Is the expression 2f + 4f + 2 – 3 equivalent to 6f – 1? 6f – 1 evaluated at f = 9 is 53. 2f + 4f + 2 – 3 evaluated at f = 9 is also 53. 6f – 1 evaluated at f = 3 is 17. what is 2f + 4f + 2 – 3 evaluated at f = 3?

Answer:

[tex](x+1)\cdot(x^2-9)[/tex]

[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]

Step-by-step explanation:

We can simplify the expression as follows:

[tex]x^3-9\cdot(x)+x^2-9[/tex]

[tex]x^3+x^2-9\cdot(x)-9[/tex]

we have a write the expression with a common factor of (x+1)

[tex]x^2\cdot(x+1)-9\cdot(x+1)[/tex]

[tex](x+1)\cdot(x^2-9)[/tex]

We can simplify (x²-9) as:

[tex](x-3)\cdot(x+3)=x^3-3\cdot(x)+3\cdot(x)-9[/tex]

Therefore the final form of the expression is:

[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]

The fourth option is the best option.

Answer:

[tex]b = \frac{v}{h}[/tex]

Step-by-step explanation:

The formula v =bh means that the volume of a prism is equal to its base area times its height.

WE need to solve for b, we need to get 'b' alone

v=bh

to get 'b' alone we need to eliminate 'h'

To eliminate any variable we always do opposite operation.'

bh mean b times h

the opposite of multiplication is division

so to eliminate 'h' we divide by 'h' on both sides

[tex]\frac{v}{h} = \frac{bh}{h}[/tex]

[tex]b = \frac{v}{h}[/tex]

The formula for the base area (b) of a prism is b = v/h.

To solve the formula v = bh for b (the base area), to isolate b on one side of the equation. Follow these steps:

Divide both sides of the equation by h:

v/h = b

The base area (b) is now isolated on one side of the equation.

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Answer:

-64

Step-by-step explanation:

Plato/Edmentum users -64 is correct.

Final answer:

The expected value of the game where you pay $3.00 to roll a die and win $5.00 for rolling a 1 or a 6 is -$0.33 per roll, indicating a loss over time.

Explanation:

The problem is asking us to calculate the expected value of the game in which you pay $3.00 to roll a fair die with the potential of winning $5.00 for rolling a 1 or a 6. To find the expected value, we need to multiply the outcomes by their respective probabilities and then sum these products.

The probability of rolling a 1 or a 6 is 1/6 for each number, so the combined probability for these winning rolls is 1/6 + 1/6 = 1/3. The probability of rolling a 2, 3, 4, or 5 is therefore 2/3 since these are the non-winning rolls.

Let's calculate the expected value (EV):

Winning: (1/3) * $5.00 = $1.67

Losing: (2/3) * -$3.00 = -$2.00

Now we add the two values:

EV = $1.67 - $2.00 = -$0.33

Therefore, the expected value of playing the game is a loss of $0.33 per roll. This means that in the long run, you can expect to lose an average of $0.33 for each time you play this game.

We are given 158 books to place them on three different shelves like A, B, and C.

It says that shelf A has eight fewer books than shelf B and five more books than shelf C.

Mathematically, it can be written as (A = B - 8) and (A = C + 5).

Or we can write it as (B = A + 8) and (C = A - 5).

If we consider there are 'x' books in shelf A, then shelf B would have 'x+8' books and shelf C would have 'x-5' books.

We know that Total books are 158, so its sum must be equal to total books.

A + B + C = 158

x + (x+8) + (x-5) = 158

3x + 3 = 158

3x + 3 - 3 = 158 - 3

3x = 155

[tex] \frac{3x}{3} =\frac{155}{3} [/tex]

x = 51.667 books

But 'x' must be an integer value because number of books can not be a decimal form.

Hence, this arrangement is "NOT possible" for this question.

Answer:

it is NOT possible

Step-by-step explanation:

Answer:

15 and 22

Step-by-step explanation:

15+22=37 and 22-15=7

Answer:

d. total amount of commission earned

Step-by-step explanation:

A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500.

This situation can be represented by the expression [tex]750+0.2(x-500)[/tex]

0.2(x-500) means total amount of commission earned.

This is because firstly its given that 20% is commission so we have 0.2.

The x-500 represents the sales over $500, where x is total sales. Like the person sold $800 worth of items so he will get 20% commission on $300.

The polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex] is classified as a 6th degree trinomial. The correct option is d) 6th degree trinomial.

To classify the polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex]:

Identify the degree of each term:

  - [tex]\( 4x^4 \)[/tex] has a degree of 4.

  - [tex]\( 4x^3 \)[/tex] has a degree of 3.

  - [tex]\( 10x^6 \)[/tex] has a degree of 6.

Determine the degree of the polynomial:

The degree of the polynomial is the highest degree of its terms, which is 6.

Count the number of terms: The polynomial has three terms.

Thus, the polynomial has 6th degree and number of terms trinomial.

The complete question is:

Choose the correct classification of [tex]4x^4-4x^3+10x^6.[/tex]

a) 4th degree trinomial

b) 12th degree trinomial

c) 3rd degree trinomial

d) 6th degree trinomial

Answer:

0.2

Step-by-step explanation:

Final answer:

The function modeling the height of the cone in terms of its radius, given the volume of 180 in³, is h(r) = 540 / (πr²).

Explanation:

The volume V of a cone with radius r and height h is given by the formula V = (1/3)πr²h, where π is Pi (approximately 3.14159). Given that the volume of the cone is 180 in³, we can solve for the height h in terms of the radius r.

Starting with the formula:

V = (1/3)πr²h

We plug in the volume:

180 = (1/3)πr²h

To solve for h, we rearrange the equation:

h = 3*180 / (πr²)

h = 540 / (πr²)

So the function modeling the height h of the cone in terms of its radius r is:

h(r) = 540 / (πr²)

Answer:

C

Step-by-step explanation:

Answer:

choosing five CDs where not all of them are pop

Step-by-step explanation:

The complement of an event is everything possible except that event.  It is found by subtracting the probability of an event from 1.

The event we have listed is April choosing 5 pop CDs.  The complement would literally be read as "not choosing 5 pop CDs."  This means she would choose 5 CDs, where some could possibly be pop, but others would not.

Using the concept of complementary events, it is found that the complement of April choosing five pop CDs is given by:

choosing five CDs where not all of them are pop.

Two events are complementary if the sum of their probabilities is of 1.

For example, either you choose five pop CDs, or you do not choose five pop CDs.

Hence the complement of this event is given by not choosing five pop CDs, that is:

choosing five CDs where not all of them are pop.

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Pythagorean theorem is used only for the right angled triangles.

For ΔABC,

Cosine rule is

[tex] a^2=b^2 + c^2-2bc$ cosA $  [/tex]

[tex] b^2=a^2 + c^2-2ac$ cosB $  [/tex]

[tex] c^2=a^2 + b^2-2ab$ cosC $  [/tex]

Here we have used one of these formulae

Hence definition of cosine or Cosine rule is the right answer

Option 2) is the right answer

The missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Given is a proof using triangles property and rule,

In △ ABC, BD ⊥ AC

Prove: the formula for the law of cosines, a² = b² + c² – 2bccos

         Statements                                                    Reasons

1.  In △ ABC, BD ⊥ AC                                               1. given

2.  In △ ADB, c²  = x²  + h²                                 2. Pythagorean thm.

3. In △ BDC, a² = (b – x)² + h²                           3. Pythagorean thm.  

4.  a²  = b²  – 2bx + x²  + h²                               4. prop. of multiplication

5. a² = b² – 2bx + c²                                           5. substitution

6. In △ ADB, cos(A) = x/6                                   6. def. cosine

7. ccos(A) = x                                                       7. mult. prop. of equality

8.  a² = b² – 2bccos(A) + c²                                8. ?

9. a² = b² + c² – 2bccos(A)                               9. commutative property

We are asked to find the reason used in step 8,

From step 5) we have, a² = b² – 2bx + c².......(i)

From step 7) we have, ccos(A) = x

So, by substituting ccosA for x in eq(i), we get the equation for step 8)

a² = b² – 2bc·cosA + c²

Hence, the missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²

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