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The function y = (x²)^(1/2) + 3 belongs to the family of square root functions.

What is a square root function?

A square root function is a function that has a variable that is the square root of the variable used in the function. A square root function has the general form:

                                           f(x) = a√(x - h) + k,

where a, h, and k are constants and a is not equal to 0.

A square root function is an inverse function to a quadratic function.

A square root function is a function that, when graphed, produces a curve with a domain (all possible values of x) of x ≥ 0 and a range (all possible values of y) of y ≥ 0, which means it is positive or zero for all values of x.

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The required scale factor with respect to the pre-image and image is equal to 2.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

In Mathematics, the scale factor of any geometric figure can be calculated by using this mathematical expression:

Scale factor = Dimension of image/Dimension of pre-image

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = -10/-5 = -4/-2

Scale factor = 2.

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Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

x = 3

Step-by-step explanation:

The traingels are similar so we can conpare sides.

3 is to 18 as 2 is to 4x or

3/18 = 2/4x

1/6 = 1/2x

6 = 2x

3 = x

Answer:

Step-by-step explanation:

3x - 18  = 8x - 9x - 21

3x - 18 = -x - 21

4x - 18 = -21

4x = -3

x = -3/4

answer is A

Answer: OPTION 3. x=-3/4

Step-by-step explanation:

This question is basically asking for to solve the equation.

------------------------------------------------------------------

Given

3(x-6)=8x-3(3x+7)

Distributive property on both sides

3x-18=8x-9x-21

Combine like terms on the right side

3x-18=-x-21

Add x on both sides

4x-18=-21

Add 18 on both sides

4x=-3

Divide 4 on both sides

x=-3/4

a. For the function f(x) = x² - 3x² on the interval -1 ≤ x ≤ 4:                    

Absolute maximum value: 0 at x = 0                                                      

Absolute minimum value: -32 at x = 4

b. For the function f(x) = x - 2x² on the interval -2 ≤ x ≤ 5:        

Absolute maximum value: 1/4 at x = 1/4                                        

Absolute minimum value: -45 at x = 5

c. For the function f(x) = (x + 2)² on the interval -3 ≤ x ≤ 3:      

Absolute maximum value: 25 at x = 3                                      

Absolute minimum value: 1 at x = -3

d. For the function f(x) = 2x³ + 3x² - 36x + 17 on the interval -3≤x≤6:

Absolute maximum value: 92 at x = -3                                          

Absolute minimum value: -11 at x = 2

To find the absolute maximum and minimum values of the given functions on each interval, we will analyze the critical points and endpoints of the intervals.

a. For the function f(x) = x² - 3x² on the interval -1 ≤ x ≤ 4:

First, let's find the critical points by taking the derivative of f(x):

f'(x) = 2x - 6x = -4x.

Setting f'(x) equal to zero, we get:

-4x = 0,

x = 0.

Next, we evaluate the function at the critical point and endpoints:

f(-1) = (-1)² - 3(-1)² = -2,

f(0) = (0)² - 3(0)² = 0,

f(4) = (4)² - 3(4)² = -32.

Therefore, the absolute maximum value is 0 at x = 0, and the absolute minimum value is -32 at x = 4.

b. For the function f(x) = x - 2x² on the interval -2 ≤ x ≤ 5:

Taking the derivative of f(x):

f'(x) = 1 - 4x.

Setting f'(x) equal to zero, we have:

1 - 4x = 0,

4x = 1,

x = 1/4.

Next, we evaluate the function at the critical point and endpoints:

f(-2) = (-2) - 2(-2)² = -6,

f(1/4) = (1/4) - 2(1/4)² = 1/4,

f(5) = (5) - 2(5)² = -45.

Therefore, the absolute maximum value is 1/4 at x = 1/4, and the absolute minimum value is -45 at x = 5.

c. For the function f(x) = (x + 2)² on the interval -3 ≤ x ≤ 3:

Since this is a quadratic function, it is always increasing. Thus, the absolute maximum value will occur at x = 3, and the absolute minimum value will occur at x = -3.

Evaluating the function at the critical points and endpoints:

f(-3) = (-3 + 2)² = 1,

f(3) = (3 + 2)² = 25.

Therefore, the absolute maximum value is 25 at x = 3, and the absolute minimum value is 1 at x = -3.

d. For the function f(x) = 2x³ + 3x² - 36x + 17 on the interval -3 ≤ x ≤ 6:

Taking the derivative of f(x):

f'(x) = 6x² + 6x - 36 = 6(x² + x - 6).

Setting f'(x) equal to zero, we get:

x² + x - 6 = 0.

Factoring the quadratic equation, we have:

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

This gives us two critical points: x = -3 and x = 2.

Next, we evaluate the function at the critical points and endpoints:

f(-3) = 2(-3)³ + 3(-3)² - 36(-3) + 17 = 92,

f(2) = 2(2)³ + 3(2)² - 36(2) + 17 = -11,

f(-3) = 2(-3)³ + 3(-3)² - 36(-3) + 17 = 92.

Therefore, the absolute maximum value is 92 at x = -3, and the absolute minimum value is -11 at x = 2.

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Answer:

The number of worms Noah started with

:)  

took the test

Answer:

The number of worms Noah started with

Step-by-step explanation:

Answer:

It is a non function.

Step-by-step explanation:

Numbers cannot repeat in functions

Answer:

x = -55

Step-by-step explanation:

Given equation,

→ 5(2 - x) - 10 = 25 - 2(3x + 40)

Now the value of x will be,

→ 5(2 - x) - 10 = 25 - 2(3x + 40)

→ 10 - 5x - 10 = 25 - 6x - 80

→ -5x + 6x = 25 - 80

→ [ x = -55 ]

Hence, the value of x is -55.

Answer:

x = -55

Step-by-step explanation:

Given equation,

→ 5(2 - x) - 10 = 25 - 2(3x + 40)

Now the value of x will be,

→ 5(2 - x) - 10 = 25 - 2(3x + 40)

→ 10 - 5x - 10 = 25 - 6x - 80

→ -5x + 6x = 25 - 80

→ [ x = -55 ]

Hence, the value of x is -55.

Answer:

42

Step-by-step explanation:

hey 42+9=51 so this can be the ✔️answer

The expected value of the sum of the two dice is 72

It is calculated by finding the weighted average of all possible sums, where each possible sum is weighted by its probability of occurring.

Let's call the 8-sided die "A" and the 9-sided die "B". Then, the possible sums are:

2 (A: 1, B: 1), 3 (A: 1, B: 2), 4 (A: 1, B: 3), ..., 16 (A: 8, B: 8)

The probability of each sum is the product of the probabilities of the individual dice outcomes:

P(2) = (1/8) * (1/9)

P(3) = (1/8) * (2/9)

...P(16) = (8/8) * (8/9)

The formula gives the expected value of the sum:

E = ∑P(x) * x

where x is each possible sum and P(x) is its probability.

Plugging in the values, we get:

E = (1/8) * (1/9) * 2 + (1/8) * (2/9) * 3 + ... + (8/8) * (8/9) * 16

E = (1/72) * (2 + 3 + ... + 16) + ... + (8/72) * (16)

E = (1/72) * [2 + 3 + ... + 16] * 8 + ... + (8/72) * 8 * 8

E = (1/9) * [2 + 3 + ... + 16]

We can now use the formula for the sum of an arithmetic series:

S = n/2 * (a + b)

where n is the number of terms, a is the first term, and b is the last term.

Applying this formula to the series [2, 3, ..., 16], we get:

S = 8/2 * (2 + 16) = 8 * (9) = 72

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Answer:

10

Step-by-step explanation:

First add: (All the classes)

24+26+28= 78 students

Then divide: (Total students by students per teacher)

78/6= 13

Then subtract: (Adult needed minus teachers)

13- 3=10

Hope this helps! :)

The range of values for which x²–5x + 6 < 0 is x < 3

The range of a function is the set of numbers that the function can produce. In other words, it is the set of y-values that you get when you plug all of the possible x-values into the function. This set of possible x-values is called the domain.

Given:

x²–5x + 6 < 0

Now, solving the above quadratic equation as

x² -3x -2x +6 < 0

x(x-3) - 2 (x-3) <0

(x - 2)(x - 3) < 0

Now, equating one by one with the inequality we get

(x - 2) <0   and (x - 3)<0

x < 2 and x < 3.

as, we can take two relation from above one is x<2 and x<3.

But, if we look towards the larger range it will be provided by x<3.

Hence, the range of the equation is at x<3.

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan A = \(\frac{sinA}{cosA}\) , cot A = \(\frac{cosA}{sinA}\)

Consider the left side

(1 + cotA + tanA)(sinA - cosA)

each term in the second factor is multiplied by each term in the first factor.

1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)

= sinA - cosA + cosA - \(\frac{cos^2A}{sinA}\) + \(\frac{sin^2A}{cosA}\) - sinA ( collect like terms )

= \(\frac{sin^2A}{cosA}\) - \(\frac{cos^2A}{sinA}\)

= ( sinA × \(\frac{sinA}{cosA}\) ) - (\(\frac{cosA}{sinA}\) × cosA )

= sinAtanA - cotAcosA

= right side ⇒ proven

The table that represents a linear relationship that is also proportional is :  x: -4, 0, 4

   y: 0, 1, 2

Option D is correct.

A linear relationship is described as being proportional if the ratio of the dependent variable  toy the independent variable x remains constant.

We analyze each table:

Table A:

x: -3, 0, 3

y: 2, 3, 4

We see that the ratio of y to x is not constant as it  changes from 2/(-3) = -2/3, to 3/0 (undefined), to 4/3.

Table B

x: -2, -1, 0

y: 4, 2, 0

We see that the  ratio of y to x is not constant as it changes from 4/(-2) = -2, to 2/(-1) = -2, to 0/0 (undefined).

Table C.

x: 0, 1, 2

y: -2, 1, 4

The ratio of y to x is not constant and changes from -2/0 (undefined), to 1/1 = 1, to 4/2 = 2.

Table D.

x: -4, 0, 4

y: 0, 1, 2

The ratio of y to x is constant and is always 0/(-4) = 0, 1/0 (undefined), 2/4 = 1/2.

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Answer:

  a) 29 men

  b) 91 cm

Step-by-step explanation:

The graph shows that 11 men have a waist measurement of 85 cm or less. That means 40 -11 = 29 men have a waist measurement of more than 85 cm.

__

The median is the value for which half the population is below the value and half is above. Here, the line for 20 men (half of 40) intersects the curve at 91 cm.

The median waist measurement is 91 cm.

The Coase theorem is an economic theory that states that in the absence of transaction costs, the allocation of resources and the distribution of wealth will be efficient regardless of how property rights are assigned.

In this context, the theorem reminds us that efficiency is all about maximizing total welfare, rather than focusing solely on the allocation of resources or the distribution of wealth. When transaction costs are low or non-existent, parties can negotiate with each other to reach mutually beneficial agreements that maximize their combined welfare. This means that ownership of property or resources is less important than the ability of parties to freely negotiate with one another.

For example, imagine two neighboring farms: one produces apples and the other produces honey. If the apple farmer's use of pesticides harms the bee population and reduces the honey farmer's production, the honey farmer could demand compensation from the apple farmer. If transaction costs are low, the two farmers could negotiate a solution that is mutually beneficial, such as the apple farmer paying for the honey farmer to relocate their bees to a safer area. In this scenario, the assignment of property rights is not as important as the ability of the two parties to negotiate and reach an agreement that maximizes their total welfare.

Overall, the Coase theorem highlights the importance of considering the broader impacts of economic decisions and recognizing that efficiency depends on maximizing the overall benefits to all parties involved, rather than just focusing on individual outcomes.

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The total cost is $44.50

Since the rug costs $27, the posters altogether cost : 44.50 - 27 = $17.50

We're given that the posters cost $2.50 each, and since they cost $17.50, the number of posters he bought was : 17.50 : 2.50 = 7 (posters)

Answer: The original price was  $125

Step-by-step explanation:

If an item is on sale for $100 and it was discounted by 20%  then we could set up an equation and solve for the original price.

Remember if there were 20% discount then 80% of the price will be left.

80% * x = 100    

0.8x =100

x = 125

Step-by-step explanation:

We have :

• Selling Price = $100

• discount = 20%

As we know

• Selling Price = Cost - Discount

Now we have

• Discount = 20%

Let cost be x

→ Selling Price = x - 20% of x

→ selling price = 80% of x

→ 80% of x = 100

→ 80/100 x = 100

→ x = 100 × 100 / 80

→ x = $ 125

Answer:

Down

Explanation:

Dependent events are events in which the outcomes are affected by previous outcomes.

In order to answer this question, the illustration below is used.

Consider a bag with 5 red and 5 blue tiles.

Since the events are dependent, the selection is made without replacement.

Observe that after each pick of the red color, the likelihood of picking a red tile decreases.

Therefore, after every pick, the likelihood of picking a particular color of tile go down.

Free samples or product trials as a type of sales promotion can be both beneficial and detrimental. They encourage consumers to try a product at reduced risk, but they can also reduce the perception of value for the product or service.

Offering free samples or product trials is a common sales promotion strategy to attract customers and encourage them to try a product or service. This approach has several benefits. Firstly, it lowers the perceived risk for consumers as they can experience the product without making a financial commitment upfront. This can be especially effective for new or unfamiliar products, as it allows potential customers to test the product's quality and functionality.

However, there can be drawbacks to this sales promotion technique. Providing free samples or trials can create the perception that the product or service has less value or is of lower quality. Consumers may develop a mindset of expecting free or discounted offerings, and it can undermine the willingness to pay the full price in the future. Additionally, if the free samples or trials are not managed effectively, it may attract individuals who are not genuinely interested in the product, leading to wastage of resources and potentially diluting the brand image.

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The slope of the new line is -3/5.

The y-intercept of the new line is -16.

The equation of the new line is y= -3/5x -16.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 5/3x +1.

The line has a slope of 5/3. If you multiply the slopes of two perpendicular lines, you get –1. So:

5/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (5/3)

slope perpendicular line= -3/5

The slope of the new line is -3/5.

The line passes through the point (-10, 3). Replacing in the expression for perpendicular line:

-10= -3/5× (-10) + b

-10= 6 + b

-10 - 6= b

-16= b

The y-intercept of the new line is -16.

Finally, the equation of the perpendicular line is y= -3/5x -16.

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The equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.

The rational function has x-2 in the denominator.

The denominator cannot be zero.

The rational function will be:

\(y=\dfrac{\left(x^{2}-16\right)}{x-2}\)

Thus, the equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.

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Answer:

its a

Step-by-step explanation:

Substituting this in equation (4), we get the final answer as ∫x sin³ (x²) cos² (x²) dx = 1/4 ∫cosu sin²u du - 1/4 ∫sin⁴u cosu du= 1/4 [cos (x²) sin² (x²) + 2 ∫sin²(x²) cos(x²)dx] - 1/4 ∫sin⁴(x²) cos (x²) dx...

The given integral is ∫x sin³ (x²) cos² (x²) dx.

Let u = x²du/dx = 2xdx

Thus the given integral becomes 1/2 ∫sin³u cos²u du

Factor out sin²u from sin³u sin³u = sin²u.sinuCos²u = cos²u .cosu = (1 - sin²u)cosu

= cosu - sin²u.cosu

Therefore, 1/2 ∫sin³u cos²u du = 1/2 ∫sin²u cosu du - 1/2 ∫sin⁴u cosu du... (1)

Using the identity sin²u + cos²u = 1, sin²u = 1 - cos²u... (2)

Substituting equation (2) in equation (1), we get1/2 ∫sin³u cos²u du = 1/2 ∫(1 - cos²u)cosu sin²u du - 1/2 ∫sin⁴u cosu du= 1/2 ∫cosu sin²u du - 1/2 ∫sin⁴u cosu du... (3)

Substituting u = x², we get the integral in terms of x as ∫x sin³ (x²) cos² (x²) dx = 1/2 ∫cos (x²) sin² (x²) dx - 1/2 ∫sin⁴(x²) cos (x²) dx... (4)

From the substitution u = x², we can write du/dx = 2x

∴ dx = du/2x

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The number -17/20 belongs to the set of real numbers.

What is the set of real numbers?

The set of real numbers is made by combining the set of rational numbers and the set of irrational numbers. Real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers.

All real numbers, including fractions and decimals, are part of the set of real numbers.

The set of real numbers includes all numbers that can be expressed on the number line, including positive and negative numbers, as well as all fractions and decimals.

This set is often denoted by the symbol "ℝ".

Hence, The number -17/20 belongs to the set of real numbers.

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Answer:

Step-by-step explanation:

1) Simplify 1/3m to m/3.

m/3 - 1 - 1/2n

2) Simplify 1/2n to n/2.

m/3 - 1 - n/2

Answer:

---------------------

The angle formed by a tangent and secant is half the difference of the intercepted arcs:

Find the measure of ∠MLJ by substituting 4 for x in the angle measure: