(06.02)The graph shows the number of weeks a movie has been in theaters and the number of tickets sold each week
Which statement best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold?

As the number of weeks increases, the number of tickets sold decreases.
As the number of weeks increases, the number of tickets sold increases.
As the number of weeks decreases, the number of tickets sold decreases.
No relationship can be determined.

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.

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 answer is 92%.

Step-by-step explanation:

5 of the 60 students reported that they like school. This means that the other 55 don't like school. You then divide 55/60 and you get 92%. So, therefore, your answer is 52%.

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

Answer: it’s 1:1

Step-by-step explanation:

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]

quotient means divide

 so 12 = x/2

x = 12*2 = 24

 x =24 fast songs

If a radius of a circle is perpendicular to a chord, then it _bisects____ that chord.

What is radius of circle?

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.

What is chord?

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.

According to question, we have to fill in the blank.

The property of the circle is that if a radius of a circle is perpendicular to a chord, then it  bisects that chord.

Hence we can conclude that Option(B) is correct.

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Final answer:

A radius of a circle that is perpendicular to a chord bisects the chord, dividing it into two equal segments.(Option b)

Explanation:

If a radius of a circle is perpendicular to a chord, then it bisects that chord. This statement is supported by a theorem in geometry which states that, in a circle, the radius bisecting an angle at the centre is perpendicular to the chord which subtends the angle and also bisects this chord. Therefore, by drawing a radius from the center of a circle to the midpoint of a chord, you create two equal segments, effectively bisecting the chord.

Thus, a perpendicular radius drawn from the center of a circle to a chord's midpoint ensures that the chord is bisected into two equal segments. This geometric principle facilitates chord division and enhances the understanding of circle properties.

The apothem of the square is equal to half the length of a side of the square, which can be calculated by doubling the radius. In this case, the apothem is 3√2.

The apothem of a square is a line segment drawn from the center of the square to any side of the square, perpendicular to that side. The apothem is equal to half the length of a side of the square.

Given that the square has a radius of 3√2, we can determine the length of a side of the square by doubling the radius. So, the length of a side is 2 * 3√2 = 6√2.

Therefore, the apothem of the square is half the length of a side, which is (6√2)/2 = 3√2.

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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1/4 = 0.25

s0 3 1/4 = 3.25

62x3.25 = 201.50 miles = 201 1/2 if you need it in fraction form

The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.

The figure provided depicts a circle with a secant (line GC) and a tangent (line GB) intersecting at point G, forming an angle. There are several angle measures given in the figure: angle ECA is 30°, angle ADB is 58°, and angle EAB is 161°. The angles x° and y° are what we need to find.

Here's how to find x and y:

1. To find x:

  - The angle formed by a tangent and a chord (GB and BA in this case) is equal to the angle in the alternate segment of the circle. Therefore, x is equal to the angle in the alternate segment, which is angle ADB (58°). So, x = 58°.

2. To find y:

  - The angle formed by a tangent and a secant (GB and GC in this case) from the external point G is equal to the difference between the measure of the intercepted arc (the large arc EAC) and the measure of the adjacent arc (the small arc EC). This can be calculated by the formula [tex]\( y = \frac{1}{2}(\text{large arc} - \text{small arc}) \).[/tex]

  - The large arc EAC is the full circle (360°) minus the small arc EBC (161°), so the measure of arc EAC is 360° - 161° = 199°.

  - The small arc EC is twice the angle ECA (which is an inscribed angle) because the measure of an arc is twice the measure of an inscribed angle that subtends it. So, the measure of arc EC is 2 * 30° = 60°.

  - Now we can calculate y using the formula: [tex]\( y = \frac{1}{2}(199 - 60) \).[/tex]

Let's calculate the exact values for x and y.

The value of x is equal to the angle ADB, which is 58°.

The value of y, calculated using the difference between the intercepted arcs, is 69.5° when rounded to the tenths place.

Therefore, [tex]\( x = 58 \) and \( y = 69.5 \).[/tex]

Answer:  three over two

Step-by-step explanation:

We know that the rate of change of a function [tex]y=f(x)[/tex] is given by :-

[tex]k=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

From the consecutive values in the table, the change in x = [tex]3-1=2[/tex]

Change in y = [tex]5-2=3[/tex]

Now, the rate of change of the linear relationship modeled in the table will be ;-

[tex]k=\dfrac{3}{\text{2}}[/tex]

For this case, the first thing we should do is define a variable.

We have then:

x: unknown number

Then, we write the algebraic expression that models the following problem:

the difference of 54 and a number.

We have then:

[tex]54-x[/tex]

Answer:

An algebraic expression that represents "the difference of 54 and a number" is:

[tex]54-x[/tex]

Answer:

A

Step-by-step explanation:

Answer:             10 min

Step-by-step explanation:

Final answer:

The bacterial culture that triples every 2 minutes will surpass 9500 cells just after 10 minutes. Since we cannot have a fraction of a minute in this context, the answer is 11 minutes (Option C).

Explanation:

The student is asking about exponential growth, specifically in a bacterial culture that triples every 2 minutes. To find out how many minutes it will take for the initial 40 cells to grow to more than 9500, we can use the formula for exponential growth:

N = N0 × 3t/2

Where N is the final number of cells, N0 is the initial number of cells (40 in this case), and t is the time in minutes.

We want N to be greater than 9500, so we solve the inequality:

9500 < 40 × 3t/2

Dividing both sides by 40 gives:

237.5 < 3t/2

Next, we find the smallest t for which the inequality holds by applying logarithms and solving:

t > 2 × (log3(237.5))

Calculating the right side, we get:

t > 10.096

So, the culture will have more than 9500 cells just after 10 minutes. The smallest whole number of minutes greater than 10.096 is 11, hence the answer is: C) 11 min

Since the growth is exponential, therefore I believe the correct form of the equation is:

P = 100 (2)^(t / 6)

Where t / 6 is the exponent of 2

So to find for the amount of time needed to exceed the population of 50,000, all we have to do is to plug in that value in the equation and find for t. Therefore:

P = 100 (2)^(t / 6)

50000 = 100 (2)^(t / 6)

500 = 2^(t / 6)

log 500 = (t / 6) log 2

t / 6 = log 500 / log 2

t = 6 * 8.96578

t = 53.8 mins = 54 mins

Answer:

D. 54 min

Answer:

True

Step-by-step explanation:

Consider triangle ABC inscribed in the circle with center at point O. Point O is a point of intersection of perpendicular bisectors of sides AC, AB and BC. According to the attached diagram, points E, F and G are midpoints of sides BC, AC and AB, respectively.

Then

Since segments OE, OF and OG are perpendicular bisectors of sides BC, AC and AB, then

You get three pairs of congruent triangles:

This gives you that

[tex]OB=OC=OA.[/tex]

Each of these segments is a radius of the circumscribed circle about a triangle ABC, then the center of the circumscribed circle about a triangle is equidistant to the vertices of the inscribed triangle.