A concession stand at the Tennis Center sells a hamburger/drink combination dinner for $7. The profit, y (in dollars), can be approximated by
y=-0.001x² +
2+3.2x-400 where x is the number of dinners prepared.
(a) Find the number of dinners that should be prepared to maximize profit.
(h) What is the maximum profit?

The required amount of 25% saline solution is 8 liters.

In mathematics, the equation that used to find an Unknow quantity is known as Linear Equation. Here we use different types of variables to represent the unknown value like x, y, z or a, b, c.. etc.

Here we have

4 liters of a 40% saline  

we need to make it a 30% of saline solution by adding a mount of 25% saline solution

Let us assume that we added x L of 25% of saline solution  

After adding x L of 25% saline into 4 liters of 40% saline to get 30% saline solution then the resultant solution is “x+4” liters of 30% saline.

The mathematical representation for the above line will be

⇒ x litres 25% saline + 4 litres 40% saline = (x+4) litres 30% saline

⇒ x(25%) + 4(40%) = (x+4)(30%)

⇒ 25x/100 + 4(40/100) = (x+ 4)30/100  

⇒ 25x + 160 = (x +4)30  

⇒ 25x + 160 = 30x + 120

⇒ 30x - 25x = 160 - 120

⇒  5x = 40

⇒ x = 8

Therefore

The required amount of 25% saline solution is 8 liters

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Answer:

5

Step-by-step explanation:

Answer:

Slope [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2x + 5y = 21  Subtract 2x from both sides of the equation

5y = -2x + 21  divide all the way through by 5

y = [tex]\frac{-2}{5}[/tex] x + [tex]\frac{21}{5}[/tex]  The slope is the coeffience of the variable (the number before the x)

Answer:

  (a)  as x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞

Step-by-step explanation:

You want to know the end behavior of the 4th-degree function shown in the graph.

The graph has an arrow on each end of the curve shown in the figure. The left arrow points upward, indicating a tendency to +∞ as x gets more negative.

The right arrow also points upward, indicating a tendency to +∞ as x gets more positive.

  As x → -∞, f(x) → ∞ and as x → ∞, f(x) → ∞.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

C(x) = 11.99 + 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

C(m) = 11.99m + 7

The equation is in the form of y = mx + c

So,

m = 11.99

c = 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

Thus,

The slope of the function is 11.99.

The y-intercept of the function is 7.

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The transformations to the graphs of each function are presented as follows:

The parent function is defined as follows:

f(x) = log2(x).

Function p(x) is defined as follows:

p(x) = 7log2(x) - 2.

The transformations are listed as follows:

Function r(x) is defined as follows:

r(x) = -2log2(x) + 3.

The transformations are listed as follows:

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Answer:

its c b a

Step-by-step explanation:

other person was wrong

The real roots of the function is {0,-2} and there are no repeated roots.

Given function:

f(x) = [tex]x^{2} +2x[/tex]

[tex]x^{2} +2x=0[/tex]

take x as common

x(x+2) = 0

x = 0 and x + 2 = 0

x+2 = 0

x = -2,0.

Therefore the real roots of the function is {0,-2} and there are no repeated roots.

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Answer:

Down Here ↓↓↓↓↓↓↓

Step-by-step explanation:

Hello!

This is all the information we need to fill up the blank spots:

Two angles whose sum is 180° are supplementary angles.

Vertical angles are formed by the opposite angles when two lines intersect.

Vertical angles are congruent/equal/equal in measure.

A linear pair of angles form adjacent angles, and the sum of their measures is 180°.

Adjacent angles share a common vertex and side.

The number of bicycles that are there is 4.

There are a Total of 11 bicycles and tricycles altogether in the shop window.

They have a total of 29 wheels.

Therefore, the number of bicycles that are there can be calculated as follows;

Bicycles has 2 wheels and tricycles has 3 wheels.

Therefore,

let

x = number of bicycle

y = number of tricycle

2x + 3y = 29

x + y = 11

Multiply equation(ii) by 2

2x + 3y = 29

2x + 2y = 22

y = 7

x = 11 - 7

x = 4

Therefore the number of bicycle is 4.

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V+12 is the expression that shows how many volunteers there are now

An expression is combination of variables, numbers and operators.

Given,

At the start of the year, the soup kitchen had v volunteers.

During the year, 12 more volunteers joined them

Joined them means added, it means 12 volunteers are added to the v volunteers

v plus twelve.

v+12

Hence v+12 is the expression that shows how many volunteers there are now

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Answer:  " x = 1 ".

    The answer for this 'system of equations' is:  " [1, 15] ".

_________

Step-by-step explanation:

To solve for x :

Given:
  y = 3x + 18

  y = 15 ;

_________
 We know that:

 3x + 18 = 15 ;  Now, subtract 18 from Each Side of the equation:

  3x + 18 − 18 = 15 − 18 ;

  to get:

  3x = 3 ; Now, divide Each Side of the equation by 3 ;

     to isolate x on one side of the equation;

      and to solve for x :
 

   3x / 3 = 3 / 3 ;

   to get:    x = 1

_________

The answer is: " x = 1 " ;

 The answer for this 'system of equations' is:
   " [1, 15] " <== { written as:  " [x, y] "} ;

                         in which: " y = 15 " ; is given in the problem.

_________
Hope this answer is helpful.
 Best wishes!
_________

Answer:

f(x) = 4x
for graph see attachment

Step-by-step explanation:

when the buyer gets 4 points for each movie purchased, the equation for the graph is f(x) = 4x

x being the movies, 4 being the amount of points per movie granted.

The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .

We know that the general form of the equation of a circle is given by the following equation:

(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.  

So the general equation of the circle is (x-5)² + (y+3)² = 9² .

Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.

The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.

(x-5)² + (y+3)² = 9²

or, x² + 10x + 25 + y² + 6y + 9 = 81

or, x² + y² + 10x + 6y - 47 = 0

Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.

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Answer:

D ,

Step-by-step explanation:

4cd(6-9c)

5(x+5)

22 members were present and 8 members were absent.

There are 30 members in a committee.

On a certain day 11/15 of the total members were present.

Let x be the number of members who were present.

So, we get an equation,

x = 11/15 * 30

We solve above fraction.

x = 11 * 2

x = 22

So, 22 members were present.

And 30 - 22 = 8 members were absent.

Therefore, 22 members were present and 8 members were absent.

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The amount of fence the farmer will need to buy is 90 ft

The area of rectangle is the product of its length to its width.

i.e., Area of Rectangle= length x width

let the length of the back of his house be x ft.

Thus, if the second side of the garden to be 30 feet longer than the back of his house,

then the length of the second side is; (x + 30) ft.

Now,

Area = Length × width

400 = x (x + 30)

400 = x² + 30x

x² + 30x - 400 = 0

Solving the quadratic equation:

x = -40 or 10

Thus, length of second side = 10 + 30 = 40 ft

Now, Perimeter of 3 sides = 10 + 2(40)

Perimeter of 3 sides = 90 ft

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The distance travelled by the tortoise in 1/4 hour is 0.5miles

A rate is a more general measure in which one quantity is divided by another quantity, where both quantities don't necessarily need to have the same unit of measure. For example , Tayo typed 500 words in 50 minutes. This means that the rate of Tayo in typing is 500/50= 10words per minutes.

The tortoise travels 2miles in 1hour. There are two terms of different unit, which are distance in miles and time in hours

if the tortoise travels 2miles in 1hour

then in 1/4 hours,

the tortoise will travel 2×1/4

= 0.5mile

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The Sum is 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

A finite series is one that has a finite number of terms.

If the series [tex]a_1[/tex]+ [tex]a_2[/tex] + [tex]a_3[/tex] +... + a has n terms and is a finite series with n terms.

As a result, [tex]S_n[/tex] is used to represent the series' sum as follows:

[tex]S_n[/tex]=∑ [tex]a_n[/tex]

Given:

1 + x + x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex]

let P= 1/ 1-x

P - Px= 1

P= 1+ Px

 = 1 + (P)x

 = 1 + (1+ Px) x

 = 1+ x + Px²

 = 1+ x + (1+ Px)x²

 = 1+ x + x² + Px³ and so on

So, 1+ x² + x³ + [tex]x^4[/tex] + [tex]x^5[/tex] + ⋯ + [tex]x^{100[/tex] = [tex]\sum^{100} _ {n=0}[/tex] 1/( 1- x)

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Answer:

8c³

Step-by-step explanation:

What is a coefficient?

A coefficient is a number that does not stand alone. For example, 3w means 3 times w, and "w" is a variable, so 3 is a coefficient.

How do we find the first term?

We can find the first term by putting the numbers from greatest to least. For example, if we had the numbers: 3x+7p+2 we would rearrange the series to this: 7p+3x+2. The number that comes first in the series would be the first term.

Answer:

Step-by-step explanation:

The train A speed is 45 mph.  The train B speed is 70 mph.

The mean number of students per Faculty is 326.

Mean simply means the average of a set of numbers.

In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:

= Total values / 9

= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9

= 2938 / 9

= 326.44

The mean is 326.

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Answer: An investor bought 500 shares of stock , some at $ 3.50 per share and some at $6.00 per share. If the total cost was $ 2187.50, how many shares of each stock did the investor buy?

(a) How will you set up the problem?

Let # of 3.50 shares be "x" ; value is 3.5x dollars

# of 6.00 shares is "500-x" ; value is 6(500-x)=3000-6x dollars

EQUATION:

value = value = 2187.50

3.5x + 3000-6x = 2187.5

-2.5x = -812.5

x = 325 (# of 3.50 shares)

500-x = 175 (# of 6.00 shares)

Step-by-step explanation:

Using dilation rules, the dilated triangle whose coordinates of the vertices are as follows: A'(-2 , 2), B'(-1,0), C'(1 , 2).

What is the rule for a dilation?

To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:

(x, y) -> (ax, ay).

suppose the coordinates of the vertices of ABC are given as follows:

A(-6,6), B(-3,0), C(3,6).

After a dilation with a scale factor of 1/3, the coordinates of the vertices of A'B'C' will be given as follows:

A'(-2 , 2), B'(-1,0), C'(1 , 2).

These coordinates are derived multiplying the coordinates of A, B and C by 1/3.

For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by 2 to generate the dilated triangle.

Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex] \sf x = 4 :: 8 : 2[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\boxed{\: x = \frac{4 \times8}{2} = \frac{32}{2} = 16 }[/tex]Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{16 : 4 :: 8 : 2}[/tex]

A number is divisible by 3 it the sum of its digits is divisible by 3. In this case, we have

which is not divisible by 3. The nearest multiples of 3 are 1623 and 1626. If you divide these numbers by 3, you have

So, the result of our division is between 541 and 542.

If these numbers are too complex to divide, we have to choose easier numbers, but we will lose some accuracy. For example, we can see that 1624 is between 1500 and 1650, which are very easily divisible by 3. We have

So, the result of our division is between 500 and 550. This is still true, but as you can see it is a much looser approximation than the one before.

The value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

First, let us know some laws of exponent:

We are given;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] and [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex].

Now, we will solve one by one;

[tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex]

[tex]= \sqrt[5]{\frac{2^{10}(x^{-10})}{(2^5x^{-15})}}[/tex]

[tex]=[({2^{10}. 2^{-5}) (x^{-10}.x^{15})}]^\frac{1}{5}[/tex]

[tex]=[({2^{10-5}) (x^{-10+15})]^\frac{1}{5}[/tex]

[tex]=[({2^{5}) (x^{5})]^\frac{1}{5}[/tex]

= 2x

So, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x.

Now,

[tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex]

[tex]=\frac{(2^3x^6y^{-3})^\frac{1}{3} }{(2^3x^3y^3)}[/tex]

[tex]=\frac{(2x^26y^{-1})}{(2^3x^3y^3)}[/tex]

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

[tex]=\frac{1}{(2^{2}x^{1}y^{4})}[/tex]

= 1 / 4xy^4

So, the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Thus, the value of [tex]\sqrt[5]{\frac{1024(x^{-1})^{10}}{(2x^{-3})^5} }[/tex] is 2x and the value of [tex]\frac{(8x^6y^{-3})^\frac{1}{3} }{(2xy)^3}[/tex] is 1 / 4xy^4.

Please find the figure for the questions below.

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The number of pennies that Anya has is equal to 15.6 pennies.

The number of dimes that Anya has is equal to 2.8 dimes.

In order to solve this word problem, we would assign variables to the number of pennies and dimes, the total number of coins, and then translate the word problem into algebraic equation as follows:

Note: 1 penny is equal to 0.05 dollar and 1 dime is equal to 0.10 dollar.

Therefore, translating the word problem into an algebraic equation, we have the following;

p = 10 + 2d                                ......equation 1.

0.05p + 0.1d = 1.06                   .......equation 2.

Substituting equation 1 into equation 2, we have:

0.05(10 + 2d) + 0.1d = 1.06  

0.5 + 0.1d + 0.1d = 1.06

0.5 + 0.2d = 1.06

0.2d = 1.06 - 0.5

0.2d = 0.56

Dimes, d = 0.56/0.2

Dimes, d = 2.8 dimes.

For the number of pennies, we have:

p = 10 + 2d

p = 10 + 2(2.8)

p = 10 + 5.6

p = 15.6 pennies.

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The features from the graph of the function are given as follows:

a) The domain is {x | x ≠ -2}.

b) The range is {y | y ≠ 1}.

c) The x-intercept is: x = 0.

d) The y-intercept is: y = 0.

The domain of the function is the set of input values of the function, hence the values of x from the graph.

From the graph, the function is not defined at x = -2, hence the domain is:

{x | x ≠ -2}.

The range of the function is the set of input values of the function, hence the values of y from the graph.

From the graph, the function has an asymptote at y = 1, hence the range is:

{y | y ≠ 1}.

The x-intercept is the value of x at which the function crosses the x-axis, hence:

x = 0.

The y-intercept is the value of y at which the function crosses the y-axis, hence:

y = 0.

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