which of the following systems of inequalities would produce the region indicated on the graph below PLZ HELP NEED ASAP!!!!!!!

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)

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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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:

125 feet

Step-by-step explanation:

Given :

On a softball field, home plate is 43 feet from the pitcher’s mound.

A ball is hit at an angle of 27° east of the pitcher’s mound.

The ball travels 162 feet before it is caught by an outfielder.

To Find : Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

Solution:

Law of cosines: [tex]a^2 = b^2 + c^2 -2bc cos A[/tex]

∠A = 27°

b = 43

c = 162

Substitute the given values

[tex]a^2 = 43^2 + 162^2 -2(43)(162) cos 27^{\circ}[/tex]

[tex]a^2 = 15679.497105[/tex]

[tex]a = \sqrt{15679.497105}[/tex]

[tex]a =125.21[/tex]

The outfielder must throw the ball 125 feet to return it to the pitcher.

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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Final answer:

Javier has 4 juice boxes, 3 of which are grape flavored. The fraction representing grape juice boxes is 3/4, with equivalent fractions being 6/8 and 9/12.

Explanation:

Javier has 4 juice boxes and three are grape flavored. To describe the part of the juice boxes that is grape in the form of a fraction, we would use the total number of juice boxes as the denominator and the number of grape juice boxes as the numerator. So, the fraction representing the grape juice boxes is 3/4 (three out of four).

To write two equivalent fractions, we can multiply the numerator and the denominator by the same number. If we multiply both by 2, we get 6/8, which is equivalent to 3/4. Similarly, multiplying both by 3 gives us 9/12, which is also equivalent to 3/4.

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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Answer:

C

Step-by-step explanation:

option: c.   graph of line going through (1, 4) and (3, 10)

It is given that:

Margo has a coin collection.

She was given 1 coin as a gift, and she adds 3 coins per year.

i.e. she started with a initial of one coin and add 3 coins each year.

That is this situation can be represented with the help of a function:

C(t) which represents the number of coins she has in 't' years.

Now,

C(0)=1

Also,

C(t)=3t+1-------------(A)

Hence, we will check each of the given functions whether at the value of t they passes through that point or not.

a)

it is given that:

Graph passes through (1,2) and (3,4)

i.e. when t=1   C(t)=2

and when t=3 C(t)=4

but on putting the value of t in equation (A) it does not hold true.

same could be done for option (b) and option (d).

But in option (c)

It hold true.

         Since,

          when t=1

            C(t)=3×1+1=4

         when t=3

            C(t)=3×3+1=10

Hence, the correct answer is:

c.)   graph of line going through 1, 4 and 3, 10

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.

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

relative minimum is -2 when x is -3