The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√

Answer:

Using the rational root theorem, we know to divide the function by (x - 1).

(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4

Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).

Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).

Using the factorized form above, the zeros of the function are 1, -2/7, and -2.

The Medication A mixed this week should be 10 milligrams.

We have,

Medications to be mixed in the proper proportions.

Last week's proportions as the doctor indicated ;

Medication A = 90 milligrams

Medication B = 72 milligrams

This week's proportions as doctor indicated;

Medication B = 8 milligrams

Let, Medication A = x milligrams

As we are instructed to mix the Medication in the proper proportions,

So,

According to the question,

90/72 = x/8

10/8 = x/8

⇒ x = 10 milligrams

Here,  the Medication A mixed is 10 milligrams.

Therefore, the Medication A mixed this week should be 10 milligrams.

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Answer:

Step-by-step explanation:

1 ft/s = 0.681818 mph

355.7 * 0.681818 = 242.5226626

355.7 ft/s = 242.5226626 mph

Answer:

D

Step-by-step explanation:

the cordinate is at (-3,2)

Answer:

1

Step-by-step explanation:

It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.

Answer: 1

Answer:

a) quantitative - continuous

b) qualitative

c) quantitative - discrete

d) quantitative - discrete

Explanation:

A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.

A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.

Answer:

Step-by-step explanation:

plug in x try numbers

x = 14.2

Part 1

[tex](g\circ h)(x)=g(x-4)=(x-4)^2 + 1=x^2 - 8x+16+1=\boxed{x^2 - 8x+17}[/tex]

Part 2

[tex](-\infty, \infty)[/tex]

The answers in the box are:

Given that the functions are

[tex]g(x)=x^2+1[/tex]

[tex]h(x)=x-4[/tex]

Since clearly g(x) and h(x) exist for all real values of x so the domain of g(x) and h(x) both are all real numbers.

Now the composition of function is given by,

[tex](g\circ h)(x)=g(h(x))[/tex]

               [tex]=g(x-4)[/tex]

               [tex]=(x-4)^2+1[/tex]

               [tex]=x^2-8x+16+1[/tex], since we know that [tex](a-b)^2=a^2-2ab+b^2[/tex]

               [tex]=x^2-8x+17[/tex]

So, [tex](g\circ h)(x)=x^2-8x+17[/tex]

It is a polynomial function so it is defined for all real values of x.

Hence the domain of composition is all real numbers, that is [tex](-\infty,\infty)[/tex]

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The next three terms will be -1/16, 1/32, and -1/64. Then the correct option is B.

Let a be term and r be the common ratio. Then the geometric sequences will be

[tex]\rm a_n = a_{n -1} \cdot r[/tex]

The sequence is given below.

-1, 1/2, -1/4, 1/8,....

The common ratio will be -1/2.

Then the next three terms will be

a₅ = a₄ x (-1/2)

a₅ = (1/8) x (-1/2)

a₅ = -1/16

a₆ = a₅ x (-1/2)

a₆ = (-1/16) x (-1/2)

a₆ = 1/32

a₇ = a₆ x (-1/2)

a₇ = (1/32) x (-1/2)

a₇ = -1/64

Then the next three terms will be -1/16, 1/32, and -1/64.

Then the correct option is B.

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Answer:

C

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

[tex]f(8+h)=8+h+10=18+h\\\\f(8)=8+10=18[/tex]

So, the average rate of change is:

[tex]\frac{(18+h)-18}{(8+h)-8}=\frac{h}{h}=\boxed{1}[/tex]

The question is wrong, the expression will not be in terms of h since it is a linear function.

Answer: 0 ≤ y < ∞

Step-by-step explanation:

   First, let us graph the function. See attached.

-> If I graphed the formatting of the square root sign incorrectly, please let me know so I can fix the answer.

  The range of the function is all of the function's output values. In this case, all of the y values.

        0 ≤ y < ∞

Answer:

y=2x+20

Step-by-step explanation:

x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20

Hope this helps :)

The associative property of adding or multiplying can be represented by (a + b) + c = a + (b + c) and a * (b * c) = (a * b) * c

An equation is an expression that shows the relationship between two or more numbers and variables.

The associative property states that when adding or multiplying it can be represented by:

(a + b) + c = a + (b + c)

For multiplication:

a * (b * c) = (a * b) * c

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Answer:

• f(g(x)) =  [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65

Step-by-step explanation:

• f(g(x)) = f(x² + 1)

         = [tex]\sqrt{x^{2} + 1}[/tex]  + 8

• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )

            = [tex](\sqrt{x } + 8)^{2}[/tex] + 1

            =  x + 16[tex]\sqrt{x}[/tex] + 64 + 1

            = 16[tex]\sqrt{x}[/tex] + x + 65

The probability that both are red marbles is 0.2391

The given parameters are:

Red =12

Blue = 12

Total = 24

The probability of selecting the first red marble :

P(Red) = 12/24

Now, there are 11 red marbles and 23 marbles in all

The probability of selecting the second red marble :

P(Red) = 11/23

The required probability is:

P =  12/24 * 11/23

Evaluate

P = 0.2391

Hence, the probability that both are red marbles is 0.2391

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Probability that the salesperson has “Fair” potential or has Above Average Sales ability is; 90.8%

A) Probability that the salesperson has “Fair” potential for advancement = (16 + 45 + 93)/500 = 154/500 = 30.8%

B)  Probability that the salesperson has “Fair” potential or has Above Average Sales ability = 30.8% + (300/500)% = 90.8%

C) Probability that the salesperson has “Fair” potential given they have Above Average Sales ability = P(A|B) = P(A ∩ B)/P(B) = (93/500)/0.6 = 0.31 = 31%

D) P(selecting 2 salespersons and finding they both have Fair potential for advancement) = (154/500) * (153/499) = 9.44%

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Considering the given equations for the revenue and the cost, it is found that 36 tickets have to be sold each night to break even.

The break-even point is when the revenue and the costs are equal.

In this problem, the equations are given as follows:

At the break-even point:

R(x) = C(x)

15x = 1.25x + 495

13.75x = 495

x = 495/13.75

x = 36.

36 tickets have to be sold each night to break even.

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Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]

Step-by-step explanation:

This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.

To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.

Inequalities help us to compare two unequal expressions. There exists no solution to the given set of inequalities.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given Inequalities can be solved as,

5 - x > 7

-x > 7 - 5

-x > 2

x < -2

2x + 3 ≥ 13

2x ≥ 10

x ≥ 5

As per the solution of the two inequalities, the value of x should be less than -2 but at the same time, it should be more than or equal to 5, which is impossible. Thus, there is no solution for the given inequalities.

This can be confirmed by graphing the two inequalities, as shown below. Since there is no area in common between the two inequalities, there exists no solution to the given set of inequalities.

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Answer:

Damien is 74 years old now

Step-by-step explanation:

Define the variables:

Given information:

From the given information, create 2 equations:

Equation 1:  d + k = 100

Equation 2:  d - 10 = 4(k - 10)

Rewrite Equation 1 to make k the subject:

⇒ k = 100 - d

Substitute this into Equation 2 and solve for d:

⇒ d - 10 = 4(100 - d - 10)

⇒ d - 10 = 400 - 4d - 40

⇒ d - 10 = 360 - 4d

⇒ d - 10 + 10 = 360 - 4d + 10

⇒ d = 370 - 4d

⇒ d + 4d = 370 - 4d + 4d

⇒ 5d = 370

⇒ 5d ÷ 5 = 370 ÷ 5

⇒ d = 74

Therefore, Damien is 74 years old now.

Answer:

  $188.06

Step-by-step explanation:

The total cost for the film will be the sum of film cost, applicable sales tax, and applicable shipping charges. The film cost will be the product of the number of rolls and the cost per roll.

__

  film cost = (18 rolls) × ($9.95 /roll) = $179.10

  sales tax = 0.05 × $179.10 = $8.96

There is no shipping charge associated with the camera shop purchase, so the total cost is ...

  camera shop cost = film cost + sales tax = $179.10 +8.96 = $188.06

__

  film cost = (18 rolls) × ($9.76 /roll) = $175.50

  shipping charge = $15.00

There is no sales tax associated with the mail order, so the total cost is ...

  mail order cost = film cost + shipping charge = $175.50 +$15.00 = $190.50

__

The price from the camera shop is the better of the two prices. The purchase there would cost you $188.06 for 18 rolls of film.

_____

Additional comment

The after-tax charge per roll of film at the camera shop is 9.95×1.05 = 10.4475. This is $0.6975 more than the basic charge per roll from the mail order company. In order to get the shipping charge of $15 to be less than $0.6975 per roll, the number of rolls ordered must be more than 15/0.6975 = 21.5.

An order of 22 rolls of film from the mail order company would cost less than from the camera shop. ($229.50 vs. $229.85)

The multiplicity of the function is 1 for each term after factorization.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a polynomial function:

[tex]\rm F(x)= 4x^3+19x^2-41x+9[/tex]

After factorization:

[tex]\rm F(x) = \left(4x-1\right)\left(x^2+5x-9\right)=0[/tex]

[tex]\rm F(x) =(4x-1)^1(\:x-\frac{-5+\sqrt{61}}{2})^1(\:x+\frac{-5-\sqrt{61}}{2})^1[/tex]

The multiplicity of the function is 1 for each term.

Thus, the multiplicity of the function is 1 for each term after factorization.

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Answer:

log12=log(2.2.3)

=log2+log2+log3

=0.30103+0.30103+0.47712

=0.60206+0.47712

=1.07918

Answer:

C = 2√(πA) units

Step-by-step explanation:

The recursive formula would be: 100 - XN = B.

When a function calls itself and uses its own previous terms to define its subsequent terms, it is called a recursive function. It is the technical recursive function’s definition, i.e., a recursive function builds on itself.

X: represents how many weeks

N: represents books per week

B: represents books she has at anytime

So the recursive formula would be: 100 - XN = B

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Answer: 925

Step-by-step explanation:

This is an arithmetic series with first term 1 and last term 3(25)-2=73, with a total of 25 terms.

Using the sum of an arithmetic series formula, we get the sum is:

[tex]\frac{25}{2}(1+73)=\boxed{925}[/tex]

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

In this case we have a cubic equation, that is, a third order polynomial. There are two strategies to determine the roots of cubic equations: (i) Cardano's formula, (ii) Numerical methods.

The quickest though most effective way consists in determining the roots by numerical methods (i.e. Newton-Raphson method). By using numerical methods we conclude that the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7

x₁ = - 1, x₂ = (- 5 + i √3)/2, x₃ = (- 5 - i √3)/2

In consecuence, the conjugate complex number x₂ = (- 5 + i √3)/2 is one of the three roots of the cubic equation f(x) = x³ + 6 · x² + 12 · x + 7. (Correct choice: D)

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The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².

The expression given in the task content whose simplest form is to be determined is;

- (4x³ + x²) + 2 (x³ − 3x²)

Hence, upon opening up the parentheses, it follows that;

-4x³ - x² +2x³ -6x²

Upon collection and summing up of like terms; -2x³ -7x².

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Part 1

[tex](f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1[/tex]

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is [tex]\boxed{[0, \infty)}[/tex]

Part 2

[tex](g \circ f)(x)=g(4x+1)=\sqrt{4x+1}[/tex]

We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,

[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]

Thus, the domain in interval notation is [tex]\boxed{\left[-\frac{1}{4}, \infty)}[/tex]