = 180° - 140°

∠TCU = 40°

So, [tex]\angle TCV = \frac{40\degree}{2}[/tex]

       ∠TCV = 20°

∴ ∠TBS = 48°

SV = 17

∠TCV = 20°

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200 rides does it take to break even.

What are the many sorts of cost?

Fixed and variable costs are the two main categories of expenses incurred by enterprises. While variable costs fluctuate with output, fixed costs do not.

                 Sometimes, fixed costs are referred to as overhead costs. They must be paid whether a company produces 100 or 1,000 widgets.

The cost function is given by

C(x ) = 15x + 1000

It is also given that it costs $25 per ride.

so,

Revenue function for x number of rides be

 R(x) = 20x

For break even:-

The cost must be equal to the Revenue i.,e

       C(x) = R(x)

  15x + 1000 = 20x

     1000 = 20x - 15x

     1000 =  5x

        x = 1000/5

        x = 200

Therefore, 200 rides does it take to break even.

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Answer:1.44

Step-by-step explanation:

Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.

To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:

-18 = a1 * r^2

9216 = a1 * r^5

Dividing these two equations, we get:

-18/9216 = (a1 * r^2) / (a1 * r^5)

-18/9216 = r^-3

r = (-18/9216)^(-1/3)

Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:

r = ((-18/9216)^(-1/3))^(1/3)

r = ((-18/9216)^(1/9))

r = (9216/-18)^(1/9)

r = (-512)^(1/9)

r = (-8)^(1/9)

r = (-2)^(2/9)

r = (-2)^(2/3)

r = (1/4)^(2/3)

r = 1/2

To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:

-18 = a1 * (1/2)^2

-18 = a1/4

a1 = -72

To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:

a4 = (-72) * (1/2)^3

a4 = -9

Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Answer:

∠AFB

Step-by-step explanation:

Vertical angles are opposite to one another and share the same vertex or endpoint. ∠DFE is ∠AFE both share the point F, and they are opposite to each other, so they are also vertical to each other.

Answer:

83

Step-by-step explanation:

(78+72+87+90+x)/5=82

327+x=82*5

327+x=410

x=410-327

x=83

Therefore the solution of this question is  the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Here,

The perimeter of the square drawn on the grid

The vertices given in the question are (3,3) & (7,7)

The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]

Thus at vertices  (3,3) & (7,7)

=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]

=>4[tex]\sqrt{2}[/tex]

Therefore the perimeter of the square = 4a

thus,

=>4*4[tex]\sqrt{2}[/tex]

=>16[tex]\sqrt{2}[/tex] units

Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

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Answer:

-1.8x^2

Step-by-step explanation:

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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Answer: I believe 140

Step-by-step explanation: This is how I found my answer:

420 / 3

= 140

420-140

=  280

420= number of all tickets sold.

140= number of adult tickets sold

280= number of student tickets sold

You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:

"the number of student tickets sold was three times the number of adult tickets."

So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!

Twice a day for 20 minutes is the required time to realize that meditation practiced is beneficial for persons physical and mental health.

Meditation practiced helps person in different ways:

Twice a week is very less time and does not make consistency.

Incorrect option.

Several hours at a stretch is not possible for all individual and it is not practical .

Incorrect option.

Twice a day for 20 minutes is the best time and helps individual to practice  meditation.

Therefore, Option C. twice a day for 20 minutes is the best time for mediation.

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The 1 dollars found near the table by your friend is likely the money for the tickets.

You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.

let

x = number of individual ticket

y = number of couple tickets = 2x

Therefore, using equation,

2x(10) + 6x = 1075

2x + x = 195

Hence,

20x + 6x  = 1075

3x = 195

x = 195 / 3

x = 65

Hence,

26x = 1075

26(65) = 1690

Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.

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Answer:

Below

Step-by-step explanation:

k = 4-a

a (4-a) = 3

-a^2 +4a -3 = 0   ====> Quadratic Formula ===>  a =  1   and k = 3

1^3 + 3^3 = 28

Answer:

$172,984.44 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=25000\left(1+\dfrac{0.065}{4}\right)^{4 \cdot 30}[/tex]

[tex]\implies A=25000\left(1.01625\right)^{120}[/tex]

[tex]\implies A=25000\left(6.9193776...\right)[/tex]

[tex]\implies A=172984.4404[/tex]

Therefore, if you deposit $25,000 now at 6.5% compounded quarterly,  you will have $172,984.44 (nearest cent) in 30 years.

In linear equation,  162 is his new weight .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Mr. Miller weigh =  180pound

10% decrease =  180 * 10/100

                        = 18

new weight = 180 - 18

                   =   162

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Answer:

Step-by-step explanation:

(2, 0), (3, 4)

(4 - 0)/(3 - 2)= 4/1 = 4