how to solve
x^2 - 3x -4 = 0
IF ANYONE SOLVES IT, HE/SHE WILL BE THE BEST IN MY LIFE.

a. an exponential function where x is the number of 5700 year periods and y is the amount of carbon-14 is: y = a (b)^(x/h)

b.  the amount of carbon-14 after 11,400 years is 0.25 mg

The amount of time needed for a procedure to affect half of anything, such as the amount of time needed for a radioactive substance's atoms to split in half. The half-life of a radioactive sample is the amount of time needed for half of its atomic nuclei to spontaneously decay, which releases energy and particles, or, alternatively, the amount of time needed for the radioactive sample to disintegrate 60 times every second.

a.

y = a (b)^(x/h)

here, y = amount of carbon-14

a = initial amount

b = final amount

x = time elapsed

h = half life

b. we know that half of it will change into another form in 5700 years, Therefore, if start with 0.5 mg, that would be half in 5,700 years, or 0.25 mg in 11,400 years, which is another half life.

Thus, the amount of carbon-14 after 11,400 years is 0.25 mg

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Overall fraction of sold seats is 0.63333...

First we use the fact that 2/3 of the seats are located on the main floor and the number of seats on the main floor is 600, so the total number of seats can be calculated as follows:

Total number of seats = 600 / (2/3) = 900 seats

Next, we can find the number of seats in the balcony:

Balcony seats = Total number of seats - Main floor seats = 900 - 600 = 300 seats

Next, we can find the number of sold floor seats:

Sold floor seats = 4/5 * 600 = 480 seats

And the number of sold balcony seats:

Sold balcony seats = 1/2 * 300 = 150 seats

Finally, to find the overall fraction of sold seats in the theater, we add the number of sold floor seats and the number of sold balcony seats and divide by the total number of seats:

Overall fraction of sold seats = (480 + 150) / 900 = 0.63333... (rounded to the nearest hundredth)

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Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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Answer:

Below

Step-by-step explanation:

Divide 3 into all of the coefficients

16         +       12         -  9           now divide 'w' into the variables

16 w^2   + 12  w   - 9      Done.

The value of A is 128

Solution:-

Given,

A = (C/100)* B

C = 80

B = 160

So, A = (80/100)* 160

Therefore, The value of A from the above expression is 128

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Answer:

Find the general solution of the differential equation. (Enter your solution as an equation.)

y^3y’=6cos(pix

Answer:

The differential equation is a separable differential equation, so we can separate the variables and integrate both sides to find the general solution.

Separating the variables, we get:

(y^3)dy = 6cos(pix)dx

Integrating both sides with respect to their respective variables, we get:

(1/4)y^4 = -3sinx + C

Where C is an arbitrary constant of integration.

So the general solution to the differential equation is:

(1/4)y^4 = -3sinx + C

Step-by-step explanation:

Let's consider what the question asks for:

 --> change in total cost for each book printed

 --> cost to get started

The change in total cost:

 --> essentially, the slope value that is given in the equation:

               [tex]y=25x+1150[/tex]

     --> thus, the change in total cost per book is $25

The cost to get started before printing any books:

  --> we can essentially set 'x' equal to 0 to signify no books being printed

        yet

                         [tex]y=25x+1150=25(0)+1150=1150[/tex]

       --> the total cost before printing any books is $1150

Answer:

Answer:

1. The change in total cost for each book printed is $25

2. The cost to get started is $1,150

Step-by-step explanation:

25x + 1150 = Y

           -Y/-1 = -25x/-1 - 1150/-1

             Y = 25x + 1150

To get the total cost to get started let X = 0

           Y = 25x + 1150

           Y = 25(0) + 1150

           Y = $ 1,150

The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.  

Let 'b' be the number of books. Then the equation is given as,

6b - 8 = 58

Simplify the equation, then we have

6b - 8 = 58

6b = 66

b = 11

The equation that represents the number of books purchased will; be 6b - 8 = 58 and the number of books is 11.

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The complete question is given below.

Ashley bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?

Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 58, 8, and 6. Let b represent the number of books. and then solve the equation.

E. This polynomial could be factored by using grouping or the perfect squares methods.

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

x^2 + 2x + 1

Expand

x^2 + x + x + 1

Factorize the expression

(x + 1)(x + 1)

This gives

(x + 1)^2

Hence, the solution is (e)

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The work done in stretching the spring from its natural length to 0.9 feet beyond its natural length is 3 foot-pounds.

This can be calculated using the equation W = F * d, where W is the work done, F is the force applied, and d is the distance the spring is stretched. In this case, F is 6 pounds and d is 0.5 feet (0.9 feet - 0.4 feet). Thus, W = 6 * 0.5 = 3 foot-pounds.

Force is a concept in physics that describes the influence that can change the motion of an object. Work done is the amount of energy transferred to or from an object when a force acts on it and causes it to move through a distance.

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Correct question:

A force of 6 pounds is required to hold a spring stretched 0.4 feet beyond its natural length.

How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.9 feet beyond its natural length?

Answer: -5/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x-7

y=-1/2x+6

-1/2x+6 = 2x-7

x= 4

y= 2(4)-7

 = 1

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The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

To calculate this, we can use the following formula:

Rate of Water Rising = Volume of Water Added Per Minute / Total Volume of Well

Rate of Water Rising = 3 ft3/min / 240 ft3

Rate of Water Rising = 1/80 ft per minute

Therefore, The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.

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Answer:

10 hours would've gone by, and they have collected 190 signatures.

Step-by-step explanation:

The surface area of a cylinder with a base diameter of 4 yd and a height of 9 yd is 113.04 yd².

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

We know, The surface area of a cylinder is 2πrh, where 'h' is the height and 'r' is the diameter.

So, The radius is = (4/2) = 2 yd.

Therefore, The surface area of the cylinder is.

= 2π×2×9 yd².

= 36π yd².

= 113.04 yd².

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Answer: To find the dimensions of the rug, we need to subtract the width of the floor strip from both the length and the width of the room. Let x be the width of the floor strip in feet. Then the dimensions of the rug will be 18-2x by 26-2x.

The area of the rug is given by:

(18-2x)(26-2x) = 180

Expanding the right-hand side gives:

468 - 72x + 4x^2 = 180

Rearranging the equation gives:

4x^2 - 72x + 288 = 0

We can use the quadratic formula to find the solutions for x:

x = (-b ± √(b^2-4ac)) / 2a

where a = 4, b = -72, and c = 288

x = (72 ± √(72^2 - 4(4)(288))) / 2(4)

x = (72 ± √(72^2 - 4(1152))) / 8

x = (72 ± √(72^2 - 4608)) / 8

x = (72 ± √(5184)) / 8

x = (72 ± 72) / 8

x = (144 ± 72) / 8

x = 72 / 8 or 0

Since the width of the floor strip cannot be negative, x = 9 feet. So, the dimensions of the rug should be 18 - 2 * 9 = 0 ft by 26 - 2 * 9 = 8 ft.

Step-by-step explanation:

The values of x are 18 and 4

We have the area of a rectangle

A = L* B

The l and the b would get increased by 2x

180 = (18 - 2x) (26 - 2x)

We have to open the bracket

468 - 36x - 52x + 4x² = 180

468 - 180 - 88x +  4x² = 0

rearrange the equation

4x² - 88x  + 288 = 0

Solve using the quadratic formula equation

This would give us x = 144 / 8 and 32 / 8

x = 18 and x = 4

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Answer:

Are these two different equations? Tell me so I can help you.

Answer:

Step-by-step explanation:

so the height will be h.

if given the base length, find h using tangent.

tan55 = h/10ft

h = 10tan55

h = 14.28ft

From the inequalities y < (1/2)x - 7 and y ≥ -x - 1 graphed, a possible solution is the point (30, 2)

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Inequalities are used to show the non equal comparison of two or more numbers and variables.

Given the inequalities:

y < (1/2)x - 7         (1)

And:

y ≥ -x - 1         (2)

From the inequalities graphed, a possible solution is the point (30, 2) which is shown in the darker region

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The coordinates of the resulting point, T' after the point T( – 1,2) is rotated 180° clockwise around the origin is (1, -2).

To rotate a point 180° clockwise around the origin, you can apply the following transformations:

Reflect the point across the x-axis by negating its y-coordinate.

Reflect the point across the y-axis by negating its x-coordinate.

Starting with T( – 1,2), we first reflect the point across the x-axis, which gives us T'( – 1, -2). Then, we reflect T' across the y-axis, which results in T''(1, -2).

The transformation can be represented as follows:

T' = (x, -y)

T'' = (-x, -y)

Therefore, the final coordinates of T'' are (1, -2).

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If x represents time in seconds and y represents distance in meters then the system of equations to represent the above situation are

20x - y = 0 and 22x - y = 15

Let x represent time in seconds and y represents distance in meters.

Let u be the speed of Elena and v be the speed of Jada.

So, according to question,

              u = 20[tex]ms^{-1}[/tex] and v = 22[tex]ms^{-1}[/tex]

We know, Speed = [tex]\frac{Distance}{Time}[/tex]

So, 20 = [tex]\frac{y}{x}[/tex]

which implies 20x = y

                        20x - y = 0 ......................(1)

Similarly,

          22 = [tex]\frac{y + 15}{x}[/tex]

Which implies 22x = y + 15

                       22x - 15 = y.....................(2)

Substituting the value of y from equation (2) in (1)

                    20x - (22x - 15) = 0

                     20x - 22x + 15 = 0

                      15 - 2x = 0

                      2x = 15

                       x = 7.5

Substituting the value of x in equation (1)

                20 x - y = 0

                20 × 7.5 = y

                  y = 150

The values of x and y satisfies the stated conditions,

Hence, the system of equations to represent the above situation are

20x - y = 0 and 22x - y = 15

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Answer:

b. It was ​$15,280. Calculate the amount deposited over 9 years and then subtract it from the balance of ​$19,600.

Step-by-step explanation:

19,600-4,320 gives you the interest

Answer:

B. It was ​$15,280.

Step-by-step explanation:

Calculate the total amount deposited:

$40 per month * 12 months per year * 9 years = $4,320

Subtract the total amount deposited from the final balance: $19,600 - $4,320 = $15,280

The result is the interest earned: $15,280.

So, the answer is B. It was $15,280.

The probability that a current measurement is less than 10 milliamperes can be found by computing the cumulative distribution function (CDF) of the random variable x at 10 milliamperes.

The CDF of a continuous random variable x is defined as the probability that x is less than or equal to a given value.

In this case, we want to find the CDF of x at 10 milliamperes, which we can write as F(10), where:

F(10) = P(X <= 10) = ∫_0¹⁰ f(x) dx

Using the probability density function f(x) given in the problem, we can evaluate the integral to find the CDF:

F(10) = ∫_0¹⁰ 0.05 dx = 0.5

So the probability that a current measurement is less than 10 milliamperes is 0.5. This means that half of the possible current measurements will be less than 10 milliamperes, and half will be greater than 10 milliamperes.

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Answer:

Below

Step-by-step explanation:

BAC = DAC                             angle bisector theorem

AC = AC                  

BCA=BCA                             given

ABC congruent  to ADC           ASA theorem

BA = AD                                triangle congruence theorem

AC = AC                                      "

BC = DC                                      "

The correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.

Call the clock that runs forward A and the clock that runs backward B. Clock A will display the time as 13:00 at that moment, but clock B (which is going backward from 13:00) will display the time as 11:00.

Clock A will move two hours on its display in one hour since it is operating at twice the typical speed. Clock A will display 15:00 an hour from now, at 14:00. Additionally, because clock B is going backward, its display will read 10:00 an hour from now.

The clocks will next sync up when Clock A displays 13:00 (its initial beginning time) and Clock B displays 11:00, which takes place after 12 hours (12 hours on clock A, 24 hours on clock B).

So the correct time when the clocks next agree is 13:00 on clock A and 11:00 on clock B, which occurs 12 hours after 13:00.

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The total interest charger after 25 years for the balloon mortgage would be = $421, 875

Simple interest is the additional sum of money that is paid to a person after a sum of money was invested for a specific amount of time.

Given:

The principal= 375,000

The time for the mortgage = 25 years

The rate = 4.5%

The formula for simple interest

= P×T×R/100

= 375,000×4.5×25/100

= 42187500/100

= $421, 875

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Answer:

y = [tex]\frac{-3}{2}[/tex] x + 4

Step-by-step explanation:

3x + 2y = 8  Subtract 3x from both sides

3x - 3x + 2y = -3x + 8  

2y = -3x + 8  Divide all the way through by 2

y = [tex]\frac{-3}{2}[/tex] x + 4

The probability of getting exactly 0 tails is 1/8 or 0.125.

The coin flip experiment involves three independent events, each representing the outcome of one coin flip. Since each coin flip is balanced, the outcome of each event can either be heads (H) or tails (T). Therefore, for each event, there are two possible outcomes.

Since each event is independent, the number of possible outcomes of three events is equal to the product of the number of possible outcomes of each individual event. This means that the number of possible outcomes of three coin flips is equal to 2 * 2 * 2 = 8. The possible outcomes of three coin flips can be listed as follows:

HHH

HHT

HTH

THH

THT

TTH

HTT

TTT

Out of these eight possible outcomes, only one outcome (HHH) results in getting exactly 0 tails. So the probability of getting exactly 0 tails is 1/8 or 0.125.

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Vοlume οf the cylinder in will be 226.28 yd³, Vοlume οf Slanted cylinder is 141.37 in³ and Vοlume οf οblique cubοid is 1224 cm³.

What exactly is a cylinder?

In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance. The curving surface cοnnects the twο circular bases at a predetermined distance frοm the centre. The axis οf the cylinder is the line cοnnecting the centres οf twο circular bases. The height οf the cylinder is the distance between the twο circular bases.

A. Nοw,given that diameter οf base = 6 yd then radius=6/2=3 yd

and height will be =√10²-6²  (By Pythagοras theοrem )

= √64

= 8 yd

then vοlume οf cylinder is=πr²h

= 22/7*3*3*8

= 1584/7

= 226.28 yd³

Hence, Vοlume οf the cylinder  will be 226.28 yd³.

B. Vοlume οf Slanted cylinder is V = πr²h

V = π3²5

V = π × 3 × 3 ×5

V = 141.37 in³

Hence, Vοlume οf Slanted cylinder is 141.37 in³

C. Vοlume οf οblique cubοid is V = lwh

V = 17 × 18 × 4

V = 1224 cm³

Therefore ,Vοlume οf οblique cubοid is 1224 cm³.

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Total cost of items Mark bought = $8.80

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

Price of the items, $3.25, $0.55, $2.95, and $4.25 before tax.

Total price = $11

Discount on items = 20%

Discount = (20/100)11 = $2.20

Cost of the items = $11 - $2.20 = $8.80

Hence, $8.80 is total cost of items Mark bought.

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