Given the linear functions f(x) = x-3 and g(x) = -2x + 4, determine (f g)(x).
O(f-g)(x) = -2x - 12
O(1-g)(x) = -2x² - 12
O(1-g)(x) = -2x2 - 2x - 12
O(f g)(x) = -2x2 + 10x - 12

Darren's monthly payment on car loan is $210.83

Given,

Cost of the car Darren purchased = $11000

The simple interest for the car loan = 3%

Time period of loan = 5 years

We have to find the monthly payment amount:

Simple interest = PRT / 100

Where,

P = Principal amount = $11000

R = Rate of interest = 3%

T = Time period = 5 years

Now,

SI = PRT / 100

SI = (11000 × 3 × 5) / 100

SI = 110 × 3 × 5

SI = 1650

Here, the simple interest for 5 years is $1650

Now,

Total amount to be paid after 5 years = Principal amount + Simple interest

A = P + SI

A = 11000 + 1650

A = 12650

The amount to be paid after 5 years is $12650

Next,

The monthly payment amount:

Number of months in 5 years = 12 × 5 = 60 months

So,

Monthly payment amount = Total amount after 5 years / Total months in 5 years

Monthly payment amount = 12650 / 60 = 210.83

That is, the monthly payment amount on car loan is $210.83

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By using differential equations' concept, we get that there is no sugar in the beginning.

A differential equation is an equation that connects the derivatives of one or more unknown functions.

Given:

Pure water = 2840 litres

sugar = 0.01kg per liter

Rate of sugar entering the tank = 4liter/min

New solution drains out at the rate = 4 litre/min

To find: sugar in the beginning.

Finding:

(a) In the beginning, the tank contains only pure water and no solution of water with sugar.

Hence, the sugar is null for t = 0.

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Answer: x = 36

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x = 36

Step-by-step explanation:

1/4 (x-8) =7

times both sides by 4

x-8=28

add 8 to both sides

x=36

The equation of the square root function is g(x) = √(x - 1) + 3

A square root function is represented as

f(x) = √x

The transformation rule is given as

Shifted up 3 units and right 1 unit

This can be represented as

(x - 1, y + 3)

So, we have

g(x) = f(x - 1) + 3

This gives

g(x) = √(x - 1) + 3

From the question, we have

It contains the point (5,7).

This means that

g(5) = 7

So, we have

g(5) = √(5 - 1) + 3

Evaluate

g(5) = 7

Hence, the equation of the square root function is g(x) = √(x - 1) + 3

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The equation of the line with slope 2/3 and y-intercept at ( 0, - 2) is y = ( 2/3 )x - 2.

The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible.

We have the slope 2/3 of a line and the y-intercept at ( 0, - 2 ).

Now, we know that

The slope-intercept form of the equation of a line with slope m and y-intercept at the point (0, c) is given by:

y = mx + c

The slope of the line is :

m = 2/3

And, the y-intercept is (0, c) = ( 0, -2)

Hence, the equation of the line in the slope-intercept form will be:

y = mx + c

y = ( 2/3 )x + ( - 2)

y = ( 2/3 )x - 2

Therefore, the slope-intercept form of the equation of the line is y = ( 2/3 )x - 2.

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Answer: -8 45/56

Step-by-step explanation:

Answer:

Answer is option A.

X cannot be equal to -4

Answer:

hi awaz are u in india server ?

Simple Interest can be defined as a method of calculating interest for a some principal amount over a period of time.

When we borrow money or take a loan , and when we pay back the loan some money is charged based in the amount borrowed and time period the loan is taken ,

that money charged is called as Simple Interest .

Simple Interest can be calculated using the formula

SI=(PxRxT)/100

where, P=principal   , R=rate of interest  , t=time taken

The main difference between the Simple Interest and Compound Interest is  the in Simple interest the principal is fixed whereas in Compound Interest the principal keeps on varying with time .

For Example : John borrowed $200 from Smith at 10% rate of interest for 5 years .

So the Simple Interest that John has to pay Smith will be

SI=(PxRxT)/100

SI=(200x10x5)/100

SI=10000/100

SI=$100

So apart from principal amount $200 John has to pay extra $100 as interest , Total John will be paying $300 to smith in return.

Therefore , Simple Interest is defined .

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The slope of the any line parallel to the line y-5 = 25/2(x+4)  is equal and its value is 25 /2 .

We have given equation y-5 = 25/2(x+4) .

On simplifying , we get

      y - 5 = 25 x/2 +50

       y = 25 x /2 +55

On comparing the above equation with slope intercept form y = mx + b ,

we get m = 25 / 2

All the lines which are parallel to any other line have equal slope.

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The height of the building is 1122.528 feet.

Angle of elevation:

Angle of elevation means an angle between the horizontal plane and oblique line from the observer's eye to some object above his eye.

Given,

The angle of elevation to the top of a building in New York is 12° from the ground and 1 mile from the base of the building.

Here we need to find the height of the building.

We know that,

The expression for the height of the building is,

h = tanΘ × x

Where the value of

tan Θ = 12°

x = 1 mile

So, When we apply the value on the formula,

The we get,

h = tan 12° x 1

So, apply the value of tan 12 degree,

h = 0.2126 x 1

h = 0.2126 mile

Simplify the above equation using the information

1 mile = 5280 ft.

That is equal to

h = 1122.528 feet.

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Answer:

it is which of the following is a reactant

Step-by-step explanation:

The two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

The equation is given as

|3x - 2| = 19

The above equation is an absolute value equation.

When it is split, the constant would be represented as positive and negative

So, the equivalent equations are

3x - 2 = 19 and 3x - 2 = -19

Hence, the two equations to set up to solve the equation are 3x - 2 = 19 and 3x - 2 = -19

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The meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

The function is given as

m(x) represents the amount of money (in dollars) it costs you to be a member at the YMCA after x months

The function notation is given as

m(0)

The function notation m(0) implies that

We determine the value of m(x) when x = 0

This represents the x-intercept of the function

The x-intercept of the function is the initial value of the function

Hence, the meaning of the function notation is the inital amount of money (in dollars) it costs you to be a member at the YMCA

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Answer:

$14988.75

Step-by-step explanation:

15 x 25 = 375

375 x $39.97 = $14988.75

Answer:

$14988.75

Step-by-step explanation:

25x15 = 375

375 x 39.97 = $14988.75

Answer:

5

Step-by-step explanation:

If you put this in a calculator it comes back with 4.79583... decimals forever.  Rounding to the nearest integer gives 5.

Answer:

5

Step-by-step explanation:

√23 : 4.795831523 whose nearest integer is 5 .

Hence, the nearest number is 5.

Answer:

[tex]f(3) = \frac{2}{5} [/tex]

Step-by-step explanation:

f(x) = 4/5x - 2

f(3)=4/5(3)−2

f(3)=4/5(3)−2

f(3)=12/5+−2

f(3)=(12/5+−2)(Combine Like Terms)

f(3)=2/5

If the number of checks are greater than 25, the Simple Checking plan cost​ less.

We have two checking account plans at Parson's bank.

We have to determine for what number of checks per month will the Simple Checking plan cost​ less.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Let for x number of checks per month the simple checking plan cost less.

For No frills plan -

Charge per check - $0.25

Therefore, for x checks, it will cost - $0.25x

For Simple Checking plan -

Fixed monthly charges - $5

Charges per check - $0.50

Therefore - for x checks - $5 + $0.50x

Now - for Simple Checking plan to cost​ less than No frills plan -

5 + 0.05x < 0.25x

5 < 0.25x - 0.05x

5 < 0.2x

x > 25

Hence, if the number of checks are greater than 25, the Simple Checking plan cost​ less.

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Answer:

108525975,11111111111111111111111

Answer: 108525975.111

Step-by-step explanation:

= (-54)

Step-by-step explanation:

ATQ

4+2(x+6)^2

6(x^2+12x+216)=0 [ {a+b}^2 = a^2+2ab+b^2 ]

6x^2 +72x+216=0

Put the value of x=(-3)

So ,

6x^2 +72x+36=0

6(-3)^2+72(-3)+216=0

6×(-9)+72×(-3)+216=0

(-54)+(-216)+216=0

= -54

Hence, the solution is -54 at x=(-3).

Thank You

Since, the sides ab || dc, ad || bc, and ad || bc . hence, the given quadrilateral abc is a prallelogram.

According to the given question.

We have the vertices of a quadrilateral abcd such that a(1, 0), b(5, 0), c(7, 2) and d(3, 2).

As we know that, a parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.

Since, we have to prove that the given quadrilateral is a parallelogram by using slope. From the definition of the parallelogram we can say that, the opposite sides of the parallelogram are parallel to each other.

Now,

slope of side ab = 0-0/(5 -1) = 0

slope of side dc = 2 -2/(3-7) = 0

slope of the side ad = 2 -0/(3 -1) = 1

slope of the side bc =  2 -0/(7 -5) = 1

Here, the slopes of the opposite sides ab and dc, and ad and bc are equals and we know that when the slope of two line are equals then the lines are parallel to each other.

Therefore,  the sides ab || dc, ad || bc, and ad || bc . hence, the given quadrilateral abc is a prallelogram.

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The force on the object will be 12 N.

We have a moving object.

We have to determine the force on object when the acceleration of the object becomes 2 m/s².

Force is necessary to bring around a change in the state of the body. Either from rest to motion or motion to rest. It can be calculated using the formula-

Force (F) = mass (m) x acceleration (a)

According to the question -

When a force of 42 N acts on the object, then using the formula of force -

F = m x a

42 = m x 7

m(Object) = 6 Kg

When the acceleration of the object becomes 2 m/s², then -

F = m(object) x a

F = 6 x 2 = 12 N

Hence, the force on the object will be 12 N.

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The probability that i will end up with one card from each suit is 3/32.

Probability:

Probability refer the possibility of the event.

The formula for the probability of the event is,

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

If i choose four cards from a standard 52-card deck, with replacement,

Then we need to find the  probability that i will end up with one card from each suit.

In the first draw, we can take one card, if it is a spade one,

Then for the second draw we have 39 options

For the third draw we have 26 options

For the fourth draw we have 13 options,

So, the probability that i will end up with one card from each suit is

=> 1 x 39/52 x 26/52 x 13/52

=> 1 x 3/4 x 1/2 x 1/4

=> 3/32

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51

1530÷30=51

30x51=1530

correct answer is random sample

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) picked at random from a larger group of people (also known as a population) with an equal probability. It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people. [1] An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that may be used in combination with other, more sophisticated sampling techniques.

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Answer:

Step-by-step explanation:

(-3, 2)

Horizontal is y = 2

Vertical is x = -3

In the same way (1, 4) is

y = 4

x = 1.

Answer: 128

Step-by-step explanation:

a whole supplementary angle adds up to 180 degrees

so 180

   - 52

     128

Answer:

2(6x²+11xy−4y²)

Step-by-step explanation:

Factor 12x²+22xy−8y²

12x+22xy−8y²

=2(6x²+11xy−4y²)

x=±a

1. take the square root of both sides