2. If f(x) = 3x³ - 4x + 6and g(x)= x³ + 3x² + x - 3, then find
A.(f+g)(x)
B.(f- g)(x)
C.(3f+2g)(x)
D. (3f-2g)(x)​

The speed of the boat in still water is 6miles/hour miles per hour.

The speed of the current is 3miles/hour miles per hour.

The distance travelled by the boat downstream(with the flow current of river) is 240 miles.

The distance travelled by the boat upstream(Against the flow current of river) is 240 miles.

Time taken to travel downstream = 20 hours.

Time taken to travel upstream = 60 hours.

Let us say the velocity of the boat is V and the velocity of the current flow of river is U.

The relative velocity of boat with respect to ground while going downstream is,

velocity of boat in downstream = V + U.

As we know,

Velocity = distance/time

Putting values of downstream motion,

V + U = 240/20

V + U = 10

Let us say this is our equation 1.

The relative velocity of boat with respect to ground while going upstream is,

velocity of boat in upstream = V - U

As we already know,

Velocity = distance/time

Putting the values of upstream motion,

V - U = 240/60

V - U = 3

Let us say this is our equation 2.

Now, on adding equation 1 and 2.

V+U+V-U = 10 + 3

2V = 13

V = 6.5 miles per hour.

Rounding off to the nearest integer,

V = 6 miles/hour.

Putting V = 6.5 miles/hour in equation 1,

6.5 + U = 10

U = 3.5 miles/hour.

Rounding off to the nearest integer,

U = 3 miles/hour

The velocity of river current is 3 miles/hour and velocity of boat is 6miles/hour.

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A boat traveled 240 miles downstream, then 240 miles back up stream. The trip downstream took 20 hours. The trip back up stream took 60 hours. Use this information to fill in the following blanks.

The speed of the boat in still water is ______ miles per hour.

The speed of the current is ______ miles per hour.

The amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.

The percentage is defined as a ratio expressed as a fraction of 100.

We know that the numbers 1 to 20 that contain the digit 2 are 2,12, and 20.

So, the quantity of the numbers is 3

It’s out of 20 numbers, this means 3/20

Calculating percentages indicated above can be readily computed using the formula below:

Percentage = (Value/Total Value) × 100

The amount as a percent = (Value/Total Value) × 100

The amount as a percent = (3/20) × 100

The amount as a percent = 15%

Thus, the amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.

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answer

11

Step-by-step explanation:

4x+1/3y^24(2)+1/3(3)^28+1/3(9)8+3

The answers are given below.

First of all, we will know about GCF and expressions.

GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.

Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)

=-2(5/6)+3(5/6)

=-5/3+5/2

2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15

3). 3/10(4m-8)+9m = 12/10m-24/10+9m

= 6/5m-12/5+9m

=6/5m+9m-12/5

=51/m-12/5

4). 2.25-2(7.5-4h)= 2.25-15+8h

= 8h-12.75

5). 3(a-7)= 3a-21

6). -6(2+x)= -12-6x

7). -5(3m-4)= -15m+20

8).  -9(-5-4c)= 45+36c

9).  4.5(3s+6)= 13.5s+27

10).  -1.4(-5+7g)= 7-9.8g

11). 2/5(6-5p)= 12/5-2p

12).  -4/3(3q-10)= -4q+40/3

13). 2(3+4y+5)= 6+8y+10 = 8y+10

14. The expression 8x + 2 factored using the GCF is= 2(4x+1)

15. The expression 3y-24 factored using the GCF is = 3(y-8)

16. The expression 14p-28 factored using the GCF is= 14(p-2)

17. The expression 6+16k factored using the GCF is= 2(3+8k)

The coefficient of the variable terms of following are given below

18. The expression 1/7a + 1/7 factored is= 1/7

19. The expression 1/3b - 1/3 factored is= 1/3

20. The expression 3/8d + 3/4 factored is= 3/8

21. The expression 2.2x+ 4.4factored is= 2.2

22. The expression 0.15c - 0.072 factored is= 0.15

23. The expression 3/8z + 1 factored is=3/8

24. The expression 6s - 3/4 factored is=6

25. The expression 5/2k - 2 factored is=5/2

26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)

27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)

28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)

29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)

30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)

31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)

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123

[tex]123 > x = 10 > 6[/tex]

The unknown side length of the right triangle is 58 units.

What is pythagoras theorem for a right triangle?
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Mathematically, Hypotenuse² = Base² + Perpendicular²

Given, the length of the perpendicular of the right triangle = 42 units
Also, the length of the base of the right triangle = 40 units
Let the length of the hypotenuse of the right triangle = 'x' units
Following the statement of the pythagoras theorem as established in literature, we have: Hypotenuse² = Base² + Perpendicular²
Substituting the values from the question given, we get:
x² = 42² + 40² = 3364 ⇒ x = √3364 ⇒ x = √58² ⇒ x = 58
Therefore, the unknown side length of the right triangle is 58 units.

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We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.

Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.

Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.

Answer: NO SOLUTION

Step-by-step explanation:

6x + 4x - 1 = 2(5x + 4)

10x - 1 = 2(5x+4)

10x - 1 = 10x + 8

-1 = 8

NO SOLUTION

Answer: (*^▽^*)        []~(￣▽￣)~*

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Answer:

7

Step-by-step explanation:

since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that

The dinner bill of Sally before the tip is $53.

Given that, Sally left an 18% tip. The tip was 9.50.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the dinner bill of Sally be x.

Now, 18% of x = 9.50

⇒ 18/100 × x = 9.50

⇒ 0.18x = 9.50

⇒ x = 9.50/0.18

⇒ x = 52.77

≈ 53

Therefore, the dinner bill of Sally before the tip is $53.

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Answer:

Axis interception points [tex]97x-9[/tex] x intercepts: [tex](\frac{9}{97} ,0),[/tex]Y intercepts:[tex](0,-9)[/tex]

Step-by-step explanation:

Slope of 97x-9 :     m=97

Domain: 97 x - 9

Range: 97 x - 9

Step-by-step explanation:

d

since you add them up you will have a certain answer that will match up

Answer:

2/3 = y

Step-by-step explanation:

to solve you got to cancel out the 7
so 7y/7.
whatever you do to one side, you do to the other.
14/3 ÷ 7 = 7y/7
14/3 ÷ 7 = 0.6666... = 2/3 = y

Select red from A and B then the probability of getting cards of same color is  12/24 * 24/48 = 1

Box A: 12 Red

          12 Black

Box B: 24 Red

          24 Black

One card is selected from Box A and placing the selected card into Box B.

One card is selected from Box B.

What is the probability that a red card is selected from Box B?

Two things can occur:

1) Select red from A and B:

12/24 * 24/48 = 1

2) Select black from A and red from B:

12/24 * 24/48 = 1

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Answer:

(x+3)(x–8)

Step-by-step explanation:

Normally you will always write factors in this form: (variable + smallest number)(variable – largest number)

Correct form: (x+2)(x–8)

Incorrect form: (x–2)(x+8)

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Answer:

Dog be 28

Phosphors apparently

Step-by-step explanation:

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Definition of the proportionality constant?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.

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The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.

The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".

Alternatively, it can be rewritten as y = b + mx.

R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.

Interpreting the equation, we can deduce the following:

The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.

The unit rate or rate of change (m) = -0.7 degrees per minute.

Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.

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The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:

The dimensions of an area, which is a two-dimensional object, refer to the length and the width.

On the other hand, the dimensions of the volume refer to the length, width, and height.

The volume of the square-based rectangular tank = 48.5ft³.

The length of each side of the surface area = 3.6468 ft (∛48.5ft)

Check:

Volume = height x length x width

= 3.6468 x 3.6468 x 3.6468

= 48.499 ft³

= 48.5 ft³

Thus, the dimensions of the surface area include the length and the width without the height.

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Step-by-step explanation:

in general, a linear function is always of the structure

y = ax + b

"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

"b" is the y-intercept (the y-value when x = 0).

so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :

2 = a×1 + b = a + b

1 = a×2 + b = 2a + b

now we can simply subtract the first equation from the second and get

1 = 2a + b

- 2 = a + b

------------------

-1 = a + 0

a = -1

1 = 2×-1 + b = -2 + b

b = 3

and the equation is

y = -x + 3

therefore, when the input is n (that means f(n))

y = output = -n + 3

We know that

Based on the given information, we define the following

The cost to rent a moving van is $51 plus an additional $7 per hour.

Based on the given information,

Answer:

D

Step-by-step explanation:

-3 ft means that it is three feet below zero. That means 0 means the sea level.

Answer:

3.75 represents how much the flower grows every week.

Step-by-step explanation:

Answer:

x = 3

or

x = -3

(explanation in the picture above)

Answer: x = 3 or x = -3

Step-by-step explanation:

Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.

3x = 9

3x = -9

x = 3 or x = -3

The two cars are 5 kilometers far apart from each other.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

Two cars leave the same parking lot, with one heading north and the other heading east.

After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car has traveled 4 kilometers.

Now,

The straight path is find by using the Pythagoras theorem as;

Straight path = √3² + 4²

                    = √9 + 16

                    = √25

                    = 5 km

Therefore,

The two cars are 5 kilometers far apart from each other.

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The polynomial in standard form is  2x³+200x-36x²-3600

A polynomial is a mathematical formula that involves only the operations subtraction, addition,  multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

We know the roots of the polynomial as 18, 10i, and −10i.

therefore the polynomial is of the form.

a(x-18)(x-10i)(x+10i)

= a (x-18)(x²-100i²)

= a (x-18)(x²+100)

= a (x³+100x-18x²-1800)

Now at x =1 The value of the polynomial is -3434

Therefore

-3434 = a(1+100-18-1800)

or, a = 2

Therefore the polynomial is of the form: (2x³+200x-36x²-3600)

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1. (3/4)x = 9. Multiply both sides by the reciprocal of 3/4: (4/3)(3/4)x = (4/3)(9)

x = 12.

2 . -4=4/7*x

        4x/7=-4

             x=-7

3. -1/5*x=6

     -x/5=6

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

x=-30

With an example, what is a reciprocal equation?

An inverse of a number or value is referred to as reciprocal. If x is any real number, then 1/x will be the reciprocal of that number. For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8. 1/8's reciprocal is equal to 8.

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Step-by-step explanation:

1st

[tex]area = \frac{1}{2} base \times hight[/tex]

2nd

[tex]32 = \frac{1}{2} base \times 4[/tex]

3rd

[tex]32 \div 4 = \frac{1}{2} base[/tex]

4th

[tex]8 \times 2 = base[/tex]

answer

[tex]base = 16ft[/tex]