The area of a circle is 18 pi square inches. If the area of a sector of this circle is 6 pi square inches, then
which of the following must be the sector's central angle?

Answer:

Step-by-step explanation:

what are your books about?

Answer:

74 is already in the simplest form. It can be written as 1.75 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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Answer:

The answer is C

Step-by-step explanation:

The intersection of those figures results to a point

Answer: 12

Step-by-step explanation: caculator

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

\(\implies (0-80)^2=4p(0-20)\)

\(\implies (-80)^2=4p(-20)\)

\(\implies 6400=-80p\)

\(\implies p=-80\)

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

\(\implies (x-80)^2=4(-80)(y-20)\)

\(\implies (x-80)^2=-320(y-20)\)

Given:

\(\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}\)

\(\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}\)

\(\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}\)

answer/explanation:

hope this helps

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

I believe that it should be 36.

Step-by-step explanation:

You got that the equation is 1/4 s^2, which I agree with. So plugging in 12, in place of s, you get:

\(\frac{1}{4} * 12^{2}\)

\(\frac{1}{4} * 144\)

\(144/4 = 36\)

Complete Question

A juggler tosses a bowling pin in the air with an initial velocity of 18 ft per second. It leaves his hand when it is five feet from the ground and he catches it when it is four feet from the ground,How long is the ball in the air?

Answer:

\(t\approx 0.1s\)

Step-by-step explanation:

From the question we are told that

Initial velocity  \(V_0= 18 ft/s\)

Initial Height    \(h_1=5feet\)

Final Height     \(h_2=4feet\)

Generally the Newtons equation for motion is mathematically given by

   \(V^2 = U^2 + 2as\)

Where

    \(s=h_2-h_1\\s=4-5\\s=-1ft\)

And

   \(a=g=>9.81\\a=32.2ft/s^2\)

Therefore

   \(V^2 = (18)^2 + 2(-32.2)(-1)\)

   \(V^2 = 388.4\)

   \(V =19.70786645\\V=19.71ft/s\)

Generally the equation for Time is mathematically Given as

   \(t=\frac{V-U}{a}\)

   \(t=\frac{19.71-18}{32.2}\)

   \(t=0.05310559006\)

   \(t\approx 0.1s\)

Therefore the time spent on air by the ball is

    \(t=0.05310559006s\)

The largest possible value is |A∩B| is |A| = 10, the minimal possible value of |A∩B| is 0 and the possible values of |A∪B| lies between 15 ≤ |A∪B| ≤ 25

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Given that, you have sets a and b with |A| = 10 and |B| = 15.

a) For any such A and B, A ∩ B ⊆, and so |A∩B| ≤ |A|, if we take A⊆B, which is possible as |A| < |B|, then A∩B = A,

So, |A∩B| = |A|

Therefore, the largest possible value of |A∩B| is |A| = 10

b) Let, A = {1, 2, 3, 4, 5, 6....10} and B = {1, 2, 3, 4, 5, 6....25},

Then, |A| = 10, |B| = 15, and A∩B = Φ

That mean,

|A∩B| = 0, But |A∩B| is a non-negative integer, so it must be the minimum possible value of the |A∩B|,

Therefore, the minimal possible value of |A∩B| is 0

c) By using the inclusion-exclusion principle for two sets, we know that,

|A∪B| = |A| + |B| - |A∩B|

= 10 + 15 - |A∩B|

= 25-|A∩B|

Since, 0 ≤ |A∩B| ≤ 10,

∴ 25-10 ≤ |A∩B| ≤ 25-0

15 ≤ |A∩B| ≤ 25

To see that all these values are possible, let A = {1, 2, 3, 4, 5, 6....10} and Bₐ = {a+1, a+2.......a+15} For some a,

If 0 ≤ a ≤ 10, then A and B both are consecutive set,

|A∪Bₐ| = {1, 2, ....a+15}

Therefore, any integer of the form a+15 where 0 ≤ a ≤ 15 is a possible size  for |A∪B|

Therefore, the possible values of |A∪B| lies between 15 ≤ |A∪B| ≤ 25

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The solution is, the profit is 18.

If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.

a). The prices that give a profit of zero dollars.

   Expression that is most useful,

   Factored form: -2(p - 3)(p - 9) = 0

   p = 3, 9

b). The profit when the price is zero .

   Standard form:

   Profit = -2p² + 24p - 54 = 0

   -p² + 12p - 27 = 0

   -p² + 3p + 9p - 27 = 0

   -p(p - 3) + 9(p -3) = 0

    (-p + 9)(p - 3) = 0

    p = 3, 9

c). The price that gives the maximum profit.

  Vertex form: -2(p - 6)² + 18

  Vertex of the given expression → (6, 18)

  Maximum profit will be at p = 6.

  Therefore, profit = -2(6 - 6)² + 18 = 18

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complete question:

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are

Standard form: - 2 p^2 + 24p - 54

Factored form: -2(p - 3)(y-9)

Vertex form: -2(p-6)^2 + 18.

Which form is most useful for finding a. The prices that give a profit of zero dollars?

b. The profit when the price is zero?

c. The price that gives the maximum profit?​

Answer:

144 km

Step-by-step explanation:

Answer:

this triangle is ABC with A(-2 ; -3), B(4; - 3) and C(3;5)

=> \(AB=\sqrt{(4-(-2))^{2}+\sqrt{(-3 -(-3))^{2} } }=\sqrt{6^{2} }=6\\\\AC=\sqrt{(3-(-2))^{2}+(5-(-3))^{2} }=\sqrt{5^{2}+8^{2} }=\sqrt{89}\\\\BC =\sqrt{1^{2}+8^{2} }=\sqrt{65}\)

using Heron theorem, we have:

\(S=\sqrt{p(p-AB)(p-AC)(p-BC)}\\\\S=\sqrt{(\frac{6+\sqrt{89}+\sqrt{65} }{2})(\frac{\sqrt{89}+\sqrt{65}-6 }{2} )(\frac{6+\sqrt{65}-\sqrt{89} }{2})(\frac{6+\sqrt{89}-\sqrt{65} }{2}) }\\\\S=24 \\\\\)

with S is the area of the triangle

       \(p=\frac{AB+AC+BC}{2}=\frac{6+\sqrt{89}+\sqrt{65} }{2}\)

Step-by-step explanation:

Area of the triangle with given vertices is equals to 24 square units.

"Area is the surface which represents the total space occupied by any two dimensional object."

"Triangle is a  polygon which has three sides and three vertices. Sum of all the interior angles of a triangle is equals to 180°."

Formula used

In ΔABC , A(x₁ , y₁) , B(x₂, y₂) and C(x₃, y₃)

Area of a triangle =  \(\frac{1}{2} [ x_{1} (y_{2} -y_{3} + x_{2} (y_{3} -y_{1} +x_{3} (y_{1} -y_{2} ]\\\)

According to the question,

Let ABC be the triangle with A(-2,-3) , B(4,-3) and C(3,5)

Area of the triangle = \(\frac{1}{2}\) [ -2(-3-5) + 4(5+3) +3 (-3 +3)]

                                 = \(\frac{1}{2}\) [ 16 +32 + 0]

                                 = 24 square units

Hence Area of the triangle with given vertices is equals to 24 square units.

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Answer:

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

I do not understand the question. But if my interpretation is correct, then:

If there are 64 players and 3 rounds, 32 will get out in the first round. 16 will get out in the second, and 8 will get out on the third. Thus, the answer is 64-(32+16+8) or just simply 8.

a. The number of red roses left t hours after the store opens \(R(t) = 400/2^{t/2}\)    

b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t

c. One possible solution is t ≈ 7.546 hours after the store opens.

d. there are 194 boxes of chocolates left.

e. you need to arrive at the store no later than 7.504 hours after it opens.

a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:

\(R(t) = 400/2^{t/2}\)

b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:

C(t) = 200 - 0.15t

c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:

\(400/2^{t/2} = 200 - 0.15t\)

Simplifying this equation, we get:

\(2^{t/2 + 1} + 0.15t - 400 = 0\)

We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.

d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:

C(3.5) = 200 - 0.15(3.5) = 194.25

We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.

e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:

\(400/2^{t/2}= 36\)

Simplifying this equation, we get:

2^(t/2) ≈ 11.111

Taking the logarithm of both sides, we get:

t/2 ≈ log2(11.111)

t ≈ 2 log2(11.111)

Using a calculator, we get:

t ≈ 7.504 hours after the store opens.

Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.

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Rested numbers in group is 33 out of 76.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

Total numbers in a group = 76.

44% of them were rested.

That is 44% of 76.

To find how many are rested we have to find the value in numbers.

Convert 44% of 76 to numbers.

For this, it can be written as

\(\frac{44}{100} *76\) = 33.44

Therefore 44% of 76  ≅ 33 numbers.(approximately)

Hence, rested numbers in group is 33.

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Answer:

Option (4)

Step-by-step explanation:

From the given circle O,

AC and BD are the diameters intersecting at point O.

∠AOB ≅ ∠COD [Vertical angles]

Therefore, length of intercepted arcs by these central angles will be same.

\(m(\widehat{AB})=m(\widehat{CD})\)

(3x - 70) = (x + 10)

3x - x = 70 + 10

2x = 80

x = 40

Since, \(m(\widehat{AB})+m(\widehat{BC})=180\) [Since AC is a diameter]

(3x - 70) + \(m(\widehat{BC})\) = 180°

3(40) - 70 + \(m(\widehat{BC})\) = 180°

\(m(\widehat{BC})\) = 180° - 50°

           = 130°

Therefore, Option (4) will be the correct option.

Answer:

130 degrees

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

8x + 5y = 48

8x + 5(-8) = 48  ==> plugin y = -8

8x + (-40) = 48  ==> simplify

8x - 40 = 48

8x = 88  ==> add 40 on both sides to simplify x

x = 11 ==> divide both sides by 8 to isolate x

Answer:

\(8x + 5y = 48 \\ put \: y = - 8 \\ 8x + 5 \times - 8 = 48 \\ 8x + ( - 40) = 48 \\ 8x - 40 = 48 \\ 8x = 48 + 40 \\ 8x = 88 \\ x = \frac{88}{8} \\ x = 11 \: anwer \: \)

Hope it will help you...

Answer:

A) 9

Step-by-step explanation:

\(m=\frac{rise}{run}=\frac{7+2}{-6+7}=\frac{9}{1}=9\)

Option A should be the answer.

Hope this helps.

Answer:

Try A

Step-by-step explanation:

Answer:

Value of LN = 19 units

Step-by-step explanation:

Given:

LN = 3 + 8x

Find:

Value of LN

Computation:

We know that LM + MN = LN

So,

8 + 6x - 1 = LN

So,

3 + 8x = 8 + 6x - 1

3 + 8x = 7 + 6x

8x - 6x = 7 - 3

2x = 4

x = 2

So,

LN = 3 + 8x

LN = 3 + 8(2)

LN = 3 + 16

LN = 19

Value of LN = 19 units

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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Answer:

24

Step-by-step explanation:

I found out that each one can have 6 possibilities with out moving so I did 6 times 4 and got 24

Answer:

You can get 12 no problem:)

Step-by-step explanation:

Answer:

x= 13 =smaller number

Step-by-step explanation:

let x=smaller number

y=2x-6=larger number

x+y=45

x+2x-6=45 (equation)

3x=39

x=13

Answer:

\(x = 13\) ..... smaller number

and

\(y = 32\) ....... larger number

Step-by-step explanation:

Greetings!!!

Let the two numbers be X and Y

\(x + y = 45........ \:equation \: 1\)

The larger number is y and is 6 less than twice the smaller number. which means:-

\((y - 6) = 2x........... \: equation \: 2\)

so, now solve for y. from equation 2

\(y - 6 = 2x \\ y = 2x + 6\)

Substitute equation 1 into equation 2

\(x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13\)

To solve for y substitute x into the first equation

\((13) = + y = 45 \\ y = 45 - 13 \\ y = 32\)

Finally, to be more sure make a cross check

\(y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26\)

If you have any questions tag it on comments

Hope it helps!!!

Answer:

1/2

Step-by-step explanation:

Answer: 1/2B

Step-by-step explanation: Because there are 3 odd numbers, meaning that you will have 3/6 which is also 1/2.

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