f(x) = x(x - 1)

g(x) = 3x

Find: (f* g)(6)


54

540

27

264

Answer:

The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!

Answer:

-6 > x

Step-by-step explanation:

First, no matter which variable and coefficient you move, you will be dividing by a negative in the end, so reverse the inequality symbol when your answer is found. Next, you move whichever term [NOT associated with a variable (negative or positive)] is near the variable and coefficient over to the left or right side of the inequality symbol depending on where they are in the inequality. Finally, you divide by the negative coefficient it gives you, and you will arrive at your answer with your inequality symbol reversed. The answer just happens to be written in reverse. Although it is written in reverse, it is still the same answer.

I hope this helps you understand the concept, and as always, I am joyous to assist anyone at any time.

Answer:

Attached

Step-by-step explanation:

The equation for the graph is

c(x)=3x+2

rewrite as

y=3x+2.............................................(1)

Then graph equation to visualize as attached.

Let the x-axis to represent minutes and the y-axis to represent cost

Answer:

The graph of required function is shown below.

Step-by-step explanation:

The given function is

[tex]c(x)=3x+2.00[/tex]

In this function c(x) is the cost for a taxi ride and x is the number of minutes.

It means, in the graph of cost function x-axis represents the time in minutes and y-axis represents the cost.

Time can not be negative. So, the function is defined for all non-negative values of x.

Table of values:

x            c(x)

0            2.00

1             5.00

2            8.00

3            11.00

Plot any two points from these points on a coordinate plane and connect them by  straight line.

Therefore, the graph of required function is shown below.

Step-by-step explanation:

The expected value is the sum of each outcome times its probability.

E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)

E = 34125

The store is expected to gain $34,125.

To calculate the expected gain or loss for the new store, we multiply each possible outcome by its probability, then sum these values. This results in an expected gain of $34,125 for the store.

The problem requires calculating the expected value of the coffee franchise's new store opening. We use probability and finance to estimate the expected gains or losses.

The expected value (EV) is calculated as follows:

Multiply each outcome by its respective probability.

Sum these products to get the EV.

So, the expected value is:

EV = (0.70 imes $50,000) + (0.05 imes $0) + (0.25 imes -$3,500)

EV = $35,000 + $0 - $875

EV = $34,125

This implies an expected gain of $34,125 for the new store.

Answer:

g(x) is option 1 or g(x) = (x + 7)^2 + 5

A quadratic equation has the general form of:

y=ax² +bx + c

It can be

converted to the vertex form in order to determine the vertex of the parabola.

It has the standard form of:y =a(x+h)² + k

where hand k represents the vertex, h represent the point in the x axis and k is thepoint in the y axis. Therefore, from the details given in the problem, the equation that represents

g(x) is option 1 or g(x) = (x + 7)^2 + 5

Answer:

Part 1) The solution of the absolute value is  (-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

Part 2) The graph in the attached figure

Step-by-step explanation:

we have

[tex]\left|2x+4\right|>8[/tex]

we know that

The absolute value has two solutions  

step 1

Find the positive case

[tex]+(2x+4)>8[/tex]

[tex]2x>8-4[/tex]

[tex]2x>4[/tex]

[tex]x>2[/tex]

The solution is the interval ----> (2,∞)

All real numbers greater than 2

step 2

Find the negative case

[tex]-(2x+4)>8[/tex]

Multiply by -1 both sides

[tex](2x+4)<-8[/tex]

[tex]2x<-8-4[/tex]

[tex]2x<-12[/tex]

[tex]x< -6[/tex]

The solution is the interval ----> (-∞,-6)

All real numbers less than -6

therefore

The solution of the absolute value is

(-∞,-6)∪ (2,∞)

Number line with open circles on negative 6 and 2, shading going in the opposite directions

step 3

using a graphing tool

see the attached figure

Answer:

Option A. 93.5°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

∠C=(1/2)[83°+2(52°)]

∠C=(1/2)[83°+104°]

∠C=(1/2)[187°]

∠C=93.5°

Answer:

Yes

Step-by-step explanation:

To be a solution of the system, it has to satisfy both the equations.

Let's check first one:

3x - 2y = -1

3 (1) - 2(2) = 3 - 4 = -1

So correct (satisfies).

Now, 2nd one:

y = -x + 3

y = -(1) + 3

y = -1 +3

y = 2

Yes, this is satisfied.

Hence, (1,2) IS A SOLUTION OF THE SYSTEM

Answer:

C. Right isosceles

Step-by-step explanation:

We have 2 angles that are the same, that means two sides have to be the same.  That makes the triangle isosceles

There are 3 angles in a triangle.  They add to 180

45+45+x = 180

90+x=180

90-90+x=180-90

x=90

The other angle is a 90 degree angle.  A ninety degree angle is a right angle.

That makes the triangle a right isosceles triangle

Answer: 3347.005 users but you cant divide people in half so its 3347 people

Answer0< x<10

Step-by-step explanation: it says reasonable so this is one of the few time it’s not all positive integers cause it’s a real world question and it’s from 2000 to 2010 so 10 years is the REASONABLE domain for this problem

Answer:

10 squared units

Step-by-step explanation:

This triangle is pretty easy since it creates a right triangle.  So the base length and height length are pretty easy to identify.

The area of a triangle is .5*base*height.

The base length after drawing the points is a horizontal so just count it or do 4-0=4.

The height length after drawing the points is a vertical so just count it or do 4-(-1)=4+1=5.

So the area of the triangle is .5*4*5=.5(20)=10 units squared.

Now if you didn't fill like drawing it and you knew how to find the determinant.

You just compute

.5 times det|  0   -1     1  |

                   |  0   4      1  |

                   |   4  -1      1  |

.5[  0 det| 4     1  |          -   -1 det|  0   1 |          +    1 det | 0   4 |      ]

              |  -1    1  |                        |  4   1 |                         |  4  -1 |

.5[ 0                           - -1(0-4)                      +   1(0-16)]

.5[  0                         -4                               -16]

.5[-20]

-10

And if you get a negative just take the absolute value of it giving you 10.  

For this case we have from the first quadrant that:

[tex]70 + A1 = 90[/tex]

Clearing angle 1:

[tex]A1 = 90-70[/tex]

[tex]A1 = 20\ degrees[/tex]

Ahors, the angle A3 of the third quadrant measures 70 degrees, it is observed that it is opposed by the vertex at the angle of 70 degrees of the first quadrant. So:

[tex]A3-A1 = 70-20 = 50[/tex]

Answer:

Option B

In order to calculate the percentage you must:

1. Divide 15.6/20.8

2. Your answer will be 0.75

3. Turn this into a fraction 75/100

4. Now turn it into a percent 75%

75% is your answer.

Answer:

-1/3 is the slope perpendicular

Step-by-step explanation:

When we have 2 points, we can use the formula

m = (y2-y1)/(x2-x1) to find the slope

m = (1-7)/(3-5)

   =-6/-2

    =3

The slope is 3

We want a slope perpendicular

Remember that is the negative reciprocal

- (1/3)

-1/3

Two lines are perpendicular when,

[tex]a_1=-a_2^{-1}[/tex]

Now solve for [tex]a_2[/tex] to get [tex]a_2=-a_1^{-1}[/tex]

First we calculate the slope [tex]a_1[/tex] from the given points [tex]E(x_1,y_1),F(x_2,y_2)\longrightarrow E(5,7),F(3,1)[/tex].

[tex]a_1=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3[/tex]

Now use the first formula and insert the data in it to find the value of the second slope [tex]a_2[/tex],

[tex]a_2=-3^{-1}=\boxed{-\dfrac{1}{3}}[/tex]

And that's it.

Hope this helps.

r3t40

Answer:

The x-term inside the radical has a negative coefficient

Step-by-step explanation:

The argument of a square root should be ALWAYS greater or equal to zero. If the domain of the function is x<7, rearranging, we have: 0<x-7

Therefore the argument is: x-7, and the function is: y = √(x-7)

The statement "The x-term inside the radical has a negative coefficient" is the right answer.

Answer: 10

Step-by-step explanation:

if we know a-b=5, to get the answer of 2(a-b) multiply 5 by 2.

Answer:

10

Step-by-step explanation:

a-b=5

Multiply each side by 2

2(a-b) = 2*5

2 (a-b) = 10

Answer:

C). This is an example of causation

Step-by-step explanation:

Causation : It can be defined as the one event is the result of the other event. It is simply the cause and its effect. There is a causal relation between the two events.

Correlation : It can described the direction of the relation between two or more events or variables.

The conclusion of the experiment is that the plant that received more than two hours of sunlight in each day grew more than the plants that received less than two hours of sunlight in each day.

This is the cause of one event and its effect on the other event.

So option C is correct because sunlight causes plants to grow.

So option C). This is an example of causation.

Answer:

C( This is an example of causation

Answer:

58 in^2.

Step-by-step explanation:

This is the sum of the area of 4 small rectangles + the area of the 2 larger  rectangles

= 2*4*1 + 2*5*1 + 2*4*5

=  8 + 10 + 40

= 58 in^2

Answer:

58in^2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Add

2 plus 3 equals 5

Step-by-step explanation:

so put two fingers up and then put three up then you get your answer.

Answer:

22 cm, 24 cm, and 24 cm.

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 70 cm. Therefore, in this question, since the sides are unknown, we can assume that:

Length of the shorter side = x cm.

Length of the other sides = y cm.

The relationship between x and y is given by:

x = (2y - 26) cm (because it is mentioned that the shortest side is 26 cm less than twice as long as the other sides).

Perimeter of a triangle = sum of all sides.

Since its an isosceles triangle, therefore:

Perimeter of the triangle = x + 2y.

Substituting the values in the perimeter formula gives:

Perimeter of the triangle = 2y - 26 + 2y.

70 = 4y - 26.

4y = 96.

y = 24 cm.

Substituting y = 24 in the equation x = 2y - 26 gives x = 2(24) - 26 = 22 cm.

So in the ascending order, the lengths are 22 cm, 24 cm, and 24 cm!!!

Answer:

A root of f(x) is x=5

Step-by-step explanation:

If (x-5) is a factor of f(x), then 5 is a root.

If (x+5) is a factor of f(x), then -5 is a root.

So we are only given that (x-5) is a factor of f(x), so we only know that x=5 is a root.

This is by factor theorem. It says if (x-c) is a factor then f(c)=0 which means c is a root of f(x) because it makes the expressions equal to 0.

G -1/6= 1/6

Move -1/6 to the other side

sign changes from -1/6 to 1/6

G-1/6+1/6=1/6+1/6

G = 2/6

Reducing: divide by 2 for 2/6

2/2= 1

2/6= 3

Answer : G= 2/6= 1/3

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=adjacent\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ \sqrt{61^1-11^2}=a\implies \implies \sqrt{3600}=a\implies 60=a[/tex]

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=\dfrac{5}{2}x+2&(1)\\2y=5x+8&(2)\end{array}\right\\\\\text{substitute (1) to (2)}:\\\\2\left(\dfrac{5}{2}x+2\right)=5x+8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)\left(\dfrac{5}{2}x\right)+(2)(2)=5x+8\\\\5x+4=5x+8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\4=8\qquad\bold{FALSE}\\\\\text{The system of equations has no solution.}[/tex]

Answer:

The patient must take [tex]2\frac{1}{2}\ tablets[/tex] per day

Step-by-step explanation:

we know that

12 1/2 grains (gr) of aspirin is equal to 12.5 grains

using proportion

Let

x -----> the number of aspirin tablets

[tex]\frac{1}{5} \frac{tablet}{gr} =\frac{x}{12.5} \frac{tablets}{gr} \\ \\x= 12.5/5\\ \\x=2.5\ tablets[/tex]

Convert to mixed number

[tex]2.5=2\frac{1}{2}\ tablets[/tex]

Answer:

Step-by-step explanation:

The ax+by+c=0 that is confusing you is just the standard form of a linear equation. It is supposed to help you formulate the linear equation. In this case, a = 1, b = -2, c = 1

Therefore,

1x -2y + 1 =0

Now, you said that you are confused on how to isolate and solve for one variable; in this case, you can't. But, you can switch around the places of the variables to solve for one variable. In this case, its best to solve for y, since linear equations are easier to understand written in Slope-intercept form:

y = mx+b

Now, you must be really confused, but look at the work I am about to do so you can learn how to make this easier for you!

1x -2y + 1 =0

-1x             -1x   --> Subtract 1x from both sides to isolate the y variable to the               left side and to keep the equation balanced

-2y + 1=0 -1x

       -1             -1   --> Subtract 1 from both sides to isolate the y variable further and to keep the equation balanced

-2y = -1x-1  

(-2y/-2) = ((-1x-1)/-2)  --> Divide by -2 on both sides to isolate the y variable even further and to keep the equation balanced

y = 1/2x+1/2

y = mx+b

This is written in slope-intercept form. It is called as such since it gives you the slope (written in front of the x variable,in this case 1/2; m = 1/2) and the y-intercept (the letter b; in this case b = +1/2). The y-intercept is where the x coordinate is equal to zero, but it is the place where the line crosses the y-axis. So your b = 1/2, which means that your y-intercept is (0, 1/2)

These are all things you use to graph a line and helps to make it easier to graph them!

Final Answer:

Answer:

-16 cents

Step-by-step explanation:

We are given that on  three rolls of a single​ die, you will lose ​$19 if a 3 turns up at least​ once, and you will win ​$5 otherwise.

We are to find the expected value of the game.

P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = [tex]1-(\frac{3}{6} )^2[/tex] = 0.875

P (other results) = 1 - 0.875 = 0.125

Random game value = -19, +5

Probabilities: 0.875, 0.125

Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents

Therefore, every time you play the game, you can expect to lose 16 cents

Answer:

It is expected to lose 5.10 dollars

Step-by-step explanation:

The probability of getting a 3 by throwing a die once is 1/6.

By throwing it 3 times the probability of not getting a 3 is:

[tex]P=(\frac{5}{6}) ^ 3 =0.5787[/tex]

Then the probability of obtaining a three at least once in the 3 attempts is:

[tex]P'=(1-0.5787)=0.421[/tex]

So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:

[tex]E(X)=P'*(X') + P*(X)[/tex]

[tex]E(X) =0.421'*(-19) + 0.5787*(5)\\\\E(X) =-\$5.10[/tex]