-4x+36 the coefficient term

Answers

Answer 1

Answer:

-4

Step-by-step explanation:

The coefficient is the number that multiplies the variable.

To find the coefficient, you'll see it right next to the variable.

Here, x is the variable.

-4x, -4 is right next to x, so it's the coefficient

:)

Answer 2

\(\bold{Hello~!}\)

♡ »»————- \({\huge{\underline{\bf{\pink{Miwsow~is~going~to~help~your~homework~!}}}}}\) ————-«« ♡

✩ ANSWER :\(= 4(-x~+~9)\)✰ EXPLANATION :

\(\sf{Factor}~- 4x~+~36:~4(-x~+~9)\)

\(\sf{-4x~+~36}\)

\(\sf{Rewrite~36~as~4}\) · \(\sf{9}\)

\(\sf{-4x~+~4}\) · \(\sf{9}\)

\(\sf{Factor~out~common~term~4}\)

\(\sf{= 4(-x~+~9)}\)

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\(\underline{Answer~:}\)

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Related Questions

The solutions to the equation 2x + x-1 = 2are X= -3/2 or x=
PLEASE HELP FAST

Answers

Answer:

1

Step-by-step explanation:

2x^2 + x -1 = 2

2x^2 + x-1-2 = 0

2x^2 + x -3 = 0

2x^2 -2x + 3x-3 = 0

2x(x-1) + 3(x-1) = 0

(2x + 3)(x-1) = 0

2x + 3 = 0

or x-1 = 0

x = -3/2 or 1

6. what are the two most generic and widely used valuation multiples?

Answers

The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.

1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.

A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.

2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).

The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.

The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.

Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.

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A cylinder has a radius of 7​ inches and a height of 9​ inches Find the exact volume of the cylinder.

Answers

To find the volume of a cylinder, we need to know its radius and height. Let's use the given values:

- Radius = 7 inches

- Height = 9 inches

The formula to find the volume of a cylinder is:

V = πr^2h

Where:

- V = Volume

- r = Radius

- h = Height

- π = 3.14 (pi)

Substituting the values in the formula, we get:

V = π(7 inches)^2(9 inches)

Simplifying the equation, we get:

V = π(49 inches^2)(9 inches)

V = 1539.75 cubic inches (approx)

Therefore, the exact volume of the cylinder is 1539.75 cubic inches.

hello! again... im so confused on this. could someone please help me figure out the answer + explanation? tysm!

hello! again... im so confused on this. could someone please help me figure out the answer + explanation?

Answers

Let’s first start with what is the parent function of a quadratic: f(x) = x^2.

Then, to get to x^2 + 1, the parent function was basically moved up by 1 on a graph.

To go from that equation to the h(x) function just follow the rules. Anything inside of a parentheses followed by a square is the opposite of what it actually is. So if you have (x - 8)^2, you’re moving the parent function 8 units to the right, instead of the left. If it’s (x + 8)^2, you are moving to the left 8. Anything outside of the parentheses that is being subtracted or added is moving the parent function down or up, respectively. Therefore, when it tells you + 5 at the end, that just means, up 5. Then if there is a negative out in front of the entire equation like you see there, it is being reflected over the x - axis. Then, the number being multiplied—in this case 3/4– is either a vertical compression or a vertical stretch. If the number is bigger than 1, it is a vertical stretch. If the number is smaller than one, it is a vertical compression.

All in all:

Vertical compression of 3/4
Vertical translation 4 units up
Reflection across the x - axis
Horizontal translation 8 units right

If you’re confused on anything, send me a comment or PM :)

What is the probability of getting 5 out of 20 numbers?

Answers

Answer:

Step-by-step explanation:

The number of events is 5 (since there are 5 red marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%.

Find the missing side.
X
34° 12
X x = [?]
Round to the nearest tenth.
Remember: SOHCAHTOA

Find the missing side.X34 12X x = [?]Round to the nearest tenth.Remember: SOHCAHTOA

Answers

Answer: 8.1

Step-by-step explanation:

Tangent is opposite over adjacent.

tan(34)=x/12

0.6745=x/12

x=12*0.6745

x=8.0941

x=8.1

the sum of a number and 4

Answers

{4,8,3,7,2,6,1,5,9}

There ^

Step-by-step explanation:

A situation where mtDNA might be used is what?
A. When there is a large amount of nuclear DNA
B. On the teeth and bones of skeletonized human remains
C. On a victim who has just died
D. When blood is present at the scene​

Answers

On the teeth and bones of skeletonized human remains is one instance where mtDNA might be used. Therefore (B) would be the correct answer.

Mitochondria are organelles in cells that transform food energy into a form that cells can use. There are hundreds to thousands of mitochondria per cell, and they are found in the fluid surrounding the nucleus (the cytoplasm). Although mitochondria have a small amount of their own DNA, the majority of DNA is contained in chromosomes within the nucleus. The term "mitochondrial DNA," or "mtDNA," refers to this genetic material. A small portion of the total DNA in cells, mitochondrial DNA in humans is made up of about 16,500 DNA base pairs.

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The probability that a student chosen at random from a class has brown
hair is 7/13
The probability that they have ginger hair is 5/26
What is the probability that a student chosen from the class at random has
either brown hair or ginger hair?
Give your answer as a fraction in its simplest form.

Answers

Answer:

5/26+7/13

5/26+14/26

19/26

The probability that a student chosen from the class at random has either brown hair or ginger hair is 19/26.

Given that, the probability that a student chosen at random from a class has brown hair is 7/13 and the probability that they have ginger hair is 5/26.

Probability that student have either brown hair or ginger hair

= 7/13 + 5/26

= 14/26 + 5/26

= (14+5)/26

= 19/26

Therefore, the probability that a student chosen from the class at random has either brown hair or ginger hair is 19/26.

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in the market for milk portrayed in this figure, which price yields an efficient outcome?

Answers

The efficient outcome in the market for milk portrayed in the figure would be where the marginal cost (MC) curve intersects with the demand (D) curve, which is at a price of $3 per gallon.


To determine which price yields an efficient outcome in the market for milk, we need to find the equilibrium price. The equilibrium price is where the supply and demand curves intersect, which represents the point at which the quantity demanded equals the quantity supplied.

                                At this price, the quantity of milk produced and consumed will be at the socially optimal level where the marginal benefit (MB) equals the MC, resulting in a Pareto efficient outcome. It is important to note that this assumes no externalities or market failures are present in the market for milk.

1. Identify the supply and demand curves in the figure. The demand curve typically slopes downward, while the supply curve slopes upward.
2. Locate the point where the supply and demand curves intersect.
3. Find the price corresponding to this point on the vertical axis (price axis).

The equilibrium price found in step 3 is the price that yields an efficient outcome in the market for milk.

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A cyclist rode 3.75 miles in 0.3 hours. How fast was she going in miles per hour? Round your answer to the tenths (first) decimal place.

Answers

Answer:

12.5 miles per hour

Step-by-step explanation:

The speed is the distance divided by time.

3.75 miles/0.3 hours= 12.5 miles per hour

Answer:

12.5 miles per hour

Step-by-step explanation:

To answer this question you have to make sure that the hours (denominator) equals to 1. To do this, divide 3.75 by 0.3, thus making the 0.3 hours into 1 hour. This results in 12.5 miles per hour, the correct answer. Hope this helped!

me ter [mee-ter] n
1. a unit of length equal to 39.37 inches
2. a device used to measure
3. the rhythm of music across time
4. the process of determining how much postage is
needed to mail a letter
Based on the sentence, which definition best describes
how the word "meter" is used in this sentence:
“My dad asked me to hold the meter while he turned
the dial."
* a unit of length equal to 39.37 inches
O a device used to measure
o the rhythm of music across time
o the process of determining how much postage is
needed to mail a letter

Answers

Answer:

B.) A device used to measure

Step-by-step explanation:

me·ter [mee-ter] n

1. a unit of length equal to 39.37 inches

2. a device used to measure

3. the rhythm of music across time

4. the process of determining how much postage is needed to mail a letter

With these defintions we can know that when the sentence says “My dad asked me to hold the meter while he turned the dial" ,so she is holding the object of measurement while her dad is moving the device ,so with this your answer is B.).

to investigate whether the consumption of beetroot juice enhances exercise performance, a researcher selected a random sample of 50 student athletes from all the student athletes at a college. the athletes in the sample were randomly assigned to one of two groups. in one group, 25 athletes were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily dose of a placebo. at the end of six weeks of exercise training, the researcher compared the performances of the two groups. based on the design of the investigation, which of the following is the largest population to which the results can be generalized?
(A) The 25 student athletes assigned to the beetroot juice group (B) The 50 student athletes in the sample (C) All student athletes at the college (D) All students at the college (E) All people who exercise

Answers

The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.

Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.

We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.

All the other options are wrong because of this reason.

Therefore, option C is correct.

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what is answers in 2 this items help me please​

what is answers in 2 this items help me please

Answers

1) missing number is 7 (answer #2)

Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)

20 minus 10 minus 3 is 7, so that's the missing number.

2) missing number is 3 (answer #4)

This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)

10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!

Hopefully this helps!

please help me with this

please help me with this

Answers

Answer:

x = -9, y = 8

or,

(-9, 8)

Explanation:

Equation 1: 2x + 3y = 6

Equation 2: 4x - y = -44

To solve by substitution, make y subject for equation 2.

4x - y = -44

-y = -44 - 4x

y = 4x + 44

Substitute this y value into equation 1.

2x + 3(4x + 44) = 6

2x + 12x + 132 = 6

14x = 6 - 132

14x = -126

x = -9

Now, find y value:

y = 4x + 44

y = 4(-9) + 44

y = 8

To check for solution, insert x and y value in either equations.

2x + 3y = 6

insert values

2(-9) + 3(8) = 6

6 = 6

Hence, the solution is correct as both sides equal.

Answer:

Therefore x = -9 and y = 8.

Step-by-step explanation:

Substitution method

Equation (1) 2x + 3y = 6

Equation (2) ——— 4x - y = -44

When using substitution method , make x the subject of equation (1).

2x + 3y = 6

2x = 6 - 3y

x = 3 - 3y/2

Substitute the value of x in equation (2) to find y.

4(3 - 3y/2) - y = -44

12 - 6y - y = -44

Subtract 12 from both sides.

12 - 12 - 7y = -44 - 12

-7y = -56

y = 8

Substitute the value of y in equation (1) to find x.

2x + 3y = 6

2x + 3(8) = 6

2x +24 = 6

Subtract 24 from both sides.

2x + 24 - 24= 6 - 24

2x = -18

x = -9

Therefore x = -9 and y = 8.

To check out the solution.

Equation (1) 2x + 3y = 6 , x = -9 , find y.

Substitute the value of x

2(-9) + 3y = 6

-18 + 3y = 6

Add 18 to both sides.

-18 + 18 + 3y = 6 + 18

3y = 24

y = 8

Substitute the value of y in equation (1) .

2x +3(8) = 6

2x + 24 = 6

Subtract 24 from both sides.

2x + 24 - 24 = 6 -24

2x = -18

x = -9

As you can see when you substitute the value of x and y in the equation(1) , you get the same value of x and y ,which is -9 and 8 respectively. So the solution is correct.

the nth term of this sequence: 1/2,4/3,9/4,16/5
URGENT

Answers

Answer: \(\frac{n^{2} }{n+1}\)

Step-by-step explanation:

The numerator (top digit) are squares. For example,

1 is \(1^{2}\)

4 is \(2^{2}\)

9 is \(3^{2}\)

and so on.

The bottom digit increases by one.

Therefore, the Nth term would be that number (N) squared on the numerator, and n+1 on the denominator.

Help please if you don’t mind!!
Thankyou so much

Help please if you dont mind!!Thankyou so much

Answers

Answer:

Step-by-step explanation:

\(F = \frac{9}{5}C+32\)

Subtract 32 from both sides

\(F-32= \frac{9}{5}C\\\)

Multiply both side by 5/9

\(\frac{5}{9}(F-32)=( \frac{5}{9})* \frac{9}{5}C\\\\ \frac{5}{9}(F-32)=C\\\)

F= 41

\(\frac{5(41-32)}{9}=C\\\\ \frac{5*9}{9}=C\\\\ \frac{45}{9}=C\\\\C = 5\\\\\)

41° F = 5° C

HELPP PLSSS IM REALLY STUCKKKK

HELPP PLSSS IM REALLY STUCKKKK

Answers

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HELPP PLSSS IM REALLY STUCKKKK

Pls answer soon, question is on pic

Pls answer soon, question is on pic

Answers

The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

How to write the inequality that models the situation?

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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The mode is ...
A) the middle number in a numerical data set when the values have been arranged in
numerical order.
B) the number or numbers occurring most frequently in a data set.
C) a measure of dispersion.
D) The difference of the highest value and lowest value in the data set.

Answers

The answer is B) the number or numbers occurring frequently in a data set. The mode is a measure of central tendency that represents the most common value or values in a data set.

Maximize 3x + 4y + 3z on the sphere x² + y2 + z2 = 16. A) There is no maximum. B) The maximum is -434 c) 2034 The maximum is – 17

Answers

Using Lagrange multipliers, The maximum value of f(x, y, z) subject to the constraint x² + y² + z² = 16 is 17√2, which is approximately 24.04. Option C is the correct answer.

To solve this problem, we will use Lagrange multipliers. We want to maximize the function f(x, y, z) = 3x + 4y + 3z subject to the constraint g(x, y, z) = x² + y² + z² = 16. We can write the Lagrangian as:

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z) - 16)

= 3x + 4y + 3z - λ(x² + y² + z² - 16)

We need to find the values of x, y, z, and λ that satisfy the following equations:

∂L/∂x = 3 - 2λx = 0

∂L/∂y = 4 - 2λy = 0

∂L/∂z = 3 - 2λz = 0

∂L/∂λ = x² + y² + z² - 16 = 0

From the first three equations, we can solve for x, y, and z in terms of λ:

x = 3/2λ

y = 2/λ

z = 3/2λ

Substituting these values into the equation x² + y² + z² = 16, we get:

(3/2λ)² + (2/λ)² + (3/2λ)² = 16

Solving for λ, we get:

λ = ±2

Substituting these values into the equations for x, y, and z, we get the following critical points:

(2√2, √2, 2√2)

(-2√2, -√2, -2√2)

We need to evaluate the function f(x, y, z) = 3x + 4y + 3z at these critical points to determine which one gives the maximum value. We get:

f(2√2, √2, 2√2) = 3(2√2) + 4(√2) + 3(2√2) = 17√2

f(-2√2, -√2, -2√2) = 3(-2√2) + 4(-√2) + 3(-2√2) = -17√2

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one point geometry contains just one point and not line. which incidence axioms does one point geometry satisfy? explain.

Answers

Since there are no lines in one point geometry, none of the incidence axioms are satisfied because all of them need multiple points and lines.

what is multiply?

Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.

Choosing two out of four is a combination issue since the order is irrelevant (no indication concerning order is given in the problem). A sample of A, B is equivalent to a sample of B, A if the population of 4 is A, B, C, and D.

There are 4C2 = 6 potential samples.

For such a tiny population, you may also list all potential samples as "A, B," "A, C," "A, D," "B, C," "B, D," and "C, D."

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1. Differentiate the function f(x) = ln (81 sin^2 (x)) f’(x) 2. Differentiate the function P(t) = in ( √t2 + 9) p' (t) 3. if x2 + y2 + z2 = 9, dx/dt = B, and dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)
dz/dt =

Answers

First you will get 4dz

Each of the following is an open sentence, where n denotes an integer. For which integers n are the following sentences true statements? (a) P (n): |n - 2| = 3
(b) P2(n): 2n2 – 5n + 2 = 0 (c) P3(n): n²> 0 (d) P4(n): n3 = 2n (e) Ps(n) : Inl + In - 1| + In - 2| = 3

Answers

The open sentence has integers that are true: (a) |n - 2| = 3, (b) 2n² – 5n + 2 = 0, (c) n² > 0, (e) |Inl + In - 1| + In - 2| = 3 and (d) n³ = 2n is false.

To determine the true value of open sentences involving integers, we can use the concept of substitution. We substitute each possible integer value into the open sentence and determine whether the resulting statement is true or false.

(a) For the first function substitute -1 and 5 into the expression |n-2|=3 and find that both result in a true statement.

The open sentence P(n): |n-2| = 3 is true for n = -1 and n = 5.

(b) For the second function substitute 1/2 and 2 into the expression 2n² - 5n + 2 = 0 and find that both result in a true statement.

The open sentence P2(n): 2n² - 5n + 2 = 0 is true for n = 1/2 and n = 2.

(c) Third function is a universally true statement, as n² is always positive for any integer except n = 0.

The open sentence P3(n): n² > 0 is true for all integers n except for n = 0.

(d) For the fourth function substitute 2 into the expression n³ = 2n and find that it results in a true statement.

The open sentence P4(n): n³ = 2n is true for n = 2 and false for all other integers.

(e) For the fifth function we need to consider several cases depending on the sign of Inl + In-1 and In-2. By systematically considering each case and the corresponding value of n, we find that the statement is true only for n = 2, 3, and 4.

The open sentence Ps(n): |Inl + In - 1| + |In - 2| = 3 is true for n = 2, 3 and 4.

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if alpha and beta are zeroes of x2-3x+q. what is the value of q, if 2 alpha+3 beta=15

Answers

The value of q is -27.

Recall Vieta's Formulas, which state that for a quadratic equation \(ax^2\) + bx + c = 0 with zeroes alpha and beta, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.

In our equation \(x^2\) - 3x + q, the sum of the zeroes alpha and beta is -(-3)/1 = 3.

We are given that 2 alpha + 3 beta = 15. Substitute alpha = (15 - 3 beta)/2 into the equation.

Replace the value of alpha in the sum of zeroes equation: (15 - 3 beta)/2 + beta = 3.

Simplify the equation by multiplying both sides by 2: 15 - 3 beta + 2 beta = 6.

Combine like terms: 15 - beta = 6.

Subtract 15 from both sides: -beta = -9.

Multiply both sides by -1 to solve for beta: beta = 9.

Substitute the value of beta into the sum of zeroes equation: alpha = (15 - 3 * 9)/2 = -3.

Since we have the values of alpha and beta, we can find q using the product of the zeroes formula: q = alpha * beta = -3 * 9 = -27.

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Look at the table showing different prices for cans of soup.

Prices for Soup
Price A
Price B
Price C
$3.87 for 3
$2.38 for 2
$8.75 for 7

Answers

The prices in order from greatest to least unit rate is Price A>Price C>Price B.

Given a table that showing different prices for cans of soup as shown in attached image.

Here, we will calculate the price of 1 quantity of each type of soup.

The Price of 3 quantities of soup price A=$3.87

Now, we will find the price of soup A for the 1 quantity.

The Price of 1 quantity of soup price A=$3.87/3=$1.29

The Price of 2 quantities of soup price B=$2.38

Now, we will find the price of soup B for the 1 quantity.

The Price of 1 quantity of soup price B=$2.38/2=$1.19

The Price of 7 quantities of soup price C=$8.75

Now, we will find the price of soup C for the 1 quantity.

The Price of 1 quantity of soup price C=$8.75/7=$1.25

Hence, the prices in order, from greatest to least unit rate from the given table which is shown in attached image is Price A>Price C>Price B or $1.29>$1.25>$1.19.

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you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?

Answers

LHL is equal to RHL then limit exist

LHL is not equal to RHL then limit does not exist.

As per the given data the graph of the function is given

Here we have to determine the limit at the indicated value of a, if it was exists.

You may have found the limit from one side instead of from both sides as notated.

Now we have to find:

\($\lim _{x \rightarrow a} f(x)$\) when a = 1

We find the left hand side limit and the right hand side limit at a = 1

So,

The Left hand limit is \($\lim _{\mathrm{x} \rightarrow 1^{-}} \mathrm{f}(\mathrm{x})=\frac{3}{2}$\)

The Right hand limit is \($\lim _{x \rightarrow 1^{+}}\) f(x) = 3

Here \($\lim _{x \rightarrow 1^{-}} f(x) \neq \lim _{x \rightarrow 1^{+}} f(x)$\)

Hence \($\lim _{x \rightarrow a}\) f(x) = DNE

From the graph we find the left hand limit and the right hand limit:

If Left hand limit = Right hand limit then limit exist

If then Left hand limit ≠ Right hand limit then limit does not exist.

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Use the graph of the given function f to determine the limit at the indicated value of a, if it exists.(If an answer does not exist, enter DNE.)

Graph attached at the end of solution

you may have found the limit from one side instead of from both sides as notated. how might you consider the limit as x approaches a from both sides?

you may have found the limit from one side instead of from both sides as notated. how might you consider

Please help me pick which ones they are. Thank you!

Please help me pick which ones they are. Thank you!
Please help me pick which ones they are. Thank you!

Answers

The correct answer for the transformation will be:

translation up π/4

vertical stretch by 2

translation right π/4

How to explain the information

The parent function of g(x) is y = sin(x), and g(x) is obtained from the parent function by performing the following transformations:

Translation: The argument of sin(x) is shifted by π/4 units to the left, which results in a horizontal translation to the right by π/4 units.

Vertical stretch: The amplitude of the sine function is multiplied by 2, which results in a vertical stretch by a factor of 2.

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There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Answers

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Given f(x) = (x - 1)(x + 2)(x − 3), what are the zeros and end behavior of the function?

Answers

A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x) = (x - 1)(x + 2)(x − 3), therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.

Hence, the zeroes of the functions are -2, 1, and 3.

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Given f(x) = (x - 1)(x + 2)(x 3), what are the zeros and end behavior of the function?

Answer:

−1, 2, −3; continues downward to the left and upward to the right

Step-by-step explanation:

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