Solve each proportion. x/7 =28/49

The length l of the hypotenuse as function of x is l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} }+x^{2} }[/tex]

Given,

A right triangle is formed in the first quadrant by x and y axes and a line through the point (3, 2).

The length of sides of triangle are y and x.

By Pythagoras theorem, the length of the hypotenuse is:

l = [tex]\sqrt{y^{2}+x^{2} }[/tex]

Now, we can choose two points to get the value of slope (x₁, y₁) = (3, 2) and (x₂, y₂) = (x, 0)

By using the formula, we get the slope:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{0-2}{x-3}[/tex] = [tex]-\frac{2}{x-3}[/tex]

The slope is same when passing through (x, 0) and (0, y) because its in the same line.

m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{y-0}{0-x}[/tex] = [tex]\frac{y}{-x}[/tex]

That is, m = [tex]-\frac{y}{x}[/tex]

These slopes are equal. So, we can equate them,

[tex]-\frac{2}{x-3}[/tex] = [tex]-\frac{y}{x}[/tex]

[tex]-\frac{2(-x)}{x-3}[/tex] = y

y = [tex]\frac{2x}{x-3}[/tex]

Substitute this to the equation,

l = [tex]\sqrt{y^{2} +x^{2} }[/tex]

l = [tex]\sqrt{(\frac{2x}{x-3})^{2} +x^{2} }[/tex]

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

That is, the hypotenuse has a length of

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

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The probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214.

A = a vehicle entering the Luray caverns has Canadian license plates

B = it is a camper

P(A) = 0.12

P(B) = 0.28

P(A∩B) = 0.09

P(A|B) = P(A∩B) / P(B)

P(A|B) = 0.09 / 0.28

P(A|B) = 0.3214

Hence,  the probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214

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Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Step-by-step explanation:

1) The graph that best models the situation is; Graph A

2)  The expression that describes the end behaviors of the function modeled by the graph is; As x increases without bound, f(x) approaches the line y = 0

We are told that Hugh wants to start a workout program. Sinmce he starts with running three times a week, we can liken this to the y-intercept. Thus; y-intercept = 3

Now, we are told that he increases the running per week by 17%. This means that the slope of the graph will be 17% or 0.17.

Looking at the given graphs, only graphs A and B have their y-intercepts at y = 3.

Now, looking at both graphs, the one with slope closest to 17% will be graph A.

2) The expressions describe the end behaviors of the function modeled by the graph is; D: As x increases without bound, f(x) approaches the line y = 0

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Step-by-step explanation:

Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.

The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330

Solve for x:

0.06x(3)+0.075(18000−x)(3)=3330

Step 1: Simplify both sides of the equation.

0.06x(3)+0.075(18000−x)(3)=3330

0.06x(3)+−0.225x+4050=3330(Distribute)

0.18x+−0.225x+4050=3330

(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)

−0.045x+4050=3330

−0.045x+4050=3330

Step 2: Subtract 4050 from both sides.

−0.045x+4050−4050=3330−4050

−0.045x=−720

Step 3: Divide both sides by -0.045.

−0.045x/−0.045=−720/−0.045

x=16000

x=16000

So, the amounts borrowed are:

Bank at 6% = 16000

Bank at 7.5% = 2000

Answer:

[tex] \frac{2b}{a} [/tex]

Step-by-step explanation:

[tex] \frac{2}{a} \div \frac{1}{b} [/tex]

[tex]\frac{2}{a} \: \times \:b[/tex]

[tex] \frac{2b}{a} [/tex]

The value of f(x)+g(x)= x²+ 3x - 1

a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

f(x) is the value of the function.

there is an x in the function f, it is replaced with the function g(x).

f(x)=3 x-2

g(x)=x²+1 .

(f+g)(x) = x²+1 + 3 x-2

f(x)+g(x)= x²+ 3x - 1

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Answer:

9:30 p.m.

Step-by-step explanation:

Starting at noon (12:00 p.m.) the temperature is 5 degrees Celsius and drops 2 degrees every hour. In the attached image I have drawn it out to better see it.

Starting at noon and subtracting 2 every hour gives us…
12:00=5

1:00 = 3
2:00 = 1

3:00 = -1

(And so on until we get)

9:00= -13 degrees

So how do we get to 14 if it is dropping 2 degrees an hour? Simple! How much does it drop every half hour? 1 degrees! So for ever 30 minutes the temperature drops 1 degrees.

This means that at 9:30 the temperature will be -14 degrees Celsius.

Answer:

1

Step-by-step explanation:

[tex]\mathrm{a^0=1~if~a \neq 0}[/tex] (Assuming a doesn't equal 0)

[tex]= 1[/tex]

Yes it is because 6/5 is the same as saying 1 and 1/5.

Answer:

2

Step-by-step explanation:

the equation of it is

y= -1/2x+5

A salaried employee will always have a(n) employment contract.

Who is a salaried employee?

A salaried employee is an individual who is said to often receives a fixed amount of money (salary), regardless of the number of hours they work each week.

It is one that  is referred to as a salaried employee because they often get compensated for 40 hours of work per week and it is one that is based on the use of an employment contract.

Since the employment contract is seen as a legally binding  form of an agreement between an employer and that of their employee, A salaried employee will always have a(n) employment contract.

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Answer:

a^3-64b^3

Step-by-step explanation:

(a-4b)(a^2+4ab+16b^2)

Multiply.

(a-4b)(a^2+4ab+16b^2)=

=a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3

Combine like terms.

a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3=

=a^3-64b^3

Hope this helps!

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Applying the rules of addition and scalar multiplication of vectors, –4w = (–8, 20) and –4u + w = (6, –7)

In the 2D coordinate system, vectors can be split into x-component and y-component.

we can write, for example, a vector r = (2,–6), which means:

x-component = 2

y-component = –6

In the given problem:

u = (-1,3), v = ( 2,4) , and w = (2,-5)

Then,

–4w =  –4(2, –5)

       = (–4 . 2, –4. (–5)) = (–8, 20)

–4u + w =  –4(-1,3) + (2, –5)

             = (–4.(–1), –4 . 3) +(2, –5)

             =(4, –12) + (2, –5)

             = (4+2, –12–(–5)) = (6, –7)

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Answer:

−3<x<3

hope this helps

Answer:

Step-by-step explanation:

The length of the shorter piece is 33 inches.

132 inches of the board is cut into 2 pieces. The board is divided into 2 parts.

One piece is three times the length of the other.

let ,one piece = x

The other piece = 3x

The length(x) of the shorter part  can be found below

x + 3x = 132

4x = 132

divide both sides by 4

x = 132 / 4

x = 33

Therefore the length of the shorter piece is 33 inches.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.

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Answer:1/2 tsp

Step-by-step explanation:

Hey there!

1/4 of 3 3/4

= 1/4 * 3 3/4

= 1/4 * 3 * 4 + 3/4

= 1/4 * 12 + 3/4

= 1/4 * 15/4

= 1(15)/4(4)

= 15/16

Therefore, your answer should be:

15/16

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The area and perimeter of the triangle are:

B. 12x; 5x + 14

The area of the triangle in the image is calculated using the formula, area = 1/2(b)(h), where:

Substitute

Area of the triangle = 1/2(8)(3x)

Area of the triangle = 4(3x)

Area of the triangle = 12x units²

The perimeter of the triangle in the image is calculated by adding the length of all three sides of the triangle, which is:

Perimeter = (x + 9) + 8 + (4x - 3)

Perimeter = x + 9 + 8 + 4x - 3

Combine like terms

Perimeter = 5x + 14 units

In conclusion: the area and perimeter of the triangle are:

B. 12x; 5x + 14

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Answer:

Below in bold.

Step-by-step explanation:

f(x)=1.8x^2-6.2x+2.5

As the coefficient of x^2 is positive this has a minimum value.

Find the derivative:

f'(x) = 3.6x - 6.2

This = 0 for a minimum value of f(x):

3.6x - 6.2 = 0

x = 6.2/3.6 = 1.722

This is the value of x when f(x) is a minimum.

So, the minimum value of f(x)

= 1.8(1.722)^2 - 6.2*1.722 + 2.5

= -2.838......

= -2.84 to nearest hundredth.

The inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

We are given the function:

f (x) = 1 / 5 x³

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 1 / 5 x³

5 y =  x³

x³ = 5 y

x = ∛ (5 y)

So, the inverse function will be:

f ⁻¹ (x) = ∛ (5 x)

Therefore, the inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

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Answer:

x = -7 and x = 4

Step-by-step explanation:

Note, I am taking the polynomial equation as
[tex]x^2 - 28 = -3x[/tex]

Otherwise it does not become a polynomial of one variable and cannot be solved

Zeros of a polynomial are the values of x where the polynomial value itself is 0

Standard equation for a polynomial of degree 2 is ax² + bx + c = 0 where a, b and c are constants

Degree is the highest exponent. Here the highest exponent is 2 so the polynomial has degree 2. Such a polynomial is called a quadratic polynomial

So we first have to convert
x² - 28 = - 3x into  this form ax² + bx + c

1. Add 3x to both sides
x² - 28 + 3x = -3x + 3x =0

==> x² + 3x - 28  = 0
With a = 1, b = 3 and c = -28

2. Factor x² + 3x - 28  = 0

Here a = 1, b = 3 and c = -28

Factoring means find two expressions x+a and x +b such that (x + a) (x + b) = x² + 3x - 28  = 0

Then we can state that
x + a = 0           ==> x = -a as one solution
x + b = 0           ==> x = -b as the other solution

To factor, find two numbers m and n(could be negative) such that mn = c and m + n = b

28 has factors 7 and 4 so that is a good start

-28 = -7 x 4 or could also be 7 x -4

How do we choose?
Add both and see what gives you +3

-7 +  4 = -3  Nope
7 + -4 = 7-4 = 3 YES

So the factors are 7 and -4

(x + m) = (x + 7)
(x + n)  = (x -4)

So the original quadratic polynomial becomes

(x + 7)(x -4) =

This means

x + 7 = 0 ==> x = -7

x -  4 = 0 ==> x = 4

So the solutions(also called roots) of x² + 3x - 28  = 0 are:

x = -7 and x = 4

Both the above values satisfy the quadratic equation

Answer:

Angle 1 = 118°

Angle 2 = 62°

Angle 3 = 118°

Angle 4 = 62°

Step-by-step explanation:

Given : Angle 4 = 62°

Here ,

=> Angle 4 + Angle 1 = 180° { linear pair }

=> 62 + Angle 1 = 180

=> Angle 1 = 180 - 62

=> Angle 1 = 118°

Angle 4 = Angle 2 { vertically opposite angle }

Angle 1 = Angle 3 { vertically opposite angles }

Answer:

ABC corresponds to DEF

BCA corresponds to EFD

CAB corresponds to FDE

Step-by-step explanation:

The questions is asking you to find where the point on the small triangle are on the larger triangle, so if it said something like B corresponds to __, your answer would be E. This one just ask for three in a row, so do the points in order. That is all you have to do!

Answer: ABC correspond to DEF.    BCA coressponds to EFD.  CAB corresponds to FED

Step-by-step explanation:

Its telling you what letters coordinate with what letters for example ; FDE corresponds to CAB  

1.9 pounds of metal was refused of her collection.

Given that

To find

So according to the question

We have,

For finding the remaining metal of her collection, we have to subtract the metal buy by recycling center from her total collection

So, we can say that

        remaining metal = her total collection - he metal buy by recycling center

Now, putting the values from question

        remaining metal = 20.3 - 18.4

                                    = 1.9 pounds of metal.

Answer:

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