If n√a=r , then which of the following are true statements? Check all that apply. A. r^n=a B. a^1/n=r C. a^r=n D. n^1/r=a

The We have given that the pairs of values of f(x) and g(x) with the corresponding values of h(x) s given below.

(x^2-9)/(x-3)

x^2-4x+3/x-3

x^2+4x-5/x-1

x^2-16/x-4

We have to match the pairs  of values of f(x) and g(x) with the corresponding values of h(x) if h(x) = f(x) ÷ g(x).

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

1)f(x)/g(x)=(x^2-9)/(x-3)=x+3

2)f(x)/g(x)=x^2-4x+3/x-3=x+1

3)f(x)/g(x)=x^2+4x-5/x-1=x+5

4)f(x)/g(x)=x^2-16/x-4=x+4

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Answer: The correct option is (D) y = -x + 2.

Step-by-step explanation:  We are to select the correct equation that describes the given graph.

We can see that the graph is a straight line passing through the points (0, 2) and (1, 1).

So, the slope of the line will be

[tex]m=\dfrac{2-1}{0-1}=-1.[/tex]

Therefore, the equation of the line with slope m = -1 and passing through the point (0, 2) is given by

[tex]y-2=m(x-0)\\\\\Rightarrow y-2=-1\times x\\\\\Rightarrow y-2=-x\\\\\Rightarrow y=-x+2.[/tex]

Hence, the equation that describes the graph is  y = -x + 2.

Thus, (D) is the correct option.

Answer:

The prime factors are:

a. 5 and 5 (5 × 5 = 25)

b. 2 and 19 (2 × 19 = 38)

c. 2, 2, 3, and 3 (2 × 2 × 3 × 3 = 36)

d. 3, 5, and 19 (3 × 5× 19 = 285)

e. 2, 5, 5, and 13 (2 × 5 × 5 × 13 = 650)

f. 2, 2, 3, 5, and 29 (2 × 2 × 3 × 5 × 29 = 1,740)

Step-by-step explanation:

straight from Penn

For this case, the first thing we must do is calculate the total profit.

We have then:

[tex] P = 850 - 500 [/tex]

[tex] P = 350 [/tex]

Then, we look for the number of coins.

For this, we need the total profit (which we already calculate) and the amount of profit per coin.

We have then:

[tex] N = \frac{350}{50} [/tex]

[tex] N = 7 [/tex]

Answer:

The amount of coins that was on the set is:

[tex] N = 7 [/tex]

Final answer:

The coin collector bought and sold a set of coins, making a total profit of $350. Dividing this profit by the $50 profit per coin reveals that there were 7 coins in the set.

Explanation:

The coin collector made a profit of $50 per coin by selling a set of coins. To find out how many coins were in the set, we need to calculate the total profit made from selling the coins and then divide that by the profit per coin.

The total profit is the selling price minus the buying price, so $850 - $500 = $350. If the collector made $50 profit per coin, then the number of coins in the set can be found by dividing the total profit by the profit per coin: $350 / $50 per coin = 7 coins.

Since no one was getting the the answer that is on the assignment I plugged  the problem into an algebra calculator, and got A 0.6616

This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).

Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:

sin θ = opposite side / hypotenuse

sin 45 = 68 miles per hr / flight

flight = 68 miles per hr / sin 45

flight = 96.17 miles per hr

Answer with explanation:

The pre image which is in blue color is parallelogram.

There are four blue parallelograms here,congruent to each other,each one of them when rotated by certain angle ,gives parallelogram in brown color.

When we rotate a polygon,after rotation neither the shape nor the size of polygon changes.The two shapes are congruent to each other.

→The Polygon being rotated to create the brown quilt block pattern is

Option C: Parallelogram

To find the equations of the directrices for a hyperbola centered at the origin with a vertex at (3, 0) and a focus at (9, 0), we use the formula x = ±a/e. The hyperbola's directrices are x = ± 1.

The student asked about the equations of the directrices for a hyperbola that is centered at the origin, with a vertex at (3, 0) and a focus at (9, 0). A hyperbola has two directrices, and each is a line that is perpendicular to the transverse axis and equidistant from the center as the foci are, but on the opposite side. The equation of a directrix can be found using the formula x = ±a/e, where 'a' is the distance from the center to the vertex and 'e' is the eccentricity, which is the ratio of the distance from the center to a focus (c) over 'a'.

In this case, the hyperbola is aligned along the x-axis. Given a vertex at (3, 0), it implies that 'a' is equal to 3. Since the focus is at (9, 0), it suggests 'c' is equal to 9. The eccentricity 'e' can be found by e = c/a, which is 9/3 = 3. Using the directrix formula x = ±a/e, the two directrices of the hyperbola would be x = ±(3/3), which simplifies to x = ± 1.

Answer:

The degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.

Step-by-step explanation:

The given polynomial is [tex]12x^4-8x+4x^2-3[/tex]

This polynomial is of one variable which is x. Hence, the degree of the polynomial is the highest exponent.

For the given polynomial, the highest exponent is 4.

Therefore, the degree of [tex]12x^4-8x+4x^2-3[/tex] is 4.

the greatest possible error when measuring in feet is 1/2 foot

 answer is B

The value of cos 53 degrees in terms of sine is,

⇒ sin 37 degree

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

⇒ cos 53 degree

Hence, We can change it into sine as;

⇒ cos 53 degree

⇒ sin (90 - 53)

⇒ sin 37 degree

Thus, The value of cos 53 degrees in terms of sine is,

⇒ sin 37 degree

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We are given the equation:

x (y + 6) – 5 (y + 6)                           ---> 1

We are to look for the missing factor in the equation: (_) (y + 6) from the given values.

Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:

(x – 5) (y + 6)                                      ---> 2

wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:

x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)

Expanding:         

x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30     (EQUAL!)

Therefore our missing factor is:

(x – 5)

The roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.

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 equation:

x³ - 7x = 6x - 12

[tex]\rm x^3-7x+12=6x[/tex]

x³ - 13x + 2 = 0

(x - 1)(x -3)(x + 4) = 0

x = 1, 3, -4

Thus, the roots of the polynomial equation x³ - 7x = 6x - 12 is x = 1, 3, -4 and graph is shown in the picture.

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Answer:

[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

Step-by-step explanation:

Given: [tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]

Simplify the expression.

[tex]\Rightarrow \sqrt{7x}(\sqrt{x}-7\sqrt{7})[/tex]

Distribute  [tex]\sqrt{7x}[/tex] over parentheses

[tex]\Rightarrow \sqrt{7x}\cdot\sqrt{x}-\sqrt{7x}\cdot7\sqrt{7}[/tex]

[tex]\Rightarrow \sqrt{7x^2}-7\sqrt{7^2x}[/tex]

square term take out from square root

[tex]\Rightarrow x\sqrt{7}-7\cdot 7\sqrt{x}[/tex]

[tex]\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

[tex]\sqrt{7x}(\sqrt{x}-7\sqrt{7})\Rightarrow x\sqrt{7}-49\sqrt{x}[/tex]

Answer:

The other answer is correct here except it is missing the answer 4pi/3

other wise its correct. The answers are 0, 2pi/3, and 4pi/3

Step-by-step explanation:

see previous answer

Answer:

The missing term is x.

Step-by-step explanation:

Given expression is,

[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}------(1)[/tex]

Since, [tex]x^2-4x+4=(x)^2-2\times (2x)+(2)^2[/tex]

[tex]\implies x^2-4x+4=(x-2)^2------(2)[/tex]    ( (a-b)² = a² - 2ab + b² )

Now,   [tex]x^2-3x+2=x^2-2x-x+2[/tex]    ( By middle term splitting )

[tex]=x(x-2)-1(x-2)[/tex]

[tex]\implies x^2-3x+2=(x-1)(x-2)------(3)[/tex]

From equation (1), (2) and (3),

[tex]\frac{x}{x^2-4x+4}-\frac{x}{x^2-3x+2}=\frac{x}{(x-2)^2}-\frac{x}{(x-2)(x-1)}[/tex]

[tex]=\frac{x(x-1)-x(x-2)}{(x-2)^2(x-1)}[/tex]

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

[tex]=\frac{x(1)}{(x-2)^2(x-1)}[/tex]

[tex]=\frac{x}{(x-2)^2(x-1)}[/tex]

Hence, the missing term in the equation is x.

Answer:

Area to be developed = 269.23 acres

Step-by-step explanation:

Let there is A acres natural area to be developed.

If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)

Now it has been given in the question that 65% of A (untouched area) = 500 acres

[tex]A.\frac{65}{100}=500[/tex]

[tex]A=\frac{500}{0.65}=769.23[/tex]

So area of the natural field = 769.23 acres

Now 35% of the natural area which is to be developed = A×35%

[tex]=769.23.\frac{35}{100}=(769.23)(.35)=269.23[/tex]

Area of the natural area to be developed is 269.23 acres

The number of acres that are to be developed is 269 acres.

Using this formula

Number of acres=(Number of acres untouched/(100%-Percentage of natural area)×Percentage of natural area

Let plug in the formula

Number of acres=500 acres/(100%-35%)×35%

Number of acres=(500 acres/65%)×35%

Number of acres=769.23×35%

Number of acres=269 acres

Inconclusion the number of acres that are to be developed is 269 acres.

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