6am air traffic controller i tracking two plane to tart plane A wa at an altitude of 1500 meter and plane B wa at an altitude of 1115 meter plane A i going altitude at 19 meter per econd and plan B wa gaining altitude at 26 meter per econd let x be the number of econd that have pae

The row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

A binomial expression is an expression that contains only two terms.

Pascal's triangle is an algorithm for finding the coefficients of a binomial expansion.

Since we require the expansion of the binomial expression (2x³ +3y³)⁷ using Pascal's triangle, we note that, the power of the binomial expression is always equal to the second and second to the last coefficient of the terms in the Pascal's triangle.

So, we see that the Row eight: 1 7 21 35 35 21 7 1, satisfies this condition.

So, the row of Pascal's triangle that is used to expand the binomial expression  (2x³ +3y³)⁷ is Row eight: 1 7 21 35 35 21 7 1.

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The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Now,

Since, The expression is,

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

Solve the expression by using distributive property as;

⇒ [ 7/5 × - 3/12 ] ± [ 7/5 × 5/12 ]

⇒ [ 7/5 ] × [ - 3/12 ±  5/12 ]

It gives two solution as;

⇒ 7/5 × [ - 3/12 + 5/12 }

⇒ 7/5 × 2/12

⇒ 7/5 × 1/6

⇒ 7 / 30

And,  7/5 × [ - 3/12 - 5/12 }

⇒ 7/5 × - 8/12

⇒ 7/5 × - 2/3

⇒ - 14 / 15

Thus, The value of expression will be;

⇒ 7 / 30

⇒ - 14/15

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Answer:  [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

===============================================

Work Shown:

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

-----------------

Explanation:

The process to find the inverse involves this outline.

This process is followed in the "work shown" portion above.

To confirm the answer, let g(x) be the inverse of f(x).

If they were inverses of each other, then these two properties would hold true:

Here's the verification for the first part.

[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]

I'll let you do the other confirmation.

The value of the angle y will be equal to 47.46. The correct option is A.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Given that the angle x is equal to 132.54°. The value of the angle y will be calculated as,

x + y = 180

132.54 + y = 180

y = 180 - 132.54

y = 47.46

Therefore, the value of the angle y will be equal to 47.46. The correct option is A.

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The average number of customers waiting in the queue is 20

In this question, we have been given that the customers arrive at the rate of two per minute.

On average a customer waits 10 minutes in a queue.

We need to find the number of customers waiting in the queue on average.

Assume that the average number of customers waiting in the queue is N.

We have the average Rate of Arrival = 2 customers per minute

So, by the formula for average waiting time under the Single-Server Queue Model,

10 = N/2

N = 10 * 2

N = 20

The average number of customers waiting according to the single-server queue model given the above conditions is 20

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Answer: The answer to this solution is 5.

Answer:

d = 5m

Step-by-step explanation:

Look at point (1, 5).

When the number of months is 1, the amount in dollars is 5.

The amount in dollars is always 5 times the number of months.

d = 5m

An expression or equation that shows how many pictures Alexa drew is 8-p.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Given, Evan drew 8 pictures.

Alexa drew p fewer pictures than Evan.

then, Alexa = 8-p

Hence, an expression or equation that shows how many pictures Alexa drew is 8-p.

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The value of x = 7 and y = 54.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:  y = 6x+12 and y = x+47

We have to solve this equation and find the value of x and y.

y = 6x+12....(1)

y = x+47.....(2)

We put the value of y in equation (1) and we get

x + 47 = 6x + 12

6x -x = 47 -12

5x = 35

x = 7

Now, we put the value of x in equation(2) and we get

y = 7 + 47

y = 54

Hence, the value of x = 7 and y = 54.

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Answer:

l

v

Step-by-step explanation:

80, 5, 30, 7, and 3,

Answer:

top right

Step-by-step explanation:

6x3=18

By using the property of congruency, it can be calculated that

Length of line segment AC is 26 units

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides are equal and the corrosponding angles are equal.

There are six axioms of congruency. They are

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

In [tex]\Delta[/tex] ABC and [tex]\Delta[/tex] XYZ,

[tex]\angle[/tex]B = [tex]\angle[/tex]Y [Given]

[tex]\angle[/tex]C = [tex]\angle[/tex]Z [Given]

BC = YZ [Given]

[tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] XYZ [ASA axiom]

AC = XZ [Corrosponding parts of congruent triangles are congruent]

AC = 26 units

Length of line segment AC is 26 units

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We have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.

                  tan∅ = sin∅/cos∅

                  cot∅ = cos∅/sin∅

Given:

tanθ.cosθ + cotθ.sinθ = sinθ + cosθ

Now LHS =  tanθ.cosθ + cotθ.sinθ

                = (sinθ/cosθ)cosθ + (cosθ/sinθ)sinθ

                = sinθ + cosθ

LHS = RHS

Hence, we have proved that tanθ.cosθ + cotθ.sinθ = sinθ + cosθ.

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The length is 28.75 inch and width is 11.25 inch.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Perimeter= 80 inches

let the width be x.

length= 3x- 5

Now, perimeter of a rectangle = 2( l+ w)

80= 2( x+ 3x- 5)

40 = 4x -5

45 = 4x

x= 11.25

and, length = 3(11.25)- 5 = 28.75

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The area of the front cover a face perpendicular to the thickness is 72in²

What is a rectangular prism?

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Here, we have

Given:

A new dictionary in the shape of a rectangular prism will have a thickness of 3 inches.

The volume of the dictionary will be 216in².

Volume = W×L×H

Surface = volume/ height

= 216/3

= 72in²

Hence, the area of the front cover of a face perpendicular to the thickness is 72in².

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The values obtained after solving the given equation is x  = 6 and y = 10.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equations are,

-5x + 3y = 0   (i)

7x - 4y = 2    (ii)

Multiply equation (i) by -7 and equation (ii) by 5.

35x - 21y = 0       (iii)

35x - 20y = 10       (iv)  

Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.

-y = -10

y = 10

Substitute y = 10 in equation (i)

-5x + 3(10) = 0

-5x = -30

x = 30/6

x = 5

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Answer:

Parallel: Y= -7/3x - 37/3

Perpendicular: Y=3/7x + 7

Step-by-step explanation:

Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.

Remember when the slope is parallel it's always the same slope in this case -7/3

When perpendicular flip it and change the sign 3/7

The correct statement regarding the exponential functions g(x) and h(x) is given as follows:

B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients of the function are described as follows:

Function h(x) is defined as follows:

h(x) = 3^x - 2.

For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:

a = 4.

When x = 1, y = 5, hence the rate of change of the function is obtained as follows:

b = 5/4.

b = 1.25.

Then function g(x) is given as follows:

g(x) = 4(1.25)^x.

Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.

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The indications of the numbers in the linear equations that produces the number of apples in Annie's basket, n = 22·t + 12, are as follows;

The domain of the function n = 22·t + 12 is R⁺ which is the set of positive real numbers, including zero, [0, ∞)

A linear equation is a equation of the line of a straight line graph. The domain of a function is the set of the input values of the function.

The equation that describes the number of apples in Annie's basket, n = 22·t + 12

The number of minutes Annie spends picking apples = t

The number of apples in Annie's basket = n

The number 22 which is the coefficient of the variable t in the linear equation, which is the slope or the rate of change of the number of apples in Annie's, which indicates the number of apples Annie picks per minute.

The number 12 is the y-intercept of the equation y = 22·t + 12

The y-intercept is the value of the function where t = 0, which is the initial value of the function.

Therefore;

The domain of the function n = 22·t + 12, are the possible values of the independent or input variable, t, which is the set of positive integers including 0

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Answer: B

Step-by-step explanation:

For [tex]f(x)=3x-\frac{1}{2}[/tex], comparing it with slope-intercept form yields that the slope is [tex]3[/tex] and the [tex]y[/tex]-intercept is [tex]-1/2[/tex].

For the graphed function, the slope is [tex]\frac{-4-0}{-2-6}=\frac{1}{2}[/tex] and the [tex]y[/tex]-intercept is about [tex]-3[/tex].

Since the absolute value of the slope of the graphed function is less than that of [tex]f(x)[/tex], option B is correct.

The slope of the given function is 0.25. The function that has  the same slope is y = 0.25x + 5. Option B is the correct option.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given table is

x         0          1            2             3

y      -0.5       -0.25      0           0.25

The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25

The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25

Now compare the equation y = -0.25x - 2 with y = mx + c

m =  -0.25

The slope of the function is -0.25.

Now compare the equation y = 0.25x + 5 with y = mx + c

m =  0.25

The slope of the function is 0.25.

Now compare the equation y = 4x - 5 with y = mx + c

m =  4

The slope of the function is 4.

Now compare the equation y = -4x + 34 with y = mx + c

m =  -4

The slope of the function is -4.

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Answer: $27,000

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

15/10 = x+12/12

180=10x+120

x=6

x+12=18=AE

The total Volume of tank = 35 liters

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the

According to the Given information

Volume of each marble = 0.04 liters

Number of marbles to be put in the water tank = 50 marbles

Volume of 50 marbles = 0.04 × 50 = 2 liters

Volume of water added to the tank = 33 liters

Total Volume of tank = 2 liters + 33 liters

                                    =     35 liters

SO,

The total Volume of tank = 35 liters

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The solutions of the quadratic equation are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

For a general quadratic:

a*x^2 + b*x + c = 0

The solutions are given by the quadratic formula

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here we have the quadratic equation:

2x^2 + x + 3 = 0

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}[/tex]

So we will have two complex solutions, these are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

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From the given ratio, there is a total of 100,000 vending machines in Osaka.

What is the ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.

Given, the ratio of vending machines to people is 1 to 24

That means, for every vending machine, there are 24 people.

In the city of Osaka, there are about 2,400,000 people.

So, the number of  vending machines = 2400000/24 = 100000

Hence, there is a total of 100,000 vending machines in Osaka.

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The value of f(x)+g(x) is 5x³+7x²+3x+10

Given that,

                 f(x)=3x³+4x²-2x+8

                 g(x)=2x³+3x²+5x+2

f(x)+g(x)=3x³+4x²-2x+8+2x³+3x²+5x+2

            =3x³+2x³+4x²+3x²+5x-2x+8+2

            =5x³+7x²+3x+10

Step-by-step explanation:

This question is a type of quadratic equation. To solve this type of question first, we have to put the values of f(x) and g(x). Then we have to put similar terms(which have similar coefficients with similar power)together. Then we add the similar term of f(x) with the similar term of g(x) like 3x³+2x³=5x³, 4x²+3x²=7x², 5x-2x=3x and 8+2=10

Therefore the value of f(x)+g(x) is 5x³+7x²+3x+10

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The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are;

a. Interest for the first quarter = $8.125

b. First quarter ending balance = $6,508.125

c. Interest for the second quarter = $8.13515625

d. Second quarter ending balance = $6,516.26015625

e. Interest for the third quarter = $8.1432520325

f. Third quarter closing balance = $6,524.40548145

g. Interest for the fourth quarter = $8.15550685975

h. The amount of interest earned in a year is about $32.56

What is an interest earned on an amount?

An interest is the amount a borrower pays to a lenders as to make use of the lender's funds.

The amount Fred deposited, P = $6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

C.I. = P[tex](1+ r/4)^{4 . 1/4}[/tex] - P

Therefore

C.I. = 6500 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6500 = 8.125

b. The first quarter ending balance is therefore;

A = P + C.I.

A = $6,500 + $8.125 = $6,508.125

c. The second quarter's interest can be found from the formula;

C.I. = 6508.125 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6508.125 = 8.13515625

The second quarter's interest is $8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 + $8.13515625 = $6,516.26015625

The second quarter ending balance is $6,516.26015625

e. The third quarters interest is therefore;

C.I. = 6516.26015625 x  (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6516.26015625 = 8.1432520325

The third quarter's interest is about $8.1433

f. The third quarter's ending balance is therefore;

A ≈ $6516.26015625 + $8.1432520325 = $6,524.40548145

The third quarter's ending balance is $6,524.40548145

g. The fourth quarter's interest can be found as follows;

C.I. = 6524.40548145 x (1 + [tex]\frac{0.5/100}{4}[/tex]) - 6524.40548145 = 8.15550685975

The fourth quarter's interest is; $8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 + $8.15550685975 = $6,532.56098831

i. The interest the account earns in a year is therefore;

$6,532.56098831 - $6,500 = $32.5609883

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