For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.
3x +8
7x
f(x)=
8x - 3: 9(x) =
8x-3

Answer:

○ \(\displaystyle \textcolor{black}{C.}\:triangle\)

Explanation:

This is a triangular prism. Its faces are triangular, but the lateral faces are rectangular. All prisms will have lateral faces shaped as rectangles. Do not ever forget this.

I am joyous to assist you at any time.

The product of the monomial 4x and the polynomial 3x²y + 7xy⁴ is 12x³y + 28x²y⁴.

The product of a monomial and a polynomial is as follows:

Step 1: multiply the monomial with each term in the polynomial

Step 2: Check for any like terms, if present adds or subtract them as per their sign.

Step 3: thus, we get the product.

The given monomial is 4x and the polynomial is 3x²y + 7xy⁴.

So, their product is

4x × (3x²y + 7xy⁴) = 4x(3x²y) + 4x(7xy⁴)

⇒ (4×3)(x × x²)(y) + (4×7)(x × x)(y⁴)

⇒ 12x³y + 28x²y⁴

Since there are no like terms and do not need any further simplification, the given product is 12x³y + 28x²y⁴.

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Answer:

B.37.68

Step-by-step explanation:

lets say pi is 3.14

12 x 3.14

37.68

The transformation of f(x) that will produce g(x) is f(x) = 4(x+2)^2.

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

Answer: x=20

Step-by-step explanation:

The two angles provided are vertical angles.

Vertical angles are equal in measurement.

This means we can set (3x+50) and (6x-10) equal to each other and solve for x

\(3x+50=6x-10\)

Add 10 to both sides

\(3x+50=6x-10\\3x+50+10=6x-10+10\\3x+60=6x\)

Subtract 3x from both sides

\(3x-3x+60=6x-3x\\60=3x\)

Divide both sides by 3

\(\frac{60}{3} =\frac{3x}{3} \\20=x\)

Answer:

Step-by-step explanation:

(3x + 50)° = (6x - 10)°

3x - 6x = -50 - 10

3x = -60

\(\frac{-3x}{-3}\) = \(\frac{-60}{3}\)

x=20°

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

The value of third side should be lesser than the the sum of other two sides ~

\(\qquad \sf  \dashrightarrow \:x < 2.8 + 2.8\)

\(\qquad \sf  \dashrightarrow \:x < 5.6\)

and, value of third side should also be greater than the difference of other two sides ~

\(\qquad \sf  \dashrightarrow \: x> 2.8 - 2.8\)

\(\qquad \sf  \dashrightarrow \:x > 0\)

Now, combine the two inequalities, we will get ~

\(\qquad \sf  \dashrightarrow \:0 < x < 5.6\)

I hope you got the required Answer ~

Answer:

3.375 or 3 3/8 or 27/8 (all the same answer just in different forms)

Step-by-step explanation:

3/8 x 9 (or 9/1)

nose si entendí bien el problema pero espero poder ayudar

Step-by-step explanation:

8 es igual a 100%, por lo que podemos guardarlo como 8 = 100% El valor que buscamos puede llamarse x Ahora sabemos que xes 72 del valor de salida, por lo que podemos escribirlo como x = 72. Así que tenemos dos ecuaciones simples: 1) 8=100% 2) = 72%Cuando comparamos estas dos ecuaciones, obtenemos: 8 / x = (100%) / (72%)Ahora solo tenemos que resolver la ecuación simple. Nosotros calculamos 72 por ciento de 8: 8 / x = 100/72(8 / x) * x = (100/72) * x8 = 1,3888888888889 * X8 / 1.3888888888889 = X5.76 = xx = 5,76

Hillary's bakery makes vanilla cakes.

She uses 18 eggs for 7 cups of sugar.

Now to find the ratio of eggs to cups of sugar.

Since there 18 eggs for each 7 cups of sugar, the required ratio is 18:7

Hence the answer is

B 18:7

The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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The horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

The noise that sounds at the end of a segment is A horn blows.

In geometry, a segment is a part of a line that connects two points.

For example, line segment AB, which is denoted by AB, connects point A and point B and can be visualized as a portion of a line.

In general, line segments are denoted by their endpoints.

A horn is a cone-shaped instrument that is often used as a warning signal or a musical instrument.

However, it is important to note that noise can occur at the end of a segment in certain contexts and situations.

For example, in the context of audio or video editing, you can apply fade-out effects or specific sound effects to signal the end of a segment.

However, these sounds are not universally applicable and depend on the specific creative choices and technical aspects of the project.

In the transportation sector, horns are commonly used to alert pedestrians and other drivers of an oncoming vehicle's presence.

The sound of a horn is usually a sharp and loud noise that is difficult to ignore.

As a result, horns are frequently used as a signal to indicate the end of a segment or a specific task. Hence, a horn blows is the noise that sounds at the end of a segment.

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Answer:

\(-3 \le h \le 1\).

Step-by-step explanation:

Apply the property of absolute values: if \(a \ge 0\), then \(|x| \le a \iff -a \le x \le a\). By this property, \(|- 3\, h - 6 | \le 3\) is equivalent to \(-3 \le -3\, h - 6\le 3\). That's the same as saying that \(-3\, h - 6 \ge -3\) and \(-3\, h - 6 \le 3\).

Add \(6\) to both sides of both inequalities:

\(-3\, h \ge 3\) and \(-3\, h \le 9\).

Divide both sides of both inequalities by \((-3)\). Note that because \(-3 < 0\), dividing both sides of an equality by this number will flip the direction of the inequality sign.

Both inequalities are supposed to be true. Combining the two inequalities to obtain:

\(-3 \le h \le 1\).

Answer:

yes

Step-by-step explanation:

The answer is "are" because it adds 3 each time!!! =)

Answer: yes

Step-by-step explanation: the answer is “are” because in the y column you add 3 to each one so it is proportional.

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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kyle regalara 16 figuras y le quedara 3/4 de ellas

Answer:

f(x) = cos(x)

Step-by-step explanation:

In a cos wave, y value is -1 when x value is pi

Answer:

minium:-2................

The function f(x) = 4x² – 16x + 6 has a minimum value is –10 when the value of x is 2. Then the correct option is B.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given below.

\(f(x) = 4x^2 -16x + 6\)

Differentiate the function, then we have

\(\dfrac{d }{dx} f(x) =\dfrac{d}{dx}(4x^2 -16x + 6) \\\\ \dfrac{d }{dx} f(x) =8x - 16 \\\)

The value of x will be

\(8x - 16 = 0\\x = 2\)

Then again differentiate the function, if the value comes negative then maxima and if the value is positive then minima.

\(f''(x) = \dfrac{d }{dx} f'(x) \\\\f''(x)=8x - 16 \\\\f''(x) = 8\\\\ f''(x) > 0\)

Then the function is minimum at 2.

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Answer:

\(\ S=\sqrt{\dfrac{3V}{H}}}\)

Step-by-step explanation:

The opposite operation of squaring is taking the square root.

\(\ S=\sqrt{\dfrac{3V}{H}}}\)

We know that the denominator of a fractional power is the index of the corresponding root:

\(\displaystyle x^\frac{1}{n}=\sqrt[n]{x}\)

For n=2, we don't usually write the index in the root symbol:

\(x^{\frac{1}{2}}=\sqrt{x}\)

In the case of this problem, ...

\((S^2)^{\frac{1}{2}}=\left(\dfrac{3V}{H}\right)^{\frac{1}{2}}\\\\S=\sqrt{\dfrac{3V}{H}}\)

Rewrite the function using the change-of-base identity as

\(e^{x^2} \log_{10}(2x) = e^{x^2} \dfrac{\ln(2x)}{\ln(10)}\)

Apply the product rule:

\(\left(e^{x^2} \log_{10}(2x)\right)' = \left(e^{x^2}\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \left(\dfrac{\ln(2x)}{\ln(10)}\right)'\)

Use the chain rule:

\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(x^2\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac{(2x)'}{2\ln(10)x}\)

Compute the remaining derivatives:

\(\left(e^{x^2} \log_{10}(2x)\right)' = 2xe^{x^2} \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac2{2\ln(10)x} = e^{x^2}\left(\dfrac{2x\ln(2x)}{\ln(10)} + \dfrac1{\ln(10)x}\right)\)

If you like, you can convert back to base-10 logarithms:

ln(2x) / ln(10) = log₁₀(2x)

1 / ln(10) = ln(e) / ln(10) = log₁₀(e)

Then

\(\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(2x\log_{10}(2x)+\frac{\log_{10}(e)}x\right)\)

I'm confused can u tell me the question in comments

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).

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The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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Answer:

It will take Ramona 25 months or 2 years and 1 month to pay back for the car.

The number of people in the set C ∩ D (customers who purchased both cats and dogs) is obtained by adding the overlap of D and C (3) with the overlap of all 3 circles (1), resulting in a total of 4 individuals.

The correct answer is 4.

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to analyze the overlapping regions in the Venn diagram.

Given information:

- Circle C (cats): 15

- Circle D (dogs): 21

- Circle F (fish): 12

- Overlap of C and F: 2

- Overlap of F and D: 0

- Overlap of D and C: 3

- Overlap of all 3 circles: 1

- Number outside of circles: 14

To determine the number of people in the set C ∩ D (customers who have purchased both cats and dogs), we need to consider the overlapping region between circles C and D.

From the information given, we know that the overlap of D and C is 3. Additionally, we have the overlap of all 3 circles, which is 1. The overlap of all 3 circles includes the region where customers have purchased cats, dogs, and fish.

To calculate the number of people in the set C ∩ D, we add the overlap of D and C (3) to the overlap of all 3 circles (1). This gives us 3 + 1 = 4.

Therefore, from the options given correct one is 4.

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Answer: 4

Step-by-step explanation:

trust me bro

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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