pls helppp!!! with geometry

The equation for the function g(x) is g(x) = (x + 4)² - 5.

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

N represents an integer.

g(x) and f(x) represent a function.

Based on the graph of the parent function f(x) = x², an equation for g(x) in vertex form after a translation of 5 units downward and 4 units to the left is given by:

g(x) = (x + 4)² - 5.

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Cost function (C(x)): C(x) = $50,000 + $6x, Marginal Cost (MC): MC = $6

Revenue function (R(x)): R(x) = $30x, Marginal Revenue (MR): MR = $30

Profit function (Π(x)): Π(x) = $24x - $50,000, Marginal Profit (MP): MP = $24

The cost function (C(x)) represents the total cost to produce x units of Furby.

Given:

Fixed costs = $50,000

Cost per Furby = $6

The cost function can be calculated as follows:

C(x) = Fixed costs + (Cost per Furby × Number of units)

C(x) = $50,000 + ($6 × x)

C(x) = $50,000 + $6x

The marginal cost (MC) represents the additional cost incurred by producing one more unit of Furby.

Since the cost per Furby is constant at $6, the marginal cost is also $6.

MC = $6

The revenue function (R(x)) represents the total revenue generated from selling x units of Furby.

Given that the price per Furby is $30, the revenue function can be calculated as:

R(x) = Price per Furby × Number of units

R(x) = $30×x

R(x) = $30x

The marginal revenue (MR) represents the additional revenue generated by selling one more unit of Furby.

Since the price per Furby is constant at $30, the marginal revenue is also $30.

MR = $30

The profit function (Π(x)) represents the total profit obtained from selling x units of Furby.

Profit = Revenue - Cost

Π(x) = R(x) - C(x)

Π(x) = ($30x) - ($50,000 + $6x)

Π(x) = $30x - $50,000 - $6x

Π(x) = $24x - $50,000

The marginal profit (MP) represents the additional profit obtained by selling one more unit of Furby.

Since the coefficient of x in the profit function is $24, the marginal profit is $24.

MP = $24

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Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

X = 27

Step-by-step explanation:

10, 20, 32, 37, 50, 60

First things first, take off 10, 20, 50, and 60.

Now, you remain with 32 and 37. Now from here it is simple.

Average of 32 and 37 = 34.83

Round 34.83 to 35

32 averaging 37 (Rounding Terms) ≈ 35

So X is 27

Answer:

The weight of the second box is 42 kilograms, since 54 - 12 = <<54-12=42>>42.

Answer:

bruh moment hdu2ebdd

Step-by-step explanation:

yqh1 badalamenti

Answer:

Step-by-step explanation:

A) The Binomial Theorem states that for any positive integer n and any real numbers a and b, the expression (a + b)^n can be expanded as a sum of the form:

(a + b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1)b^1 + C(n,2)a^(n-2)b^2 + ... + C(n,n)a^0b^n

where C(n,k) = n!/(k!(n-k)!) is the binomial coefficient.

Applying this to the expression (1 + x)^2, we have:

(1 + x)^2 = C(2,0)1^2 x^0 + C(2,1)1^1 x^1 + C(2,2)1^0 x^2

= 11^21 + 21x + 1*x^2

The first four terms of the polynomial are: 1, 2x, x^2

B) The binomial theorem states that the first term is a constant term and the second term is linear. When x is less than 1, the linear term 2x is much smaller than the constant term 1, so the linear term can be ignored as a good approximation. Therefore, 1 + nx will be a good approximation of the expression (1+x)^2 when x is less than 1.

Answer:

Option (3)

Step-by-step explanation:

If the triangle FGH is dilated by a scale factor 'k', then the sides of the image triangle F'G'H' will get dilated by 'k' times but the angles will measure the same.

In simpler words, both the triangles will be similar

Therefore, sin(F) and sin(F') will measure the same.

Option (3) will be the correct option.

Answer:

$1274.13

Step-by-step explanation:

To start, we need to turn this percentage into a fraction out of 1

\(43\% = 0.43\)

Now that we have this, we can multiply

\((0.43)(891) = 383.13\)

Last step is to add the new number to the original number

\(383.13 + 891 = 1274.13\)

Answer:

x=y-3/5

Step-by-step explanation:

y=5x+3

y-3=5x

y-3/5=x

x=y-3/5

Hopefully this the correct answer 15 percent I am not sure

Step-by-step explanation:

Answer:

y = 1/2x+2

Step-by-step explanation:

first find x intercepts : to find x intercept put 0 in y

1/2x+2 = 0

1/2x= -2

x = -4 the graph shows x intercept at 4

next find y intercept : to find y intercept put 0 into x

=1/2*0+2

=2

the graph shows y crosses at 2.

Answer:

y = 1/2x+2

Answer:

c

Step-by-step explanation:

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The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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Answer: a + 3b = 8

Step-by-step explanation:

a + b = 4 is true, since (2,2) works:  2 + 2 = 4

Try (2,2) in the options to find which one is true for (2,2):

A)  2 + 3*2 = 4?  No.

B)  4 + 4 = 2?  No.

C)  8 + 8 = 8?  No.

D)  2 + 6 = 8?  YES.

Therefore, a + 3b = 8 can be another valid equation.

Answer:

D. a + 3b = 8

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiStep-by-step explanation:

Answer:

3x+6=9

Step-by-step explanation:

thre are 3 x's on one side and 6 1's

the other side has nine ones

Answer:

$838.09

Details:

750.44 after one year.

771.45 after two years.

793.05 after three years.

815.26 after four years.

838.09 after five years.

Answer:

-9.5 would be less than -9.05

b

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1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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Answer:

\(( - {6x}^{3} - {x}^{2} - 6x + 2)(6x - 2) \\ = ( - 36 {x}^{4} - 6 {x}^{3} - 36 {x}^{2} + 12x + 12 {x}^{3} + 2 {x}^{2} + 12x - 4) \\ = ( - 36 {x}^{4} + 6 {x}^{3} - 34 {x}^{2} + 24x - 4)\)

The correct location of the table are;

                   6x            - 2

- 6x³           - 36x⁴          12x³

  - x²           - 6x³           2x²

- 6x           - 36x²         12x

   2              12x           - 4

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

Given that;

The expression is;

⇒ (−6x³ - x² - 6x + 2) (6x - 2)

Now,

Solve the expression as;

⇒ (−6x³ - x² - 6x + 2) (6x - 2)

After multiplying, we get;

⇒ - 36x⁴ + 12x³ - 6x³ + 2x² - 36x² + 12x + 12x - 4

Thus, The complete table is,

                   6x            - 2

- 6x³           - 36x⁴          12x³

  - x²           - 6x³           2x²

- 6x           - 36x²         12x

   2              12x           - 4

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The area of the circle r = 18 sinθ as an integral in polar coordinates is 81π.

We must evaluate the integral of the function r = 18sinθ with respect to θ in order to determine the circle's area in polar coordinates, where r stands for the radius and θ for the angle.

The whole revolution of the circle should be covered by the limits of integration for θ. Our bounds of integration will be 0 to 2π(or 0 to 360 degrees), which is the range of a whole revolution.

The following is the formula for the area in polar coordinates:

A = (1/2)\(\int[a, b] r^2 d\theta\)

A = 0 and b = 2 in this instance. The radius at every given angle is represented by the function r = 18sinθ, which must be squared to get r².

We can now determine the area:

A = (1/2) \(\int[0, 2\pi] (18sin\theta)^2 d\theta\)

Simplifying the integrand:

A = (1/2) \(\int[0, 2\pi] 324sin^2\theta d\theta\)

Using the trigonometric identity sin²θ = (1/2)(1 - cos2θ):

A = (1/2) \(\int[0, 2\pi] 324(1/2)(1 - cos2\theta) d\theta\)

A = (1/4) \(\int[0, 2\pi] (162 - 162cos2\theta) d\theta\)

Integrating term by term:

A = (1/4) [162θ - 81sin2θ] evaluated from 0 to 2π

Plugging in the limits:

A = (1/4) [(162(2π) - 81sin(4π)) - (162(0) - 81sin(0))]

Simplifying further:

A = (1/4) [324π - 0 - 0 - 0]

A = (1/4) (324π)

Finally, we can calculate the area:

A = 81π

Therefore, the area of the circle r = 18sinθ in polar coordinates is 81π square units.

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Answer:

$60

Step-by-step explanation:

Answer:

5 and -15

Step-by-step explanation:

5 × -15 is -75.

5 + -15 is -10

Answer:

$1.47 per yard

Step-by-step explanation:

3 feet = 1 yard

9 feet = 3 yards

set up a proportion

\(\frac{3}{4.41} = \frac{1}{x}\)

cross multiply; 3x = 4.41 * 1

3x = 4.41

divide both sides by 3

x = 1.47

$1.47 per yard

The polynomial function with rational coefficients that has the roots -6, 3, and -15i is P(x) = x⁴ + 9x³ + 225x² + 486x - 8100.

A polynomial function with rational coefficients that has the given roots -6, 3, and -15i, we can use the concept of complex conjugate roots. Since -15i is a root, its conjugate 15i is also a root.

The polynomial can be formed by multiplying the linear factors corresponding to each root:

(x - (-6)) × (x - 3) × (x - (-15i)) × (x - 15i)

Simplifying:

(x + 6) × (x - 3) × (x + 15i) × (x - 15i)

To remove the complex numbers, we can multiply the conjugate pairs:

(x + 6) × (x - 3) × ((x + 15i) × (x - 15i))

(x + 6) × (x - 3) × (x² - (15i)²)

(x + 6) × (x - 3) × (x² + 225)

Expanding:

(x + 6) × (x³ - 3x² + 225x + 6x² - 18x - 1350)

(x + 6) × (x³ + 3x² + 207x - 1350)

Finally, multiplying further:

x⁴ + 3x³ + 207x² - 1350x + 6x³ + 18x² + 1242x - 8100

Simplifying and combining like terms:

P(x) = x⁴ + 9x³ + 225x² + 486x - 8100

Therefore, the polynomial function with rational coefficients that has the roots -6, 3, and -15i is P(x) = x⁴ + 9x³ + 225x² + 486x - 8100.

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Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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