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Which function is the inverse of

[tex]f(x)=x^2-16[/tex]

if the domain of f(x) is x ≥ 0?

The inverse funtion of the given function is given by

[tex]\mathbf{f(x)=\sqrt{x+16}}[/tex]

where the domain is x ≥ -16.

Given the function is,

[tex]f(x) =x^2-16[/tex]

Let, y = f(x)

[tex]y = x^2-16[/tex]

Adding 16 to both sides we get,

[tex]y + 16 = {x}^{2} - 16 + 16[/tex]

[tex] {x}^{2} = y + 16[/tex]

Now, square rooting to both sides we get, since x ≥ 0

[tex]\sqrt{x^2}=\sqrt{y+16}[/tex]

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

[tex]f^{-1}(y)=\sqrt{y+16}[/tex]

Hence substituting x in place of y,

[tex]f^{-1}(x)=\sqrt{x+16}[/tex]

Above function is the required inverse function where the domain of that is given by, x ≥ -16.

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Answer:

Brand A is the best buy.

Step-by-step explanation:

Brand A has a pack of 28 pencils for 5.29 dollars. This means that the unit cost of one pencil in Brand A would be 5.29/28 = 0.2$ per pencil rounded up to the nearest tenth.Brand B has a pack of 48 pencils for 8.47 dollars. This means that the unit cost of one pencil in Brand B would be 8.47/48 = $0.8 per pencil rounded up to the nearest tenth.Since $0.2 is lesser than $0.8, it means that Brand A is the best buy.

Answer:

B) y = 4/5x - 2

Answer:

B

Step-by-step explanation:

First, we can find the slope of the graph.

The distance of x between the two points is 5, and the distance of y between the two points is 4.

The slope formula is (Increase in y)/(increase in x)

So the slope will be 4/5.

The y-intercept is (0,-2), so the number at the very end of the equation will be -2.

With all this in mind, we can be sure that our answer is B: y=4/5x-2

Answer:

the answer is (D) F-1 (X) = 7x - 3

Step-by-step explanation:

Answer:

x could be anything but might be 3<4 or 5?8 u really never kno

Answer:

(0, 0)

Step-by-step explanation:

Ok so you have the equation: [tex]y = log_2{(x+2)}-1[/tex]. To find the zero you simply set the y equal to zero and then solve for x

[tex]0 = log_2{(x+2)}-1[/tex]

Add 1 to both sides

[tex]1 = log_2{x+2}[/tex]

Rewrite the equation in exponential form:

[tex]2^1=x+2[/tex]

Subtract 2 from both sides

[tex]0 = x[/tex]

So the zero of the function is at the origin (0, 0)

The slope of the line is 4.5

The points are given as:

(2,9) and (4, 18)

The slope (m) is calculated using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (18 - 9)/(4 -2)

Evaluate

m = 4.5

Hence, the slope of the line is 4.5

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Answer:

(-5, -3)

Step-by-step explanation:

Isolate x:

x - 3y = 4

x = 3y + 4

Substitute to get y:

-3x + 2y = 9

-3(3y + 4) + 2y = 9

-9y - 12 + 2y = 9

-7y = 21

y = -3

Substitute to get x:

x = 3y + 4

= 3(-3) + 4

-9 + 4

= -5

The coordinates of X in the pre-image of the figure is (3.2, 0.6) if the  transformation rule is T_(-5.2, 1.4)(x, y)

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we can see in the figure.

The transformation rule is T_(-5.2, 1.4)(x, y)

X'(-2, 2)

Before the transformation:

X = (-2+5.2, 2-1.4)

X = (3.2, 0.6)

Thus, the coordinates of X in the pre-image of the figure is (3.2, 0.6) if the  transformation rule is T_(-5.2, 1.4)(x, y)

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Answer:

[tex]\frac{(x-2)(x+4)}{x+2}[/tex]

Step-by-step explanation:

[tex]\frac{(x+4)^2}{x+2} :\frac{(x+2)(x+4)}{(x+2)(x-2)} =\frac{(x+4)^2(x+2)(x-2)}{(x+2)(x+2)(x+4)}=\frac{(x-2)(x+4)}{x+2} .[/tex]

An equation is formed when two equal expressions. The company is planning to produce 25 mountain bikes and 15 trail bikes.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of mountain bikes produced by the company be x, while the number of trail bikes produced by the company is y.

The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. Also, the budget of the company is $1,600. Therefore,

1600 = 40x + 40y

x + y = 40

y = 40-x

The cost of labour to manufacture a mountain bike is $90, and the cost of labour to manufacture a trail bike is $30. Also, the budget for labour is $2,700.

2700 = 90x + 30y

2700 = 90x + 30(40-x)

2700 = 90x + 1200 - 30x

1500 = 60x

x = 25

Substitute the value of x,

y = 40 - x

y = 15

Hence, the company is planning to produce 25 mountain bikes and 15 trail bikes.

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Answer: {-1, 3, 15}

Step-by-step explanation:

[tex]f(1)=-1\\\\f(3)=3\\\\f(5)=15[/tex]

So, the range is {-1, 3, 15}.

Answer:

38 pills

Step-by-step explanation:

To find the number of pills, you need to divide the weight of each pill by the total weight needed.

0.76 grams / 0.02 grams = 38 pills

Mark Achin's economic order quantity in units is D. 120​ units.

The economic order quantity (EOQ) is the optimal order quantity that minimizes the total costs (ordering, receiving, and holding inventory).

The formula for the economic order quantity is the square root of [2(setup costs)(demand rate)] / holding costs.

Annual demand = 3,600

Cost price per unit = $200

Ordering cost = $40

Holding cost per unit = $20

Working days per year = 360

Lead time = 5 days

Economic order quantity (EOQ) = square root of: [2(setup costs)(demand rate)] / holding costs.

= square root of (2 x $40 x 3,600)/$20

= 120

Thus, Mark Achin's economic order quantity in units is D. 120​ units.

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Following the prescription, You will need to administer a 0.7 tablespoon per dose.

We can determine the number of tablespoons that are administered by using equivalent expressions.

From the standard conversion rate, we know that:

Using equivalent expressions:

7.5 mg/1.01442 tbsp = 5 mg/x tbsp

x = (1.01442 × 5)/7.5 tbsp

x = 0.67 tbsp

x = 0.7 tbsp per dose.

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Based on the calculations, the average selling price for these properties is equal to $127,865.

Mathematically, the average selling price for these properties would be calculated by using the following formula:

Average price = [F(x)]/n

Note: The total number of properties is equal to 5.

Substituting the given parameters into the formula, we have;

Average price = [118,450 + 126,500 + 128,000 + 130,425 + 135,950]/5

Average price = 639,325/5

Average price = $127,865.

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Complete Question:

Property taxes are based on the value of the property. city officials use the average selling price of similar properties to estimate the value. the selling prices of similar properties are listed below. $118,450 $126,500 $128,000 $130,425 $135,950. What is the average selling price?

Answer: B. When finding the midpoint between two points on a vertical line, keep the x-coordinate and find the average of the y-coordinates

Answer:

3

Step-by-step explanation:

The relationship between lines m & n is (a) the lines M and N have positive slope

The points are given as:

From the above points, we can see that:

As  x increases, the y values of both lines increase

This is an illustration of positive slope

Hence, the lines M and N have positive slope

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Answer:

second transformation

Answer:

A. arc

Step-by-step explanation:

The circumference is the entire boundary of a circle.

A portion of the circumference is called an arc.

Answer:

xxfdjdjwkoq9w Woow Kike sosl

Option b) and c) is correct, i.e. 2/3 and 0.66(line over 66)7

6/9 is a rational number.
similar ration number can be given as -

Rational numbers are the numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3 etc.

From the option, by above definition 2/3, 0.66(line over 66)7 seems to be an equivalent rational numbers because
6/9=2/3= 0.66(line over 66)7.

Thus, Rational numbers 2/3, 0.66(line over 66)7 are equivalent to 6/9.

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[tex]\frac{2}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\\\=\frac{2\sqrt{13}-2\sqrt{11}}{13-11}\\\\=\boxed{\sqrt{13}-\sqrt{11}}[/tex]

The solution is: our final quotient is:  (√13 - √11).

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation

Since we have radicals in the denominator, we need to rationalize our expression.

To do it we just need to multiply both numerator and denominator by the conjugate of the denominator.

Remember that the conjugate of a binomial is the same binomial with the sing in between changed.

given that,

2/ (√13 + √11)

Now, we can simplify the denominator:

multiplying by  (√13 - √11)

we get,

2 *  (√13 - √11) / (√13 + √11)*  (√13 - √11)

The only radical that we can simplify in the numerator is , which simplifies to:

2 (√13 - √11) / 13 - 11

=  2(√13 - √11) /2

= (√13 - √11)

So, our final quotient is:  (√13 - √11)

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A ratio shows us the number of times a number contains another number. The correct option is A.

A ratio shows us the number of times a number contains another number.

The ratio of fertilizer to soil is,

Fertilizer/Soil = 12 ounces / 10 pounds

The amount of fertilizer that the farmer need to mix for 120 pounds of soil is,

Fertilizer/120 pounds = 12 ounces / 10 pounds

Fertilizer = (12 ounces × 120 pounds)/10pounds

Fertilizer = 144 ounces

Hence, the correct option is A.

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Answer:

[tex]f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=3\sqrt{x}+7[/tex]

To find the inverse of the function

Swap f(x) for y:

[tex]\implies y=3 \sqrt{x}+7[/tex]

Subtract 7 from both sides:

[tex]\implies y-7=3 \sqrt{x}+7-7[/tex]

[tex]\implies y-7=3\sqrt{x}[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3\sqrt{x}}{3}=\dfrac{y-7}{3}[/tex]

[tex]\implies \sqrt{x}=\dfrac{y-7}{3}[/tex]

Square both sides:

[tex]\implies \left(\sqrt{x}\right)^2=\left(\dfrac{y-7}{3}\right)^2[/tex]

[tex]\implies x=\left(\dfrac{y-7}{3}\right)^2[/tex]

Swap the x for [tex]f^{-1}(x)[/tex] and y for x:

[tex]\implies f^{-1}(x)=\left(\dfrac{x-7}{3}\right)^2[/tex]

The AA postulate can be used to verify that the two triangles shown below are a similar option (C) is correct.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We can utilize the AA postulate since we know two of each triangle's three angles.

In every triangle, they are the same. We may also determine each triangle's third angle.

They are comparable because both triangles have the same angles.

Thus, the AA postulate can be used to verify that the two triangles shown below are similar.

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Answer:1333.3 Contiuous

Step-by-step explanation:

 .

4000/3,=1333.3x1,=1333.3

 I'm not sure

Answer:

976cm squared

Step-by-step explanation:

that's all I could do .hope it helps. in case of any questions please ask.