Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long will it take the object to reach the ground?

If a ball is dropped from 2120 feet, it will take approximately_________ seconds to reach the ground.

Answer:

The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.

Factoring the equation:

x²+12x+43=(x+7)(x+6)=0

x+7=0 or x+6=0

x=-7 and x=-6

Therefore, the solutions for the equation are x=-7 and x=-6.

Alternatively, you can use the quadratic formula:

x = (-b± √(b²-4ac))/2a

Where a=1, b=12, c=43

x = (-12± √(12²-4143))/2*1

x = (-12± √(144-172))/2

x = (-12± √(-28))/2

x = (-12± i*√28)/2

x = (-12+ i2√7)/2 or x = (-12- i2√7)/2

These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)

The graph of the exponential function y = 200(1 + 0.05)ˣ starts with a curve and increases non-linearly or exponentially at any given time

Mathematical functions that rise or decrease in value at a rate proportional to their existing value are known as exponential functions. An exponential growth or decay function is another name for it. An exponential function is represented by the equation y = bx, where b denotes the base and x the exponent.

In this problem, we can use the basic form of an exponential function to represent this.

y = p(1 + r)ˣ

Substituting the values into the formula above;

y = 200(1 + 0.05)ˣ

The equation above is an exponential function that represents the growth over a period of time "x"

The graph of an exponential function curves from it's starting point and increases non-linearly steadily till it reaches it's peak.

Kindly find attached graph below

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The total amount owed to the lender equals $2,330.

In our calculate, we are using a simple interest because it is only an interest charge that borrowers pay lenders for a loan. It is calculated by using the principal only and does not include compounding interest.

Data

Loan = $2000.00

Interest rate = 5.5%

Time = 3 years

The total amount owed:

= Loan + Interest.

To get our Interest, we will use "S.I. = PRT/100"

= 2000.00 * 5.5% * 3

= $330

Hence, the total amount owed equals to

= $2,000 + $330

= $2,330.

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The sorrect option: y - 4 = 5x - 10, is the equation of the line, in point-slope form.

The slope of the line;

Slope m = 5.

Passing points: (x1, y1) =  (-2, 4).

So, general equation of the line,

y - y1 = m(x - x1)

y - 4 = 5(x + 2)

y - 4 = 5x - 10

Thus, the equation of line, in point-slope form, that has a slope of 5 is found as : y - 4 = 5x - 10.

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She will make $ 10130 more per year as an accountant than a public relations expert by frequency .

Frequencies are arranged into visual displays known as frequency distributions in order to make the information more understandable. Absolute or relative frequencies, such as ratios or percentages, can be shown in a frequency distribution. A frequency distribution can be shown using a graph or a frequency table. In a frequency distribution, the precise number of observations and the percentage of observations falling inside each range may both be shown. The distribution in the latter case is known as a relative frequency distribution. An observation's frequency is the frequency with which it appears in the data. For example, the frequency of the number 9 in the following list of integers is 5. (because it occurs 5 times). 1,

given

$58,020 Public Relations Specialist

$68,150 for an accountant

How much more will she make working as an accountant compared to a public accountant? $68,150 - $58,020, or $ 10130.

She will make $ 10130 more per year as an accountant than a public relations expert.

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Answer: Let one of the number be X and the other no will be x +18, this is as per given sum.

By sum,

Step-by-step explanation: x + x + 18 = 128

or, 2 x = 128 - 18 = 110

Therefore x = 55 & the other no will be 55 + 18 = 73

Hence, 55 & 73 are the two numbers.

w = 0  and z= -2  are the value in linear equation.

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.

3w-4z= 8

2w+3z=-6

multiply both sides of the equation of a

  6w - 8z = 16

    3(2w +3z ) = - 6 * 3

calculate the quotient

         6w - 8z = 16

        3(2w +3z ) = - 6 * 3

    6w - 8z = 16

    6z + 3z = -18

substract the two equation

                  6w - 8z - (  6z + 3z) = 16 - (-18)

                            -17z = 34

                               z = -34/17

                                 z = - 2

put the value of z in equation

           6w - 8 * -2  = 16

          6w + 16  = 16

               6w = 0

                 w = 0

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Answer:

(n+5)(n-2)

Step-by-step explanation:

n^2+3n-10

(n+5)(n-2)

When a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1, synthetic division is used. Any polynomial equation, regardless of degree, can, for instance, be divided by x + 1, but not by x2+1.

Additionally, the binomial must be of degree 1; synthetic division cannot be used to divide by a binomial such as x2 + 1. Here are the steps for performing synthetic division on a polynomial by a binomial.

To get the quotient and the remainder, write down the coefficients and divide them by the linear factor's zero. Q(x) + (R/(x - a)) = (P(x)/(x - a)).

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The remainder when the function f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 is 49. Therefore f(2) = 49

An equation is used to show the relationship between numbers and variables.

Polynomial is an expression composed of variables, constants and exponents using mathematical operations such as addition, subtraction, multiplication and division.

The remainder theorem states that when a polynomial f(x) is divided by (x - a), it gives a remainder equal to f(a).

Given that f(x) = x⁴ + 2x³ + 4x² + x - 1 is divided by (x - 2) to get x³ + 4x² + 12x + 25 with a remainder of 49

Applying the remainder theorem to the above polynomial:

x - 2 = 0

x = 2

Hence:

f(2) = 49

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The measure of arc GH is 102°.

What is inscribed angle?

In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.

Given:

The measure of inscribed angle ∠FHG is 39°.

We have to find the measure of arc GH.

Since,

FG = 2*m ∠FHG

FG = 2(39°)

FG = 78°

Let FH = 180°

⇒ GH = FH = FG

   GH = 180° - 78°

   GH = 102°

Hence, the measure of arc GH is 102°.

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The line of best fit to represent the given data would be y = 13.5x + 10.

What is the best-fit line in statistics?

A best-fit line, also known as a line of best fit, is a straight line that is used to model the relationship between two variables in a set of data.

A line of best fit is a straight line that is the best approximation of the data points. To find a line of best fit, you can use the method of least squares, which involves minimizing the sum of the squared differences between the data points and the line.

Given the data (x,y) = {(0,10), (1,12), (2,15), (3,20), (4,30)}, the slope of the line can be calculated using the formula:

slope = (NΣ(xy) - Σx * Σy) / (NΣ(x^2) - (Σx)^2)

Where N is the number of data points.

Plugging in the data:

slope = (5*(10+24+30+60+120) - (0+1+2+3+4)(10+12+15+20+30)) / (5(0+1+4+9+16) - (0+1+2+3+4)^2)

slope = 270/20 = 13.5

y-intercept can be calculated using the formula:

y-intercept = (Σy - slopeΣx)/N

y-intercept = (10+12+15+20+30 - 13.5(0+1+2+3+4))/5

y-intercept = 10

So, the equation of the line of best fit would be:

y = 13.5x + 10

This equation represents a line with a slope of 13.5 and a y-intercept of 10. This line of best fit can be used to make predictions about the ticket price for a given number of years since 1980.

Hence, the line of best fit to represent the given data would be y = 13.5x + 10.

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27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

The unit technique is a strategy for addressing issues that entails first figuring out the price of a specific unit, then multiplication that value to figure out the needed value. Simply put, the unit method is employed to derive a single unit value from a multiple that is supplied. For example, 40 pens could cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, abstract algebra, mathematical analysis, or mathematical skills of matrices or operators.

given

6 logs in 4 hours

18hrs= ?x

then you multiply and cross.

so,18x6= 4x

4x/4=108/4

x=27 logs

27 logs Teresa can keep the fire going for 444 hours with 666 logs instead of having to maintain it for 181818 hours.

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The equation that represent how many gallon of water are left in the tub after it ha drained for x minute is A(n) = -8x + 300.

In the given question, we have to write and equation that represent how many gallon of water are left in the tub after it ha drained for x minute.

From the given question, a hot tub that hold 300 gallon of water.

Hot tub drain at a rate of 8 gallon per minute.

So the slope will be = -8 , the negative sign is there because the water is leaving the tub.

Let the amount of water left in the tub at time n minutes is A(n) gallons.

The initial value of A(n) is 300 gallons.

Thus when n = 0, the value A(n) will be 300.

So, we can write the relation as

A(n) = -8n + 300

We need to find the amount left after x minute. So n = x

Now the equation is A(n) = -8x + 300.

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You need to show what you have problem with and then I could help you.

Around 100 hours will take for both vats to contain the same amount of liquid.

How do you calculate the rate of evaporation of a liquid?

The equation indicates that the evaporation rate,

W = (95+0.425*V)*(Pw-Pa)/Y, where W is the evaporation rate, V is the air velocity at the water surface,  Pw is the saturation vapor pressure at water temperature.

To find out how many hours it will take for both vats to contain the same amount of liquid, we need to compare the rates at which the liquid is evaporating from each vat.

We can set up the following equation:

(35 - x) / 0.25 = (40 - x) / 0.35

where x is the amount of liquid in both vats at the time they reach the same level.

We can then solve for x by multiplying both sides by 0.25 and 0.35 and then subtracting one equation from the other:

35 - x = 40 - x

x = 5

So, both vats will contain 5 liters of liquid at the time they reach the same level.

To find out how many hours it will take to reach this point, we can use the rate of evaporation for either vat.

For Vat A:

35 - 5 = 30 liters

30 liters / 0.25 liters/hour = 120 hours

For Vat B:

40 - 5 = 35 liters

35 liters / 0.35 liters/hour = 100 hours

So, It will take around 100 hours for both vats to contain the same amount of liquid.

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The equation that represents the relationship between the number of fruit Tyler ate and Han ate is x = y + 34

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Also a linear equation can be defined as an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The number of fruits Tyler ate is represented by x

The number of fruits Han ate is represented by y

Han ate 34 less than tyler, this means that y = x-34

and also making x the subject,

x = y + 34

Therefore the equation that represents the relationship between the number of fruits Tyler ate and Han ate is x = y+34

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2,5,4,6,1,7,3 is the correct order to construct a square.

So looking at the 7 available steps, only the step "Construct horizontal PQ" is possible since that's just a matter of drawing a straight line and labeling the endpoints P and Q. In any case, here are the 7 steps in order. The number in parenthesis after the 1st number is the original scrambled order of that step.  

1. Construct horizontal PQ

2. Construct a circle with point P as the center and a circle with point Q as the center, each circle having a radius PQ

3. Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S

4. Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T

5. Construct a circle with point T as the center with a radius TQ

6. Label the point of intersection of circles T and RS closest to point R, point U, and the point of intersection of circles T and RS closest to point S, point V.

7. Construct PU, UQ, QV, and VP to complete square PUQV.

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First twenty prime numbers among the set of prime numbers are as follow :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

As given in the question,

Prime numbers are defined as the numbers which has only two factors one and the number itself.

Prime number does not exactly get divided by any other integer by leaving remainder equals to zero.

Prime numbers present in the number between 1 to 100 are equal to :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

As prime numbers are already written in ascending order.

First twenty prime numbers are as follow :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

Therefore, the first twenty prime numbers are given by :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.

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A circle has a circumference of 91.688 millimeters. The above statement indicates that the circle's radius is 14.6 millimeters.

The radius of a circle or other curvy geometric object pertains to its length. It is the boundaries across another two-dimensional circular surface measured linearly in one dimension. The length of something like a circle's contour is referred to as its circumference, while the length of a form with straight sides is referred to as its perimeter.

Circumference of a circle = 91.688 millimeters

π = 3.14

Radius = ?

Therefore, cicumference of a circle = 2 * π * r

91.688 = 2 * 3.14 * r

r = 91.688/6.28

r = 14.6 millimeters.

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Answer:

Step-by-step explanation:

The half-life of bismuth-210 is given as follows:

5 days.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

For this problem, we have that:

Hence the decay rate is obtained as follows:

[tex]6.64 = 122(1 - r)^{21}[/tex]

[tex](1 - r)^{21} = \frac{6.64}{122}[/tex]

[tex]((1 - r)^{21})^{\frac{1}{21}} = \left(\frac{6.64}{122}\right)^{\frac{1}{21}}[/tex]

1 - r = 0.8706

r = 1 - 0.8706

r = 0.1294.

Hence the function is given as follows:

y = a(0.8706)^t.

The half-life is the value of t for which:

y = 0.5a.

Hence:

0.5a = (0.8706)^t.

(0.8706)^t = 0.5

log((0.8706)^t) = log(0.5)

tlog(0.8706) = log(0.5)

t = log(0.5)/log(0.8706)

t = 5 days.

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Using the concept of rates and ratio, it will take approximately 0.12 days to finish 4 bananas

When comparing two or more similar amounts or numbers using the same units, a ratio is utilized. In spoken language, we state the ratio of one quantity "to" the second quantity, and it is frequently written with a colon. For instance, a class has a 3:4 (or 3:4) ratio of boys to girls. When comparing two quantities, for example, some issues may only give you two numbers, but other problems might have more than two. For example, the proportions of the various ingredients used in a recipe.

We can use the concept of ratio or proportions to determine the number of days they will consume 4 banana

4 days = 13 banana

1 day = x banana

Cross multiply both sides and solve for x

x * 4 = 13 * 1

4x = 13

x = 13 / 4

x = 3.25

Now, we can find the number of days it will take to consume 4 banana

1 day = 3.25 banana

x days = 4 banana

Cross multiply both sides and solve for x

4 * 1 = 3.25x

x = 4 / 3.25

x = 0.12 days

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Answer:y=-4, x=-1

Step-by-step explanation:

Answer:

d.) y > 41

Step-by-step explanation:

33 < y - 8

41 < y

The solution is

a) The equation of line that has infinitely many solutions is y = ( -3/4 )x + 4

b) The equation of line passing through the point ( 0,1 ) is y = ( -3/4 )x + 1

c) The equation of line passing through (0,2) is y = ( -1/4 )x + 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

a)

Let the first point be P ( 0,4 )

Let the second point be Q ( 4 ,1 )

Now , the slope of the line passing through the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 4 ) / ( 4 - 0 )

Slope m = -3/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = ( -3/4 ) ( x - 0 )

y = ( -3/4 )x + 4

b)

The equation which passes through the point R ( 0 ,1  ) is given by

Substituting the values in the equation , we get

y - 1 = ( -3/4 ) ( x - 0 )

On simplifying the equation , we get

y = ( -3/4 )x + 1

c)

Now , the equation of line passing through the point ( 0 ,2 ) and has a solution at ( 4 , 1 ) is

Slope m = ( 1 - 2 ) / 4 - 0 )

Slope m = -1/4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 2 = ( -1/4 ) ( x - 0 )

y = ( -1/4 )x + 2

Hence , the equations are solved

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The slope of y = -9 is 0.

In mathematics, the slope of a line is a number that describes both the direction and the steepness of the line. It is commonly denoted by the letter "m".

The slope is defined as the ratio of the "rise" (change in the y-coordinate) to the "run" (change in the x-coordinate) between any two distinct points on the line. It is also known as the gradient of the line.

A line with a positive slope goes up as it goes to the right, while a line with a negative slope goes down as it goes to the right. A line with a slope of zero is horizontal, and a line with undefined slope is vertical.

The equation y = -9  is a horizontal line, hence, the slope is 0.

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The values are calculated using the basic properties as follows.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Trigonometric functions are also called as Circular functions.

Given sin θ = [tex]\frac{3}{7}[/tex] and cot θ = [tex]\frac{2\sqrt{10} }{3}[/tex]

In order to solve this, you need to know some of the basic trigonometric properties.

1. cot θ = 1 / tan θ

tan θ = sin θ / cos θ

So, cot θ = cos θ / sin θ

[tex]\frac{2\sqrt{10} }{3}[/tex] = cos θ /  [tex]\frac{3}{7}[/tex]

cos θ =  [tex]\frac{2\sqrt{10} }{3}[/tex] ×  [tex]\frac{3}{7}[/tex]

cos θ = [tex]\frac{2\sqrt{10} }{7}[/tex]

2. tan θ = 1 / cot θ

tan θ = 1 / [[tex]\frac{2\sqrt{10} }{3}[/tex]]

tan θ = [tex]\frac{3}{2\sqrt{10} }[/tex]

3. sec θ = 1 / cos θ

sec θ = 1 / [[tex]\frac{2\sqrt{10} }{7}[/tex]]

sec θ = [tex]\frac{7}{2\sqrt{10} }[/tex]

4. csc θ = 1 / sin θ

csc θ = 1 / [[tex]\frac{3}{7}[/tex]]

csc θ = [tex]\frac{7}{3}[/tex]

Hence the values of the trigonometric functions are calculated.

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