Given f(x) = x³- 6x2 - 13x + 42, which statements are true? Select all that apply.

A. f(2)= 0, therefore (x + 2) is a factor of f(x).

B.f(2)= 0, therefore (x - 2) is a factor of f (x).

C. (x+3) is a factor of f (x) because f (x) divided by (x+3) has a remainder of 0.

D.(x-3) is a factor of f (x) because f (x) divided by (x-3) has a remainder of 0.

E.(x + 7) is a factor of f (x).

F. (x-7) is a factor of f(x).

Answer:14 cm

Step-by-step explanation:

 The value of r should be greater than 8 in order for the area of the shaded region to be greater than 12.

An inequality is an inequation separated by <,>≥,≤

Given here:  A rectangle with dimensions r and 3 units

Thus area of the square is given by a=3r

Now area of the shaded region is given by

3r-1/2 ×3×r where ( 1/2×3×r is the area of the non-shaded triangle)

3r-1.5r

1.5r

Again the area of the shaded region is given by

1.5r>12

r>8

Hence,  The value of r should be greater than 8 in order for the area of the shaded region to be greater than 12.

Learn more about inequality here:

https://brainly.com/question/28823603

#SPJ1

The correctly expresses that algorithm in pseudocode

numFreezing ← 0

numDays ← 0

FOR EACH temp IN temps

IF (temp ≤ 32)

{numFreezing ← numFreezing + 1}

{numDays ← numDays + 1}

DISPLAY(nonfreezing/numDays)

For this situation, Pseudocode B would be appropriate. Two variables are created by this code for the overall number of days (numDays) and the number of freezing days (nonfreezing). Then, it does a loop over the complete collection of data to determine whether each temperature is less than or equal to 32 degrees.

If so, it adds it to nonfreezing; otherwise, it skips the step while still increasing the number of days after each loop by 1. Contrary to answer A, which prints the ratio after each loop iteration, this answer only prints the ratio once the loop has been completed.

numFreezing ← 0

numDays ← 0

FOR EACH temp IN temps

IF (temp ≤ 32)

{numFreezing ← numFreezing + 1}

{numDays ← numDays + 1}

DISPLAY(nonfreezing/numDays)

Know more about algorithm

https://brainly.com/question/24953880

#SPJ4

The full question:

A programmer for a weather website needs to display the proportion of days with freezing temperatures in a given month.

Their algorithm will operate on a list of temperatures for each day in the month. It must keep track of how many temperatures are below or equal to 32. Once it's done processing the list, it must display the ratio of freezing days over total days.

Which of these correctly expresses that algorithm in pseudocode?

Step-by-step explanation:

There are two curves on this graph. One that is higher than the other. The higher one is the max and the lower one is the min

Let's find the coordinate of the higher one. Looks like it's at (2,3). This means The function has a maximum of 3 at x=2

The lower on is the same process. Looks like that ons is at (-3,-2). This means The function has a minumum of -2 at x=-3

The slope of the tangent line is 12.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, a function f(x) = 3x²+1, has a rate of change at x = 2

We are asked to calculate the instantaneous rate of change and slope of secant,

Instantaneous Rate of Change

We can approximate to the value of the slope of one function P(x) by computing the slope of the secant line as:

m = f(x+Δx) - f(x) / Δx

Where Δx is an infinitesimal change of x, as small as we want.

The given function is = f(x) = 3x²+1

Let Δx = 0.1

m = f(2+0.1) - f(2) / 0.1

= 14.23 - 13 / 0.1

= 12.3

Now we use a smaller infinitesimal or differential

Δx = 0.01

m = f(2+0.01) - f(2) / 0.01

= 0.1203 / 0.01

= 12.03

We can see the slope is getting closer to 12 as the infinitesimal tends to 0,

Hence, we can estimate the slope of the tangent line is 12

Learn more about slope, click;

https://brainly.com/question/3605446

#SPJ1

The solution to the inequality is 1/3 ≤ x < 7

For the first inequality:

2x + 1 ≤ 5x

Solving for x:

2x + 1 - 5x ≤ 0

-3x + 1 ≤ 0

-3x ≤ -1

x ≥ 1/3

For the second inequality:

3x + 5 > 4x - 2

Solving for x:

3x + 5 - 4x + 2 > 0

-x + 7 > 0

x < 7

The set of all real numbers that satisfy both inequalities is:

1/3 ≤ x < 7

Graphically, this is represented on the number line

|----|---|---|---|---|---|---|---|---|---|

1/3                                        7

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Based on the information, it can be inferred that the required numbers are 1010 and 1313.

To find the required numbers we must find the HCF, that is, the highest number by which these two numbers can be divided (303 and 101). We have tried this procedure with different numbers as shown below:

Once we have these digits, we must find the numbers whose difference is 303; these numbers are 1010 and 1313.

Learn more about High Common Factor in: https://brainly.com/question/25299251

#SPJ1

Answer:

101,168

Step-by-step explanation:

The value of 6 in the given number 35,629 is the hundreds value.

35,629.

You are trying to find a number in which the number 6 is in 1/10th of the value of the original number. In this case, divide the hundreds value by 10:

100/10 = 10

Place the value 6 in the tens digit place value for any number.

101,168 can be a answer choice.

Learn more about place values, here:

https://brainly.com/question/27734142

The amount of the discount 10% on this bill is, $11.767

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

Discount  amount 10%  =  117.67x10/100

                                      =  11.767

Hence, the discount amount is $11.767

To know more about Percentage check:

brainly.com/question/29306119

#SPJ1



The probability that an event will occur is determined by the likelihood of each possible outcome and the number of possible outcomes.

In this scenario, the binomial variable is the number of wins for the two people with equal skills playing a game for 50 days.

The probability of success (a win) is the same for each game, and the number of trials is fixed at 50, making this a binomial experiment.

Probability is the measure of how likely it is that an event or outcome will occur. It is usually expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that it is certain to occur. The probability that an event will occur is determined by the likelihood of each possible outcome and the number of possible outcomes.

Learn more about probability

https://brainly.com/question/28185528

#SPJ4

Complete question:

A binomial variable in the context of this scenario would be the number of wins out of 50 games, since there are only two outcomes that can occur: a win or a loss.

Answer: The machine packs 10 sandwiches in 3 minutes, so it packs 10/3 = 3.33 sandwiches per minute.

Step-by-step explanation:

The machine packs 10 sandwiches in 3 minutes, so it packs 10/3 = 3.33 sandwiches per minute.

To pack 100 sandwiches, it would take 100/3.33 = 30 minutes, or 30/60 = 0.5 hours.

Answer:

10:3

100:?

10*10=100

3*10=30

100:30

Step-by-step explanation:

Answer:

lets say you decide to take three part-time jobs: Work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour. What will your average hourly wage be? Enter your answer up to two decimal places. its on edmentum.

For this it's going to be 13.75. The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job): 0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.

Answer:

Step-by-step explanation:

I'll do the first part for you:

The number of 3/4 in 2 is [tex]=2/\frac{3}{4}[/tex]

That is the division equation.  Rearrange it to make the multiplication equation.  keep...change...flip.  Change the division to a multiplication and flip the fraction:

The number of 3/4 in 2 =[tex]=2.\frac{4}{3}[/tex]

Answer:

21

Step-by-step explanation:

15 ≤10

15 ≤12

15 ≤14

15 isn't less or equal to 10, neither is 12 and 14.

Answer:

y=2x+9

Step-by-step explanation:

Point of intersection of y=3 & x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]y=2x+6+3

y=2x+9

Answer:

15/20

Step-by-step explanation:

5students=a

10students=b

15/20

please tell me if i got it right

Answer:

40 hot dogs and 90 sodas were sold at the football game.

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations. Let's use:

➽"x" to represent the number of hot dogs sold

➽"y" to represent the number of sodas sold

We are given the following information:

♦The total revenue from hot dogs and sodas is $300.

♦The number of sodas sold is 10 more than two times the number of hot      dogs sold.

From this information, we can create the following equations:

▷[tex]\tt{3x + 2y = 300}[/tex] (The total revenue from hot dogs and sodas)

▷[tex]\tt{y = 2x + 10}[/tex] (The number of sodas sold is 10 more than two times the    number of hot dogs sold)

Now, we can solve this system of equations using the substitution method. Substitute the second equation into the first equation:

Simplify and solve for x:

Now that we have the number of hot dogs sold (x = 40), we can find the number of sodas sold by substituting x back into the second equation:

So, 40 hot dogs and 90 sodas were sold at the football game.

________________________________________________________

Number of hot dogs sold = 40

Number of sodas sold = 90

The school earned $300 in total, this confirms our answer.

Learn more on how to solve system of equations

↳https://brainly.com/question/31856581

#BTH1

________________________________________________________

The clock, which is equal to 30 cm multiplied by pi (3.14), or 94.2 cm, in one hour.

Clock is an instrument used to measure and indicate time. It is one of the oldest human inventions, measuring time in units of seconds, minutes, hours, days, weeks, months, and years. Clocks are used in many different contexts, including to regulate the timing of activities, to measure the duration of events, to indicate the time of day, to give a signal at a specific time, and to keep track of time.

The tip of the minute hand of a circular clock moves around the circumference of the clock in one hour. The circumference of the clock is equal to the diameter of the clock multiplied by pi (3.14). The diameter of the clock is equal to twice the length of the minute hand, or 30 cm. Therefore, the tip of the minute hand moves around the circumference of the clock, which is equal to 30 cm multiplied by pi (3.14), or 94.2 cm, in one hour.

To learn more about clock
https://brainly.com/question/24051741
#SPJ1

The vertex is (21, 125210)

The vertex shows that the overall value of home in 21 years after 2020,i.e., in 2041 is 125210 dollars.

What is quadratic equation in math?

A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.            

                         Equations with quadratic terms are another name for them. The quadratic equation is expressed in its general form as ax2 + bx + c = 0. When the numerical coefficients a, b, and c are present and x is an unknown variable.

The overall value of a home is modeled by

v(x) = 210x²-4400x+125000

This is a quadratic function which is of the form ax²+bx+c ⇒ x²+(b/a)x+(c/a)

The vertex of a quadratic function is the point where the rate of change of function is zero.

x-coordinate of the vertex is given by (-b/2a) and the y-coordinate is the corresponding y-value to the x-coordinate of the vertex.

Hence here, x-coordinate = -(-4400/210) = 20.95 ≈ 21

y-coordinate = 210 x 21²-4400 x 21+125000 = 125210

The vertex is (21, 125210).

The vertex shows that the value of home in 21 years after 2020,i.e., in 2041 is 125210 dollars.

Learn more about the quadratic equation

brainly.com/question/30098550

#SPJ1

The nearest tenth of a year, about 11 years 5 months  long will it be until the value of the car is 7900 dollars

For $25,000, a brand-new car is bought. The automobile loses 14% of its value annually.

x=6.3.

Using the conditions stated, come up with:

20500 . 1 - 14% x 7900

Determine the difference or total:

First, we convert R percent to r a decimal,

which is 14%/100, which is 0.14 each year. Next, we solve for t by using the ratio

(1/0.14)(20500/7900) - 1),

which gives us 11.39 years.

At a basic interest rate of 14% per year, it will take 11.39 years to accumulate a total of $20,500.00 from the principle and interest on a $7,900.00 starting point (about 11 years 5 months).

To learn more about interest rate refer to:

https://brainly.com/question/25793394

#SPJ1

Answer: 6.3

Step-by-step explanation: just because

Answer:

18%

Step-by-step explanation:

Celia=100%-Mark-Juan-Mary

Celia=100%-36%-29%-17%

Celia=100%-82%

Celia=18%

Answer: 5,211 dollars

Step-by-step explanation: Our first approch to this is to find the number of Gala and Honeycrisp(HC) Trees are there.

We are given the number of total trees (81 trees) and the ratio between Gala and HC trees  (5 to 4). This means for every set of 9 trees, 5 will be Gala and 4 will be HC. We can create the equation

9x = 81

5x = number of gala trees

4x = number of HC trees

x represents the number of sets of 9 trees so in this case, there will be 9 sets if you solve for x.

9x = 81

divide both sides by 9

x = 9

We can plug this back into the 2 other equations that represent the number of each tree so

5(9) = 45 gala trees,

4(9) = 36 HC trees

This makes sense since 45+36 = 81 so it adds up

Now to find the amount of money just take the amount of each trees we have and multiply it by the pounds each tree made then multiply it by the price each pound makes.

45 gala trees * 25 pounds * 1.52 dollars = 1,710 dollars

and

36 HC trees * 25 pounds * 3.89 dollars = 3,501 dollars

Finally, add both of them up to get the total profit

1,710 + 3,501 = 5211 dollars

Answer:

To find the measures of each angle, we first need to determine the total measure of all three angles in the triangle. Since the sum of the measures of the angles in any triangle is 180 degrees, we can find the total measure of all three angles by multiplying the ratio 2:5:3 by 180.

We can find the total measure of all three angles by using the rule of three.

2/5+5/3+3/2 = 180/x

Solving for x:

x = 1802532/ (2+5+3) = 180*60/10 = 1080

So, the total measure of all three angles is 1080 degrees.

Then, we can find the measure of each angle by multiplying the fraction of the ratio that represents that angle by the total measure of all three angles.

The measure of the first angle is: 2/10 * 1080 = 216 degrees

The measure of the second angle is: 5/10 * 1080 = 540 degrees

The measure of the third angle is: 3/10 * 1080 = 324 degrees

By integration by parts, the integral ∫ 4 · x · e³ˣ dx = (4 / 3) · x · e³ˣ - ∫ (4 / 3) · e³ˣ dx is an alternative form of integral ∫ 4 · x · e³ˣ dx. (Correct choice: A)

Herein we find the case of an integral of a product of two functions that cannot be integrated by means of a single integral and algebraic substitution, this can be found alternatively by definition of integration by parts:

∫ u dv = u · v - ∫v du

First, define functions u and dv:

u = 4 · x

dv = e³ˣ dx

Second, find functions du and v:

du = 4 dx

v = (1 / 3) · e³ˣ

Third, find the alternative integral equation:

∫ 4 · x · e³ˣ dx = (4 / 3) · x · e³ˣ - ∫ (4 / 3) · e³ˣ dx

To learn more on integration by parts: https://brainly.com/question/1550271

#SPJ1

The value vt= 305 shows the distance travelled.

Given:

If a car travels at a constant speed of v miles per hour for t hours, it will travel vt miles.

we have v= 61 and t= 5

So, vt = 61 x 5 = 305

As, we know from the formula

speed = distance/ time

distance = speed x time

here speed= v, time= t

So, the value vt= 305 represents the distance travelled when speed is 61 and time is 5.

Learn more about Speed- distance here:

https://brainly.com/question/12759408

#SPJ1

The situations described are A : subjective, B : classical, C : empirical, D : subjective and E : empirical.

In Classical probability, probability of an event is found using the basic probability formula assuming the outcomes in a sample space are equally likely.

In Empirical probability, experiment is actually done and record the outcomes.

In subjective probability, probability is based completely on the intuition or guess.

A : Recruiters are making a wild guess that there is an 80% chance that remote hiring will increase in 2023. This is a subjective probability.

B : This is classical probability because the probability is found by the basic formula, Number of nurses divided by total number of medical employees = 10/20 = 0.50.

C : This is an empirical probability because the experiment of survey is already done to find that there is a 73% chance that a randomly selected adult will say that he/she is playing games on mobile phones.

D : This is a subjective probability because the climate change expert made a educated guess.

E : This is an example of empirical probability because, the probability is known according to the Sharaf DG records.

Hence the situations are classified as classical empirical and subjective probability.

Learn more about Classical, Empirical and Subjective Probability :

https://brainly.com/question/29776548

#SPJ1

The cartesian equation and domain and range will be Domain: - 2 ≤ x ≤ 2;

Range:  - 2 ≤ y ≤ 2;

We square the following equations to obtain the cartesian equation, and then we add:

Suppose that P0 has coordinates x0,y0,z0, and n has components a,b, and c. Let P, with coordinates x,y, and z, be an arbitrary point on the plane. A Cartesian equation of the plane is what this is. in which d is a constant ax0 + by0 + cz0.

x2(t) = 4cos2(t), y2(t) = 4sin2(t).

So, x2 + y2 = 4(cos2(t) + sin2(t)), or x2 + y2 = 4

We have a circle with a radius of two and a center at the origin.

Domain: - 2 ≤ x ≤ 2;

Range:  - 2 ≤ y ≤ 2;

Know more about Cartesian equation

https://brainly.com/question/14869452

#SPJ4

The full and correct question would be:

find the cartesian equation and domain and range of this

For the pair of parametric equations below, eliminate the parameter to find its Cartesian equation. Also, specify the domain and range of your equation using interval notation.

x(t)=2cos(t)

y(t)=2sin(t)

The total amount earned by Kedar is $2285.1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Kedar's salary is $2200. The commission amount is 3.7%. The total earnings will be calculated as:-

Total earning = 2200 + ( 4500 - 2200 ) x 0.037

Total earning = 2200 + 85.1

Total earning = $2285.1

Therefore, the total amount earned by Kedar is $2285.1.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ1

4 thread of 2(1/7) inches can be made from 8(3/4) inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Thread = 2(1/7) inches

Total length = 8(3/4) inches

The number of 2(1/7) inches thread.

= 8(3/4) ÷ 2(1/7)

= 8(3/4) / 2(1/7)

= 35/4 x 7/15

= 7/4 x 7/3

= 49/12

= 4.08

= 4

Thus,

4 thread of 2(1/7) inches can be made.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1