A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)

There are numerous reasons to use number lines to teach positive and negative numbers. But the following which is not used number line is B) Number lines match several familiar situations, like altitude, temperature, and football.

What is number line?

   A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6). Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers on the left are smaller than the integers on the right. For instance, 0 is lower than 1 and -1

Here the reasons we use number line for to teach positive and negative numbers is ,

=> Children are taught the fundamentals of addition and subtraction in mathematics using number lines with negative and positive numbers. It can also be used to multiply by skipping counts. The use of positive or negative signs makes it challenging to solve equations involving negative integers on a number line.

=> Number lines can be utilised in a variety of various ways, despite the fact that it may seem like addition, subtraction, and multiplication principles are best taught to children using number lines. The negative number line and positive number line are used by people to compute and measure specifics. These lines display the values' substantial increases and decreases.

Therefore the correct option is B)Number lines match several familiar situations, like altitude, temperature, and football.

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Answer:

it can be 100 because percentages are out of 100

Answer:

y = 4/3 x + 4/3

Step-by-step explanation:

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

y+4 = 4/3 (x +4)

y + 4 = 4/3 x + 16/3

y = 4/3 x +16/3 -4

y = 4/3 x + (16- 12)/3

y = 4/3 x + 4/3

y = 4/3 x + 4/3

Answer:

y=4/3x+4/3

Step-by-step explanation:

-4=4/3(-4)+9

-4=-16/3+9

-4=-5 1/3+9

-4= 4 1/3

4+4 1/3=8 1/3

9-8 1/3=2/3

-4=4/3(-4)+2/3

-4=-16/3+2/3

-4=-14/3

-4=-4 2/3

2/3+2/3=4/3

-4=4/3(-4)+4/3

-4=-16/3+4/3

-4=-12/3

-4=-4

A. The equation that represents the situation is $9.98 = c + $2.47

B. The solution using a related equation $.7.51

C. The solution of the equation represents the initial cost of the toy before the increment of price.

Equation:

Basically, the equation means the mathematical statement that is made up of two expressions connected by an equal sign.

Given,

Because it is popular, a store owner increases the cost of a toy by $2.47. The new cost of the toy is $9.98.

Here we need to find the following:

A. The equation that represents the situation

B. The solution using a related equation

C. The solution of the equation represent.

Here we know that the new cost of the toy is equal to the original cost of the toy plus the amount by which cost was increased.

So, the equation is written as,

=> New cost of the toy = original cost + amount of increase

=> $9.98 = c + $2.47

Here we need to determine the value of c, make c the subject of the formula by combining similar terms

So, the equation is rewritten as,

=> c = $9.98 - $2.47

=> c = $7.51

Therefore, the initial cost of the toy is $.7,51

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Answer:

the answer is 100...........

Answer:

64 marbles

Step-by-step explanation:

hope it helped :)

y=−1/2x+1/2

Step-by-step explanation:

The total surface area of the cylinder is 175.84 squared inches

The surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface.

The formula is given as

A = 2πrh + 2πr²

We can substitute the values into the equation and solve

A = 2(3.14 * 4 * 3) + 2(3.14 * 4²)

A = 175.84 in²

The cylinder has a surface area of 175.84 in²

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Answer: 175.84

Step-by-step explanation:

By using natural logarithm properties we will see that the solutions of the two equations are:

17) x = 3.11

19) p = 2.02

Here we will use the property of natural logarithms:

Ln( a^x) = x*ln(a)

17) We have the exponential equation:

5^(x - 2) = 6

If we apply the natural logarithm in both sides, we will get:

ln( 5^(x - 2)) = ln(6)

(x - 2)*ln(5) = ln(6)

(x - 2) = ln(6)/ln(5)

x = ln(6)/ln(5) + 2

x = 3.11

19) Now the exponential equation is:

7^p = 51

We will do the exact same thing, apply the natural logarithm in both sides:

ln(7^p) = ln(51)

p*ln(7) = ln(51)

p = ln(51)/ln(7) = 2.02

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The shape of units you would get that has a perimeter of 22 and an area of 30 is a rectangle, which is shown in the image below.

A rectangle is a quadrilateral that has two opposite sides that are equal and are longer than the other two opposite sides that are equal and parallel to each other.

Assuming that the shape being referred to is a rectangle that has an area of 30 units² and a perimeter of 22 units, therefore, the dimensions of the rectangle is shown in the image attached below, and they are:

Length of rectangle = 6 units

Width of rectangle = 5 units

Therefore:

Area of the rectangle = 6 × 5 = 30 units².

Perimeter of the rectangle = 2(6 + 5) = 2(11) = 22 units.

This implies that the shape of units with an area of 30 units² and a perimeter of 22 units is most likely a rectangle.

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Answer:

5n + 12p + 12m

Step-by-step explanation:

Perimeter means you are adding up all three sides.

4m + 3n + 8m + 10p + 2p + 2n

= 2n+3n + 10p+2p + 4m+8m

Combine like terms.

= 5n + 12p + 12m

Answer:

shsjsjsjsjshsh#6#7#7##+-##6#3

The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (1 + r/n) nt

Now, We can put r = 0.1 , n = 12 and t = 2 in above equation as;

⇒ (1 + r/n) nt

⇒ (1 + 0.1/12) 12 x 2

⇒ (1 + 0.008) 24

⇒ 1.008 x 24

⇒ 24.192

Thus, The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

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Answer:

(x +5)/-16=-1 this is the answer

The true equations are 24 over 2 squared equals 50 minus 6 squared minus 8 and  56 divided by 8 plus 3 squared equals 2 times 2 cubed.

The equation one is given as

39- 3(6) = 6(10/4)+4

After solving we get,

39 - 18 = 15 +4

21 = 19

Which is not a true equation.

2nd equation we have

24/(2^2)=50 -6^2-8

24/4 = 50 -36 -8

6 = 50 - 44

6 = 6

which is a true equation.

3rd equation we have

56/8+3^2= 2(2^3)

7 +9 = 2(8)

16 = 16

which is true equation.

4th equation, we have

8^2-5^2 = 4^2-7

16-10 = 16-7

6 = 9

Which is not a true equation.

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The function F(x) = -3x² + 18x + 3 has a maximum value of 30 at x = 3

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

F(x) = -3x² + 18x + 3

A quadratic function is represented as

F(x) = ax² + bx + 3

By comparison, we have

a = -3

For a quadratic function to have a maximum value, the value of a must be less than 0

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

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The derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

The chain rule is a method for calculating the derivative of composite functions, which are created by joining one or more functions.

The given function is y = tan⁻¹(x³ -4)³.

The derivative of tan⁻¹(x) is 1/(1+x²).

Use the above fact and the chain rule to differentiate the function as follows:

[tex]y = \tan^{-1}(x^3-4)^3\\\\\frac{dy}{dx} = \frac{1}{1+((x^3-4)^3)^2}\cdot\frac{d}{dx}(x^3-4)^3\\\\=\frac{1}{1+(x^3-4)^6}\cdot3(x^3-4)^2\cdot3x^2\\\\=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex]

Hence, the derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

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The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

Two or more expressions with an equal sign are defined as an equation.

The given equation is Three-fifths(30x -  15) = 72.

Simplify the equation as follows:
Three-fifths(30x -  15) = 72

3/5(30x - 15) = 72

18x - 9 = 72

Which is equivalent to "18x minus 9 = 72".

Solve for the  value of x:

18x -9 = 72

18x = 72 + 9

18x = 81

x = 81/18

x = 27/6

x = 4.5

Now, solve the equation in the first option:

18x - 15 = 72

18x = 87

x = 4.83

Solve the equation in the second option:

50x - 25 = 72

50x = 97

x = 1.94

The third equation is already shown to be equivalent to the given equation.

The solution to the fourth equation is:

3(6x - 3) = 72

18x -9 =72

Which is the same as the given equation.

The last equation is x = 4.5

Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".

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The minimum number of nickels that Jaxson could have is 9.

Given that, Jaxson has some pennies and some nickels.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of pennies be P and the number of nickels be N.

So, P + N > 13

Therefore

P×0.01 + N×0.05 ≥ 0.33

Because he has at most, $0.33

If  P = 4

4×0.01 + N0.05 ≥ 0.33

∵ $0.33 - $0.04 = $0.29

N×0.05≥ 0.29

N = 0.29/0.05 = 5.8

The number of nickels that he might have is 9.6, but because he cannot have 0.6 of a nickel, we have to round the figure down to 9.

Now that we also know that he had at least 15 coins in total, we can use that equation to get the smallest possible number for N.

4 +  N  > 13

N > 13 - 4

N> 9

So we have the range:

9 < N ≤ 5.8

Therefore, the minimum number of nickels that Jaxson could have is 9.

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The number of terms in the arithmetic sequence {-8, 1, 10, 19, 28, ..., 469} is 54 terms

The number of terms in the sequence { -8, 1, 10, 19, 28, ..., 469 } is calculated from the formula

Un = a1 + (n - 1) d

where a1 = first term

d = common difference

n = number of terms

a = -8

d = second term -  first term

= 1 - -8

= 9

solving for n

Un = a1 + (n - 1) d

469 = -8 + (n - 1)9

469 + 8 = (n - 1)9

collecting like terms

(n - 1) = 477 / 9

n - 1 = 53

n = 54

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The simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

The expression is given in the question

4(3x + 2) −2

Apply the distributive property of multiplication,

4×3x + 4 × 2 −2

12x + 8 - 2

Apply subtraction operation,

12x + 6

The expression is given in the question

20b − 16

To determine the factor of the expression

20b − 16

5 × 4 × b - 4 × 4

Factor out 4 in the above expression

4 (5b - 4)

Thus, the simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).

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Answer:

Take a look at the attachments...

Hope this helps! :)

x>1

below is the graph.

any questions in the comments:

The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.

What is a computer network?

Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.

A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.

Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).

In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.

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Answer: 33 1/3 percent

Step-by-step explanation:

First, we need to find the volume of the tennis ball can, which is a cylinder.

The formula for the volume of a cylinder is pi r^2 h.

The radius of a tennis ball is 3.2 cm, so the radius of the cylinder would be 3.2 cm as well.

The height is equivalent to the height of three tennis balls, which is the diameter of 3 tennis balls. The diameter of one tennis ball is 6.4 cm, and we can multiply this by 6 to get 38.4 as our height.

We can plug in these values to our equation for the volume of the cylinder.

pi * 3.2^2 * 38.4

The volume of the cylinder is 393.216 pi.

Now, we need to find the volume of one tennis ball and multiply that by six.

The volume of a sphere is 4/3 pi r^3

We know our radius, 3.2, so we just have to substitute that into the equation.

4/3 pi 3.2^3 = 4/3 * pi * 32.768 = 43.69 and 2/3 pi for the volume of one tennis ball. If we multiply this by six, we get the volume of all the tennis balls, which is 43.6 and 2/3 *3 = 262.144 pi.

Now we have to find the percentage of the cylinder not occupied, so we can find one percent of the container and divide that by 262.144 pi.

1% of 393.216 = 3.93216

262.144 divided by this = 66 and 2/3, so 33 and 1/3 percent of the can is not occupied. The answer depends on how many places to round to, or whether or not to keep the answer as a fraction.

For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1             2

Cost in dollars      :    $11.50      $23

As given in the question,

Given equation to represents the total cost to watch a movie related to number of tickets of movie.

c = 11.5t

Where t is the number of tickets to watch movie and c is the total cost to watch movie.

Table which represents the given situation is given by:

Option A:

Number of tickets cannot be in decimals that is 0.09 and 0.17.

Incorrect.

Option B.

Number of ticket  = 1

cost 'c' = 11.5(1)

          = $11.5

when t = 2

c = 11.5(2)

  = $23

Correct.

Option C:

Number of tickets cannot be in decimals that is 11.5.

Option D:

when t = 1

c = $0.09 is incorrect.

Therefore, For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1               2

Cost in dollars      :    $11.50      $23

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The equation 36-7p=-7p-35 has no solution.

What is equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

Here the given equation is

=> 36-7p=-7p-35

=>-7p+7p=-35-36

=>0=71

Then the statement is false for any value of p.

Hence the given equation has no solution.

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The number of hours at which both companies' rental costs will be the same is nearly 6 hours.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions displayed on the left and right sides have an equal connection. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Let the number of hours = h The deposit price at the first canoe rental company = $10

Cost per hour to rent a canoe = $8.25/h

The total cost for rental for the first company is given by

C(A) = 10 + 8.25h

The deposit price at the second canoe rental company = $12.50

Cost per hour to rent a canoe = $7.85/h

The total cost for rental for the second company is given by

C(B) = 12.50 + 7.85h

The number of hours at which both company's rental costs will be the same is given as

C(A) = C(B)

10 + 8.25h = 12.50 + 7.85h

8.25h - 7.85h = 12.50 - 10

0.4h = 2.5

h = 2.5/0.4

h = 6.25

h ≈ 6 hours

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In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

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