A ball is thrown upward and outward from a height of 5 feet. The height of the ball, y, in feet, can be modeled by y=-0.4x^2+1.6x+5 where x is the​ ball's horizontal​ distance, in​ feet, from where it was thrown.
a. What is the maximum height of the ball and how far from where it was thrown does this​ occur?
b. How far does the ball travel horizontally before hitting the​ ground?
c. Graph the equation that models the​ ball's parabolic path.

The profit function for the concert is presented as follows;

y = -100•x² + 2,000•x - 1,000

The maximum profit is $9,000

A profit function is one that gives the profit of a business which is the difference between the business's revenue and the costs of the business.

Profit = Revenue - Cost

Revenue = Quantity × Ticket price

Cost = Quantity × unit cost

Which gives;

y = Q•x - Q•c = Q•(x - c)

Given that the quantity, Q, varies, and Q•(x - c) is the product of two variables, a quadratic function is used as follows;

y = a•x² + b•x + c

When x = 0, y = -1000

Which gives;

y = a×0² + b×0 + c = -1000

c = -1000

When x = 3, y = 4,100

Which gives;

4,100 = a•3² + b•3 - 1000 = 9•a + 3•b - 1000

4,100 = 9•a + 3•b - 1000

5,100 = 9•a + 3•b

When x = 6, y = 7,400

Which gives;

7,400 = a•6² + b•6 - 1000 = 36•a + 6•b - 1000

7,400 = 36•a + 6•b - 1000

8,400 = 36•a + 6•b

Solving gives;

a = -100, b = 2,000

Which gives;

y = -100•x² + 2,000•x - 1,000

The profit function is therefore;

The maximum profit is therefore at point, x = -2000/(2×(-100)) = 10

Which gives;

Max profit = -100×10² + 2,000×10 - 1,000 = 9,000

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Answer:

11/20

Step-by-step explanation:

4/5 - 1/4

We need to get a common denominator of 20

4/5 * 4/4 = 16/20

1/4 *5/5 = 5/20

Replacing the fractions with their equivalent fractions

16/20 - 5/20

11/20

Answer: 4

Step-by-step explanation: Divide both sides by -3 so the x is by itself. When you divide both sides by -3, you get x =4.

Answer:

4

Step-by-step explanation:

Divide -3 on both sides so that x is by itself

-3x = -12

-3      -3

-3 is cancelled out

-12 divided my -3 is 4

Since both numbers are negative it would end up positive.

If the numbers are both positive then it would be positive as well.

And if one number is positive and the other is negative then the answer would be negative.

The answer would be: 4

I hope it helps! Have a great day!

The statement that shows Sam's purpose for making the investment,  is; Sam wants an investment that offers a higher return than stocks.

We know that bonds refers to a type of investment that could be held for a while the hope of making returns. Both the bonds and the stocks are common types of investments that are traded in the equities market. They are held by buyers with the sole hope that they could yield returns.

However, the bonds tend to be more secure than the stocks. The stocks are actually an overly volatile kind of investment. The bonds when mature tends to provide a high return on investment for the investor compared to the stocks.

Hence, the statement that shows  Sam's purpose for making the investment,  is; Sam wants an investment that offers a higher return than stocks.

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Answer:

80,000 numbers.

Step-by-step explanation:

Since the number is 6-digits and is larger than 599,999, it would be between 600,000 and 999,999.

Between those two numbers (included), there are [tex]999999 - 600000 = 399999[/tex] numbers.

In addition, we know that the number is a multiple of 5. Therefore, we should divide this number by 5 to find how many of the numbers in that group are divisible by 5.
Since it's difficult dividing 399,999 by 5, I would divide 400,000 by 5, as we must also include 600,000.

[tex]\frac{400000}5 = 80000[/tex]

The value of x for the equation 4 log₃2-2 log₃x=1 is 2.30946

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a set number, base b, must be increased in order to obtain a specific number x, is represented by the logarithm of that number.

Given,

4 log₃2-2 log₃x=1

log₃ 2⁴ - log₃ x² = 1

using logₐ(m - n) = logₐ(m/n)

log₃(2⁴ / x²) = 1

2⁴ / x² = 3¹

x = 4/√3

x = 2.30946

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x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).

This is further explained below.

Generally, the equation for is  mathematically given as

Differentiate both sides of the equation of the circle with respect to x, treating y=y(x) as a function of x:

[tex]x^2+y^2=5 \Longrightarrow 2 x+2 y \frac{\mathrm{d} y}{\mathrm{~d} x}=0 \\\\ \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{x}{y}[/tex]

This gives the slope of any line tangent to the circle at the point (x, y). Rewriting the given line in slope-intercept form tells us its slope is

[tex]x=2 y+5 \\\\ y=\frac{1}{2} x-\frac{5}{2} \\\\ slope =\frac{1}{2}[/tex]

In order for this line to be tangent to the circle, it must intersect the circle at the point (x, y) such that

[tex]-\frac{x}{y}=\frac{1}{2} \\ \\\\ y=-2 x[/tex]

In the equation of the circle, we have

[tex]x^2+(-2 x)^2=5 x^2=5 \\\\ x=\pm 1 \\\\ y=\mp 2[/tex]

If x=-1, then

[tex]-1=2 y+5\\\\ y=-3 \neq 2[/tex]

If x=1, then

[tex]1=2 y+5 \\\\ y=-2$[/tex]

In conclusion, as expected. Therefore x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).

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Adult tickets that were sold were 210 .

Let the no. of children be x and no. of adults be y .

According to ques .

x + y = 385     - eq 1

4 x + 6 y = 1960          - eq 2

Solving linear equation in 2 variable by method of substitution ,

multiply   - eq 1 by 4 ,

4 x + 4 y = 1540     - eq 3

multiplying  - eq 3 by - 1

- 4 x - 4 y = - 1540         - eq 4

Adding  - eq 2 and   - eq 4

2 y = 420

y = 210

Hence , 210 adult tickets were sold .

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Answer:

x=3

Step-by-step explanation:

The solution 'x' of the expressed logarithmic expression is 17.65.

A logarithmic equation one in which the variable x contains a logarithm.

The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.

Now, as per the stated log expression;

3 ln x + ln 5 = 7

Apply the Power Rule on the first term of the given equation;

ln x³ + ln 5 = 7

Now, by the Product Rule, we can re-write the equation in the form;

ln (x³×5) = 7

ln (5x³) = 7

Using the exponent form of the log on both side.

e∧ln (5x³)  = e⁷

As, we have the same base for the obtained expression. Use the exponent rule;

(5x³)  = e⁷

x³ = e⁷/5

Substitute the value of exponent e = 2.72

x³ = (2.72)⁷/5

x³ = 5507.5

Take cube root on both side;

x = 17.65

Thus,  solution for the value of 'x' for expressed logarithmic expression is 17.65.

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The formula for r will be C/2π.

The radius of the yo-yo will be 6.02 feet.

It should be noted that circumference simply means the distance round the circle.

In this case, the circumference is given as 37.8 feet.

The formula is illustrated as:

C = 2πr

r = C/2π

The radius will be:

r = C / 2π

r = 37.8 / (2 × 3.14)

r = 37.8 / 6.28

r = 6.02

Therefore, the radius of the yo-yo will be 6.02 feet.

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The value of x in the absolute value inequality is given as5 - 10|3x + 3| < 95 is all set of real numbers

The absolute value inequality is given as

5 - 10|3x + 3| < 95

Subtract 5 from all sides of the absolute value inequality

So, we have

- 10|3x + 3| < 90

Multiply -1/10 to all sides of the absolute value inequality

So, we have

|3x + 3| > -9

This means that the value of x is all set of real numbers

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Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

[tex]x+6=0[/tex]

Subtract 6

[tex]x+6-6=0-6[/tex]

Simplify arithmetic

[tex]x=0-6[/tex]

Simplify arithmetic(again)

[tex]x=-6[/tex]

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!

Answer:

5x = 15

2x = 6

10x = 30

8x = 24

21x = 63

Step-by-step explanation:

The equations that can give you an answer of 3 are the following

[tex]3x=9[/tex]

[tex]6x=18[/tex]

[tex]11x=33[/tex]

[tex]10x=30[/tex]

[tex]7x=21[/tex]

The equations above are one step linear equations

and many many more

Answer:

c - 12 = 4

Step-by-step explanation:

Hello!

Decreasing a number by something is subtracting that number with something.

c decreased by 12 can be represented as c - 12.

When something is something, we set it equal to each other. We can set that equal to 4 to find our equation.

Equation: c - 12 = 4

Answer:-55

Step-by-step explanation:

-11 times 5= -55

Step-by-step explanation:

-by-step explanation:

y=\frac{2}{x+1}-3y=

x+1

2

−3

asymptotes:

x+1 = 0

x = -1

y = -3

asymptotes: x = -1, y = -3

x int: (-\frac{1}{3}, 0)(−

3

1

,0)

y int: (0, -1)

D: (-infinity, -1) (-1, infinity) x cannot be -1

R: (-infinity, -3) (-3, infinity) y cannot be -3

Expression as a single logarithm of 5 log₇2-2 log₇y is Log (2x/3y).

Log a + Log b = Log ab

Log a - Log b = Log (a/b)

so starting with the bracket, we have;

Log 2 + Log X - Log 3y

Furthermore, we have;

Log 2x - Log 3y

Finally, we have;

Log (2x/3y)

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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The closest side length of each side of the garden is 7 feet .

It is given that Billy is planting a square garden that is 48 ft.²

Putting A = 48 ft.² in equation (1) , we get

       [tex]48=a^2\\a=\sqrt{48} \\a=6.92[/tex]

which is approximately equal to 7

Hence , closest side will be 7 ft.

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Answer to this question is:

Domain of given function is (0,∞),{x|x>0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is 9/x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(0,∞)

Set-Builder Notation:{x|x>0}

The set of all valid y values constitutes the range.Graph may be used to find the values.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (0,∞),{x|x>0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is 9/x²

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Answer: A, C and F

Step-by-step explanation:

Answer: $75 difference per shirt

Step-by-step explanation:

The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.

Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.

Fir example, if we want to select 2 players from 6. This will be:

= 6! / 2! (6 - 2)!

= 15 ways

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The inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore, the inverse of the fuction y = 3 x + 2 is y = x/3 - 2/3.

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Answer:

4

Step-by-step explanation:

because if it has two Pairs that's 2 on each side of the side of the shape

so, when you have a figure of 2 parallel sides id would be a parallelogram

Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!

Aircraft a has 371 seats and Aircraft b has 235 seats.

A linear equation is an algebraic equation that has highest degree of 1.

The total number of seats in both aircraft is 606.

Assuming aircraft b has x number of sheets.

∴ Aircraft a has (x + 136) number of sheets.

From the question itself we can form a numerical expression which is

x + (x + 136) = 606.

2x + 136 = 606.

2x = 606 - 136.

2x = 470.

x = 470/2.

x = 235.

So, Aircraft b has 235 seats and Aircraft a has ( 235 + 136) = 371 seats.

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Answer:

4

Step-by-step explanation:

Well, 2*2 = 4, so the answer is 4

Answer:

[tex]A = 4x^2 - 50x + 150[/tex]

Step-by-step explanation:

Since we are given that the path is `x` meters wide, e can express both the length and the width of the pool by subtracting `2x` from the length and width of the outside edge of the path.

[tex]w = 15 - 2x\\l = 10 - 2x[/tex]

Therefore, we can express the area of the pool using [tex]x[/tex] by substituting the values of [tex]w[/tex] and [tex]l[/tex] into the formula for the area of a rectangle.

[tex]A = w \times l\\A = (15-2x)(10 - 2x)\\\to A = 15 \times 10 - 15 \times 2x - 2x \times 10 - 2x \times (-2x)\\\to A = 150 - 30x - 20x + 4x^2\\\to A = 4x^2 - 50x + 150[/tex]