does this represent quntitites that are proportional

In calculus, we can find the maximum and minimum value of any function or variable without on looking at the graph of the function.

Maxima will be the giant point on the curve within the given range and minima would be the minimum point on the curve. The combination of both is extrema.

Since 0 ≤ x^2 + y^2 ≤ 6, we have e^ (6*0) ≤ e^ (6(x^2 + y^2)) ≤ e^ (6*6) on D.

So, ∫∫ 1 dA ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ ∫∫ e^36 dA

==> 6π ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ 6π * e^36, since the area of D is 6π.

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The function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ

An average rate measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

The functions are given as:

f(x) = x² --- quadratic

g(x) = 2ˣ --- exponential

The exponential function has the same base as the power of the quadratic function.

This means that the exponential function would increase faster from the point where f(x) = g(x)

This is illustrated using the following table

x      0   1   2   3   4    5

f(x)  0    1   4   9   16   25

g(x)  1   2    4   8   16   3

Hence, the function that increases at a faster rate on 0 to infinity is g(x) = 2ˣ

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The measure of ∠Q is equivalent to 21°.

Congruent triangles have both the same shape and the same size.

Given is that in △QRS, SQ ​≅ RS and m ∠R=21°.

Now, it is given that SQ ​≅ RS, this means that -

SQ = RS

Angles opposite to equal sides are equal.

∠R = ∠Q = 21°

Therefore, the measure of ∠Q is equivalent to 21°.

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Domain of the relation will be {-3,-4,1,0} and

Range of the relation will be {1,-4,-3,8}.

What is range and domain of a function?

Domain

The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).

Range

The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

Now,

As inputs in the given relation are  {-3,-4,1,0}

and outputs are {1,-4,-3,8}.

Hence,

          Domain of the relation will be {-3,-4,1,0} and

          Range of the relation will be {1,-4,-3,8}

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Answer:

im sorry but i need the points

The number of cups of milk that she will need would be = 20 cups.

A ratio is defined as the expression that shows the relationship between two numbers of the same unit.

The ratio used by Aunt Janelle to make hot chocolate is as follows;

The quantity of milk to cocoa = 5 cups : 2 cups respectively.

Therefore the cups of milk to 8 cups would be = X

That is, 5 cup of milk = 2 cups of cocoa

X cup of milk = 8 cups of cocoa

make X the subject of formula;

X = 5 × 8/2

X= 40/2

X = 20

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The value of percent in 1 decimal point is, 52.7%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

There 19 out of 36 in a class are girls.

Hence, The percentage of girls is,

⇒ 19 / 36 × 100 %

⇒ 1900/36 %

⇒ 52.7%

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Answer: 32

Step-by-step explanation:

32+33+34 = 99

They are consecutive numbers.

y=2x²+4x+4 and y=3x²+6x+9 are two instances for the provided standard form, y=ax²+bx+c.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A condition on a variable (or variables) such that two expressions in the variable (variables) have equal value is referred to as an equation. • The solution or root of the equation is the value of the variable for which the equation is fulfilled.

Here,

given standard form,

y=ax²+bx+c

examples of this,

y=2x²+4x+4

y=3x²+6x+9

The 2 examples for given standard form, y=ax²+bx+c is y=2x²+4x+4 and y=3x²+6x+9.

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By applying the required transformation, the coordinates of the translated point Q' are (-1, -11).

A translation is a type of transformation in geometry that moves every point of a figure in a fixed direction and by a fixed distance, without changing its size or shape. It is one of the basic geometric transformations along with rotation, reflection, and dilation.

Coordinates are a set of values that determine the position of a point in a certain space. In a two-dimensional space, coordinates are usually represented by an ordered pair of numbers (x, y), where x is the horizontal distance from a fixed point called the origin and y is the vertical distance from the origin. In a three-dimensional space, coordinates are represented by an ordered triple of numbers (x, y, z). Coordinates are often used to locate points in space, to describe the position of objects, and to plot graphs.

To find the coordinates of the translated point Q', we can use the rule that in a translation, the x-coordinate is decreased by the horizontal translation distance and the y-coordinate is decreased by the vertical translation distance.

Given that point Q has coordinates (5, -6) and is translated 6 units left and 5 units down, we can find the coordinates of the translated point Q' as follows:

x' = x - 6 (horizontal translation distance)

y' = y - 5 (vertical translation distance)

So the coordinates of the translated point Q' are:

x' = 5 - 6 = -1

y' = -6 - 5 = -11

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86 ml of dirt will remain after 9 passes

An equation is an expression showing the relationship between numbers and variables.

Let y represent the amount of dirt on the floor after x passes, hence:

y = abˣ

During each pass, 17% of the dirt is removed, therefore b = 100% - 17% = 0.83

If the floor initially has 460.0 ml of dirt, then a = 460.

The equation becomes:

y = 460(0.83)ˣ

After 9 passes:

y = 460(0.83)⁹ = 86

86 ml of dirt will remain

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The inequality for the expression is x≥83

inequality, In mathematics is a statement of an order relationship. The signs in inequality includes: greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

greater than( >)

less than (<)

less than or equal to ≤

greater than or equal to ≥

Kami needs to score at least 83 on her quiz, this means that kami need to score a mark greater than or equal to 83 in her quiz.

If we represent the score of kami by x, this means the expression can be represented as:

x ≥ 83

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Answer:

x+9

Step-by-step explanation:

for example x is 18 , add 9 to it will become 18+9=27

The Taylor series up to the degree 4 terms is:

e^8 + (x - 8)e^8 + (x - 8)^2/2! e^8 + (x - 8)^3/3! e^8 + (x - 8)^4/4! e^8

The Taylor series of a function f(x) at point a is an infinite sum of terms that approximates the value of the function near point a. The general form of the Taylor series of f(x) at a is:

f(x) = f(a) + (x - a)f'(a) + (x - a)^2/2! f''(a) + (x - a)^3/3! f'''(a) + ...

Where,

In the case of e^x, the function is infinitely differentiable, so all its derivatives are equal to itself. Hence the Taylor series at a=8 is:

e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8 + ....

by taking the degree 4 terms we can find the Taylor series of e^x at a = 8 up to the degree 4 terms, which is

e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8

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The enclosed area between the 2 equations, x = 7y² and x = 4 + 6y² is 32/3 sq units

Here equation 1 is x = 7y²

and equation 2 is x = 4 + 6y²

To find the area enclosed between the region, we need to first find the points where these two lines meet.

This implies,

eq 1 = eq 2

or, 7y² = 4 + 6y²

or, y² = 4

or, y = ±2

Now if we see the graph with respect to y, the area between the y-axis and eq 2 is greater than that of the y-axis and equation 1.

Now area is enclosed between 2 lines with respect to x. Hence it will be

= ∫eq 2 dy - ∫eq 1 dy with limts of 2 and -2

= ∫4 + 6y²dy - ∫7y²dy with limits 2 and -2

= [4y + 2y³ - 7/3 y³] with limits 2 and -2

= 8 + 16 - 56/3 + 8 + 16 - 56/3 sq. units

= 48  - 112/3

= 32/3 sq units

Hence the enclosed area is 32/3 sq units

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The cost of bag of popcorn is $7.5 and that of one drink is $5.

The formula for finding the general equation of a straight line is -

[y] = [m[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.

Assume that the cost of one popcorn bag is $[x] and one drink is $[y].

Then we can write -

6x + 4y = 65

6x + 4y = 659x + 8y = 107.5

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.

Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.

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Answer:

$7.5 and 5

Step-by-step explanation:

i did this on my assignment

Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay

Discount Formulas can be used to solve Discount problems in mathematics. It aids in boosting sales. Where M.P. (Marked Price) denotes the item's full retail cost without any discounts. The selling price, or S.P., is what consumers pay for the item. A percentage of the marked price is the discount.

The loyalty card gives a 15% discount so Madison should multiply the price on the tag by (1-0.15) = 0.85 to find the price she would have to pay, before tax, in one step.

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Answer:

79 degrees

Step-by-step explanation:

there are 180 degrees in a triangle

if you deduct the sum of 15 and 86, which is 101, the third angle must measure 79 degrees

In this question, we use the theory of LCM (Least Common Multiple) for finding the numbers which are divisible by 2,5 and 10. As we know, in arithmetic, the LCM is the smallest or least positive integer that is divisible by both a and b. So, in this question we need to calculate the LCM of 2,5

step 1

Solution

LCM of 2,5,10 is 10

So, if a number is divisible by 10 then it will be divisible by 2,5,10

Like 60,100,120,450,600

step-by-step answer:

For example, let us take two positive integers 4 and 6. Multiples of 4 are: 4,8,12,16,20,24… Multiples of 6 are: 6,12,18,24…. The common multiples for 4 and 6 are 12,24,36,48…and so on.

2, 5 and 10 (LCM by Division Method).

LCM of 2, 5 and 10 = 2X5

                                 = 10

we get LCM of 2, 5 and 10 is 10.

So, if a number is divisible by 10

Then it will be divisible by 2,5,10.

Therefore, any number which is multiple of 10 or which is divisible by 10. We say it will be divisible by 2,5,10.

Like- 10, 20, 30, 40, 50, 60, 70, 80 etc.

Thus, 10, 20, 30, 40, 50 are 5 numbers which are divisible by 2,5 and 10.

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Using simultaneous equations, the price of one adult ticket is $4 and one student ticket is $7.

Simultaneous equations are two or more equations solved concurrently.

Sales of Tickets:

                                            Adult     Student   Sales Revenue

First day of ticket sales         1               8               $60

Second day of ticket sales   5              4               $48

Let the price per adult ticket = a and students ticket = s

Equation 1: a + 8s = 60

Equation 2: 5a + 4s = 48

Multiply equation 1 by 5:

Equation 3: 5a + 40s = 300

Subtract equation 2 from equation 3:

5a + 40s = 300

-

5a + 4s = 48

36s = 252

s = 7

= $7

In equation 1, substitute s = 7:

a + 8s = 60

a + 8(7) = 60

a + 56 = 60

a = 4

= $4

Thus, the price of one adult ticket is $4 while the price of one student ticket at Kali's school is $7.

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The mathematical expression for the given algebraic expression is,

⇒ k / 5

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

We have to given that;

The algebraic expression is,

⇒ One-fifth of a number, k

Now, We can write the mathematical expression for the given algebraic expression is,

⇒ One-fifth of a number, k

⇒ 1/5 of k

⇒ 1/5 × k

⇒ k / 5

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Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.

The characteristics of the quadratic function graphed in the figure must be identified.

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Answer:

56 pages per hour

Step-by-step explanation:

Penny reads 14 pages in 1/4 of an hour.

An hour is 4 times more than 1/4 of an hour (you could think of it as 15 minutes compared to 60 minutes)

Multiply the amount penny reads in 1/4 of an hour (14 pages) by 4 to get the rate she reads in 1 hour.

14 x 4 = 56

Now add the rate of time (per hour) to get that she reads a total of 56 pages per hour.

Hope this helps!

On solving the provided question, we can say that quadratic equation x² - 5x+7=0 => x = 1 , -3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

x² - 5x+7=0

x(x-1) +3(x-1)

(x-1)(x+3) = 0

x = 1 , -3

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Therefore , the solution of the given problem of area is largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

The term "area" refers to how much room a 2D structure or surface occupies. We use these units to measure surface in cm2 or m2. By dividing the length by the breadth of a form, you can determine its area.

Area = length times breadth and Perimeter = 2 (length + width)

Here,

Given: 2 feet by 3 feet is the size of the map.

8 by 10 inches is the size of a sheet of paper; in inches:

12 inches per foot

24 inches are equal to two feet, or two times twelve.

36 inches are equal to three feet, or three times twelve.

Scale factor is 24/36, or two-thirds.

Paper's longer side equals ten inches.

Using the scale, determine how long the shorter side is:

2/3 = x/10

the cross-multiply

3x = 2 × 10

3x = 20

x = (20 ÷ 3)

x=6.23 inches

The largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

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Answer:

  x = -2 and 4

Step-by-step explanation:

You want a plot of the x-intercepts of H(x) = (x -1)² -9.

The x-intercepts are the points where the graph crosses the x-axis, the points where H(x) = 0. Solving, we get ...

  H(x) = (x -1)² -9

  9 = (x -1)² . . . . . . . . add 9

  ±3 = x -1 . . . . . take the square root

  ±3 +1 = x = {-2, 4} . . . . . add 1

The attached graph shows the coordinates of the x-intercept points on the x-axis. The coordinates of the vertex of the parabola are also shown.

Answer:

Step-by-step explanation:

J:  y = 29 cm + (1 cm/mo)x

Z:  y = 12 cm + (2 cm/mo)x

29 cm + (1 cm/mo)x =  12 cm + (2 cm/mo)x

Solve for x to find how many months it will take for them to have the same length of hair:

29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x

17 cm = (1 cm/mo)x

x = (17 cm) / (1 cm/mo) = 17 months

Plug this value for x (17 months) into the equations to find how long their hair will be:

J:  y = 29 cm + (1 cm/mo)(17 mo) = 46 cm

Z:  y = 12 cm + (2 cm/mo)(17 mo) = 46 cm

This shows that it will take 17 months for each girl's hair to be 46 cm long.

The catcher must throw the ball in a distance of 127.2 feet to force a runner out at second base.

From the figure we understands that it is a right angled triangle.

The hypotenuse of a right triangle is formed by the line from home plate to second base. The triangle's two sides are each 90 feet.

We can calculate the length of the hypotenuse using the Pythagorean theorem:

90² + 90² = c²

= 8100 + 8100 = c²

= 16200 = c²

c = √16200

c = 127.2

c = 127 feet

As a result, the distance that the catcher must throw the ball to get a runner out at second base is 127 feet.

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Yes , watching TV helps you live longer  by using correlation coefficient.

How to interpret a correlation coefficient?

The statistical measure of how well changes in the value of one variable predict changes in the value of another is called a correlation coefficient. The value rises or falls together when the variables are positively linked.

The r represents the correlation coefficient which has a value 0.89 for the given case.

we can say that there is a positive association between the life expectancy of citizen and the average number of TVs in households.

the r value is close to +1 which means that the association is close to linear relation .

 so we put it like

               R² = 0.89² = 0.7921

now  0.7921 signifies that almost 79% variation in life.

So we can say that  watching TV helps you live longer.

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