The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.

An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?

0 = –4.9t2 + 19.6t + 24.5
0 = –4.9t2 + 24.5t + 19.6
19.6 = –4.9t2 + 24.5t
24.5 = –4.9t2 + 19.6t

Answer:

5-1, known colloquially as four, 4, or 1+3.

Step-by-step explanation:

Answer: It is correct.

The first step here is to distribute the numbers

4 times 2x is 8x

4 times -5 is -20

Therefore, you're left with 8x-20

I hope this helps!

Answer:

r = -10

Step-by-step explanation:

1. Distribute

1-(r+2)=9

1-r-2=9

2. Subtract the numbers

1-r-2=9

-1-r=9

3. Rearrange the terms

-1-r=9

-r-1=9

Solution: r = -10

The value of BC the nearest hundredth is 15.01 .

From the image , we are able to see that CA = seven and angle A = 65°

Using ,Trigonometric Ratios , we get

Tan A = Perpendicular / Base

Tan 65° = BC / CA

2.144 =BC / 7

2.144 ×7 = BC

15.011 = BC

On rounding off to the closest hundredth , we have a tendency to get BC = 15.01

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Answer:

tan A +tanb

Step-by-step explanation:

1-tan a tan b

i think so

The average rate of change of 2|x| on the interval [-3, 5] is 0.5

The function is given as

2|x|

Rewrite as

f(x) = 2|x|

The interval is given as

[-3, 5]

So, we have

f(-3) = 2|-3| = 6

f(5) = 2|5| = 10

The average rate of change of 2|x| on the interval [-3, 5] is then calculated as

Rate = (f(5) - f(-3))/(5 --3)

This gives

Rate = (10 - 6)/(5 --3)

Evaluate

Rate = 0.5

Hence, the average rate of change of 2|x| on the interval [-3, 5] is 0.5

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Answer:

You start with 18.000 gallons and want to know when you reach 6.000 gallons, with a daily use of 450 gallons. This means you need to know how many days it take to use 18.000 - 6.000 = 12.000 gallons. This can simply be calculated with 12.000/450, which gives 26 2/3 day

Step-by-step explanation:

The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

Transformation involves changing the position and size of a shape.

The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

From the figure, we have:

So, the scale of dilation from shape A to B is:

Scale = 1/2

Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees

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Answer:

7 14/15

Step-by-step explanation:

The vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

It is given that:

The coordinates are:

Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).

After applying dilation with a scale factor of 3:

E(−3, 4) → E'(-3x3, 4x3) = E'(-9, 12)

Similarly,

F(−2, 4) → F'(-6, 12)

G(−2, −2) → G'(-6, -6)

H(−3, −2) → H'(-9, -6)

Thus, the vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

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The four rational number between -5/6 and -4/9 are (-43/54, -37/54, -35/54 and -31/54).

First we will make the denominator of -5/6 and -4/9 same by multiplying the numerator and denominator of -5/6 by 9 and multiply the numerator and denominator of -4/9 by 6, we get

-5x9/6x9 = -45/54 and -4x6/9x6 = -24/54

Now, we have -45/54 and -24/54 whose denominator are same.

we can choose or pick any four integers as numerator in between -45 and -24 with denominator as 54.

-43/54, -37/54, -35/54 and -31/54 are the four rational number having numerator in between -45 and -24 with denominator as 54.

Therefore, -43/54, -37/54, -35/54 and -31/54 are the four rational number between -5/6 and -4/9.

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For any function, we call x the numerator value and y is the denominator value.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

For any function in Mathematics, we call x the numerator value while y is the denominator value.

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The bone is approximately 16384 years old, as solved by basic algebra and logarithm.

The properties of logarithms and exponents so used are:  [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex]

Let 'a' be the original amount of the object.

Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).

We are also given that: y = a [tex]e^{-0.00012t}[/tex]

On substituting the value of y, we get: 0.14a = a [tex]e^{-0.00012t}[/tex]

By basic algebra, we can solve it as:

=> 0.14 = [tex]e^{-0.00012t}[/tex]

=> ln (0.14) = ln ([tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)

=> ln (0.14) = - 0.00012t (as [tex]log_b(a)^m=m(log_b(a))[/tex]; further  [tex]log_e(e) = 1[/tex])

=> [tex]\frac{ln(0.14)}{-0.00012}[/tex] = t

=> t = 16384 years (approx.)

Hence, the bone is approximately 16384 years old, as solved by basic algebra and logarithm; The properties of logarithms and exponents so used are:  [tex]log_b(a)^m=m(log_b(a))[/tex], [tex]log_e(e) = 1[/tex].

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Sam would need to drive for the two plans to cost the same is 130 miles.

Let, x = Number of miles driven

      y = Total cost

The first plan:

Initial fee = $65

Cost of 1 mile = $0.3

Cost of drive x mile = $0.3x

In total, you will pay

y = 0.3x + 65 for the first plan.

The second plan:

There are no initial costs, but

Cost of 1 mile = $0.80

y = 0.80x

Now we have two equations

y = 0.3x + 65

y = 0.80x

As we know that y is equal to both 0.3x + 65 and 0.80x, this means we can equate the right hand sides and solve for x.

    0.3x + 65 = 0.80x

0.80x - 0.3x = 65

            0.5x = 65

                 x =  65÷0.5

                 x =  130

The cost of two plans will be same when Sam drive 130 miles.

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Solution of exponential equation  is , x=2

In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa is also possible . The basic form of the exponential function can be written as   .

   [tex]a^n = x[/tex]

where, a = the base of function

            x = main expression

            n = exponential

Mathematically, if  [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as    [tex]a^n = x[/tex] .

There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.

According to given statement,

2^3x = 4^(x+1)

the equation can also written as :

[tex]= > 2^{3x} = 2^{2(x+1)}\\= > 3x = 2(x+1)\\= > 3x = 2x +2\\= > x=2[/tex]

Thus solution for this equation is  x = 2.

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The complete question is :

Solve each equation.

[tex]2^{3x} = 4^{(x+1)}[/tex]

The result of simplifying the expression  x³/₅ / x³/₁₀  using the exponent rules is [tex]\sqrt[10]{}[/tex](x³)

To solve this exercise we have to resolve algebraic operations following the exponent rules.

[(x)³/₅ ] /  [(x)³/₁₀]

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

x⁽³/⁵ ⁻³/¹⁰⁾

(x)⁽⁶⁻³⁾/¹⁰

(x)³/¹⁰

As we have a fractional exponent, you must convert the exponent to root:

[tex]\sqrt[10]{}[/tex](x³)

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

85

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order. The two consecutive numbers are 42 and 43.

42+43=85

Answer:

42 & 43

Step-by-step explanation:

Let the two consecutive numbers be x and x+1 .

Here it is given that the sum of two consecutive numbers is 85.

So we get the equation,

x + (x+1) = 85

We get,

x + x + 1 = 85

2x + 1 = 85

Transposing +1 to RHS,

2x = 85 - 1

2x = 84

Transposing 2 to RHS,

x = 84 ÷ 2

Therefore, we get x = 42

Therefore, the two numbers are x and x+1, so they are: 42 and 43.

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Answer:

15hw.

Step-by-step explanation:

Note 5wh is the same as 5hw, so we have:

7hw+5hw + 3hw

= 15hw.

Or, if you like, you could write it as 15wh.

A composite function exists as a function that depends on another function. The value for (f(1+h)-f(1)) / h = 2

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the function be f(x) = 2x - 3

f(1+h) = 2 (1+h) -3 = 2h - 1

f(1) = 2(1) - 3 = -1

(f(1+h)-f(1)) = (2h - 1 ) + ( -1) = 2h

simplifying the equation, we get

(f(1+h)-f(1)) / h = 2h/ h

(f(1+h)-f(1))/h = 2

Therefore, the value of (f(1+h)-f(1))/h = 2.

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The vertex is (2,-3)So the Answer isY=(x-2)-3

In the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.

So, (a+1)(2a²-3)(-4):

Therefore, in the given expressions (f x g)(-4) is -8a³ - 8a² + 12a + 12.

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Answer:

Step-by-step explanation:

The answer is just 5

f(5)=5

The given expression can be rewritten as  [tex]6 ^{-9}=\frac{1}{6^9}[/tex].

There are different power rules, as presented below:

For solving this exercise, you should identify the power rules you will apply. For this question, you can apply the following rule:

"Power -  repeat the base and multiply the exponents."

Lilke the base is 6 and the exponents are 3 and -3, then you can rewrite the expression as:

[tex](6^3) ^{-3}=6 ^{-9}=\frac{1}{6^9}[/tex]

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The approximate length is 12.755 year or 4653.75 days.

A year is the time it takes for a planet, moon, or other celestial body to make one orbit around the Sun. ( when we take our solar system as an example). In the case of other exoplanets, the celestial bodies, moon and other planets orbit around the main star. The period of the moon's orbit around the earth is related to the moon.

The reference point is very important in determining the exact length of a year. The length is dependent upon the reference point used for the orbital movement.

Jupiter completes a Single orbit once every 4333 days, due to which one Jupiter year is equivalent to 11.86 earth years.

The complete calculation is done below. (Image Attached)

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Answer: 20 quarts for two "standard" sized pots.

Step-by-step explanation:

Answer:

y =x - 3

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

 slope = m = 1

 y = 1x + b

Substitute the point (2,-1) in the above equation and find 'b'.

   -1 = 1*2 + b

   -1 = 2 + b

-1 -2 = b

     b = -3

Equation of the line:  y = x - 3

The students chose pizza as their favorite school lunch based upon the data will be 130 students.

Let the assumed fraction for those who choose pizza be 3/10.

From the information, 400 students were surveyed about their favorite school lunch.

Therefore, the students chose pizza as their favorite school lunch based upon the data will be:

= Fraction for pizza × Total students

= 3/10 × 400

= 120 students

Note that an overview was given as the graph wasn't found.

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The distance is  mathematically given as

D=1066.66667

The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.

While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours. Additionally, the function's capabilities include the ability to merge several values into a single time value.

formula= TIME (hour, minute, second)

distance = rate X time

D = RT

T = D/R

20 feet per second = 1200 feet per minute

16 feet per second = 960 feet per minute

(D/R) + 19 + (D/R) = 21

(D/R) + 19 + (D/R) = 21

(D/1200) + 19 + (D/960) = 21,

This is the equation we can use to find the distance from the flowerbed to the​ hive.

(D/1200) + (D/960) = 2

(D(1200)(960))/1200 + (D(1200)(960))/960 = 2(1200)960

960D + 1200D = 5(1200)960

2,160D = 2304000

D=1066.66667

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Answer: 20/12

Step-by-step explanation: