Mathematics College

Let R(x)=3x^3+2x^2+x and S(x)=4+1. Find R(x) * S(x)

Pls help!!!!

Let R(x)=3x^3+2x^2+x And S(x)=4+1. Find R(x) * S(x) Pls Help!!!!

Answers

Answer 1

3x^3 x 4x^2 = 12x^5

3x^3 x 1 = 3x^3

2x^2 x 4x^2 = 8x^4

2x^2 x 1 = 2x^2

1x x 4x^2 = 4x^3

1x x 1 = 1x

12x^5 + 3x^3 + 8x^4 + 2x^2 + 4x^3 + 1x

Simplify

12x^5 + 7x^3 + 8x^4 + 2x^2 + 1x

Thus, answer is B

Hope this helps!

Related Questions

Which relation is also a function
{(2,0),(3,2),(2,3)}

Answers

3,2

because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.

In an olimpiad , each of the 25 questions is worth 3 marks. So every correct answer is awarded 3 marks. But for every incorrect answer 1 mark is subtracted. lesley scored 55 marks out of a possible 75. how many problems did leley get correct.

Answers

An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.

The total number of questions can be written as,

x + y = 25

Solving the equation for y,

y = 25 - x

The total marks can be written as,

3x - 1y = 55

Substitute the value of y,

3x - 25 + x = 55

4x = 80

x = 20

Hence, the number of questions that Lesley answered correctly is 20.

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what term is defined by the formula b^2 = a^2 + c^2 - 2ac(cosB)

Answers

Answer:

It is cosine theorem

Step-by-step explanation:

It is cosine theorem.

Which inequality does the shaded region correspond to?

Answers

Answer:

y < x + 1

Step-by-step explanation:

identify 2 points along the line (-1,0) and (0,1)

gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]

let us choose point (0,0) which is within our origin and substitute

0 = 0 +1

0 = 1

but we know 0 < 1

so the region is well represented by : y < x + 1

Answer:

y > x + 1

Step-by-step explanation:

→ As the line is upward sloping we can eliminate the 2 negative equations options

y < x + 1 or y > x + 1

→ As the region shaded is above the line y = x + 1, it must be y > x + 1

Convert 3 tons, 569 pounds into pounds

Answers

Answer:

6,569 pounds

Step-by-step explanation:

Ton= 2,000 pounds each

Therefore, 3 x 2,000 (pounds) = 6,000(pounds). You can use a shortcut by multiplying 3 x 2 and adding the three zeros at the end. 6,000 pounds + 569 pounds will result in 6, 569 pounds.

What is an equation of the line that passes
through the point (5,
-2) and is parallel
to the line 2x
- 5y = 35?

Answers

2x-2y

parallel means that the x part is the same

and it is -2y because the y-coordinate is -2

given the function f(c)=4|x-5|+3, for what values of x is f(x)=15?

Answers

All you have to do is plug in 15 to f(x) to get

15=4|x-5|+3 then solve for x
12=4|x-5|
3=|x-5|

3=x-5
-3=x-5

x=8, -2

Hope this helped :)

Find the volume of a rank 5cm long, breadth 5cm and height 5cm

Answers

Answer:

125cm³

Step-by-step explanation:

To find volume, we multiply length × width × height

(length × breadth × height)

here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm

length : 5cm

width/breadth: 5cm

height: 5cm

so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)

length × width × height

5  ×   5  ×  5= 125

*note: we write volume as cubed (unit³)

So, we know our volume is 125cm³

hope this helps! have a lovely day :)

Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.

StartFraction 5 Over 6 EndFraction divided by 10

Which expression is equivalent to Balin’s expression?

Answers

The expression that is equivalent to  Balin's expression is 5/6 x 1/10.

What is the equivalent expression?

Division is the mathematical operation that is used to determine the quotient of a number.

In order to determine the distance ran by each member, divide the total distance ran by the total number of people.

5/6 ÷ 10

5/6 x 1/10

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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10

Division of fraction

Combined distance = 5/6 mileNumber of Balin’s soccer team = 10

Distance each member ran = Combined distance ÷ Number of Balin’s soccer team

= 5/6 ÷ 10

= 5/6 × 1/10

= 5/60

= 1/12 mile

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The linear function has the domain (-2, -1, 0, 1, 2). Find the range or output of. h(x) = 2x + 3

Answers

If the linear function has the domain (-2, -1, 0, 1, 2). Then the range of the function h(x) = 2x + 3 will be (-1, 1, 3, 5, 7).

What are domain and range?

The domain means all the possible values of x and the range means all the possible values of y.

The function is given as

h(x) = 2x + 3

The linear function has the domain (-2, -1, 0, 1, 2).

For x = -2

h(-2) = 2 (-2) + 3

h(-2) = -1

For x = -1

h(-1) = 2 (-1) + 3

h(-1) = 1

For x = 0

h(0) = 2 (0) + 3

h(0) = 3

For x = 1

h(1) = 2 (1) + 3

h(1) = 5

For x = 2

h(2) = 2 (2) + 3

h(2) = 7

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find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x2-y2 and 2xy

Answers

The expression for hypotenuse is √4x^4 + y^4.

What is Pythagoras theorem?

A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.

Given:

one leg = 2x²- y²

another leg = 2xy

H² = (2x²- y²)² + (2xy)²

H² = 4x^4 + y^4 - 4x²y² + 4x²y²

H²= 4x^4 + y^4

H= √4x^4 + y^4

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2 factored expressions equivalent to -20x-30

Answers

The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression

What are Expressions ?

Expressions are the mathematical statement consisting of variables , constants and mathematical operators .

The expression given is

-20x -30

-2(10x +15)

-20x -30

-5x ( x+6)

Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.

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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second. What does point I represent in this context?

CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah.

Explanation: Point I is on line b, so it does represent Chana's distance at a certain time. Also, point I is below line a, so it represents a distance that is less than Josiah's distance.

Answers

The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.

How to solve for the line B

The point I is the distance of Chana at a particular point in time. This distance is the line a.

At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.

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Maria is going to purchase celery and onions for a new black bean soup recipe. The recipe calls for 1.5 times as many pounds of onions as celery. If she has $8.10, what is the most pounds of celery she can buy if celery costs $1.80 per pound and onions cost $1.50 per pound?

Answers

The maximum pounds of celery she can buy is  3.25 pounds.

What are the linear equations that represent the question?

1.5c = o equation 1

1.50o + 1.80c = 8.10 equation 2

Where:

o = pounds of onions

c = pounds of celery

How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1

1.50(1.50) + 1.80c = 8.10

2.25 + 1.80c = 8.10

1.80 = 8.10 - 2.25

1.80c = 5.85

c = 5.85 / 1.80

c = 3.25 pounds

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Which table represents a linear function?
X
1
2
34
y
3 1/1/2
O
777772
X
1
2
3
4
O
11121314
X1234
y
X1234
7
6
13
21
y
0
6
16
30

Answers

Answer:

2

Step-by-step explanation:

The first table represents the linear function.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The first table represents a linear function because the slope remains constant through out the function

Hence, the first table represents the linear function.

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For the pair of
functions, f and g, determine the domain of f + g.
f(x) = 4x + 19, g(x) = 12x + 14

Answers

Answer: (-∞,∞)

Step-by-step explanation:

f(x)=4x+19

g(x)=12x+14

f + g=  4x +19 + 12x + 14 = 16x + 33

Domain of 16x + 33 = (-∞,∞)

On a coordinate plane, a line goes through points (negative 2, negative 2) and (4, 2).The graphed line can be expressed by which equation?

Answers

Answer:

y=⅔m-8 or 3y=2m-8

Step-by-step explanation:

put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c

A television game show has 12 ​doors, of which the contestant must pick 3. Behind 3 of the doors are expensive​ cars, and behind the other 9 doors are consolation prizes. The contestant gets to keep the items behind the 3 doors she selects. Determine the probability that the contestant wins at least one car.

Answers

The probability that the contestant wins at least one car is 3/5.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

For 1 car, we consider two possible outcomes:

P(1 car) = 2/6 x 4/5 + 4/6 x 2/5

P(1 car) = 8/15

For no car in either door

P(no car) = 4/6 x 3/5

P(no car) = 2/5

The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:

P(2 cars) = 2/6 x 1/5

= 1/15

P(1 car) + P(2 cars) = 8/15 + 1/15

= 3/5

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Choose the most convenient method to graph the line y=−3.

Select the correct answer below:


Recognize the equation as that of a vertical line passing through the x-axis at −3

Recognize the equation as that of a horizontal line passing through the y-axis at −3

Identify the slope and y-intercept and then graph

Find the x- and y-intercepts and then graph

Answers

Answer:

Recognize the equation as that of a horizontal line passing through the y-axis at −3

Find the equation of the line through the points (3,-4) and (0,2) answer in slope intercept form

Answers

Answer:

y= -2x+2.

Step-by-step explanation:

1) according to the condition interception is '2' (point (0;2));

2) slope is: (2+4)/(0-3)= -2;

3) finally the required equation is: y=-2x+2.

P.S. the suggested option is not the only one.

1. Given
G(n) = 4n-5
H(n) = 2n + 1
Find G(H(8))

Answers

Answer:

first H(8)= 2×8+1=16+1=17

and G(17)= 4×17-5=68-5=63

Question Write an equation of the line that passes through (1, −2) and is parallel to the line y=7x+7. An equation of the parallel line is y= .

Answers

Answer:

Step-by-step explanation:

7 = (y+2)/(x-1)

Parallel lines have equal slopes.

You can "massage" the form into any form you need.

what is the surface area of the walls of a hall measuring length 14m,width9m and height 4m?​

Answers

Answer:

184 m²

Step-by-step explanation:

lateral area of a prism = perimeter of base × height

A = 2(14 m + 9m) × 4 m

A = 184 m²

Which of the following rational expressions has the domain restrictions x = -6 amd x = 1?

Answers

Answer:

The answer is A)

Step-by-step explanation:

There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :

(1-1)(-6+6)=0

The Denominator can't be zero

Hope it helps!

Help me please im trying to do this but dont understand it at all.

Answers

The attached graph represents the graph of the function g(x)

How to determine the function g(x)?

The function f(x) is an absolute value function.

An absolute value function is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have:

(h, k) = (-3, -2)

So, we have:

y = a|x + 3| - 2

Also, we have:

(x, y) = (-1, 0)

So, we have:

0 = a|-1 + 3| - 2

This gives

0 = 2a - 2

Solve for a

a = 1

Substitute a = 1 in y = a|x + 3| - 2

y = |x + 3| - 2

This means that

f(x) = |x + 3| - 2

We have:

g(x) = 2f(x)

This means that:

g(x) = 2(|x + 3| - 2)

So, we have:

g(x) = 2|x + 3| - 4

See attachment for the graph of g(x)

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Last year, about 2,400 people participated in a local event. This year, about 3,200 people participated. What was the approximate percent increase in participation?

Answers

Answer:

33 %

Step-by-step explanation:

3200 - 2400 = 800

800 / 2400 x 100

1 /3 x 100

100/ 3

33 %

                                                                                                                                                                                         

Please help!!! Select the quadratic equation that has no real solution.

Answers

Answer:

2x² + 6x + 20

Step-by-step explanation:

See the picture

Solve for x in the diagram below.

Answers

Answer:

35 degrees

Step-by-step explanation:

Given all 3 angles add up 180(Sum of angles in a straight line)

[tex]2x + 30 + 40 + 40 = 180 \\ 2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ x = 35deg[/tex]

SOLVING

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Solve for x in the diagram below.

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Notice that all 3 of those angles together make a linear pair, or a [tex]\bf{180^\circ}[/tex] angle.

This is the key to solving this problem, because the sum of these angles is 180 degrees.

[tex]\bf{2x+30+40+40=180}[/tex] | arrange the like terms

[tex]\bf{2x+30=180-40-40}[/tex] | arrange the like terms

[tex]\bf{2x+30=100}[/tex] | subtract 30

[tex]\bf{2x=70}[/tex] | divide by 2

[tex]\bf{x=35}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                    [tex]\bf{=m\angle x=35^\circ}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]

The terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y). What are the exact values of sinθ and cosθ?

Answers

The exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.

Given that the point of intersection of the terminal side of θ an the unit circle is:

(16/19,y)

The exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

The given parameters is represented by:

(16/19,y)

This means that :

(cosθ ,sinθ )=(16/19,y)

Using the following trigonometric identity:

cos²θ +sinθ =1

We have:

(16/19)²+y²=1

Expand fraction:

(256/361)+y²=1

Collect like terms:

y²=1-(256/361)

Take LCM:

y²=(361-256)/361

y²=105/361

Take square roots

y=(√105)/19

Substitute value for y in

(cosθ ,sinθ )=(16/19,y)

By comparison:

cosθ =16/19

sinθ =(√105)/19

So the exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

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Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle is either in the circle or in the trapezoid.

Answers

The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The area of the rectangle = 30×21 = 630 square m

The total outcomes = 630 square m

The favorable outcomes = area of the circle + area of the trapezoid

= π(5)² + [(11+15)/2]×5

= 78.53 + 65

= 143.53 square m

Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):

= 143.53/630

= 0.227 ≈ 0.23

Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

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Answer:

0.13

Step-by-step explanation:

I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3

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