A cannonball i fired directly upward from a height of 0 feet with an initial velocity of 208 feet per econd. When will the cannonball be at a height of 640 feet for the firt time?
12 econd
5 econd

Answer:

To prove that cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA, we can start by multiplying both sides of the equation by sinA cosA:

cosA/sinA -sinA/cosAsinA cosA = (2cos^2A-1)/sinA cosAsinA cosA

Now we can simplify the left side of the equation by using the identity sin^2A + cos^2A = 1:

cosAcosA -sinAsinA = (2cos^2A-1)cosAsinA

Now we can simplify the right side of the equation by using the identity cos^2A = 1 - sin^2A:

cosAcosA -sinAsinA = (2(1 - sin^2A)-1)cosAsinA

Finally, we can simplify the right side of the equation by using the identity sinAcosA = (sinAcosA)/(sinA*cosA):

cosAcosA -sinAsinA = (2(1 - sin^2A)-1)(sinAcosA)/(sinA*cosA)

Since both sides of the equation are equal, we can conclude that the statement is true.

The value h(x) = f(x)g(x) is h(x) = f(x)g(x) = (2x - 4g(x) + 1)(g(x)) = 2xg(x) - 4g(x)^2 + g(x)

Factorization is the process of finding the factors of a number or expression. In mathematics, factorization or factoring is the breaking apart of a polynomial into a product of other smaller polynomials, or the breaking apart of a number into a product of other smaller numbers. For example, the factorization of the polynomial x^2 + 2x + 1 is (x+1)^2, and the factorization of the number 15 is 3*5.

It can then be concluded that the equation of f(x) = 2x - 4 g(x) + 1 what is h(x) = f(x)g(x) is (2x - 4g(x) + 1)(g(x)) = 2xg(x) - 4g(x)^2 + g(x)

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The length of the rectangle is L = 29 meters

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the length of the rectangle be represented as L

Let the width of the rectangle be represented as W

Now , Perimeter P of rectangle = 2 ( Length + Width ) = 74 meters

And , length of a rectangle is three meters less than four times its width

Substituting the values in the equation , we get

L = 4W - 3

And , 74 = 2 ( 4W - 3 + W )

Divide by 2 on both sides of the equation , we get

37 = 5W - 3

Adding 3 on both sides of the equation , we get

5W = 40

Divide by 5 on both sides of the equation , we get

W = 8 meters

Now , the length of the rectangle L = 4 ( 8 ) - 3

Length of the rectangle L = 32 - 3 = 29 meters

Hence , the length of the rectangle is 29 meters

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The probability that fewer than 30% of the rolls result in a two is 0.450.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

To find the probability that fewer than 30% of the rolls result in a two, we can use a normal distribution to model the number of twos rolled in 50 rolls.

Let's assume that the mean number of twos rolled in 50 rolls is μ = 50 * (2/6) = 16.67 (since the probability of rolling a two is 2/6). The standard deviation can be calculated as σ = sqrt(50 * (2/6) * (4/6)) = 2.94.

Now, we can use the normal distribution to find the probability that the number of twos rolled is less than 15 (30% of 50 rolls), which is P(X < 15) = P((X - μ) / σ < (15 - 16.67) / 2.94). We can use a standard normal table (z-table) to find this probability, which is approximately 0.450.

Therefore , the probability that fewer than 30% of the rolls result in a two is 0.450.

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There is a 0.450 percent probability that fewer than 30% of rolls will produce a two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

We can predict the frequency of twos rolled in 50 rolls using a normal distribution to determine the likelihood that less than 30% of the rolls produce two.

Given that the probability of rolling a two is 2/6, let's assume that the mean number of twos rolled in 50 rolls is = 50 * (2/6) = 16.67.

Calculating the standard deviation is as follows:

sqrt(50 * (2/6) * (4/6) = 2.94.

The chance that the number of twos rolled is less than 15 (30% of 50 rolls) can now be calculated using the normal distribution, and it is given by P(X 15) = P((X - ) / (15 - 16.67) / 2.94). It is possible to determine this probability, which is around 0.450, using a common normal table (z-table).

As a result, 0.450 represents the likelihood that fewer than 30% of rolls will produce a two.

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Answer:

3/4 square points

Step-by-step explanation:

An equilateral triangle is a triangle with all sides of equal length.

To find the area of an equilateral triangle, we can use the formula:

Area = (√3/4) * (side length)^2

In this case, the side length is √3/4 * 1 point. To calculate the area, we need to square the side length first.

(√3/4 * 1)^2 = (√3/4)^2 * 1^2 = (3/4) * 1 = 3/4

So, the area of the equilateral triangle is 3/4 square points.

Answer: 1,2,4,7,14 and 28

Step-by-step explanation:  Todos los Factores de 28 = Factors of 28

By solving a system of equations we will see that:

t = 33 and u = 308

The two triangles will be congruent if the correspondent sides have the same measure, then we can write two equations (or a system of equations) like the one below:

16t = 6u

20t -44 = 2u

So we have a little system of equations to solve.

We can isolate u on the second equation to get:

u = (20t - 44)/2

u = 10t - 22

Now we can replace that on the other equation to get:

16t = 6*( 10t - 22)

16t = 60t - 132

We can solve this for t to get:

132 = 60t - 16t

132 = 44*t

132/44 = t

33 = t

And the value of u is:

u = 10t - 22

u = 10*33 - 22 = 308

The values are t = 33 and u = 308

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The product of three fractions is acquired by multiplying the numerators and then multiplying the denominators of the three fractions to get the product fraction.

To find the product of any 3 fractions, multiply the three numerators. After that, multiply the three denominators. After the product of numerators and denominators, write them as fractions. This method will provide the product of 3 fractions in fractional form. To obtain this fraction in decimal form, divide the numerator of the fractional product by its denominator.

For example, consider the fractions 1/5 × 2/5 × 3/5.

In this, first multiply all the numerators: 1×2×3 = 6

Similarly, multiply all the denominators: 5×5×5 = 125

Now, the product of the three fractions is 6/125.

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The length of the original piece of fabric is 61 1/2 inches.

Let x be the length of the original piece of fabric.

If the first cut is 1/3 of the length of the original fabric, then we can express that as an algebraic expression 1/3x.

The next two cuts made from the remaining fabric is 10 inches and 5 inches.

10 + 5 = 15 inches

Therefore, the total length that was cut off was 1/3x + 15 inches = 35 1/2 inches.

With the algebraic equation written, solve for x.

1/3x + 15 = 35 1/2

To solve for x, isolate the terms containing the variable x on one sie and the constant terms on the other side.

1/3x = 35 1/2 - 15

1/3x = 20 1/2

Multiply both sides by 3 to get x.

1/3x = 20 1/2

x = 61 1/2 inches

Therefore, the original length of the fabric was 61 1/2 inches.

We can check our solution by adding the length of the cuts off to the original length:

1/3(61 1/2 inches) + 10 inches + 5 inches = 20 1/2 + 10 + 5 = 35 1/2

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There are four systems of equations in mathematics, namely linear equations, quadratic equations, polynomial equations, and exponential equations.

Each has its own unique properties that can be exploited for solving problems. Linear equations are the simplest system of equations and are the basic building blocks of more advanced systems of equations. Quadratic equations use the product of two terms to solve one equation. For example, 5x + 6y = 20 can be rewritten as 2x + 5y = 20. Polynomial equations use the power of a term squared to solve one equation. For example, x^2 + 7x + 12 = 55 can be written as x2 + 9x + 22 = 55. Exponential equations use the power to the base to solve one equation. For example, x^3 + 3x^2 - 10x - 16 = 0 can be written as x^3 + 3x^2 - 10x - 16 = 0e^-3 = e. These systems can be used to represent real world scenarios such as population growth,

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Using Algebraic expressions,  the number of baskets Desiree can assemble in 6 hours is 4.5. It will take her 5.5 days to complete the order.

We are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3 x+ 3 x+3 .

According to the question,

Using Algebraic expressions,

Each basket takes her 3/4 of an hour to put together

5 baskets already assembled that Desirae can use for this order

a) the number of baskets Desiree can assemble in 6 hours = 3/4 × 6

= 4.5 baskets

b) Total baskets to prepare = 25

Days it will take her to complete the order = 25/4.5

= 5.5 days.

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Only table {1} represents a exponential function.

       [tex]$e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }[/tex]

Given are the function tables as shown in the question.

       {x} → 0  1  2  3  4

       {y} → 0  1  4  9  16

Therefore, only table {1} represents a exponential function.

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The exponential growth model is given by the equation y = 2000(1.06)ˣ

An equation is an expression showing the relationship between numbers and variables.

An exponential function is in the form:

y = abˣ

a is the initial value and b is the multiplication factor. if b > 1, it is an exponential growth whereas if b < 1, it is an exponential decay.

A Exponential growth model initial value 2,000 growth rate 6%, hence a = 2000, b = 100% + 6% = 1.06

The exponential model becomes y = 2000(1.06)ˣ

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The solution of the given equations is x= 0.4 and y= 1.

The system of equations is y = -5x + 3 and y = 1. To find the solution, we can substitute the value of y from the second equation into the first equation.

To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y = -5x + 3

y = 1

We can see that the second equation is already in the form y = a, which means that the y value is constant and equals to 1. Now we can substitute this value of y in the first equation:

1 = -5x +3

So the solution to the system of equations is x = 0.4, y = 1.

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To read and plot coordinates, first you need to understand what the coordinates are and what they represent. Coordinates are used to indicate the position of a point on a graph or map.

They are typically composed of two or three numbers that represent an x- or y-axis on a graph.

To plot coordinates, start by plotting the x-coordinates on the x-axis and the y-coordinates on the y-axis. When plotting a point, start by drawing a circle at the coordinates. Then, draw a line connecting the point to the origin (the point where the x- and y-axes intersect). Finally, label the point with its coordinates.

When plotting multiple points, start by plotting each point individually and then connecting them with straight lines. This will create a graph with the points connected in a specific order.

When plotting coordinates, it is important to make sure that the data is accurate. Any mistakes in the coordinates can lead to wrong results. Additionally, it is important to use the same scale when plotting coordinates so that the points are accurately represented.

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The degree of 3x^1 is 1.

A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.

To find the degree of a polynomial, you can do the following:

→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.

→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.

3x^1 is a monomial with a coefficient of 3 and an exponent of 1. It is also called a linear term. The degree of a monomial is the exponent of the variable. So in this case, the degree of 3x^1 is 1.

Therefore, the degree of 3x^1 is 1.

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The nth term of an arithmetic sequence is given by aₙ = a + (n – 1).

A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A formula for the nth term of the AP could be derived from this kind of progression. Because it follows a pattern where each number is acquired by adding 4 to the preceding term, the sequence 2, 6, 10, 14,... is an example of an arithmetic progression (AP). In this series, the nth term equals 4n-2. By changing the nth term to n=1,2,3,..., the sequence's terms can be obtained. i.e.,

First term when n = 1 is 4n-2 = 4. (1)

-2 = 4-2=2

second term = 4n-2 = 4 when n = 2 (2)

-2 = 8-2=6

The third term is 4n-2 = 4 for n = 3. (3)

-2 = 12-2=10

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The relation should be written as a set of ordered pairs as follows: A. . ordered pairs: {(0, 2), (2, 6), (4, 10)}.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (x-value or domain) to an output variable (y-value or range).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

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Answer:

15

Step-by-step explanation:

becaue o was thinking and i was like oh search it u0 and i got snswer

Answer:4 hours and 23 minutes

Step-by-step explanation:1:40-5:40 is 4 hours. Then add 20 minutes and you get to 6 o'clock. Then finally add 3 minutes and you get to 6:03. When you add 4 hr + 20 min + 3 min you get 4 hours and 23 minutes.

Answer:

4 km per hour

Step-by-step explanation:

Use the point (15,1)  Since the line is proportional, the slope is y/x or 1/15

1/15 this is in minutes

1/15 x 60/1  To convert  to hours

4 km per hour

Answer:

4 Km per hour

Step-by-step explanation:

average speed (S) is calculated as

S = [tex]\frac{D}{T}[/tex] ( D is distance and T is time, in hours )

the distance ( vertical axis )  from her home to the newspaper shop is 1 Km

time ( horizontal axis )

from 09 00 to 09 30 has 6 divisions

then 1 division = 30 minutes ÷ 6 = 5 minutes

time to walk to the shop is 3 divisions = 3 × 5 = 15 minutes

15 minutes = [tex]\frac{15}{60}[/tex] of an hour = [tex]\frac{1}{4}[/tex] hour

then average speed from home to newspaper shop is

S = [tex]\frac{1}{\frac{1}{4} }[/tex] = 4 Km per hour

To work out the value of 3 2/5 × 10, we need to first convert the mixed number 3 2/5 into an improper fraction. To do this, we multiply the whole number (3) by the denominator (5) and add the numerator (2) to get:

3 2/5 = (3 x 5) + 2 / 5 = 15 + 2 / 5 = 17/5

Now that we have the improper fraction, we can multiply it by 10:

17/5 x 10 = (17 x 10) / (5 x 10) = 170 / 50 = 34 / 10

The answer is 34/10, which can be simplified to 17/5. Therefore, the value of 3 2/5 × 10 is 17/5.

The range would be [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range.

You may recall this by saying "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" stand for "left to right," "R" stands for "range," and "B" and "T" stand for "bottom to top," and "R" stands for "range." Since the function doesn't approach 250, as can be seen in the graph, 250 is not inside the range.

Between the minimum and greatest value are the numbers that make up the range. The range would be [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range. The collection of values that can be plugged into a function's domain are called its parameters.

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Because the lowest Y value is 75 and the highest one is around 212.5, the range would be [75,212].

You may remind yourself of this by repeating "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" are "left to right," "R" is "range," "B" and "T" are "bottom to top," and "R" is "range." Since the function doesn't approach 250, as can be seen in the graph, 250 is not inside the range.

1. The numbers that make up the range lie between the lowest and highest value. Because the lowest Y value is 75 and the highest one is around 212.5, the range would be [75,212].

The set of values that can be plugged into the domain of a function is referred to as its parameters.

Thus, the range would be [75,212] because the lowest Y value is 75 and the maximum is somewhere around 212.5.

2. The set of all temperatures that the water can attain is the function's range. The temperature of the water rises quickly at first, then more gradually, and after 30 minutes, it levels off and stops rising altogether, as shown by the graph.

As a result, the range of the function is a range of temperatures, beginning at the water's initial temperature and ending at the water's highest temperature.

3. The time at which the water reaches a temperature of 0 degrees Fahrenheit is represented by the equation W(t) = 0. We can observe from the provided graph that the water temperature rises quickly at first and subsequently more gradually.

The water is therefore unlikely to ever reach a temperature of 0 degrees Fahrenheit. As a result, W(t) = 0 cannot be solved.

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Answer: 77.05

Step-by-step explanation:

The correct option is a. At least 5 which indicates the number of pants that can be bought.

To avail discount Nina needs 30 shirts. So, calculating the cost on buying minimum required number of t-shirts.

So, 150 × 30 = php 4,500

Total php available with Nina = 8,000

Now, leftover money for pants = total money - money spent on t-shirts

Leftover money for pants = 8000-4500

Leftover money for pants = 3500

Now, total pants Nina can buy = leftover money divided by php for pants

So, 3500/600=5

Thus Nina should buy atleast 5 pants.

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Answer:8u6

Step-by-step explanation:

8+9_rjs_+5

In a case whereby Rowan spends 20% of his monthly salary on food while spending 30% of the remainder on transport the percentage of the salary does he save for clothes is 50%.

The concept that will be used here is the percentage. A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is.

The percentage of overall value  is always 100%

Given :  monthly salary on food  = 20%

              monthly salary on transport = 30%

The percentage of the salary  save for clothes = 100% - 30%  -  20% = 50%

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To find the domain and range from given points on a graph: the set of all x-coordinates is the input and the set of all y-coordinates is the output.

We know that the domain of function is the set of all possible input values for which the function is well defined.

And the range of function is the set of all possible output values for given input.

To find the domain and range of function we can graphical methhod.

We know that the input values of function are shown on the x-axis and the output values of the function are shown on the y-axis.

This means, the domain of a graph shown on the x-axis. Whereas the range is shown on the y-axis.

To find the domain and range when points on a graph are given:

the set of all x-coordinates would be the domain and the set of all y-coodinates is the range of function.

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