if a/b - d = 2c/b, find the value of c when a = 3, b = 4 and d = 5 ​

The area enclosed by the track is 7,530.64 m².

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr² and the area of a rectangle is (length×width).

By observing the diagram the total area enclosed by the track is the

sum of the area of a rectangle having a length of 104m and a complete circle having a diameter(2r) of 52 m and the diameter is equal to the width of the rectangle.

Therefore, The area of the track is,

= (104×52) + π(26)².

= 5408 + 2,122.64 m².

= 7,530.64 m².

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The required lowest cost for the trip of 200km is given as $657.1.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
A truck travelling at x km/h, where 30 ≤x≤ 120, uses gasoline at the rate of r(x) L/100 km, where r(x) = 1/400(4900/x + x)

Since,
For r(x) maximum, r(x) = 0
1/400(4900/x + x) = 0
4900 = x²
x = 70 km/hr

Now,
Cost of the fuel for 200km = 200 / r(70) × $1.15/L
                                         = 200/(1/400× (4900/70 + 70)) × 1.15
                                         = $657.1

Thus, the required lowest cost for the trip of 200km is given as $657.1.

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well, we can simply find how much for each tulip in each store.

store left has them for £9.8 for 4, that means 9.8 / 4 = 2.45, so £2.45 for each tulip.

store right had them for £4.2 each, but they went down by 1/3, so hmm a whole is 3/3 so if we take away 1/3 from 3/3, 3/3 - 1/3 = 2/3, so the new discounted price is really 2/3 of £4.2, that's (2/3) * 4.2 = 2.8, so £2.8 each.

so store left has them cheaper, doesn't matter at a dozen or less or more.

how much is it at store left for 12?  12 * 2.45 = 29.4, or £29.4.

1. PM:MQ and KM:ML  (Given)

2. KM/MQ = PM/ML (Property of cross multiplication)

3. ∠ PMK = ∠ LMQ (vertical angles are congruent)

4. ΔPMK ~ ΔLMQ  (SAS~)

Similar triangles are triangles that have the same shape, but their sizes may vary, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Given,

PM:MQ and KM:ML

To prove

ΔPMK ~ ΔLMQ

By the figure,

PM:MQ = KM:ML (Given)

Cross multiplying

KM/MQ = PM/ML

∠ PMK = ∠ LMQ (vertical angles)

Using Side - Angle - Side theorem

ΔPMK ~ ΔLMQ

Hence,

1. PM:MQ = KM:ML , since its given

2. KM/MQ = PM/ML using cross multiplication

3. ∠ PMK = ∠ LMQ both are vertical angles

4.  ΔPMK ~ ΔLMQ using side-angle-side theorem of similarity

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Answer:

2/36

Step-by-step explanation:

there are a total of 36 possible rolls

and the only to ways to get an 11 on two fair six-sided dice is when it is (5,6) or (6,5)

The description of the parts of the expression are:

The coefficient of x² is 1/2.

The coefficient of x is 1.

The constant is 7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(1/2)x² + x + 7

Now,

The coefficient of x² is 1/2.

The coefficient of x is 1.

The constant is 7.

Thus,

The description of the expression is given above.

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Answer:

The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1

Step-by-step explanation:

The value of function at f(-1) = -13,

f(0) = -8 and f(2) = 10.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given equations,

f(x) = 9x - 4 where x < 0

f(x) = 9x - 8  where x ≥ 0

to find f(-1),

substitute value in equation f(x) = 9x - 4 where x < 0

f(x) = 9x - 4

f(-1) = 9(-1) - 4

f(-1) = -13

now f(0) and f(2),  substitute in equation f(x) = 9x - 8  where x ≥ 0

f(x) = 9x - 8

f(0) = 9(0) - 8

f(0) = -8

f(2) = 9(2) - 8

f(2) = 10

Hence  f(-1) = -13,

f(0) = -8 and f(2) = 10.

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Answer:

h(6) = 13

Step-by-step explanation:

Functions! One of my favorites to answer :)

h(x) = 2x + 1

So, now we plug in h(6). Remember that when we replace the x with the number, we replace it in the right side of the equation as well:

h(6) = 2(6) + 1

Now we multiply 2 * 6:

h(6) = 12 + 1

Now 12 + 1:

h(6) = 13, final answer.

Hope this helps :D

Answer: 13

Step-by-step explanation:

h(x) = 2(x) + 1

h(6) = 2(6) + 1 = 12 + 1 = 13

For the equation  Y=5+3x the solution for x is (y-5)/3=x.

Two or more expressions with an Equal sign is called as Equation.

The given equation is Y=5+3x

y equal to five plus three times of x

In the given equation x and y are the variables.

We have to solve for variable x.

Subtract 5 from both the sides

y-5=3x

Divide both sides by 3

(y-5)/3=x

Hence, for the equation  Y=5+3x the solution for x is (y-5)/3=x.

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The total revenue can be calculated as "2.50a" dollars.

What is the dozen?

A dozen is a grouping of twelve objects, shapes, or numbers. It is abbreviated as doz or dz. Dozen is one of the most primitive customary units of numbers. The number system with the base number 12 is called duodecimal or dozenal.

In this scenario, Adam is selling pencils in dozens and the price he charges for each dozen is $2.50.

To calculate the total revenue, we need to multiply the number of dozens sold (represented by "a") with the price per dozen ($2.50).

The expression "2.50a" represents this calculation, where "a" represents the number of dozens sold and "2.50" represents the price per dozen.

Hence, the total revenue can be calculated as "2.50a" dollars.

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When graphed, a linear equation always produces a straight line since each element in the equation has an exponent of 1.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3 or x∈(−∞,3)

At x=3, the lines y=3x-2 and y=2x+1 will both intersect.

The dark line unmistakably depicts the 3x-2<2x+1 solution.

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Answer:

A and D

Step-by-step explanation:

Given the function:

[tex]\displaystyle{f(x)=\sqrt{5-x^2}}[/tex]

In order to find the first-order derivative of square root function, we have to convert the form of surd to exponent form. Therefore:

[tex]\displaystyle{f(x)=\left(5-x^2\right)^{\frac{1}{2}}}[/tex]

Since the exponent is a constant and that the base is an expression with variable, we can apply the chain rule (power rule variation):

[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]

Therefore:

[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-1} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-\frac{2}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}[/tex]

Deriving 5 - x²:

[tex]\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = 0 - 2x^{2-1}}\\\\\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = -2x}[/tex]

Thus:

[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot (-2x)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}(-2x)\left(5-x^2\right)^{-\frac{1}{2}} }\\\\\displaystyle{f'(x)=-x\left(5-x^2\right)^{-\frac{1}{2}} }[/tex]

You can also convert to the square root form of:

[tex]\displaystyle{f'(x)= \dfrac{-x}{\sqrt{5-x^2}}}[/tex]

Therefore, A and D are correct.

The number of students that have been to Germany or Spain but not France is given as follows:

18.

The amounts are obtained considering the Venn diagram in the problem.

For the 20 students that went to Spain, we have that:

Hence the value of x is obtained as follows:

x + 3 + 3 + 6 = 20

x + 12 = 20

x = 8.

The number of people who have gone to Spain or Germany but not France is given as follows:

6 + 4 + 10 = 18.

(or means at least one of Spain or Germany).

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Answer:

Below

Step-by-step explanation:

1/16    is     1  ÷  16     use calculator to find = .0625

Answer:

1.06

Step-by-step explanation:

Step 1: divide numerator (1) by the denominator (16):

1 ÷ 16 = 0.0625

Step 2: add this value to the integer part:

1 + 0.0625 = 1.0625. So,

1 1/16 = 1.0625

On solving the provided question, we can say that by percentage 9.6  gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

by percentage

mix with 96 gallons of a 10% sugar solution

the resulting mixture is an 18%

10/100 X 96 = 9.6

9.6  gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution

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The graph of the equation x^2 - 4x + 4y - 4 = 0 is a circle, so it doesn't have a direction of opening.

From the question, we have the following parameters that can be used in our computation:

x^2 - 4x + 4y - 4 = 0

The equation x^2 - 4x + 4y - 4 = 0 is of a conic section

i.e. the equation of a circle

The equation of a circle does not have a particular direction it opens to

Hence, it is a closed shape

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A point that is a solution to this system of linear inequalities is (0, 1).

From the question, we have the following parameters that can be used in our computation:

y ≥ 2x - 4

x > -3

y < 5

Using the point (0, 1)

To see why this is a solution, we need to check if it satisfies each of the inequalities:

Since the point (0, 1) satisfies all of the inequalities, it is a solution to the system of linear inequalities.

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Therefore , the solution of the given problem of linear equation comes out to be  x = 21.75.

A linear regression curve is built on the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is sometimes referred as a "mathematical equation merging multiple variables," even if y or y are independent parts. The only variables in bivariate linear equations are two. There are no known solutions to application issues involving linear equations. Y=mx+b, also written as mx+b, is the expression for a straightforward system of equations.

Here,

Given :

From a mixed number, you must convert it to a decimal number. You can do this by following the instructions below:

In order to start, you must reduce the fraction's denominator by its numerator.

Step 2: You must now multiply the resulting quotient by the whole number component.

You therefore obtain:

=> 7 1/4 = 7 + 0.25 = 7.25

The scale picture that transforms "Figure a" into "Figure b" is then: 1: 71

The specified length of the appropriate side of "Shape a" must then be multiplied by in order to determine the value of "z."

The outcome is as follows:

=>x = (3)(7.25)

=> x = 21.75

Therefore , the solution of the given problem of linear equation comes out to be  x = 21.75.

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The complete question is "Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x

Both figures are triangles

Figure a is smaller than figure b

Figure a to the right has a 3

Figure b to the right has a x"

Therefore , the solution of the given problem of probability comes out to be probability of winning a  3 game out of 5 is 0.5 .

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any quantity between 0 and 1, whereby 1 frequently represents certainty range 1 and 0 normally denotes possibility, can be used to represent chance. A probability diagram illustrates the likelihood that a particular event will take place.

Here,

Given :

Since,

the probability to win a game is 50% .

So they have to win 3 games ,

and so , the probability to win the game is:

=> 1/2 * 1

=> 0.5

thus,

probability of winning a  3 game out of 5 :

=> 0.5

Therefore , the solution of the given problem of probability comes out to be probability of winning a  3 game out of 5 is 0.5 .

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The value of the expressions will be:

2x² + 3x + 4, when x=1 is equal to 9.

(x+y)², when x=2 and y=2 is equal to 16.

5x² + 2x, when x=2 is equal to 24.

(x+y)³, when x=7 and y=3 is equal to 1000.

2x² + 3x + 4, when x=1 is:

= 2(1)² + 3 + 4

= 2 + 3 + 4

= 9.

(x+y)², when x=2 and y=2 is equal to:

= (2 + 2)²

= 4²

= 16.

5x² + 2x, when x=2 is equal to:

= 5(2)² + 2(2)

= 20 + 4

= 24.

(x+y)³, when x=7 and y=3 is equal to:

= (7 + 3)³

= 10³

= 1000.

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Answer:

The task is to calculate the total amount spent by Mr. Spendalot. To do this, you need to calculate the amount of inventory purchased, apply the discount, calculate the sales tax, and add the tip. Here's one way to do it:

Calculate the amount of inventory purchased: 31% of $1,000,000 is 31/100 * $1,000,000 = $310,000

Determine the discount: Based on the purchase amount of $310,000, Mr. Spendalot qualifies for a discount of 10%. So, the discount is $310,000 * 10% = $31,000.

Calculate the sales tax: 8.5% of the purchase amount after discount is 8.5/100 * ($310,000 - $31,000) = $2,067.50

Add the tip: 15% of the purchase amount after discount and sales tax is 15/100 * ($310,000 - $31,000 + $2,067.50) = $52,101.13

Calculate the total: The total amount spent by Mr. Spendalot is ($310,000 - $31,000 + $2,067.50 + $52,101.13) = $393,168.63.

So, the total amount spent by Mr. Spendalot is $393,168.63.

Step-by-step explanation:

Determine the amount of purchase before discount: Mr. Spendalot bought 31% of Mr. Shine's inventory, which is $1,000,000. Therefore, his purchase before discount is 31% of $1,000,000, or $310,000.

Calculate the discount: Based on the information in the discount table, Mr. Spendalot's purchase qualifies for a 40% discount. Therefore, the discount amount is $310,000 * 40%, or $124,000.

Determine the amount of purchase after discount: After getting the 40% discount, Mr. Spendalot's purchase is $310,000 - $124,000, or $186,000.

Calculate the sales tax: Mr. Shine charged an 8.5% sales tax on Mr. Spendalot's purchase after discount. Therefore, the sales tax amount is $186,000 * 8.5%, or $15,791.

Determine the tip: Mr. Spendalot gave Mr. Shine and his staff a 15% tip on his purchase after discount and sales tax. Therefore, the tip amount is $186,000 + $15,791 * 15%, or $31,328.

Calculate the total cost: Adding up the purchase after discount, sales tax, and tip, we get the total cost of $186,000 + $15,791 + $31,328, or $233,119.

Conclusion: Mr. Spendalot's total purchase cost is $233,119.

The task requires you to calculate the total amount spent by Mr. Spendalot at Mr. Shine's store Ice Box. Mr. Shine has an inventory worth $1,000,000 which he marks up by 150%. Mr. Spendalot bought 31% of this inventory, and was given a discount based on the amount he spent:

Spend 100k+ and get 10% off

Spend 250k+ and get 20% off

Spend 500k+ and get 30% off

Spend 750k+ and get 40% off

Spend 1 million+ and get 50% off

After the discount, Mr. Spendalot was charged 8.5% sales tax. He also left a 15% tip for Mr. Shine and his staff. Your goal is to calculate the total amount spent by Mr. Spendalot.

The value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.

The link between the quantity demanded for a commodity (the dependent variable) and its price is represented by the demand function (independent variable).

a) At the price of Gh¢10 , then

Qd= 500 - 5P

Qd= 500 -5(10)

Qd= 500-50 = 450 units

The value of quantity demanded at unit price Gh¢10 is 450 units.

b) If there are 200 units,then

Qd= 500- 5P

200 = 500-5P

5P = 500-200

P= 300/5

P= Gh¢60

The price to sell 200 units is Gh¢60

c) if demand is zero, it mens Qd= 0

Qd= 500- 5P

0= 500-5P

5P= 500

P= Gh¢100

The price for 0 demand is Gh¢100.

d) If P= 0, then

Qd= 500-5P

Qd= 500-5(0)

Qd= 500 units

The quantity demanded at zero price is 500 units.

Hence, the value of quantity demanded at unit price Gh¢10 is 450 units. b. The price to sell 200 units is Gh¢60. c. The price for 0 demand is Gh¢100. d. The quantity demanded at zero price is 500 units.

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The amount after the discount is applied would be $21.25.

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

As per the question, the given data as:

Bill amount = 25$

Coupon for 15% off

The amount after the discount can be calculated as:

⇒ 25$ - 15% of 25$

15%  is expressed as 15/100 in fractional form

⇒ 25 - (15/100)(25)

15/100  is expressed as 0.15 in decimal form

⇒ 25 - (0.15)(25)

⇒ 25 - 3.75

⇒ 21.25

Thus, the final amount would be $21.25.

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Answer:

22

Step-by-step explanation:

550x4%=550x0.04=22

Answer:

$22

Step-by-step explanation:

550 x 4% = 550 x 0.04 = $22

The mean of the numbers is 22.625

The average of all the data in a set. The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

The mean or average of the set of the data is calculated thus

(6+7+5+8+6+7+6+8)/8

181/8 = 22.625

Therefore,  the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8 is 22.625

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The cosine of the angle  θ  is 8/17 whose terminal side passes through the given point

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent

Given here: The terminal side goes through the point (8/17, -15/17)

Thus we have cosθ =8/17 and sin θ =-15/17

now tan θ =sinθ /cosθ

         tanθ    = -15/8

               θ = -61.9275

Hence, cosθ =8/17

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The surface area of a right rectangular prism is 250 m².

Option C is the correct answer.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

From the figure,

Width = w = 5 m

Height = h = 5 m

Length = l = 10 m

The surface area of a right rectangular prism.

= 2 (lw + lh + wh)

= 2 (10 x 5 + 10 x 5 + 5 x 5)

= 2 (50 + 50 + 25)

= 2 (125)

= 2 x 125

= 250 m²

Thus,

250 m² is the surface area of a right rectangular prism.

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Answer:

250m 2

I hope this helps <3

The value of the sum of the series is are 315, 1600 and 104

In an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:

Sn = n/2 * (a1 + an)

Where "a1" is the first term and "an" is the nth term.

For the first series, we have

In this series, a1= 3 , an= 42 , n= 14

Plugging these values into the formula, we get:

Sn = 14/2 * (3 + 42)

Sn = 315

For the second series, we have

In this series, a1= −20 , n= 25 , an= 148

Plugging these values into the formula, we get:

Sn = 25/2 * (-20 + 148)

Sn = 1600

For the third series, we have

In this series, a1=5 , d=1/2 , n=13

So, we have

an = a + (n - 1)d = 5 + 12 * 1/2 = 11

Plugging these values into the formula, we get:

Sn = 13/2 * (5 + 11)

Sn = 104

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The estimated area of Laurens's circle is 642 squared.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Parker:

Area = 40 squared

This means,

πr² = 40

r² = 40/3.14

r² = 12.74

r = √12.74

r = 3.6

Laurens:

r = 4 x 3.6

r = 14.3

Area = πr²

Area = 3.14 x 14.3 x 14.3

Area = 642

Thus,

Laurens's circle area is 642 squared.

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