The monthly rents (in dollars) paid by 10 people are given below. (Note that these are already ordered from least to greatest.) 735, 935, 960, 995, 1005, 1050, 1065, 1075, 1100, 1120 Suppose that one of the people moves. His rent changes from $735 to $535. Answer the following.

a) The function velocity of the particle is v(t) = 0.5 · t² + 6 · t + 7, b) The distance traveled by the particle is 467 feet.

In this problem we have the equation that represents the acceleration of a particle. The function velocity (v) is obtained by integrating the function acceleration (a) and the function position is obtained by integrating the function velocity. Now we present the definitions of each function:

Velocity

v(t) = ∫ a(t) + C

Position

s(t) = ∫ v(t) + C

Where C is the integration constant.

The distance traveled during the time interval is found means of definite integrals:

Δs = [tex]\int\limits^b_a {v(x)} \, dx[/tex]= s(b) - s(a)

a) First, determine the function velocity of the particle:

v(t) = ∫ (t + 6) dt + C

v(t) = 0.5 · t² + 6 · t + C

7 = C

v(t) = 0.5 · t² + 6 · t + 7

b) Second, determine the distance traveled in the given time interval:

Δs = s(10) - s(0)

Δs = 0.167 · 10³ + 3 · 10² + 7 - 0.167 · 0³ - 3 · 0² - 7

Δs = 467

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Answer:

8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7

                    Hope this helped answer your question!

Answer:

7

Step by Step Explanation:

The Incenter of triangle ABC is I =  (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).

Given:

Let I be the incenter of triangle ABC.

Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.

Let a,b and c are lengths of the sides AB,BC and AC.

we know that:

Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)

we can find a, b and c values using the distance formula between the vertices.

AB = a =  [tex]\sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]

AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]

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Answer:

Rate = 72 km per hour
Distance traveled in 2 hours = 144 km

Step-by-step explanation:

The car speed is given as 20 meters per second

There are 3600 seconds in an hour

So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour

There are 1000 meters in a kilometer

So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour

In 2 hours the car would travel 72 x 2 = 144 km

Answer: 11.99 + 0.45t ≤ 16 The most toppings you can have is 8

Step-by-step explanation:

11.99 + 0.45 is a basic cheese pizza plus one topping
11.99 + 0.45t represents a pizza plus an undefined amount of toppings
11.99 + 0.45t ≤ 16 The cost of the pizza has to be 16$ or less
Subtract 11.99 from each side
0.45t ≤ 4.01
Divide both sides by 0.45
t ≤ 8.9111
You can't have a partial number of toppings, and 9 is too much, so we round down to 8.

Answer:

8%

Step-by-step explanation:

1. Subtract:

  55000 - 50600 = 4400

2. Divide:

   4400/55000 = 0.08

Answer: I hope this is helpful mark me brainlist if this apply to you

Step-by-step explanation:

The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .

A function is defined as a relation between a set of inputs having one output each.

Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.

The function is generally written as "f(x)" where x is the input value.

let us take an example-

f(x) = x/2

here, f(x) is a function because each input "x" has a single output "x/2":

• f(2) = 1

• f(5) = 2.5

• f(−12) = −6

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The answer to this Question is A we can use basic knowledge from linear equations to find the answer

What is Linear Equation?

Linear Equation is a equation in which degree of variables is 1 only

Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options

together cole and maggie have won 30 games and we are also given that  out of those 30 maggie has won 4 games

we should closely see at Linear Equations given in Options.

therefore cole has won 26 games which is more than 13

Hence the answer to the Question is Yes

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The area of the paperboard remaining after a semicircle is cut out of it is 235.52 in².

The area is the amount of space within the perimeter of a 2D shape.

To calculate the area of the rectangular board that remain, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paperbaord left is 235.52 in².

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El espacio que ocupa la casa sería 6/15, el espacio que ocupa el huerto sería 4/15 y el espacio restante del terreno sería 5/15.

Para representar en forma de fracciones el área de los diferentes espacios del terreno de Pedro debemos tener en cuenta que el total tiene 15 metros. Adicionalmente, cuando representamos una fracción estamos informando cuántas unidades de un número x de unidades estamos utilizando. Por ejemplo, en este caso del total (15 metros) del terreno que tiene Pedro, él esta utilizando 6 metros para su casa. Esta fracción se representaría así:

6 / 15

Por otra parte, la fracción para representar el área del huerto de Pedro debe seguir los mismos lineamientos que la anterior, es decir en el numerador (número de la parte de arriba) ponemos el número de unidades que utilizamos y en el denominador (número de la parte de abajo) ponemos el número total de unidades disponibles. Entonces la fracción del huerto sería:

4 / 15

Por ultimo, para saber cuántas unidades quedan disponibles del terreno de Pedro, debemos restarle al total de terreno la cantidad de espacio que usamos:

15 - 4 - 6 = 5

De acuerdo con lo anterior, el espacio disponible serían 5 metros, que expresado en fraccionarios sería:

5 / 15

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The algebraic expression √((x²-1)²) simplifies to x²-1

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Given: sqrt((x^(2)-1)^(2))=x^(2)-1

√((x²-1)²)

The square root will cancel out the square:

Thus, √((x²-1)²)  = x²-1

Therefore,  √((x²-1)²) simplifies to x²-1

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Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

The maximum value of the parabola is represented by y-vertex whose value is 9.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).

             y = a(x - 1)² + k  ->  points (2, 6.5) and (-1, -1), thus

            6.5=a(2-1)² + k (1)

            -1=a(-1-1)² + k   (2)

         Simplifying the equations

             6.5=a(1)² + k  ( 1 )

            -1=a(-2)² + k  (2)

            6.5=a+ k      ( 1 )

            -1=4a+ k      (2)

         Multiply equation 1 by -1

            -6.5=-a- k    ( 1 )

            -1=4a+ k      (2)

          Sum equations 1 and 2

           -7.5=3a

              a= -2.5

        If a= -2.5, from equation 1, you have

            -6.5=-a- k    

            -6.5=-(-2.5)- k  

            -6.5=2.5- k

            k=2.5+6.5

            k=9

Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:

y=-2.5(x²-2x+1)+9

y= -2.5x²+5x-2.5+9

y= -2.5x²+5x+6.5

[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]

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The number of points gained overall by Julia playing the game is 30 point

From the question, we have the following parameters that can be used in our computation:

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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Answer:

this 1

Step-by-step explanation:

same doubt pease any help

Hence, yes we can solve the triangle with the help of Law of Cosines.

What is trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given that,

Some people are saying it is possible to use the Law of Cosines to solve a triangle if given only three angles, and some are saying it is not possible.

Yes, with the help of Law of Cosines we can solve the triangle and the formula for it is

[tex]c^2=a^2+b^2-2abcos(C)[/tex]

where, [tex]a,b,c[/tex] are the side lengths of the triangle and [tex]C[/tex] is the angle.

Hence, yes we can solve the triangle with the help of Law of Cosines.

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Comparing the box-and-whisker plots for both data of each city, we have:

a. City B had more noon temperatures above 76°F

b. Both had the same interquartile range.

c. City B had a larger median noon temperature

d. City A had the largest noon temperature.

The box-and-whisker plot has the following values it displays about a data distribution:

Interquartile range = Q3 - Q1

Analyzing the box-and-whisker plots given above, we have the following to conclude:

a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.

b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7

Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7

Both had the same interquartile range.

c. Median for City A = 70

Median for City B = 78

City B had a larger median noon temperature

d. City A had the largest noon temperature of 85.

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To match equivalent expression is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

In mathematics, equivalent fractions are those with the same denominator and differing numerators.

According to equivalent fractions, two or more fractions are considered to be equal if both provide the same fraction following simplification. Let's imagine that two fractions, a/b and c/d, were simplified to provide comparable fractions, e/f. In this case, the two fractions are equal to one another.

For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.

We have to find how do we match equivalent expression.

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Answer: [tex]\frac{11+\sqrt{146}}{5}[/tex] seconds

Step-by-step explanation:

[tex]10=-5t^2 +22t+15\\\\5t^2 -22t-5=0\\\\t=\frac{22 \pm \sqrt{(-22)^2 -4(5)(-5)}}{2(5)}\\\\t=\frac{11+\sqrt{146}}{5} \text{ } (t > 0)[/tex]

Answer:

Step-by-step explanation:

its a

The intersection of these lines is the answer to the given system of equations. → (-1, -2)

Given the system of equations,

y = x - 1

y = 3x + 1

Now, equating both the given equations,

x - 1 = 3x + 1

3x - x = -2

2x = -2

x = -1

From, y = x - 1

          y = -1 - 1

          y = -2

The answer to the given system of equations is located at the intersection of these lines.

⇒ (-1, -2)

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Answer:11x

Step-by-step explanation:

The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

In the given question we have to define which symbol is represent function.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function f at an element x of X, denoted by the symbol f(x), is regarded to as the picture of x as per f or the value of f implemented to the input x.

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Answer: 1.41 meters

Step-by-step explanation:

14.1 decimeters to meters
Decimeters are 10 times smaller than meters, so you divide the value by 10 to get meters
14.1/10 = 1.41
1.41 meters

It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

[tex]y=5^x[/tex]

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

[tex]y=5^{-x}[/tex]

this function can be rewritten in this way:

[tex]y=(1/5)^x[/tex]

Here, base between 0 and 1, the function decays

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The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A system of equations as discussed above is a set of equations that seek a common solution for the variables included.

1.

y = -2x + 3 ...eq(i)

y = 1/2x - 7 ...eq(ii)

The solutions to the linear equations (x,y) are (4, -5)

2.

y = 2x - 7 ...eq(i)

y = 5x + 5 ...eq(ii)

The solutions to the linear equations (x,y) are (-4, -15)

3.

3y = -12x + 6 ...eq(i)

y = -4x + 2 ...eq(ii)

The linear equations (x, y) have infinitely many solutions

4.

y = -2x + 3 ...eq(i)

y = 2x - 1 ...eq(ii)

The linear equations (x,y) have solutions of (1, 1)

5.

y = 5x + 4 ...eq(i)

y = 5x - 2 ...eq(ii)

The linear equations have no solutions

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The area of the shaded region is calculated as: 6.88 yd²

The area of the shaded region in the diagram = area of rectangle - area of semicircle.

Given the following:

Area of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²

Area of the rectangle = length × width = 8 × 4 = 32 yd²

The area of the shaded region = 32 - 25.12 = 6.88 yd²

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The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

A triangle is a three-sided polygon.

The triangle's three points are known as vertices.

Several triangle-related points:

Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

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1.4t - 0.4(t-3.1)=5.8

Combine terms in paratheses

1.4t - 0.4t + 1.24 = 5.8

Combine t's

(1)t + 1.24 = 5.8

Subtract 1.24 over