What is the slope of the line that passes through the points (2,-6) and (6,-12)
Write your answer in simplest form.

I suppose you're given [tex]f(x) = x^2 + 2[/tex], which would mean [tex]f^{-1}(x) = \sqrt{x-2}[/tex]. Then

[tex]f^{-1}(f(x)) = f^{-1}(x^2 + 2)[/tex]

and

[tex]f^{-1}(x) = \sqrt{x - 2} \implies f^{-1}(x^2+2) = \sqrt{(x^2+2) - 2}[/tex].

You should have [tex]x^2+2[/tex] where you wrote [tex]x+2[/tex]. This then simplifies to [tex]\sqrt{x^2} = x[/tex] (as long as [tex]x\ge0[/tex]).

The solution of the system of equation by graphing is (1,2)

According to the question we have been given two equation which are :

       x + y = 3       and  y = 3x - 1

We need solve this system of equation by graphing that is we have to find the value of x and y from the graph.

For the solution of the system of equation from graph we need to find the intersecting point.

First we will plot the graph of both the equation

For , x+y = 3

      the coordinates are (0,3) and (1,2)

For, y = 3x-1

      the coordinates are (0,-1) and (1,2)

Hence the below image is the graph of both the equation

From the graph we will see the point where both the lines are intersecting.

Thus the point where they intersect is (1,2).

Hence the solution is (1,2)

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Answer:

6.984×10^8 km

Step-by-step explanation:

Your calculator can tell you the answer to this.

15.15×10^8 -8.166×10^8 = 6.984×10^8

The difference between the distances is about 6.984×10^8 km.

_____

Additional comment

If you're paying attention to significant figures, you must round this to 6.98×10^8 km. The precision of the Saturn distance does not allow any better precision in the difference.

Answer:

 the value of cos(x) is ±√3/2 and tan(x) is ±1/√3.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The  f(x) - k shifts the function g(x) by  √0.8x units downwards

Let us consider

f(x) = g(x) + k

g(x) = f(x) - k

where f(x) = √x and

          g(x) = √0.2x

Substituting these values in the above equation

√0.2x = √x - k

-k = -√x + √0.2x

k = √x - √0.2x

k = √0.8x

which means that the f(x) - k shifts the function g(x) by √0.8x units downwards.

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Answer:  $24

Step-by-step explanation:

14+14+14+14=56

56+24=80

80/5

16

The 5th shirt cost $24 if the average after the 5th shirt was purchased changed to $16 per shirt.

Let's consider the total cost of the first 4 shirts:

Total cost of first 4 shirts = 4 shirts * $14/shirt = $56

Now, let's assume the cost of the 5th shirt is "x" dollars. After purchasing the 5th shirt, the total cost of all 5 shirts would be:

Total cost of all 5 shirts = $56 + x

Given that the average price after the 5th shirt was purchased is $16, we can set up an equation using the average formula:

Average price = Total cost / Number of shirts

$16 = ($56 + x) / 5

Solving for x:

$16 * 5 = $56 + x

$80 = $56 + x

x = $80 - $56

x = $24

So, the cost of the 5th shirt (x) is $24. This means that the person purchased the 5th shirt for $24 in order to bring the average price of all 5 shirts to $16 per shirt.

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The amount of profit each of them received $49625 and $36625 respectively

To solve the problem, we need to write a system of equations.

Let

Given that a profit of $86,250 was shared by the two partners of a business, we have that

x + y = 86,250 (1)

Also, since one partner received $13,000 more than the other, we have that

x - y = 13,000  (2)

We now solve for x and y in the system of equations

x + y = 86,250 (1)

x - y = 13,000  (2)

Adding equations (1) and (2), we have

x + y = 86,250 (1)

+

x - y = 13,000  (2)

2x = 99250

x = 99250/2

x = $49625

From equation (2) y = x - 13000

Substituting x into the equation, we have

y = x - 13000

= 49625 - 13000

= $36625

Since x = $49625 and y = $36625,

So, the amount of profit each of them received $49625 and $36625 respectively

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A basketball team sells tickets that cost $10 $20 or VIP seats, $30.

The no. of three types of tickets = x, y, z

;

The team has sold 492 tickets over all.

x + y + z = 492

:

It has sold 177 more $20 tickets than $10 tickets.

y = x + 177

:

The total sales are $8580.

10x + 20y + 30z = 8580

:

How Many tickets of each kind have been sold?

:

Replace (x+177) for y in the 1st and 3rd equations

x + (177+x) + z = 492

2x + z = 492 - 177

2x + z = 315

and

10x + 20(x+177) + 30z = 8580

10x + 20x + 3540 + 30z = 8580

30x + 30z = 8580 - 3540

30x + 30z = 5040

Simplify, divide equation by 30

x + z = 168

:

Using these two equations for elimination

2x + z = 315

x + z = 168

---------------subtracting eliminates z

x = 147 ea $10 tickets sold

:

y = 147 + 177

y = 324 ea $20 tickets sold

;

Find z using the 1st equation

147 + 324 + z = 492

471 + z = 492

z = 492 - 471

:

Check solution in the $$ equation

10(147) + 20(324) + 30(21) =

1470 + 6480 + 630 = 8580; confirms our solutions

The number of $10 tickets sold is 1094.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Number of $10 tickets = x

Number of $20 tickets = x + 158

Number of $30 tickets = y

Total tickets = 3227

Total sales = $62410

We can make two equations.

x + (x + 158) + y = 3227

2x + y = 3227 - 158

2x + y = 3069 ____(1)

10x + 20(x + 158) + 30y = 62410

10x + 20x + 3160 + 30y = 62410

30x + 30y = 62410 - 3160

30x + 30y = 59250

30 (x + y) = 59240

x + y = 1975 ____(2)

From (1) and (2).

 2x + y = 3069

 x + y = 1975  

(-)   (-)    (-)      

x = 3069 - 1975

x = 1094

And,

Substituting x = 1094 in (2)

x + y = 1975

y = 1975 - x

y = 1975 - 1094

y = 881

The number of $10 tickets.

= x

=1094

Thus,

The number of $10 tickets is 1094.

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The simplified answer is 6.01* 10^6.

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

Given:

(4.1 x 10^5) + (5.6 x 10^6)

Solving further

4.1 * 10^5 + 5.6 * 10^6

4.1* 10^5 + 5.6*10*10^5

4.1* 10^5 + 56*10^5

(4.1 + 56 ) * 10^5

60.1* 10^5

6.01* 10^6

Hence, the simplified answer is 6.01* 10^6

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Answer:             4x +10

Step-by-step explanation:

Distribute the 2 to both terms

2*2x + 2*5

4x + 10

The commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

Given that the commission rate is 6%

If the sales done is 33000 dollars then the commission received by the agent would be:

33000 * 0.06 = 1980

Now if the sale doubles we would have 33000 x 2

= 66000 dollars

then the commission received would be

66000 x 0.06

= $3960

Hence we would say that the commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

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Answer:

Step-by-step explanation:

Answer:

domain of the given function is i don't know sorry

Step-by-step explanation:

Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.

We are given that:

Ishmael claims:

the square root of a number is always less than the number under the radical symbol.

Laurie claims:

there are lots of numbers whose square root is larger than the number and the radical.

Laurie can convince Ishmael by giving examples like 1/4 whose square root is 1/2 which is greater than 1/2.

Another number is 1/9 whose square root is 1/3.

Therefore, Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.

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The most convenient method to graph the line is to plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The equation is given as

3x + 2y = 12

The above equation is a linear equation

All forms of equation can be conveniently plotted by a graphing utility

However, the best way is to start by simplifying the equation

So, we have

3x + 2y = 12

Divide through the equation by 2

So, we have

3/2x + y = 6

Make y the subject of the equation

So, we have

y = -3/2x + 6

This means that  we plot the equation y = -3/2x + 6 to represent the equation 3x + 2y = 12

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Answer:

  [-4, 0]

Step-by-step explanation:

You want the set -4 ≤ x ≤ 0 expressed using interval notation.

In interval notation, an interval is expressed as an ordered pair, with the first number of the pair being the lower end of the interval, and the second number being the upper end.

When the inequality symbol used to describe the interval is "less than" (<), the bracket used is a round bracket (parenthesis). When the symbol is "less than or equal to" (≤), a square bracket is used. The brackets need not be of the same kind.

When one end of the interval is an infinity (positive or negative), a round bracket is used.

The interval

  -4 ≤ x ≤ 0

is written using the ordered pair ...

  [-4, 0]

The number sequence x satisfying-4< x <0 is an interval containing -4,0 as well as all numbers between -4 and 0.

[-4, 0]

A graph for interval notation is created when we describe the solution set of an interval on even a number line.

Intervals are represented in rectangular brackets as well as parentheses, and two numbers are separated by a comma. The two numbers are referred to as the interval's endpoints. The number on the left represents the smallest element or lower bound.

Interval notation is a technique for representing any subset of the real number line. To write interval notation, we utilize different symbols depending on the type of interval.. For instance, the set of numbers x satisfying 1 x 6 is an interval containing 1, 6, and all values between 1 and 6.

The ordered pair is used to write the interval -4 x 0.

[-4, 0].

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Answer:

-1/12

Step-by-step explanation:

-⅓ + ¼

= (-4 + 3)/12

= -1/12

For the given coordinates, The equation of line is x - 3y + 8 =0

The equation of line is given by -

y − y 1 = m ( x − x 1 )

here x1,y1 = (1,-5)

m = x2 - x1/ y2 - y1

m = 4-1/4+5

m = 3/9

m = 1/3

y - 1 = 1/3 (x +5)

3y - 3 = x + 5

x - 3y = -8

x - 3y + 8 =0

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Based on the fact that the vehicle's fuel efficiency is not less than 35 miles per gallon, using f to represent the vehicle's fuel efficiency gives f ≥ 35.

The fuel efficiency of the vehicle is no less than 35 miles per gallon. This means that the fuel efficiency is either 35 miles per gallon, or greater than 35 miles per gallon.

Assuming f is meant to represent this fuel efficiency of a vehicle, this means that f can be shown as being either greater than, or equal to 35 miles per gallon.

A representation of this would be:
f ≥ 35

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Answer: 1

Step-by-step explanation:

The range of the function is (11, -4, 29}.

What is the range of a function?

The set of all a function's outputs is its range. In the function, f : A→B, A is the domain and B is the co-domain. The range is then created by this function's output. "Set of even natural numbers" defines the range. The mapped elements of the co-domain are referred to as the images, while domain elements are referred to as pre-images. The set of all images representing the domain's elements, or the set of all its outputs, defines the range of the function f in this case.

The range in this case is (11, -4, 29}.

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The value of angle x in the triangle is 5

The given parameter is represented by the figure

By the external opposite angle of a triangle theorem, we have the following equation

22x + 3 = 6x + 4 + 79

Collect the like terms

So, we have

22x - 6x = 4 + 79 - 3

Evaluate the like terms

So, we have

16x = 80

Divide both sides by 16

So, we have

x = 5

Hence, the value of angle x in the triangle is 5

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Take the base-5 logarithm on both sides and simplify.

[tex]x^{16 \log^3_5(x) - 68 \log_5(x)} = 5^{-16}[/tex]

[tex]\left(16 \log^3_5(x) - 68 \log_5(x)\right) \log_5(x) = -16[/tex]

[tex]16 \log^4_5(x) - 68 \log^2_5(x) + 16 = 0[/tex]

[tex]4 \log^4_5(x) - 17 \log^2_5(x) + 4 = 0[/tex]

Factorize the left side.

[tex]\left(4 \log^2_5(x) - 1\right) \left(\log^2_5(x) - 4\right) = 0[/tex]

Then

[tex]4 \log^2_5(x) - 1 = 0 \implies \log^2_5(x) = \dfrac14 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm \dfrac12 \\\\ ~~~~~~~~ \implies x = \dfrac1{\sqrt5} \text{ or } x = \sqrt5[/tex]

or

[tex]\log^2_5(x) - 4 = 0 \implies \log^2_5(x) = 4 \\\\ ~~~~~~~~ \implies \log_5(x) = \pm 2 \\\\ ~~~~~~~~ \implies x = \dfrac1{25} \text{ or } x = 25[/tex]

and the product of these solutions is of course 1.

Answer:

[tex]x = 1[/tex] or [tex]x = -5[/tex]

Step-by-step explanation:

[tex]4|2x + 4|-7 = 17\\\to4|2x + 4| = 24\\\to |2x + 4| = 6[/tex]

Case 1) 2x + 4 is positive
[tex]2x + 4 = 6\\\to 2x = 2\\\to x = 1[/tex]

Case 2) 2x + 4 is negative

[tex]2x + 4 = -6\\\to 2x = -10\\\to x = -5[/tex]

The explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.

A graph is a function when there are exactly one y-value for every x-value that is plotted on the graph.

This implies that, no single x-value can have two different y-values in a graph that represents a function. If there are two different y-values for a single x-value, then the graph is not a function.

In the graph given below, the x-value, 4, has two different y-values, -2 and 4. This makes the graph not a function.

Therefore, the explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.

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Answer:

Step-by-step explanation:

It is not a function because there are two different y-values for a single x-value.

Using simple interest, the better deal is given by Bank B.

The options are missing, but they are given as follows:

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

For Bank A, the balance, without the fee, will be given by:

A(1) = 500(1 + 0.1) = $550.

Removing the fee:

550 - 12 x 5 = $490.

For Bank B, the balance is given by:

A(1) = 500(1 + 0.02) = $510.

No fee, 510 > 490, hence Bank B offers the better deal.

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Answer:

27

Step-by-step explanation:

-2x+3(y-5x)-x --- distribute the parenthesis

-2x+3y-15x-x --- evaluate by combining similar terms

3y-18x --- plug in -1 for x and 3 for y

3(3)-18(-1) --- evaluate

9+18 --- evaluate

27

Answer:

27

Step-by-step explanation:

-2(-1)+3{3-5(-1)}-1(-1)

2+3(3+5)+1

2+3(8)+1

2+24+1

=27