For f(x) = 4x + 1 and g(x) = x2 - 5, find (f- g)(x).

In the quadratic equation f(x) = a(x - h)² + k , then the graph is given on the right

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

According to the question, given that

the quadratic equation f(x) = a(x - h)² + k

Axis of symmetry : x = h = 3

The coordinates of the highest point is (3,8)  {it is the ordinate of the    highest point of the image}

so, k = 8

f(x) =  [tex]a (x- 3)^{2} + 8[/tex]

plug in (0,- 10)

       - 10 = 9a + 8

          a  = - 2

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

Therefore, f(x) = a(x - h)² + k quadratic equation we get the value of f(x),

f(x) = [tex]-2 (x- 3)^{2} + 8[/tex]

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

The parent quadratic function connects the locations whose coordinates have the type f(x) = x2 and is of the kind (number, number2). This function, which normally has the form f(x) = a (x - h)2 + k, is capable of being transformed. It can also be changed to take the form f(x) = ax2 + bx + c.

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Step-by-step explanation:

I assume this actually is

revenue : R(x) = 12x

cost : C(x) = 5x + 20

profit : P(x) = R(x) - C(x) = 12x - 5x - 20 = 7x - 20

In order to find the quotient and remainder of the division, let's divide the polynomials doing the following steps:

x³ divided by x: x².

x² times (x + 2): x³ + 2x²

x³ + 6x² + 17x + 11 minus (x³ + 2x²): 4x² + 17x + 11

4x² divided by x: 4x

4x times (x + 2): 4x² + 8x

4x² + 17x + 11 minus (4x² + 8x): 9x + 11

9x divided by x: 9

9 times (x + 2): 9x + 18

9x + 11 minus (9x + 18): -7

Therefore the quotient is x² + 4x + 9 and the remainder is -7

Correct option: first one.

to make a perpendicular function from another we must take its slope and make two transformations

the slope of y=1/3x is 1/3

the transformations:

1.

reverse the number

2.

and change the sign

ok we have the slope now need the general equation of the line

where m is the slope , b a cut point and (x,y) a point

so, we have the slope=-3 , and the point (2,-3) we can replace to find b

now we can replace b and the slope to have the final equation

The unit cost for a pair of shoes at FootAction is $33.33.

The unit cost is a function of the total cost divided by the number of units.

The unit cost is the cost per one (pair).

The unit cost is also described as the unit rate, which gives a unit's cost.

Unit costs can be computed using a division operation.

The cost of 2 pairs of Nikes at FootLocker = $69.98

The cost of 3 pairs of shoes at FootAction = $99.99

1 pair of shoes at FootAction will cost = $33.33 ($99.99/3)

Thus, based on their unit costs, we can conclude that a pair of shoes costs $34.99 at FootLocker and $33.33 at FootAction.

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Answer:

5y=3x+5

Step-by-step explanation:

y-(-2) 1-(-2)

_____ = _____

x-(-5) 0-(-5)

y+2 3

____ = __

x+5 5

5y+10=3x+15

5y=3x+5

Explanation

Step 1

Let

initial position= 10m

Answer:

Step-by-step explanation:

lets represent:

Hours of Loading and Unloading = X

Hours of packing = y

Weekday move: 8 hours of loading and unloading services. 6 hours of packing and unpacking service. $890 total cost.

Equation 1:  18x + 6y = 890

Weekend Move: 5 hours of loading and unloading services. 3 hours of packing and unpacking services. $515 total cost.

Equation 2:  5x + 3y = 515

-

Multiply Equation 1 by 5 and Equation 2 by 4

Equation 3:  90x + 30y = 4450

Equation 4: 20x + 12y = 2060

We Subtract Equation 4 from 3

70x = 2390

x = 2390/70

x = $34.14

Solving for y

-Equation 1-

18x + 6y = 890

18(24.14) + 6y = 890

434.52 + 6y = 890

6y = 890 - 434.52

6y = 455.48

y = 75.91

y = $75.91

Hours of Loading and Unloading rates= x = $34.14

Hours of packing rates = y = $75.91

Using the given linear functions, it is found that:

a) The test average for your math class after completing test 2 is of 76.6.

b) The test average for your science class after completing test 2 is of 84.

c) The science class had a higher average after completing test 4.

The grades change by a constant rate in each of the classes, science and math, hence the functions are called linear.

The average grade function, after x tests, for each class, is defined according to the following rule:

After the second test, the numeric values for items a and b are found replacing the lone instance of x in each equation by 2, hence the grades are as follows:

After the fourth test, the grades are given as follows:

80 > 77.2, hence the science class had a higher average.

The science class grade after test x is given by the following rule:

g(x) = 88 - 2x.

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Answer:

I don't think so. It's a coincidence -- maybe. But it's a fun question to answer.

Step-by-step explanation:

Comment

So ice cream on this particular beach causes more sharks to come closer to shore and attack. That's the premise.

I'd like to say it is a coincidence, or the data is biased in some way, but there is no way of telling without checking out the stats (which I would guess there are none).

Perhaps sharks like sugar and lot of someones drop their ice cream cones in the water. It's a test. Or it could be made into one.

Perhaps the sharks are annoyed by the ice cream and take it out on the person holding the ice cream. Again it's a test.

Perhaps they smell the ice cream and are attracted to it. I wouldn't want to test this with offering a shark a sugar cube put in water.

Considering the definition of an equation and the way to solve it, the price of a T-shirt was $11.

An equation is an algebraic equality between two expressions, called members, in which letters (unknowns) appear with unknown value. These unknown values appear related to known elements through mathematical operations.

The equality between two algebraic expressions is only verified or true for certain values of the unknown. So finding the solution to an equation involves finding the value that satisfies the equality.

To solve an equation, keep in mind:

Being "x" the cost of one T-shirt, you know that:

The total purchase can be calculated through the equation:

Total purchase =  Cost of book + Cost of T-Shirt

Substituting the corresponding values:

23= 12 + x

Solving:

23 - 12= x

11=x

Finally, a T-shirt cost $11.

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Considering the measure of each "small square" 1 x 1:

Each side of the complete square (a) measure 3 units.

Thus, since the area (A) is A = a², the area is:

Answer: 9 sq units.

Since Vito's bid is the highest, he gets the bus and has to compensate the others to make the division fair. The amount of money that Tim get from Vito is: $1,581.25.

Fair shares:

Rob: 3600 4 = 900

Sue: 5000 /4 = 1250

Tim: 4800 / 4 = 1200

Vito: 6500 / 5 = 1625

Since Vito gets the bus the amount he pay the group is:

Amount = 6500 - 1625

Amount = 4,875

Since everybody gets their fair share, the amount remaining is:

Amount left = 4,875 - 900 - 1250 - 1,200

Amount left = 1,525

Hence,

The amount Tim get is calculated as :

Amount = 1200 + (1525 /4)

Amount  = $1,581.25

Therefore Tim get $1,581.25.

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Answer: 32 dollars each week

Step-by-step explanation: Divide 768 by 24 and get 32

Answer:

32$ each week.

Step-by-step explanation:

This is simply division. 768 divided by 24 equals 32.

Answer:

15 ft

Step-by-step explanation:

3 ft / 2 in    *  10 in = 15 feet tall

So if you let x and y be the two numbers...

the sum of the two means you add them together... so you get:

x+y=56: the difference means you subtract them.. so

x-y = 16

now you have two equations and two unknowns... which you can solve with various methods... you can use elimination, substitution, or trial and error.

x+y=56

x-y = 16

I will use the elimination method: Because there is a plus y and a negative you cancel that out and add the 2x's. Therefore:

2x=72

x=36

Now, you can plug 36 into one of your original equations:

36+y=56

y=20

Those are your two numbers!

Answer:

15/20-8/20

Step-by-step explanation:

3/4-2/5=0.35

15/20-8/20=0.35

It is equivalent.

The conclusion regarding the statement is true will be f(-2) = g(-2). Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

From the graph, the lines intersect at (-2, 4). That means the value of the functions f(x) and g(x) will be 4 at x = -2.

The conclusion regarding the statement is true will be f(-2) = g(-2). Then the correct option is D.

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The complete question is attached below.

Answer:

x³ + 8x² + 11x - 20

Step-by-step explanation:

(x + 5)(x² + 3x - 4) =

= (x + 5)[x² + 3x + (-4)] =

= (x + 5)(x²) + (x + 5)(3x) + (x + 5)(-4)

= x³ + 5x² + 3x² + 15x + (-4x) + (-20)

= x³ + 8x² + 11x - 20

Answer:

Step-by-step explanation:

Given conditional:

→ If a number is a natural number, then is it also a whole number.

If P then Q.

P= "a number is a natural number"-hypothesis

Q="is it also a whole number"-conclusion

Inverse negates both the hypothesis P and the conclusion Q.

If not P then not Q.

→ If a number is not a natural number, then is it also not a whole number.

Converse interchanges hypothesis P for the conclusion Q.

If Q then P.

→ If a number is a whole number, then is it also a natural number.

Contrapositive interchanges hypothesis for the conclusion of the inverse

or negates both the hypothesis and conclusion of converse.

If not Q then not P.

→ If a number is not a whole number, then is it also not a natural number.

Biconditional

P if and only if Q

→ A number is a natural number if and only if is it also a whole number.

For the student the lift increased for the weight will be 50%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A student doing resistance exercise.

After one week, She can lift the weight = 2 kg

And, After four weeks, she can lift the weight = 3 kg

Since, We know that;

Percent = (increased weight - Actual weight) / Actual weight  x 100

Substitute all the values, we get;

Increased percent = (3 - 2) / 2 x 100

Increased percent = 1 / 2 x 100

Increased percent = 100 / 2

Increased percent = 50%

Therefore,

For the student the lift increased for the weight will be 50%.

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The value of cos I as a fraction in simplest terms is 4/5.

This is a problem based on trigonometry. Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The length of the hypotenuse is 25. The length of the perpendicular is 15. The length of the base is unknown. We know that the angle ∠IJK = 90°.

We need to find the value of Cos(I). But we don't know the value of the length of the base of the triangle. So, we will first find Sin(I).

Sin(I) = 15/25

Sin(I) = 3/5

We know the trigonometric identity that Sin²θ + Cos²θ = 1.

Sin²I + Cos²I = 1

Cos²I = 1 - Sin²I

Cos²I = 1 - (3/5)²

Cos²I = 1 - (9/25)

Cos²I = (25 - 9)/25

Cos²I = 16/25

Cos(I) = √(16/25)

Cos(I) = 4/5

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the angle is a reflex angle

reflex angle is when two sum of angles is 90

equating both angle to 90

X = 90

That should be the answer

The population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the point estimate.

From the question:

The population parameter value and the point estimate differ because a sample is not a census of the entire population , but it is being used to develop the point estimate.

Sample proportion p, is a point estimate of the population proportion.

So it is proved that correct option is point estimate.

Hence the population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the point estimate.

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Answer:

Slope = -9/7

Step-by-step explanation:

       (-3 , 7) ⇒  x₁= -3 & y₁ = 7

       (4 , -2)   ⇒ x₂ = 4  & y₂ = -2

 [tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf = \dfrac{-2-7}{4-[-3]}\\\\=\dfrac{-9}{4+3}\\\\=\dfrac{-9}{7}[/tex]

The best estimate of the cost of renting a car if you plan to drive 268 miles is 234.72 or round off to 235 dollars.

There must be an equal sign (=) in an equation. You can imagine an equation as having a left side and a right side since there will be a mathematical expression on either side of it. Unknowns are a necessary part of algebraic equations. A symbol, such as x, y, or z, is used to symbolize this.

According to the given values in the question,

y = 0.54x + 90

Where y represents the cost of renting the car and x represents the number of miles.

The plan is to drive 268 miles, so the cost according to that will be :

y = 0.54(268) + 90

y = 234.72 or,

y = 235.

Hence, the round-off cost will be 235 dollars.

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Answer:

If its asking what kind of slope it would be an undefined slope  

Step-by-step explanation:

Answer:24 kids

Step-by-step explanation: a dozen is equal to 12 so 12+12=24

We have the following:

We can calculate the angle by means of the trigonometric cosine ratios, as follows:

replacing:

Therefore the angle formed is 57.6 degrees