Theater tickets are marked down 15%. How
much are the tickets if they originally cost
$55?

To find the derivative dy/dx of the equation \(x^2\)y - 2\(x^2\) - 8 = 0 implicitly, we differentiate both sides of the equation with respect to x.

Differentiating both sides of the equation \(x^2\)y - 2\(x^2\) - 8 = 0 implicitly with respect to x, we apply the product rule and chain rule as necessary. The derivative of \(x^2\)y with respect to x is 2xy + \(x^2\)(dy/dx), and the derivative of -2\(x^2\) with respect to x is -4x. The derivative of -8 with respect to x is 0, as it is a constant.

So, the derivative expression is: 2xy + \(x^2\)(dy/dx) - 4x = 0.

To find the value of dy/dx, we can rearrange the equation:

dy/dx = (4x - 2xy)/(\(x^2\)).

Now, substituting the given point (2, 4) into the derivative expression, we have:

dy/dx = (4(2) - 2(2)(4))/(\(2^2\)) = 0.

Therefore, the slope of the curve at the point (2, 4) is 0.

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Answer:

I believe that would be 225.  (Hope that helps!)

Answer:225:)

Step-by-step explanation:

Answer:

9 + 4(1) \(\neq \\\) 17

Step-by-step explanation:

to satisfy inequality

9 + 4(1) < 17

13 < 17

The value of polynomial p(x) when x=0 is 35.

What is a polynomial?

An expression made up of indeterminates and coefficients and utilising solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables is referred to as a polynomial.

The complete question is as follows:

Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).

Given,

p(x) is a polynomial of smallest degree where

    p(-3) = p(√7) = p( 1-√6) = 0

     p(-1) = 8

 So the factors of p are (x+3),(x-√7) and (x - 1+√6)

Given p has rational coeffecients. So we should remove √7 and √6. This can be done by multiplying with conjugates.

(x-√7)*(x+√7) = x²-7

(x-1+√6) * (x-1-√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5  

Now the polynomial can be written as

p(x) = c (x+3)(x²-7) (x²-2x-5 )

Here c is a constant and can be determined using p(-1) = 8

p(-1) = c ( -1+3)(-1² - 7 )(-1²-2*(-1) -5)

8 = c(2)(-6)(-2)

c = 1/3

Now the polynomial p(x) = 1/3(x+3)(x²-7) (x²-2x-5 )

Therefore p(0) = 1/3 (3) (-7)(-5) = 35

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Elww Mate..........

.........

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

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Answer: 60 shirts.

Step-by-step explanation: Camila: 40/hr Evelyn: 20/hr

20 + 40 = 60

Answer:

7

Step-by-step explanation:

We can solve this problem by making an equation for the monthly bill. First, the cost is $59.99 per month, and that cannot be decreased, so we must add all costs to that amount. Next, it costs $5.49 per first run movie, so for each first run movie, we add $5.49 to the total. Therefore, we can write our equation as

59.99 + 5.49 per first run movie = monthly bill

Representing the number of first run movies as r, we can say

59.99 + 5.49 * r = monthly bill

Next, the monthly bill should be less than or equal to 100, so we can say

monthly bill ≤ 100

59.99 + 5.49 * r = monthly bill ≤ 100

Moreover, we want to maximize r, or the amount of first run movies. Because we add money to the monthly bill for each movie, to maximize r, we have to find the maximum money we can spend on the monthly bill that is still less than or equal to 100. To do this, we set the monthly bill to its maximum limit, or 100, so we have

59.99 + 5.49 * r = 100

subtract 59.99 from both sides to isolate the f and its coefficient

40.01 = 5.49 * r

divide both sides by 5.49 to isolate the variable

r ≈ 7.29

Since we can't buy .29 of a movie, and rounding up to 8 movies would cause us to go past 100 dollars, the maximum movies he can watch if he wants to keep his monthly bill ≤ 100  is 7

Answer:

*

Step-by-step explanation:

Answers

8 x - 1/2 = -4 - middle line

-3/4 x 8 = - 6 - side line

-3/4 - - 1/2 = -1/4 - top line

-1/2 - 1/2 = -1 - vertical line

Step-by-step explanation:

first you can 1.9 7 times then you do it again but to the 10 power

The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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The period of the function given in the graph is 9.

Given is a graph.

We have to find the period of the function.

The period of a function is defined as the distance between the points where the function is repeated.

In the given function, take any two points where the function is repeated.

If we take the top points which are near to each other, they are points for which the function is repeated.

Consider the two points which corresponds to y = 2.

The x values are x = 1 and x = 10

So period = 10 - 1 = 9

Hence the period of the function is 9.

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Answer:

b = $2.40

d = $5.70

Step-by-step explanation:

d = hot dog and b = hot dog buns

Equations:

2d + 5b = $23.40

3d + 2b = $21.90

-------------------------------subtract these two equations

-d + 3b = $1.50

3b - $1.50 = d

Substitute:

3d + 2b = $21.90

3(3b - $1.50) + 2b = $21.90

9b - $4.50 + 2= $21.90

11b = 26.40

b =  $2.40

Substitute again but this time with b:

3d + 2b = $21.90

3d + 2($2.40) = $21.90

3d + $4.80 = $21.90

3d = $21.90

d = $5.70

The domain and range of the function are [-3, 3] and [-2, 4], respectively and The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

Given that the graph of the function is shown below, the domain and range of the function need to be determined along with finding the function values for (a) f(−1), (b) f(0), (c) f(1) and (d) f(2).Graph of the function:Graph of the function for the given graph of the function, we can observe that the domain of the function is from -3 to 3 as the graph is defined within these limits.In order to find the range of the function, we need to look at the range of the y-coordinates.

The minimum value of y is -2 and maximum value of y is 4.Range of the function: [-2, 4]a) f(-1) means the function value for x = -1. As we can observe from the graph, the point where x = -1 is on the graph of the function is (1, 0). Therefore, f(-1) = 0b) f(0) means the function value for x = 0. As we can observe from the graph, the point where x = 0 is on the graph of the function is (0, -2).

Therefore, f(0) = -2c) f(1) means the function value for x = 1. As we can observe from the graph, the point where x = 1 is on the graph of the function is (2, 4). Therefore, f(1) = 4d) f(2) means the function value for x = 2. As we can observe from the graph, the point where x = 2 is on the graph of the function is (3, 3). Therefore, f(2) = 3

Thus, the domain and range of the function are [-3, 3] and [-2, 4], respectively. The function values for (a) f(-1), (b) f(0), (c) f(1) and (d) f(2) are 0, -2, 4, and 3, respectively. The total number of words used is 163.

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Explanation:

A function has each x value map to exactly one y value. Choice A demonstrates this, which is why it's a function. Note how none of the x values are repeated in this table.

Choices B, C and D have repeated x values, which in turn means that we have an x input lead to multiple y outputs. For instance, choice B says that the input x = -5 has the two outputs y = -5 and y = 5; this is sufficient to show that table B is not a function. Choices C and D are a similar story.

A 1% error in r will lead to a larger error in the volume.

A 1% error in r will cause a larger error in the volume, since the percentage increase in volume is proportional to the square of r.

The volume of a cylinder of radius r and height h is V = πr2h. The linear approximation to the volume of a cylinder is given by V ≈ πr2(h + r).

Thus, the percentage increase in volume when r and h are each increased by c is given by 100% × (Vnew - Vold) / Vold = 100% × (π(r + c)2(h + c + r) - πr2h) / πr2h = 200c/r + 100c/h.

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Answer: Perpendicular

Step-by-step explanation: x-y=5 —-> subtract x from both sides to give you y alone. -y= -x+5 —-> next step is to continue to get y alone so you have to divide both sides by -1. y=x-5 now the first one is done

x+y=-10 —-> solve to get y alone so subtract both sides by x making it y=-x-10 Meaning that the two lines are perpendicular to each other.

Please make me brainliest!

Answer: √25 = ±[5]

Step-by-step explanation:

5 × 5 = 25

-5 × -5 = 25 (negative times negative = positive)

Answer:36

Step-by-step explanation:

Concept,

Two chords with a shared termination point on the circle make an inscribed angle in a circle. The vertex of the angle is this shared terminal point. An inscribed angle is equal to half the length of the intercepted arc.

Given,

We have been given a figure in which the line \(BD\) is the tangent to the circle at the point \(B\) and the measure of the arc \(AC\) is \(108^{\circ}}\). And also we have some options:

A. \(38^{\circ}}\)

B. \(18^{\circ}}\)

C. \(118^{\circ}}\)

D. \(72^{\circ}}\)

To find,

We have to choose the correct option which tells the measure of the angle of \(CBD\).

Solution,

In the figure, we can see that \(\angle ABC\) is an inscribed angle and we know that the inscribed angle is half of the measure of the intercepted arc.

And from the figure arc \(AC\) is the intercepted arc.

Thus, we can write

\(\angle ABC=\frac{\widehat{AC}}{2}\)

\(\angle ABC=\frac{108}{2}\)

\(\angle ABC=54^{\circ}\)

So, the measure of \(\angle ABC=54^{\circ}\).

Now given that \(BD\) is a tangent to the circle at the point \(B\).

Thus, we will get

\(\angle ABC+\angle CBD=90^{\circ}\)

\(54^{\circ}+\angle CBD=90^{\circ}\)

\(\angle CBD=90^{\circ}-54^{\circ}\)

\(\angle CBD=36^{\circ}\)

Thus, the measure of the angle \(CBD=36^{\circ}\).

So, the correct option is A. \(36^{\circ}\).

In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

45

Step-by-step explanation:

f(x)=2^6x-19

f(1)=2^(6(1))-19=2^(6)-19=2^6-19=64-19=45

Answer:

(3•22g4h5)

Step-by-step explanation:

Step 1:  ((3gh2 • 4) • g3) • h3

Step 2:   ((3•22gh2) • g3) • h3

Step 3:   3.1 h2 multiplied by h3 = h(2 + 3) = h5

Final answer:   (3•22g4h5)

(IF THIS HELPED PLEASE GIVE BRAINLIEST OR RATE IT 5 STARS!)

The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.

An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.

Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.

Angle ABC = Angle ABD + Angle ACD

replacing the specified values:

110° = Angle ABD + 75°

Simplifying:

Angle ABD = 110° - 75°

Angle ABD = 35°

Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:

AC / CD = AB / BD

replacing the specified values:

AC / 10 = 16 / 8

Simplifying:

AC = 20

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Complete Question:

Find the angle ∠ABD jn the given figure

Step-by-step explanation:

where is the steps to this question you can't answer it without a question too it SMH

Answer:

5%

Step-by-step explanation:

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given:

Substitute the given values into the simple interest formula and solve for r:

\(\implies 500=5000 \cdot r \cdot 2\)

\(\implies 500=10000r\)

\(\implies r=\dfrac{500}{10000}\)

\(\implies r=0.05\)

\(\implies r=5\%\)

Therefore, the interest rate is 5%.

Answer:

Interest rate = 5% (or) 0.05

Step-by-step explanation:

Now we have to,

→ find the required interest rate.

Formula we use,

→ I = P × R × T

→ PRT = I

→ R = I/PT

Then the interest rate will be,

→ R = I/PT

→ R = $500 ÷ ($5000 × 2 years)

→ R = 500/(5000 × 2)

→ R = 500/10000

→ R = 0.05 × (100)

→ [ R = 5% ]

Hence, the interest rate is 5%.

the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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Answer:

-4≤x<5

Hope This Helps!!!

Answer:

4x4 =16 so 7x4=28

Answer =28