Decrease £19064.67 by 9.5%
Give your answer rounded to 2 DP.
​

Slope of line PQ is 2.

What is slope ?

In arithmetic, the slope or gradient of a line may be a range that describes each the direction and also the steepness of the road. Slope is commonly denoted by the letter m;

Main body:

Slope of line OP = 1

Slope of line OQ = 7

Let us assume point P = (x, y)

slope = y/x

slope of OP = 1 , so x = y

so point P = (3,3)

slope of OQ =7 , so y = 7x

assume the point Q = (1, 7)

Slope of line QP = y/x

(7-3)/ (3-1)

4/2

2 = slope of line QP.

Hence slope of line QP is 2.

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The answer is: x+x^4

Applying a subtraction operation, it is found that his new ERA was of 3.17.

ERA is a baseball concept, but understanding of baseball is not relevant to this question.

One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:

ERA = 3.91 - 0.74 = 3.17.

His new ERA was of 3.17.

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a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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By applying unitary method it can be obtained that Ryan drank 2 liters of water in one hour.

What is Unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method is used In \(\frac{3}{4}\) of an hour, Ryan drinks \(1\frac{1}{2}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(1\frac{1}{2} \div \frac{3}{4}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(\frac{3}{2} \div \frac{3}{4}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(\frac{3}{2} \times \frac{4}{3}\) liters of water at a constant rate.
In 1 hour, Ryan drinks \(2\) liters of water at a constant rate.

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Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Step-by-step explanation:

Step-by-step explanation:

product : 0.56×0.3 = 0.168

hope this helps you.

Answer:

7x6+5=47

6x5+7=37

7x5+6=41

The union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

What is an interval?

⇒ An interval is an expression that involves a subset of numbers on the actual line. These intervals contain all the actual numbers between the two numbers in the interval.

There are three types of intervals, these are:

⇒ The intervals can be joined if in the math problem the result is between one end of the real line and the other end of the real line. There are two intervals with the sign of union in the middle of them.

The representation of the union of these intervals is given as follows:(2,3]∪[3,4]  , the union is denoted by ∪

Now as in every interval the three is part, we can express this union of this set as one in the following way:

⇒ (2,4]

Hence, the union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

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For the provided points (-7,-8) and (-5,-6) on the line, the slope is 1.

The slope of a line is a measure of its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

Here,

Slope=(y2-y1)/(x2-x1)

=(-6-(-8))/(-5-(-7))

=2/2

=1

The slope of the line for given point (-7,-8) and (-5,-6) will be 1.

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The x- and y-intercepts of the graph of x + y = 18 both have the values of 18

The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0

The equation of the graph is given as

x + y = 18

To calculate the x-intercept, we set the value of y to 0

This is represented as

y = 0

So, we have the following equation

x + 0 = 18

Evaluate the like terms

x = 18

To calculate the y-intercept, we set the value of x to 0

This is represented as

x = 0

So, we have the following equation

0 + y = 18

Evaluate the like terms

y = 18

This means that the x-intercept has a value of 18 and the y-intercept has a value of 18

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y + 1 = 3(x-6) in Ax + By = C form is 3x - y = 19. A quadratic function's standard form is written as f(x) = ax2 + bx + c, where c is the y-intercept of the function's graph.

A quadratic function is the polynomial function that a quadratic polynomial defines. f(x) = ax2 + bx + c, where a, b, and c are constants and a = 0 represents a quadratic function. The quadratic term, abbreviated as ax2, the linear term, abbreviated as bx, and the constant term are all names for the function (abbreviated as c). Three points produce a quadratic function of the formula f(x) = ax2 + bx + c. A quadratic function can be determined by finding a, b, and c algebraically given three locations on the graph.

The y-intercept is the location on a graph where the y-axis crosses. To get 3x - 18 on the right side, we shall first distribute the 3 through the parenthesis. Bring down your y + 1 to the left to obtain y + 1 = 3x - 18. Subtract 1 from both sides to get y = 3x - 19, then transfer the 1 to the right side. To get -3x + y = -19, subtract 3x from both sides now. The x term's coefficient in standard form must be positive. Thus, subtract -1 from both sides to get 3x - y = 19.

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Answer:

Rise/Run

or

\(\frac{rise}{run}\)

Step-by-step explanation:

The formula for slope is referred to rise over run,

Because the fraction consists of the rise (the change in y, going up or down) divided by the run (the change in x, going from left to the right).

A rise over run equation would be formatted like this:

Rise/Run

or

\(\frac{rise}{run}\)

(i used to struggle with slopes, and i understand how much of a pain they are)

Answer:

24c+37

Step-by-step explanation:

The values of x that make the triangle acute are:

2 < x < sqrt(20)

or approximately:

2 < x < 4.47

To determine the values of x that make the triangle acute, we need to use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's apply this theorem to the given triangle. Since the longest side has a length of 12, we have:

2x + 8 > 12     (1)

2 + 8 > 2x      (2)

12 + 2x > 8     (3)

Simplifying each of these inequalities, we get:

1) x > 2

2) x < 5

3) x > -2

To make sure that the triangle is acute, we also need to ensure that the sum of the squares of the two shorter sides is greater than the square of the longest side. That is,

(2x)^2 + 8^2 > 12^2

Simplifying this inequality, we get:

4x^2 + 64 > 144

4x^2 > 80

x^2 > 20

x > sqrt(20) or x < -sqrt(20)

Since x must be greater than 2, we have:

x > sqrt(20)

Therefore, the values of x that make the triangle acute are:

2 < x < sqrt(20)

or approximately:

2 < x < 4.47

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Agility, balance, coordination, speed, reaction time, and power are all components of Skill -related fitness.

The skill-related component of physical fitness is specifically related to skills used in sports and is often (but not always) combined with other components of fitness. For example, power is strength at speed. Agility is a combination of strength and balance. The six basic fitness components related to ability are flexibility, balance, coordination (hand-eye or foot-eye), strength, reaction time and speed. If you already meet ACSM guidelines and want to train more for specific fitness-related goals, consider his six fitness components related to ability. The health component of fitness is of universal importance. Performance-related fitness components are better suited to specific athletes. For example, everyone benefits from a daily walk, but someone who walks just to get their heart pumping doesn't need to be fast enough to run a 5-minute mile.

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Answer:

p=(-0.0125n) + 42.5

Step-by-step explanation:

Let p= price

n = number of shirts

m = slope of the line (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

There are two points which are (1000, $30) and (3000, $5)

Our slope m = (p1-p2)/(n1-n2)

Filling in from our points m = (30-5)/(1000-3000)

m = 25/-2000

m = -0.0125

Since we have determined our slope, we can now find our equation

p-p1=m(n-n1)

p-30=(-0.0125)(n-1000)

p-30= (-0.0125n) + 12.5

p=(-0.0125n) + 42.5

Then, we can double check with the other point there:

p=(-0.0125n) + 42.5

5? (-0.0125x 3000) + 42.5

5= 5

Therefore,linear equation in the form p(n) is

p=(-0.0125n) + 42.5

The frequency of a radio wave that is 300 meters long is 160 kilohertz.

The frequency varies directly with the length.

To solve this problem, we can set up a proportion based on the given information. Let's represent the frequency as f and the length as l.

The frequency varies directly with the length, so write the proportion:

f₁ / l₁ = f₂ / l₂

Where f₁ = 400 kilohertz, l₁ = 750 meters, f₂ is the unknown frequency, and l₂ = 300 meters.

Plugging in the values, we have:

400 / 750 = f₂ / 300

To find f₂, we can cross-multiply and solve for it:

400 * 300 = 750 * f₂

120,000 = 750 * f₂

Dividing both sides by 750:

f₂ = 120,000 / 750

f₂ = 160 kilohertz

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Answer: 49 in^2

Step-by-step explanation:

Trapezoid area formula = (a+b/2) x h

So...

(5+9/2) x 7

= 49 in^2

\( \huge \boxed {\longmapsto\mathcal {\purple {Answer}}}\)

Area of trapezoid :

\( \boxed{ \frac{1}{2} \times sum \: of \: parallel \: sides \times height }\)

=》

\( \boxed {\frac{1}{2} \times (9 + 5) \times 7}\)

=》

\( \boxed {\frac{1}{2} \times 14 \times 7}\)

=》

\(\boxed{7 \times 7}\)

=》

\(\boxed{49}\)

\( \boxed {\mathfrak{area = 49 \:in {}^{2} }}\)

Answer:

3

Step-by-step explanation:

3x=9

3(3)=9

3/3=0=9/3=3

answer=3

Answer: 6 miles is 9.656064km

Answer:

-2.5w<6.8

-2.5w/-2.5<6.8/-2.5

w>-2.72

The derivative of \(f(x) = ln(sin^−1(e^(x^2)))\) using chain rule is \(f'(x) = 2x * e^(x^2) / √(1-e^(2x^2)).\)

To find the derivative of the function\(f(x) = ln(sin^−1(e^(x^2)))\), we can use the chain rule and the properties of logarithmic and trigonometric functions.

Let's break down the problem step by step:

The inner function is \(sin^−1(e^(x^2))\). The derivative of \(sin^−1(u) is 1/√(1-u^2).\)

Therefore, the derivative of \(sin^−1(e^(x^2))\) with respect to \(x is 1/√(1-(e^(x^2))^2) * d/dx(e^(x^2))\).

The derivative of \(e^(x^2) with respect to x is 2x * e^(x^2).\)

The derivative of \(f(x) = ln(sin^−1(e^(x^2)))\) can be written as:

\(f'(x) = 1/√(1-(e^(x^2))^2) * 2x * e^(x^2).\)

Simplifying the expression further, we have:

\(f'(x) = 2x * e^(x^2) / √(1-e^(2x^2)).\)

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We have shown that for any two elements x and y in G, xy = yx, and hence, G is abelian.

The key step in the proof was the left-right cancellation property of G, which allowed us to substitute xy for zx and obtain x = y. This property implies that the group is abelian, and hence, all elements commute with each other.

To prove that the group G is abelian, we need to show that for any two elements x and y in G, xy = yx.

Let x and y be any elements of G. Consider the element z = xy. Then, we have:

xy = zx

Multiplying both sides by y^-1, we get:

x = zy^-1

Now consider the element w = yx. Then, we have:

yx = zw

Multiplying both sides by y^-1, we get:

x = zy^-1

Since z = xy, we can substitute it in the above equation:

x = xy y^-1

Simplifying, we get:

x = y.

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G is an abelian group since the commutative property holds for any elements x and y in G.

To prove that g is abelian, we need to show that for any x or y in the group g, we have xy = yx.

Let's take x and y in g. By the property given, we know that xy = xz implies y = z for any z in g.

Now let's consider the products xy and yx. We have:

xy * yx = x(yy)x (associativity of the group operation)
      = x(y^2)x

Let z = y^2 in the property given. Then we have:

xy * yx = x(y^2)x implies y2 = yx.

Using the same property again with z = x, we have:

yx * xy = y(x^2)y implies x2 = xy.

Multiplying the two equations, we get:

y2x2 = xyxy

Since the group operation is associative, we can also write this as:

(yx)^2 = xyxy

But we just showed that y2 = yx and x2 = xy, so we can substitute and simplify:

(yx)2 = xyxy
      = y^2x^2
      = (yx)(xy)
Compute x(xy) and (xy)x:

x (xy) = (xx)y = ey (since xx = e, the identity element)
(xy)x = y (xx) = y (since xx = e)

So, ey = y = yx, which implies that xy = yx for any elements x and y in G. Cancelling (yx) on both sides, we get:

yx = xy

Therefore, G is an abelian group since the commutative property holds for any elements x and y in G.

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Answer: 42

Step-by-step explanation: