A water rocket is launched froni a platform. The height,
h in metres, of the water rocket at time & seconds after
it is launched is h= -212 + 74 + 4. When does the water
rocket hit the ground?​

Answer:

  -5/4

Step-by-step explanation:

To evaluate the function, put the value of the argument where the variable is and do the arithmetic.

  f(x) = -x -3x²

  f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x

  f(1/2) = -2/4 -3/4 = -5/4

The value in simplest form is ...

  f(1/2) = -5/4

Answers:

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Explanation:

Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).

If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.

If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.

In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.

Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.

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Problems 3 and 4 are linear functions of the form y = mx+b

m = slope

b = y intercept

This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.

If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.

On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.

Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.

The correct answer is A. 5 + 9 = 9 + 5 is an example of the commutative property of addition.

The commutative property of addition states that the order of the numbers being added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a. In this example, 5 + 9 = 9 + 5, which shows that the order of the numbers being added does not change the sum.

B. (9 + 2) + 8 = 9+ (2 + 8) is an example of the associative property of addition.

C. 4+ 7 = 3 +4 is not an example of commutative property as its not true 4+7 != 3+4

D. 6 x 1 = 6 is an example of identity property of multiplication.

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Answer:

D.) x = 2y²

Step-by-step explanation:

You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.

As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]

They spoke of a bicycle that is 1-foot long. the revolutions the tire will make when it is ridden one mile is 1681.52 revolutions.

Generally, The circumference of a tire is equal to the diameter times pi

C = d * pi.

Since the spoke of the bicycle is 1 foot long, the diameter of the tire is also 1 foot.

Therefore, the circumference of the tire is 1 * pi = approximately 3.14 feet.

To find out how many revolutions the tire will make when it is ridden one mile, you need to divide the distance traveled (1 mile) by the circumference of the tire.

One mile is equal to 5280 feet, so to find out how many times the tire will revolve, you would divide

5280/ 3.14

=1681.52 revolutions.

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The angle of elevation that the instruments have to record to be at the correct height is given as 79°

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

Given that?

First, we determine the length of side c using the law of cosines.

c = √( a² + b² - 2ab( cosC ) )

We substitute in our values

c = √( 20² + 13² - 2×20×13( cos 139° ) )

c = √( 400 + 169 - 520( cos 139° ) )

c = √( 569 + 392.44898 )

c = √961.44898

c = 31 cm

Next, we find Angle A, using the law of cosines.

A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]

We substitute in our values

A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 )  ]

A = cos⁻¹[ ( 169 + 961 - 400) / 806]

A = cos⁻¹[ 730 / 806]

A = cos⁻¹[ 0.9057 ]

A = 25°

The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

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Answer:

Maybe the answer must be 90°

The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5

From the table in the question, we are given;

Number of blackberry muffins = 10

Number of banana nut muffins = 25

Number of Chocolate chip muffins = 1

Number of blueberry muffins = 11

Number of pumpkin spice muffins = 3

Total number of muffins = 10 + 25 + 1 + 11 + 3

= 50

Probability = number of successful outcomes/Total number of outcomes

Thus;

P(banana nut muffin) = 25/50

= 0.5

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y(x)  = [tex]\frac{1}{3-x^2}[/tex] is the solution of the given differential equation.

A differential equation is an equation that relates a function and its derivatives; it describes how a quantity changes with respect to another. and its solution is a function that satisfies the equation for all values of the independent variable

y'=2x[tex]y^2[/tex]

where y' is dy/dx

so dy/dx = 2x[tex]y^2[/tex]

=> dy/ [tex]y^2[/tex] =2xdx

integrating on both side we get:

-1/y = [tex]x^2[/tex] +c   --- (i)

where c is a constant

given that y(1) =2

putting the value of y = 1/2 and x=1 in equation (i) we get

so  -2 = 1+c

=>  c= -3

y(x) = 1/(3-[tex]x^2[/tex])  is the required solution of the differential equation.

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Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

The given polynomial function has 1 relative minimum and 1 relative maximum.

The given function is

f(x) = 2x³ - 2x² + 1

derivating the above function,

f'(x) = 6x² - 4x

At slope = 0, f'(x) = 0 (for maximum and minimum values)

⇒ 6x² - 4x = 0

⇒ 2x(3x - 2) = 0

2x = 0 or 3x - 2 = 0

∴ x = 0 or x = 2/3

Then the y-coordinates are calculated by substituting these x values in the given function,

when x = 0;

f(0) = 2(0)³ - 2(0)² + 1 = 1

So, the point is (0, 1)

when x = 2/3;

f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27

So, the point is (2/3, 19/27)

Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.

So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.

Thus, option A is correct.

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Answer:

1/9, 3, 27

(A / the first option listed)

Step-by-step explanation:

Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression

first,

x = -2

3ˣ → 3⁻²

when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:

3²  =  3 · 3 =  9

so, 3⁻² =  [tex]\frac{1}{9}[/tex]  (1/9)

next,

x = 1

3ˣ → 3¹

now, here we have something raised to the power of 1, which is always itself, so  3¹ = 3

   (think of ^to the power of  as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)

and finally,

x = 3

3ˣ → 3³

here, we can multiply 3 by itself 3 times:

3 · 3 · 3 = 27

so, 3³ = 27

[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}

So, our answers in order are:

1/9, 3, 27 (the first option listed)

hope this helps! let me know if I should clarify anything :)

Step-by-step explanation:

x, y = 2 numbers

x = 2y

y - x/2 = 20

this is impossible to solve. there is no solution.

because the first equation tells us

y = x/2

and so the second equation is

x/2 - x/2 = 20

0 = 20

so, again, no solution.

The value of x-y from the given condition is 14.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The given ratio is x:y=5:3.

So, x/y =5/3

3x=5y

To the equation x+y=56, multiply 5 on both side, we get

5x+5y=280

5x+3x=280

8x=280

x=35

Substitute x=35 in equation x+y=56, we get

35+y=56

y=21

Now. x-y is

35-21=14

Therefore, the value of x-y from the given condition is 14.

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The six types of algebraic expressions are:

Monomial: An expression with only one term, such as 5x or 2[tex]y^3[/tex].

Binomial: An expression with two terms, such as 3x + 4y or 7a - 5b.

Trinomial: An expression with three terms, such as 2[tex]x^2[/tex] + 4x - 6 or 5[tex]a^2[/tex] + 3ab - 2[tex]b^2[/tex].

Polynomial: An expression with more than one term, such as 2[tex]x^3[/tex] + 4[tex]x^2[/tex] - 6x + 8 or 5[tex]a^4[/tex] - 3[tex]a^2[/tex]b + 2[tex]b^3[/tex].

Rational expression: An expression that is the ratio of two polynomials, such as (2x+3)/(x-4) or (5[tex]a^2[/tex]-3b)/(a-2b).

Radical expression: An expression that contains a square root, cube root, or any other root of a number or a variable, such as √x or 3√(2y+5)

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The domain of a relation or function are the input values. In this image the domain is represented by the begining of the arrows (the values on the x column).

What is a one one function?

In Maths, an injective function or injection or one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. We can say, every element of the codomain is the image of only one element of its domain.

The range are the output values. In this case they are the ends of the arrows (the values on the y column

• Domain: {5, 10, 15, 20}

• Range: {-3, -1, 1, 3}

• Description: ,this is an injective function, because it is a one to one relation

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the area of a triangle with base 16 cm and height 8 cm is 64 cm^2

What is triangle?

" Triangle is defined as the two dimensional geometric shape with three vertices, three sides, and three interior angles enclosed in it."

Standard formula A= 1/2 bh

Area of the triangle =1/2 bh

According to the question,

Given,

Given formula of the area of the triangle

b represents the base of a triangle=16

h represents the height of a triangle

Area of the triangle =?

Height of the triangle =8

Substitute the value in the given formula we get,

=1/2*8*16

= 64

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On solving the provided question, we can say that the solution of the System of Equation  3000 + 500x = 1000*

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.

The equation for Appleville is

3000 + 500x,       in x years after the year 2000

The equation for Bananaville is

1000*   , in x years after the year 2000

The solution of the equations

3000 + 500x = 1000*

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Answer:

w is greater than or equal to 15

Step-by-step explanation:

15(5)=75

The linear correlation coefficient unknown population is denoted by the statistic r and correlation strength is denoted by the parameter p, respectively.

As a result, correlations are generally portrayed by the two integers r and p. A number of +1 denotes a fully linearly positive correlation, while a number of -1 denotes a fully linearly negative connection. The correlation coefficient has a range of -1 to +1. The linear correlation becomes weaker as r approaches closer to zero.

The sample correlation coefficient evaluates the scatter plot points and a linear regression line constructed from those points (r). The correlation coefficient, denoted as r, ranges in value from -1 to 1. A p-value is a measure of statistical significance.

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Answer: [tex]g(x)=5^x - 10[/tex]

Step-by-step explanation:

g(x) is the graph of f(x) translated 10 units down.

There is a total of 420 Oranges were sold on Friday.

What is a fraction?

A fraction is a mathematical expression that represents a ratio of two numbers. It is written as a ratio of two integers, with the numerator (top number) representing the number of parts being considered and the denominator (bottom number) representing the total number of parts in the whole. The fraction can be written with a slash (/) or a horizontal line.

let the original number of orange be x

total orange sold = 2x/7 + 3x/8 + x/5 = 241x/280

Oranges left = x - 241x/280 = 39x/280

now, 39x/280 = 156

x = 1120 were there.

According to question

number of oranges sold on Friday = 3/8 * 1120

= 420 Oranges were sold on Friday.

Hence, there is a total of 420 Oranges were sold on Friday.

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Answer:

[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple