pls help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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

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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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:

Step-by-step explanation:

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  

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]

Answer:

2

Step-by-step explanation:

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:)

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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the equation of it is

y= -1/2x+5

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:

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:

1

Step-by-step explanation:

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

[tex]= 1[/tex]

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:

X=1

Search it up on a calculator next time

Answer:

solution:

x=1

Step-by-step explanation:

2x + 6=4x+4

2x -4x +6-4=0

-2x +2 =0

-2x = -2

x = -2/-2

× = 1

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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Expanded form of logarithm  log√x²-4 / (x+3)² is 1/2log(x²-4)-2log (x+3).

By considering the given logarithm function

log√x²-4 / (x+3)²

log√x²-4 -log (x+3)²

1/2log(x²-4)-2log (x+3)

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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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.

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

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:

I think it's an error it should be correct and in the right spot or whatever it an error

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:

−3<x<3

hope this helps

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: