pls help me i will mark brainliest:)
Simplify −5g(3g + 4).

−15g + 4

−15g − 20g

−15g2 + 4

−15g2 − 20g

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

222

Step-by-step explanation:

The diameter is always radius squared. Therefore, the answer is:

111 + 111 = 222

1) the supply and demand schedule for Blue-ray movie "Frozen is attached accordingly.

Equilibrium price and quantity are $20 and 40 units respectively.

2) At a price of $30, quantity demand  and supplied are 20 and 60 units respectively

This is an example of supply surplus.

To get the price back to equilibrium, they have to setthe price at $20 /unit

3) at $10 the quantity demand and supplied are 60 units and 20 units respectively.

This is an example of supply shortage.

increasing the price to $20 per unit will help achieve equilibrium.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.

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The option that is not true about polynomial functions is:

Option D. The deg (f ^ 3) = 3m​

For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:

Option A: deg(f + g) = max(m, n)

This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.

Option B: deg(f * g) <= m + n

This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.

Option C: If g is a factor of f, then deg(f) <= m

This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.

D. The deg(f ^ 3) = 3m

This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.

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\(p(t)=1650e^{0.11t}\implies \stackrel{p(t)}{2479}=1650e^{0.11t}\implies \cfrac{2479}{1650}=e^{0.11t} \\\\\\ \log_e\left( \cfrac{2479}{1650} \right)=\log_e\left( e^{0.11t} \right)\implies \log_e\left( \cfrac{2479}{1650} \right)=0.11t \\\\\\ \ln\left( \cfrac{2479}{1650} \right)=0.11t\implies \cfrac{ ~~ \ln\left( \frac{2479}{1650} \right) ~~ }{0.11}=t\implies 3.7\approx t\)

at that moment, the population will reach 2479, and right after that, it'll exceed it.

\(\text{A}_{\square}=\text{a}^2\\\\a\longrightarrow\text{x}+1\\\\\text{A}_{\square}=(\text{x}+1)^2=(\text{x}+1)(\text{x}+1)=\text{x}^2+\text{x}+\text{x}+1=\boxed{\text{x}^2+2\text{x}+1}\)

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

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Answer:

240

Step-by-step explanation:

The average rate of a function f(x) is interval [a,b] is given by :-

R = (f(b) - f(a)) / (b-a)

Now, the given function : F(x) = 4(5)^x

Interval : [1,3]

Now, the average rate of change over the interval [1, 3]  is given by :-

R = F(3) - F(1) / (3 - 1)

= 4(5)^3 - 4(5)^1 / 2

= 4(5^3 - 5) / 2

= (4(125 - 5) / 2) = 240

Hope It helped

that Solving for the retail price of a parrot with 20% markup and 3% taxes

We want to know the retail price of a parrot if it costs us $159.95 , knowing that we want to obtain 20% of profit and we're getting taxed 3%

Firts, we have to calculate the 20% of the original value ($159.95), and add that up. Then, we calculate the 3% of that value ($159.95 + 20% markup) and add it up, asl following:

Thus, the retail price of the parrot, with 20% markup and 3% taxes, should be $197.70

The dimensions listed above are thus neither exact nor precise.

In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.

It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.

The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.

The dimensions listed above are thus neither exact nor precise.

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Answer:

A. Similar triangles

Step-by-step explanation:

Triangle ABC

35° + 90° + x = 180°

125° + x = 180°

x = 180° - 125°

x = 55°

They are similar due to the occurrence in angles

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

the height of the flag = 12cm

Step-by-step explanation:

inclide ladder length = 15m (hypotenuse)

distance between ladder foot and flag foot= 9m (base)

according to Pythagoras theorem,

(h)^2 = (p)^2 + (b)^2

(15)^2 = (p)^2 + (9)^2

(p)^2 = (15)^2 - (9)^2

(p)^2 = 225-81

p = √144

p= 12 cm

Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.

A discount is an amount that reduces the price of a retail item.

Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.

Discount rate on offer = 20%

Discounting factor = 80% or 0.8 (100 - 20%)

Manufacturer's coupon off the price = $200

Let the price of the bureau = x

The price after the discount (discounted price) is given by D(x)

D(x) = 0.8x

The price after the coupon = C(x) = x - 200

The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200

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Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).

The statement is true because 4 × 30%=120

In the first month, the price of the avocado is said to have been raised by 30 percent.

While already raised by 30 percent, another 30 percent raise would make the increase to be 60 percent.

While is at 60 percent, the third month the raise would be = 90 percent because 30 * 3 = 90

Then at 90 percent if there is another raise of 30 percent, the increase would grow to be 120 percent.

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Answer:

A. y = 3/2x

B. you need 3 chocolate squares and 2 graham crackers to make 1 smore

C. 0, 0 chocolate squares and 0 graham crackers make 0 smores

Step-by-step explanation:

A. rise/run = 3/2

B. slope = 3/2

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

The correct answer is  (f + g)(x)= -5x²-9x+11.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

you have two functions f(x) and g(x) the sum of them f(x) + g(x) is represented as (f + g)(x)

then if our functions are f(x) =2-9x,

and g(x) = -5x² + 9

then (f + g)(x)

= f(x) + g(x)

= -5x²-9x+11

Hence, The correct answer is -5x²-9x+11.

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Answer:

try -8/-5 -10

Step-by-step explanation:

The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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Answer:

5

Step-by-step explanation:

if u add al of these it equals 35 divided by 7 equals 5

Answer:

$2.25

Step-by-step explanation:

Red: $2

Blue: $6

Green: $6 + $5 (original cost of game) = $11

Yellow: $20

The total number of slots on the spinner is 4, with one slot for each color. Since the spinner can land on any color with equal probability, the probability of it landing on each color is 1/4 or 0.25.

Therefore, the expected value of the game is:

(0.25 x $2) + (0.25 x $6) + (0.25 x $11) + (0.25 x $20) - $5 = $2.25

Answer:

\(\dfrac{90}{341}\)

Step-by-step explanation:

3rd grade:

Number of girls = 16

Number of boys = 15

Total number of students = 31

4th grade:

Number of girls = 15

Number of boys = 18

Total number of students = 33

Formula for probability of an event E can be observed as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

Probability of picking a boy from 3rd grade, \(P_{1} = \dfrac{15}{31} ..... (1)\)

Probability of picking a boy from 4th grade, \(P_{2} = \dfrac{18}{33} ..... (2)\)

These are two independent events of picking a boy from 3rd grade and 4th grade.

So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.

\(P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}\)

Answer:

a

Step-by-step explanation: