Determine the domain and range of (g ○ f)(x) if f of x is equal to 2 over the quantity x squared minus 1 end quantity and g(x) = x + 1.

Answer:

y + 1/2 = 3(x - 2)

Step-by-step explanation:

We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:

y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

The correct option is (3).

The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.

As per the given data:

We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.

As we know a point at the slope of the line, we can use the point slope form:

[tex]y - y_1 = m(x-x_1)[/tex] , where m is the slope and [tex](x_1, y_1)[/tex] is the point through which the line passes.

y - (-1/2) = 3(x - 2)

y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

Hence, The equation of the line is y + 1/2 = 3(x - 2).

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The Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], where a and b are two legs of a right triangle and c is the hypotenuse (the longest side).

We're given a triangle with the following:

We can plug these values into the Pythagorean theorem as a, b and c:

[tex]a^2+b^2=c^2\\2^2+b^2=6^2[/tex]

Now, isolate b:

[tex]b^2=6^2-2^2\\b=\sqrt{6^2-2^2}\\b=\sqrt{36-4}\\b=\sqrt{32}[/tex]

[tex]b=\sqrt{32}[/tex]

Answer: [tex]52.6^{\circ}[/tex]

Step-by-step explanation:

Let the angle of depression be x.

[tex]\sin x=\frac{27}{34}\\\\x=\sin^{-1} \left(\frac{27}{34} \right) \approx 52.6^{\circ}[/tex]

You can by 42 combinations of items from the store

The given parameters are:

Envelop = 7

Stamp = 6

The number of combination is:

Combination = Envelop * Stamp

So, we have:

Combination = 7 * 6

Evaluate

Combination = 42

Hence, you can by 42 combinations of items from the store

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Answer:

QR=17

Step-by-step explanation:

[tex](12)(x-2)=(3)(3x-1)\\12x-24=9x-3\\3x-24=-3\\3x=21\\x=7[/tex]                

 [tex]x=7\\\\QR=12+x-2\\=12+(7)-2\\QR=17[/tex]

Answer:

375

Step-by-step explanation:

Since they started at the same point and went in opposite directions, add the 2 distances.

162.5 + 212.5 = 375

Answer:

Step-by-step explanation:

255 people

Using the binomial distribution, we have that:

A. The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

B. There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The expected number of trials until q successes are found is:

[tex]E(X) = \frac{q}{p}[/tex]

In this problem, the probability of a success is of p = 0.65, hence:

[tex]E(X) = \frac{1}{0.65} = 1.54[/tex]

The salesperson should expect 1.54 customers until he finds a customer that makes a purchase.

The probability is p = 0.65 multiplied by P(X = 0) when n = 3, hence:

0.65 x (0.35)³ = 0.0279.

There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

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Answer:

dan is 24

I had to redo this one

The age of Margo and Dan will be 32 years and 24 years, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Margo is 8 years older than her brother Dan. The sum of their ages is 56.

Let M be the age of Margo and D be the age of Dan. Then the equations are written as,

M = D + 8               ...1

M + D = 56            ...2

From equations 1 and 2, then we have

D + 8 + D = 56

2D + 8 = 56

2D = 56 - 8

2D = 48

D = 48 / 2

D = 24 years

Then the age of Margo will be given as,

M + 24 = 56

M = 56 - 24

M = 32 years

The age of Margo and Dan will be 32 years and 24 years, respectively.

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Answer:

A: The rate of change is 10% per year.

Step-by-step explanation:

The rate of change is simply the change in value divided by the change in time. In this case, the change in value is $1080 - $720 = $360, and the change in time is 12 years. Therefore, the rate of change is $360 / 12 years = $30 per year.

Using the GREAT decision-making model, one could consider telling the driver not to drive after drink, getting out of the car and looking for another, or riding in the same car while ignoring the situation.

The options we have in this situation are:

Option 1:

Option 2:

Option 3:

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At step 2, we arrive at

(2x + 3) (x + 3) = 0

and the next step (which isn't actually shown) is to use the so-called zero-product property that says if [tex]ab=0[/tex], then [tex]a=0[/tex] or [tex]b=0[/tex]. This means

2x + 3 = 0   or   x + 3 = 0

and solving the first equation leads to the rational solution.

2x + 3 = 0

2x = -3

x = -3/2

The area of the shaded region in the task content is; 251.2.

It follows from the task content that the area of the shaded region is;

= Area of semicircle IL - Area of semicircle JK + Area of semicircle IJ + Area of semicircle KL.

Hence, since the radius of each semicircle are as follows;

R(IL) = 12

R(IJ) = R(JK) = R(KL) = 4.

Hence, the Area of the shaded region can be evaluated as;

= (π/2)(12² - 4² + 4² +4²).

= π (144 +16)

= (3.14/2) × 160 = 251.2

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[tex]\huge\boxed{10}[/tex]

[tex]\sqrt{100}[/tex] means that you are looking for the number that, when multiplied by itself, produces [tex]100[/tex]. That number is [tex]10[/tex], because [tex]10\cdot10=100[/tex], meaning that [tex]\sqrt{100}=10[/tex].

Answer: Probability = 44%

Step-by-step explanation:

To find the probability of finding 2 black balls in a row, we first need to find the probability of finding 1 black ball at a time.

To do that, we need to divide the amount of total black balls by the number of total balls.

Black balls = 6

Total balls = 3 + 6 = 9

6 divided by 9 = 0.(6)

If you multiply 0,(6) by 100%, it will give you 66% (rounded) of getting a black ball.

Now, to find the chances of getting 2 black balls in a row, we need to multiply [tex]\frac{6}{9}[/tex] by [tex]\frac{6}{9}[/tex]. What we are doing is squaring the chances of getting one black ball, by the number of times we want to get it.

That is equal to 0,(4)

Multiply 0,(4) by 100%, and it will give you 44%(rounded) chances to get a black ball 2 times in a row.

Probability = 44%

Hope I Helped!

Answer:

a fraction

Step-by-step explanation:

this will produce a fraction, for example:

3^-1 = 1/3

and (-2)^-3 = -1/8

The largest possible volume of the box is x²y

It is important to note that the given figure is a rectangle

Area of the box is given as 100 square feet

Formula for volume of a rectangle

Volume = length × width × height

Length = x

Width = x

Height = y

Substitute the values in the formula

We have;

Volume = x × x × y

Volume = x²y

Thus, the largest possible volume of the box is x²y

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Answer:

88 square units

Step-by-step explanation:

     a  and b are the length of the parallel sides.

      a = IL = 15

      b = JK = 7

      h = height between the parallel lines = 8

[tex]\sf \boxed{\bf Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]

                                   [tex]\sf =\dfrac{(15+7)*8}{2}\\\\=\dfrac{22*8}{2}\\\\= 11*8\\\\= 88 \ square \ units[/tex]

The total interest for 4 years with a principal amount of $500 and a rate of 2% is $40.

The formula for the simple interest is,

I = PTR

where

I is the interest, P is the principal amount, T is the period, and R is the rate of interest.

The given data is,

Kaitlin wants to save $500 in her savings account. I.e., P = $500

For 4 years i.e., T = 4 years and the rate R = 2%  i.e., R = 0.02

Then,

the total interest for 4 years with no more deposits is

I = PTR

 = $500 × 4 × 0.02

 = $40

Therefore, the total interest that Kaitlin will earn for 4 years is $40.

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The theorems that apply are A(HL) D(SAS) E(LL)

Two triangles are said to be similar if their corresponding angles are equal and their corresponding lengths are in the same proportion.

Analysis:

The two triangles are similar according to the HL theorem since the hypotenuse of the two triangles are equal and one of the sides is same in both triangles. HL theorem applies.

The two triangles are similar according to LL theorem since the other lengths apart from the hypotenuse are also equal.

since two sides of both triangles are equal and there is an included angle 90 degree between the equal sides, the triangles are similar based on SAS.

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The final amount of the compound interest after 6 years would be $ 294, 122, 500

The formula for the final amount is given as;

[tex]A = P( 1 + \frac{r}{n}) ^n^t[/tex]

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = [tex]2500[/tex] [tex]( 1 + \frac{6}{1}) ^1^*^6[/tex]

A = [tex]2500 ( 7)^6[/tex]

A = [tex]2500[/tex] × [tex]117, 649[/tex]

A =$ [tex]294, 122, 500[/tex]

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

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Answer:

See Below

Step-by-step explanation:

Since they are lines, and if two lines have angles that are congruent, then it has to be perpendicular. Angles sum up to 180, and since they are equal, it is 90.

Hence, the area of base is [tex]x^2 - 2x - 9[/tex]

Division in maths is breaking a number into equal parts and finding out how many equal parts can be made.

The volume of a rectangular prism is,

        Volume = Area x Height

Substituting the given expressions,

[tex]x^3 + 2x^2 - 17x - 36 = Area x (x + 4)[/tex]

Area = [tex](x^3 + 2x^2 - 17x - 36) / (x + 4)[/tex]

Now, let's use synthetic division,

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is [tex]x^2 - 2x - 9[/tex]

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The probability that a person will be entertained by either books or TV is 0.55

Express the given percentages as probabilities.

Let the probability of people being entertained by books be represented as

P(A)=0.36

Probability of people entertained by watching TV,

P(B)=0.32

Probability of people entertained by both books and TV,

P(A∩B)=0.13

P(A) + P(B) - P(A and B) is the formula for calculating the either/or probability for overlapping events. This formula is identical to the non-overlapping events, but we need to take the likelihood that the outcomes could occur simultaneously into account.

Thus, the probability of people being entertained by either books or TV is,

P(AUB)=P(A)+P(B)-P(A∩B)

           =0.36+0.32-0.13

           =0.68-0.13

          =0.55          

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It will take the company 20.3 years to have a financial worth of $11.4

The estimate of profit is given as;

Profit = $0.6 million per year

This means that the engineers based their estimate per year

Hence, the unit of time is year

To do this, we make use of any variable of our choice.

In this case, we let x represents the variable of the amount of time.

In (a), we have:

Profit = $0.6 million per year

So, the expected financial status is 0.6x

This is the amount taken as loan by the engineers.

So, the financial status at the beginning is 1.8

Using the expressions above, we have the yearly worth to be:

y = 0.6x - 1.8

When the financial status is $11.4 million, we have:

0.6x - 1.8 = 11.4

Evaluate the like terms

0.6x = 12.2

Divide both sides by 0.6

x = 20.3

Hence, it will take the company 20.3 years to have a financial worth of $11.4

See attachment for the graph of y = 0.6x - 1.8

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Since there are no patterns for the rate of change of the function, it is quadratic.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, while if the rate increases in a proportional way, the function is exponential.

In this problem, no patterns of linearity or of exponentiality can be established, hence the function is quadratic.

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Answer:

The Framers are offering a better price and are cheaper by $1.35

Step-by-step explanation:

I've been framed price:

50% off of 115 = 0.5*115 = 57.5

10% off of sale price = 0.9*57.5 = $51.75

the Framers price:

30% off of 120 = 0.7*120 = 84

40% off of sale price = 0.6*84 = $50.40

Difference: 51.75-50.40 = $1.35

The number of people who are not Democrats , do not wear glasses, and don not like ice-cream by using sets are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

Given total people of 1000 people, 595 democrats, 595 wearing glasses, 550 like ice cream, 395 of them are democrats who wear glasses,350 of them are democrats who like ice cream and 400 of them wear glasses as well as like ice cream ,250 of them are democrats as well as wear glasses and like ice cream.

We have to find the number of people who are not democrats , do not wear glasses ,do not like ice cream and the number of people who do not wear glasses and do not like ice cream.

let X shows the number of democrats and G be number of people who wear glasses and I be the number of people like ice cream.

So,

D=595, G=595 AND I=550

Now D∩G=395

D∩I=350

G∩I=400

so D∩G∩I=250

Formula will be :

D∪G∪I=D+G+I-(D∩G)-(G∩I)-(D∩G)+(D∩G∩I)

=595+595+550-(395+350+400)+250

=845

845 are either democrats or wear glasses as well as like ice cream.

So 1000-845=155

Number of people who are democrats, do not wear glasses and do not like ice cream=D-(D∩G)-(D∩I)+(D∩G∩I)

=595-(395+300)+250

=845-695

=150 people.

Hence the number of people who are not Democrats , do not wear glasses, and don not like ice-cream are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

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Answer:

D

Step-by-step explanation:

on a graph, look at the points (-3,0) (-1,0) and (2,0). Then, see if the line passes through those points. You will see that graph D passes through all those points. If you're confused on how to turn the (x,y) format into points on a graph, remember that the first point tells you how left/right you want to be, and the second point tells you how up/down you want to be.

The value of y if the perimeter of the figure is 5y is 15meters.

The perimeter of a polygon is the sum of the length of the whole sides.

Therefore,

perimeter = y + 2y + 30

perimeter = 5y

Hence,

5y = 3y + 30

5y - 3y = 30

2y = 30

divide both sides by 2

2y / 2 = 30 / 2

y = 15

Therefore, the value of y is 15m.

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