To get to the different parts of the race course you need to use local transport. One bus company offers a 10 trip ticket, with each trip costing £6.74. How much will the 10 trip ticket cost?

Answer:

Solutions given:

4sin B=3sin (2A+B)............(1)

let B=A+B-A

and

2A+B=A+B+A

again

substituting value we get

Or, 4sin[ A+B-A]=3sin[ A+B+A]

Or,4Sin [(A+B)-A]=3sin[ (A+B)+A]

Or,4(Sin(A+B)cosA-Cos(A+B)sinA)=

3(Sin(A+B)cosA+Cos (A+B)sin A)

Or,4Sin(A+B)Cos A-4Cos(A+B)sinA=

3Sin(A+B)cosA+3cos(A+B)sinA

Or, 4Sin(A+B)CosA-3Sin(A+B)cosA=

3cos(A+B)sinA+4Cos(A+B)sinA

OrSin(A+B)CosA=7Cos(A+B)sinA

or

7cos(A+B)/Sin (A+B)=Cos A/Sin A

7Cot (A+B)=CotA.

7Cot (A+B)=CotA.Proved.

For the provide inquilty problem,

a) The feasible region lies in between the following equations,

b) The extreme points of feasible region are (2,5) , (6,1) ,(0,0),(6,0),(0,5).

Let consider, x = A and y = B, this changes your inequalities and equations as follows: Maximize x + 2y, such that:

x ≤ 6

y ≤ 5

2x + 2y = 14

x,y ≥ 0

We use graphical method, for getting the solution of problem. So, first change the Inequalities into equality equations.

we would then find the region of feasibility by looking at the areas on the graph that satisfy the inequalities and equations,

x ≤ 6

y ≤ 5

2x + 2y = 14 (this is an equation)

x ≥0

y ≥ 0

a) The graph will look like as present above : we can see that the feasible region is the area on the graph that is:

on or below the line y = 5

on or to the left of the line x = 6

on or above the line y-axis , y = 0

on or to the right of the x-axis, x = 0

on the line 2x + 2y = 14

This says is that your solution has to be on the line of 2x + 2y = 14, have an x-coordinate that is greater than or equal to 0 and less than or equal to 5 and have a y-coordinate that is greater than or equal to 0 and less than or equal to 5. The maximum or minimum value should be at the corner points of the feasible region.

b) The corner points would be at (x,y) = (2,5) and (x,y) = (6,1). Also, plotted some other points on the line just to show the max/min value of function on the corner points of the feasible region.

(2,5) = 12

(4,3)= 10

(3,4) = 11

(6,1) = 8

the maximum solution is at the coordinate of (2,5) and all of your constraints have to be satisfied at the this point. The solution is that the maximum value is when x = 2 and y = 5, that is one of the corner points of the feasible region.

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Complete question:

Consider the following linear program:

Max. 1A+2B , s.t.

1A ≤6

1B≤5

2A+2B=14

A,B>0

a. Show the feasible region.

b. What are the extreme points of the feasible region?

The length of ST is 16 units.

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

We have to given that;

Point P is the midpoint of ST.

SP = x + 4, and ST = 4x

Since, P is the midpoint of ST.

Hence, We get;

⇒ SP = PT

And, ST = 2 SP

Substitute all values we get;

⇒ 4x = 2 (x + 4)

⇒ 4x = 2x + 8

⇒ 4x - 2x = 8

⇒ 2x = 8

⇒ x = 4

Thus, The value of ST = 4x

                                  = 4×4

                                  = 16

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Answer:

14

Step-by-step explanation:

200 / 10 = 20

20 miles a gallon

280 / 20 = 14

:)

Answer:

14 gallons

Step-by-step explanation:

200 miles takes ten gallons, and 280 is equal to 100 percent plus 40 percent of 200, and 140 percent of 10 is 14. if that makes sense

Answer:

4w4 + 10w5 - 5w3

Step-by-step explanation:

Answer:

4.30 inches

Step-by-step explanation:

Given data

Volume of basket ball= 334cubic inches

We know that the expression for the volume of a sphere is given as

Volume of sphere= 4/3πr^3

334= 4/3πr^3

334=4/3*3.142*r^3

334=4.189*r^3

r^3= 334/4.189

r^3=79.73

cubic root both sides

r= ∛79.73

r=4.30 inches

Answer:

(f/g)x = (x - 3)/(2x - 3)

Step-by-step explanation:

Try and see if f(x) can be factored.

g(x) = (2x - 3) (2x + 3)

That means that perhaps f(x) has one of these two factors.

(2x   3)(x   3)

You want the 2x and 3 to multiply. The middle term has to be -, so when 2x and 3 multiply likely it is 3 that gives you the minus answer.

(2x + 3)(x - 3) should be the way f(x) factors, and it is.

f(x) / g(x) = (2x + 3) (x - 3)

                 (2x + 3)(2x - 3)

2x + 3 cancels. The answer is

(f/g)x = (x - 3)/(2x - 3)

The process of solving the 3 variable with 2 equation is explained below.

The term equation is defined as a relationship between two terms on either side of an equal sign.

Here we have the following steps to solve the 3 variable for two equation is solved accordingly.

First of all we have to take any two equations and solve it for one variable.

And then again we have to take another two pair of equations and solve for the same variable.

Now, we have a system of two equations with two unknown variables.

Then we have to solve the equation by using the appropriate arithmetic operations.

and then substitute it accordingly until all the value of the variable are solved.

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The sales tax rate on the item = 8%

We know that the sales tax is nothing but the purchase price times the percentage of tax.

An item costs $430 before tax.

This means, the purchase price is 430 dollars.

The sales tax is $34. 40

To find: the sales tax rate as a percentage

First we find a ratio of the sales tax to the cost of the items before tax.

Sales tax / Pre-tax value of item = (34.40) / 430

Now we write a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

i.e., (34.40) / 430 = sales tax percent / 100

So, the sales tax percent  = 8%

Therefore, the sales tax is of 8%

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Answer:

GCF = 4

add to:  -14

multiply to:  45

4(x-5)(x-9)

Step-by-step explanation:

Answer:

84 cm

Step-by-step explanation:

Area=a, length=l, width=w

[tex]A=lw[/tex]

If area is 5376 cm², and width is 64 cm,

[tex]5376=64l[/tex]

Divide each side by 64,

[tex]l=84[/tex]

So, the length of the rectangle is 84 cm.

Answer:

28x^2+3x-18

Step-by-step explanation:

Formula: (a+b)(a+b) = a^2 + a*b + a*b + b*b

Following this: 28x^2 -21x +24x -18

Then you combine like terms: 28^2 +3x-18

hope this helped!! :)

Answer:

[tex]28x^{2} + 3x - 18[/tex]

Answer:

the answer is (3,4) and (2,3)

Step-by-step explanation:

that's my answer

Answer:

ppppppppppppppppppppppppppppppppppp dogwater freee

Step-by-step explanation:

There are 4 cassette tapes.

Given that,

Let x be the number of compact discs

Then 5 times the number of CD's= 5x and 10 less than 5 times the number of CDs is 5x-10

Therefore the number of cassettes is 5x-10

Now we are told that the ratio of cassettes to CDs which is

((5x-10)/x) equals 5/2 so our equation to solve is:

(5x-10)/x=5/2 multiply both sides by 2x to get rid of the fractions and we get:

2(5x-10)=5x

Further solving this equation, we get:

10x-20=5x

5x=20

x= 4 (number of compact discs)

Thus, there are in total 4 cassette tapes.

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Using trigonometric ratios, the value of x is as follows:

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the angle of a right angle triangle can be found using trigonometric ratios as follows:

Hence, let's find angle x

Therefore,

sin x = opposite / hypotenuse

opposite side = 7 ft

hypotenuse side = 18 ft

Hence,

sin x = 7 / 18

x = sin⁻¹ 7 / 18

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An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.

Here, (17, 570) and (29, 822)

Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)

= (822-570)/(29-17)

= 252/12

= 21

Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get

570=21×17+c

570=357+c

c=213

Substitute, m=21 and c=213 in y=mx+c, we get

y=21x+213

Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

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Answer:

∠8 and ∠5

Step-by-step explanation:

Vertical angles are angles that are across from each other.

∠8 and ∠5 are across from each other.

Here the exact values of circle is not given.so in general .Area of Circle = πr² or πd2/4 in square units, where (Pi) π = 22/7 or 3.14.

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle's radius, is the formula for c

Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

Area of Circle:

[tex]\pi[/tex]×r²

Where [tex]\pi[/tex]=3.14

But Here we need correct values to find the area of the circle.

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Answer:

C.11

Step-by-step explanation:

a perimeter is the total length of all sides of a rectangle. so

rectangle has 4 sides and it says that the shorter side is 5 so 5+5 for the shorter side and it's 10

32-10=22

22÷2= 11

(basta yan lang alam ko, sorry kung mali.)

Answer: [tex]21.6\ s[/tex]

Step-by-step explanation:

Given

The initial velocity of the ball is [tex]u=150\ ft\s[/tex]

Angle of projection [tex]\theta=45^{\circ}[/tex]

The time of flight of the ball is given by

[tex]T=\dfrac{2u\sin \theta}{g}\\\\[/tex]

Insert the values

[tex]T=\dfrac{2\times 150\times \sin 45^{\circ}}{9.8}\\\\T=\dfrac{212.132}{9.8}\\\\T=21.6\ s[/tex]

if a²+b²>c², the triangle is acute, if a²+b2²=c², the triangle is a right triangle,  and if a²+b²<c², the triangle is obtuse.

where a and b are the lengths of the two shorter sides of the triangle and c is the length of the longest side.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

An acute triangle has three angles that each measure less than 90°. In an acute-angled triangle, all three internal angles of the triangle are acute, that is, they measure less than 90°.

An obtuse triangle is a triangle with one angle that is greater than 90° degrees, it is not possible for a triangle to have more than one obtuse angle.

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Answer: 6

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

AB = 4x + 6 and BC = 7x + 15  AC is the sum of AB and BC

so 4x + 6 + 7x + 15 = 120 add like terms

11x + 21 = 120 subtract 21 from both sides

11x = 99 divide both sides by 11

x = 9

Answer:

What he did right was doing the first part correctly, wher it;s 46000x1.05, which is 48300. But then the student thought that every year, Carlos' salary will increase by 48300, and after 3 years it got to 144900, which is nuts. The real thing is to do 46000 x 1.15, because on the 3rd year, your salary will be 115% of your salary, if that makes sense, you do 5x3 = 15, then you add 15% to 100 which is 115 % =1.15. then you do 46000x1.15= 55545$

hope that answers your question

comment if your confused about something.

Step-by-step explanation:

Salary after 3 years of increment by 5% annual rate is given as $53,250.

Carlos accepts a new job with a starting salary of $46,000. He will earn a 5% increase after each year. What will be his salary after 3 years.

It is defined as the fee you pay to borrow money or the fee you levy to lend money. Interest is considerable and frequently recalled as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Incorrect solution,
$46,000 • 1.05 • 3 = $144,900 is Carlos’ salary after 3 years.

Correct solution,
Principal amount = $46,000
rate of increase in salary each year = 5%
After t = 3 years what will be the salary = ?

following identity is used to calculate the increments in principal amount.
[tex]Amount = principal(1+r)^t[/tex]

[tex]Amount = 46000(1+0.05)^3\\Amount = 46000(1.05)^3\\[/tex]
Amount = 456000 * 1.16
Amount = 53,250

Thus, salary after 3 years of increment is given as $53,250.

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Answer:

6.333... but you would have 6.3 with a line over the 3

Step-by-step explanation:

19 divided by 3

Answer:0.275

Step-by-step explanation:

Answer:

D. 3600ft^3

Step-by-step explanation:

First you have to find the volume of one box:

Volume = Length*Width*Height

Volume = 48ft^3

Multiply 48 by 75 to find the volume of 75 boxes:

48*75 = 3600ft^3

Answer:  A.  X=4

Step-by-step explanation:

Since the line is on the X axis you can see its touching x,4 y,0