is this a function?

Answer:

c = 169

Step-by-step explanation:

To make the trinomial a perfect square

add ( half the coefficient of the x- term )², that is

x² + 2(13)x + 13²

= x² + 26x + 169

= (x + 13)² ← a perfect square

Answer:

c = 49

Step-by-step explanation:

\(x^{2} -14x+49\)  

\(=(x-7)(x-7)=(x-7)^{2}\)

Hope this helps

A wheel is rotating 600 times per minute.  108,000° in 1/2 seconds degrees does a point on the edge of the wheel move in 1/2 seconds.

We know that one complete revolution of a circle is equal to 360°.

Therefore, the angle of rotation of the wheel can be calculated as:Angle of rotation of the wheel = (number of revolutions) × (360°/revolution)

Since the wheel rotates 600 times per minute, the number of revolutions it makes in 1/2 seconds can be calculated as:

Number of revolutions = (600 rotations/minute) × (1/2 minute) = 300 rotations

Therefore, the angle of rotation of the wheel in 1/2 seconds can be calculated as:

Angle of rotation of the wheel = (300 revolutions) × (360°/revolution) = 108,000°

Therefore, a point on the edge of the wheel will move 108,000° in 1/2 seconds.

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45% of 315 = 141.75

When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )

0.45 x 315 = 141.75

Answer:

141.75

Step-by-step explanation:

To do this question, first, we can write 45% as 45/100.

Now, we have to multiply.

45/100x315

=141.75

Hope that helped!

:D

Answer:

Edge 2021

Answer:

C

Step-by-step explanation:

i jut got it right

the gradient of the function y = x⁴ - 3x² + 5x - 2 at x = 0.5, calculated from first principles using the definition of a derivative, is 2.5.

To find the gradient of the function y = x⁴ - 3x² + 5x - 2 at x = 0.5 using the definition of a derivative, we need to calculate the limit of the difference quotient as δx approaches 0.

The difference quotient is defined as:

f'(x) = lim(δx→0) [(f(x + δx) - f(x)) / δx]

Substituting the given function into the difference quotient, we have:

f(x) = x⁴ - 3x² + 5x - 2

f(x + δx) = (x + δx)⁴ - 3(x + δx)² + 5(x + δx) - 2

Expanding (x + δx)⁴ and (x + δx)², we get:

f(x + δx) = x⁴ + 4x³δx + 6x²(δx)² + 4x(δx)³ + (δx)⁴ - 3x² - 6xδx - 3(δx)² + 5x + 5δx - 2

Simplifying the equation:

f(x + δx) = x⁴ + 4x³δx + 6x²(δx)² + 4x(δx)³ + (δx)⁴ - 3x² - 6xδx - 3(δx)² + 5x + 5δx - 2

Now, we can substitute the expressions for f(x) and f(x + δx) into the difference quotient:

f'(x) = lim(δx→0) [(f(x + δx) - f(x)) / δx]

f'(x) = lim(δx→0) [(x⁴ + 4x³δx + 6x²(δx)² + 4x(δx)³ + (δx)⁴ - 3x² - 6xδx - 3(δx)² + 5x + 5δx - 2 - (x⁴ - 3x² + 5x - 2)) / δx]

Simplifying further:

f'(x) = lim(δx→0) [(4x³δx + 6x²(δx)² + 4x(δx)³ + (δx)⁴ - 6xδx - 3(δx)² + 5δx) / δx]

f'(x) = lim(δx→0) [4x³ + 6x²δx + 4x(δx)² + (δx)³ - 6x - 3δx + 5]

Now, we can take the limit as δx approaches 0:

f'(x) = 4x³ + 6x²(0) + 4x(0)² + (0)³ - 6x - 3(0) + 5

f'(x) = 4x³ - 6x + 5

Finally, substitute x = 0.5 into the derivative expression:

f'(0.5) = 4(0.5)³ - 6(0.5) + 5

f'(0.5) = 0.5 - 3 + 5

f'(0.5) = 2.5

Therefore, the gradient of the function y = x⁴ - 3x² + 5x - 2 at x = 0.5, calculated from first principles using the definition of a derivative, is 2.5.

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The translations on the graph are: Horizontal translation = 2 and Vertical translation = 4

The equation of the function is  y = ∛(x - 2) + 4

From the question, we have the following parameters that can be used in our computation:

The graph

The parent function of the function is a cube function i.e. y = ∛x

On the graph, we can see that

This means that

Horizontal translation = 2

Vertical translation = 4

Also, it means that the equation of the function is

y = ∛(x - 2) + 4

Hence, the graph is represented by y = ∛(x - 2) + 4

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The standard form of the equation of f(x) is option a -x² - 6x + 7

Given,

The graph shows a downward open parabola.

The vertex points are:

(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)

Now,

We have to find the standard form of the function f(x):

As from the graph:

Parabola opens downward, so the function will be negative.

We have the options with:

a = -1, b = -6 and c = 7

Now,

Use x = -b/2a

x = 6/2 × -1 = 6/-2 = -3

Now,

f(x) = -x² - 6x + 7

f(-3) = -(-3)² - 6(-3) + 7

f(-3) = -9 + 18 + 7

f(-3) = 9 + 7

f(-3) = 16

That is, the points for the vertex in this equation is (-3, 16)

Then, the standard form of the equation of f(x) is option a -x² - 6x + 7

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The equation 3x² - 8xy²z² = 7 can be expressed in cylindrical coordinates as 3(r cosθ)²- 8(r cosθ)(r sinθ)²z² = 7.

In cylindrical coordinates, a point is represented by (r, θ, z), where r is the radial distance from the origin, θ is the angle measured from a reference direction (usually the positive x-axis), and z is the vertical distance from the xy-plane.

To express the equation 3x² - 8xy²z² = 7 in cylindrical coordinates, we substitute x = r cosθ, y = r sinθ, and leave z as it is. Thus, we have:

3(r cosθ)²- 8(r cosθ)(r sinθ)²z² = 7.

By applying trigonometric identities, we can simplify the equation further. Using the identity cos²θ + sin²θ  = 1, we have:

3r² cos²θ - 8r³ cosθ sin²θ z² = 7.

Now, we can rewrite the equation in its final form:

3r² cos²θ - 8r³ cosθ sin²θ z² - 7 = 0.

This is the equation in cylindrical coordinates corresponding to the given equation in Cartesian coordinates.

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Answer:

D. x=4 and x=6 (A P E X)

Answer:

-17 9/10

Step-by-step explanation:

Answer:

Vertical

Step-by-step explanation:

I got this correct :) and also because if it would be supplementray, those angles would be placed different (on one line) had they’re not corresponding or alternating. So its C - vertical. :) Can you please mark me as brainliest?

Answer:

If that says 6 and 8 then they are vertical. If it's 6 and 3 then they are alternate interior. Forgive me for I am blind.

Answer:

3(p+1)²-7

Step-by-step explanation:

(5p² - 3p + 4) - (2p² - 9p + 8) =3p²-12p-4=3(p+1)²-7

Answer:

\(3p^2+6p-4\)

Step-by-step explanation:

\((5p^2-3p+4)-(2p^2-9p+8)\)

Now, combine like terms.

\((5p^2-2p^2)+(-3p+9p)+(4-8)\)

\(3p^2+6p-4\)

Answer:

48.33%

Step-by-step explanation:

if you ever have problems with percents

you should probably use calculator soup :)

have a nice day!

This statement is - true.

Two angles that lie in the same plane and have a common vertex and a common side but have no common interior points are the meaning of adjacent angles.

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Answer:

A. x^2 - 6x - 16

Step-by-step explanation:

FOIL it

x * x = x^2

2 * x = 2x

-8 * x = -8x

2 * -8 = -16

x^2 + 2x - 8x - 16.     combine like terms

x^2 - 6x - 16

Answer:

A

Step-by-step explanation:

expand

x*x +2x-8x-16

x^2 -6x-16

Answer:

x=3

Step-by-step explanation:

2x+(3x)=15

5x=15

x=3

solving for y:

3(3)=9

y=9

Answer:

(y,x) (9,3)

Step-by-step explanation

a)The expected profit is $4,000. b)The standard deviation for the profit is approximately $4,898.98.

a) To calculate the expected profit, we multiply the profit by the probability of it happening:

Expected profit = Profit * Probability

Given:

Profit = $10,000

Probability = 40% = 0.4

Expected profit = $10,000 * 0.4 = $4,000

Therefore, the expected profit is $4,000.

b) To find the standard deviation for the profit, we need more information about the probability distribution of the profit. If we assume that the profit follows a Bernoulli distribution (with only two possible outcomes: getting the contract or not), we can calculate the standard deviation using the formula:

Standard deviation = √(Probability * (1 - Probability) * Profit^2)

Given:

Profit = $10,000

Probability = 40% = 0.4

Standard deviation = √\((0.4 * (1 - 0.4) * $10,000^2)\)

                = √(0.4 * 0.6 * $100,000,000)

                = √(24,000,000)

                ≈ $4,898.98

Therefore, the standard deviation for the profit is approximately $4,898.98.

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The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

An expression of two terms having a degree n can be represented as,

(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).

Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).

(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.

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Answer:

To solve the quadratic equation x^2 + 9x +25 = 5 by factoring, we first rearrange the equation to get:

x^2 + 9x +20 = 0

Next, we need to find two numbers that multiply by 20 and add to 9, the coefficient of x. The two numbers are 4 and 5.

So, we can factor the quadratic as:

(x + 4)(x + 5) = 0

Setting each factor to zero and solving for x, we get:

x + 4 = 0 or x + 5 = 0

Solving for x in each equation, we get:

x = -4 or x = -5

Therefore, the solutions to the quadratic equation x^2 + 9x +25 = 5 are x = -4 and x = -5.

Answer:

0.003,0.032,0.302, and then 0.320

Step-by-step explanation:

A recent report estimates that four out of every five dentists recommend a brand of toothpaste situation involves Inferential statistics.

Inferential statistics are widely employed to compare the differences between the treatment groups. Inferential statistics compare the treatment groups and make generalizations about the subject population using data from the experiment's sample of subjects. To offer answers for a situation or phenomena, inferential statistics is helpful. It differs fundamentally from descriptive statistics, which do not allow for result extrapolations and merely report the data that has already been measured.

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Answer:

D and E

C

Step-by-step explanation:

Answer:

x=71

Step-by-step explanation:

The magnitude of the expected shortfall at a 95% confidence level is not provided. Please provide the necessary information to calculate the expected shortfall.

The expected shortfall at a specific confidence level, we need additional information, such as the distribution of returns or loss data. The expected shortfall, also known as conditional value-at-risk (CVaR), represents the average value of losses beyond a certain threshold.

Typically, the expected shortfall is calculated by taking the average of the worst (1 - confidence level) percent of losses. However, without specific data or parameters, it is not possible to determine the magnitude of the expected shortfall at a 95% confidence level.

To calculate the expected shortfall, we would need a set of data points representing returns or losses, as well as a specified distribution or methodology to estimate the expected shortfall. Please provide the necessary details so that the expected shortfall can be calculated accurately.

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The weights are 25 kg for weight X, 20 kg for weight Y, and 15 kg for weight Z. Thor's new total lift would be higher if he replaced one weight Z with a weight Y.

a) To determine the three separate weights, let's assign variables to each weight. Let X represent the weight of weight X, Y represent the weight of weight Y, and Z represent the weight of weight Z.

From the given information, we have the following equations:

4X + 3Y + 5Z = 295

2X + 5Y + 3Z = 295

3X + 4Y + 5Z = 310

We can solve this system of equations to find the values of X, Y, and Z.

Multiplying the first equation by 2 and the second equation by 4, we get:

8X + 6Y + 10Z = 590

8X + 20Y + 12Z = 1180

Subtracting the first equation from the second equation, we obtain:

14Y + 2Z = 590

Multiplying the third equation by 3 and subtracting the first equation multiplied by 2, we get:

3X + 12Y + 15Z - 8X - 6Y - 10Z = 930 - 590

-5X + 6Y + 5Z = 340

Multiplying this equation by 14, we have:

-70X + 84Y + 70Z = 4760

Adding this equation to the previous equation, we obtain:

-68X + 86Y + 72Z = 5350

Dividing by 2, we get:

-34X + 43Y + 36Z = 2675

Now we have two equations:

14Y + 2Z = 590

-34X + 43Y + 36Z = 2675

Solving this system of equations, we find:

X = 25 kg

Y = 20 kg

Z = 15 kg

Therefore, the weights are 25 kg for weight X, 20 kg for weight Y, and 15 kg for weight Z.

b) If Thor replaced one weight Z by a weight Y, it would change the result of the competition. The total lift for Thor is currently 295 kg. If Thor replaces one weight Z with a weight Y, the new total lift would be:

2X + 6Y + 2Z = 2X + 6Y + 2(15) = 2X + 6Y + 30

This new total lift would be greater than the original 295 kg, as 2X + 6Y + 30 is greater than 295. Therefore, Thor's new total lift would be higher if he replaced one weight Z with a weight Y.

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Using complementary angles, the numerical value of the given expression is as follows:

2.

Complementary angles are angles whose sum of the measures is of 90º.

The relevance of complementary angles in the context of this problem is that if a and b are complementary angles, then the sine of one angle is the cosine of the other angle, as follows:

sin(a) = cos(b).

Considering the angles of 40º and 50º in this problem, we have that:

Hence these following simplifications are applied:

Then the numerical value of the expression is given as follows:

1/1 + sin²(40º) + cos²(40º) = 1 + 1 = 2.

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Answer:

The answer is DF

Step-by-step explanation:

The opposite side is 4 or EF, so the ADJACENT side would be 3 or DF according to SOH CAH TOA.

Answer:

D

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainlies!

Answer:

D is for sure a function and just so you know A is never a function.

Step-by-step explanation:

To determine the value for X, which represents the total relative frequency for the full price column, we need to subtract the respective discounted relative frequencies from 1. The correct value for X is 0.96.

In the original frequency table, the fourth column represents the total number of beach towel sales for each month. To convert it to a conditional relative frequency table by row, we divide each entry in the second and third columns by the respective total in the fourth column. This gives us the relative frequencies for full price and discounted sales.

In the conditional relative frequency table, the entries in the fourth column represent the total relative frequency for each month, which should sum up to 1.0. Therefore, we need to determine the value for X, which represents the total relative frequency for the full price column.

To find X, we subtract the respective discounted relative frequencies from 1.0. In month 1, the discounted relative frequency is 0.02, so X = 1.0 - 0.02 = 0.98. In month 2, the discounted relative frequency is 0.04, so X = 1.0 - 0.04 = 0.96. In month 3, the discounted relative frequency is 0.192, so X = 1.0 - 0.192 = 0.808. Since X should be rounded to the nearest hundredth, the correct value is 0.96.

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