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\(\theta =\cfrac{20\pi }{3}\implies \theta =\cfrac{6\pi +6\pi +6\pi +2\pi }{3} \\\\\\ \theta =\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{2\pi }{3}\implies \theta =2\pi +2\pi +2\pi +\cfrac{2\pi }{3}\)

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The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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Answer:

Step-by-step explanation:

\(C=\pi d\\ \\ \text{Since the diameter of II is 12 and diameter of I is 10, circle II has the greater circumference. B is the answer.}\)

Based on the time the clock is set to, and the minutes lost every hour, the time the clock would show the next day at 10 am is 8:57 am

To find the time that the clock would show the next day, first find the difference between the 1 pm and 10 am the next day:

This difference is:

= 10 am the next day - 1 pm

= 10 + (12 - 1)

= 10 + 11

= 21 hours

The number of minutes lost is:

= 21 x 3 minutes per hour

= 63 minutes

The time the clock would be showing is:
= 10 am  - 63 minutes

= 8:57 am

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Answer: the 3rd one, 11x^3-6x^2+5x

Step-by-step explanation:

Answer:

Step-by-step explanation:

C.  11x^3 - 6x^2 + 5x

The powers of x are listed from greatest to least

Answer:

Your answer will be \(12\) cups of popcorn.

Step-by-step explanation:

To find out how much the new bags hold, you need to find out the discount.

\(\frac{20}{100 } = .2\)

\(15 * .2 = 3\)

We know that the discount is \(3\).

To figure out how much the new bags hold, subtract by the old bags.

\(15 - 3 = 12\)

The new bags hold 12 cups of popcorn.

Answer:

The domain should be X

Step-by-step explanation:

I'm a bit unsure but I think it's correct

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Step-by-step explanation:

This is an equation, where we need to find the value of x.

To solve this equation, we can first use the distributive property to expand 3.4(x + 7) which gives 3.4x + 3.4 * 7 = 3.4x + 23.8

Now we have the equation:

3.4x + 23.8 - 2.1 = 35.5

Next, we can add 2.1 to both sides of the equation:

3.4x + 23.8 = 37.6

Then, we can subtract 23.8 from both sides of the equation:

3.4x = 13.8

Finally, we can divide both sides of the equation by 3.4 to find the value of x:

x = 4

Therefore, the value of x that solves the equation is 4.

Answer:

1 and -3

Step-by-step explanation:

Answer:

1 and -3

Step-by-step explanation:

that's. the right answer

Answer:

In screen shot

Step-by-step explanation:

To find the answer for 1.00  

you have to divide .48 by 8.00 which gives you .06

I feel like you should get it by now

The cost of a lamp in city 1 is $26.50 and the cost of a lamp in city 2 is $27.00.

Given that, shopping in Two Different Cities. Different cities have different sales tax rates.

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

Let the total cost of an item in city 1 be x and the total cost of an item in city 2 be y.

So, the cost of lamp in city 1 is

x=25.00+1.50

x=$26.50

Now, the cost of lamp in city 2 is

y=25.00+2.00

y=$27.00

Therefore, the cost of a lamp in city 1 is $26.50 and the cost of a lamp in city 2 is $27.00.

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BD is the whole segment, while BC is one part and the CD segment is the other. The sum of two parts must be equal to the whole.

Applying the expressions for each part we can solve for "x".

The equation of the line containing the paints A and B is y = -1/3x + 4

from the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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Answer:

12 1/2

Step-by-step explanation:

2 x 5 = 10

1/2 x 5 = 2 1/2

10 + 2 1/2 = 12 1/2

With the help of probability we can say that, DUM={GG,BB,GB,BG).

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

hence, DUM={GG,BB,GB,BG)

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By solving a linear equation for the concentration we will see that the guy needs to use 18 ounces.

We know that the guy used 10 ounces of 6% solution with x ounces of a 12% solution to make a 8% solution, then we can write the concentration equation:

0.06*12 + 0.12*x = (12 + x)*0.08

So we just need to solve a linear equation for x.

0.06*12 + 0.12*x = (12 + x)*0.08

0.06*12 + 0.12*x = 12*0.08 + x*0.08

0.12*x - 0.08*x = 12*0.08 - 0.06*12

0.04*x = 0.06*12

x = 0.06*12/0.04 = 18

Which means that the guy needs to use 18 ounces of the 12% substance.

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Answer:

are you looking for a mixed number if so its 2 4/5

Step-by-step explanation:

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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By definition of real field and algebra properties we conclude that the product of three positive integers is always equal to a positive integer.

First, we state the conjecture: The product of three positive integers equals a positive integer. Second, we prove if the conjecture is true:

Integers are part of the real field, which mean that the product of two integers is also an element of that field. By algebra we know that the product of two positive integers is equal to another positive integer. Thus, the product of three positive integers is always equal to a positive integer.

Here is an example:

2 × 5 × 7

10 × 7

70

In a nutshell, the conjecture has been proved true.

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The Corollary to the polygon is explained below and the  formula to find the measure of each interior angle is  " (n - 2)×180°/n "   .

The Corollary to the polygon Angle Sum Theorem states that : the sum of the interior angles of a regular n gon is written as :

that means , ⇒ Sum of interior angles = (n - 2) × 180° ...equation(1)

In a regular "n-gon" , all the interior angles are said to be congruent.

Let "x" be  measure of each interior angle of a regular n-gon.

So , we can write ;

⇒ Sum of interior angles = (n)×(x)  ;

Equating the above expressions with equation(1),

⇒ (n)×(x) = (n - 2) × 180°  ;

On Solving for x,

⇒ x = (n - 2)×180°/n  ;

Therefore, the measure of each interior angle of a regular "n-gon" is x = (n - 2)×180°/n  .

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Answer:

(2a^3a^4)^5 simplifies to 32a^35.

Step-by-step explanation:

To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5

Next, we can simplify the expression inside the parentheses by multiplying the exponents:

a^3a^4 = a^(3+4) = a^7

Substituting this into our expression, we get:

(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35

Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:

2^5 * a^35 = 32a^35

Therefore, (2a^3a^4)^5 simplifies to 32a^35.

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer:

16864

Step-by-step explanation:

16694 + 170 = 16864

Hey there! I'm happy to help!

To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!

16×16×16=4096

You can also write it as 16³=4096

This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!

I hope that this helps! Have a wonderful day!

x = y² - 7 is the simplified inverse equation of the equation y = x² - 7.

Inverse function is a function which reverse one function to another.

If a function f takes the variable x to y, then the inverse of a function must takes y to x.

To get the inverse of the function, we have to interchange the variables.

Given equation is y = x² - 7

Now interchange the variable x to y and y to x,

we get  x = y² - 7

Hence, the required equation is x = y² - 7

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Answer: 9 bottles in each box and they bought 2, 4 & 5 boxes respectively.

Step-by-step explanation:

As it is clearly mentioned at the start of question that store only sells 'boxes' of juice bottles so all three of them bought perfect boxes.

So we'll find out how many boxes they'd have bought.

The largest possible divisor of 18, 36 and 45 is 9 so each box contains 9 juice bottles and guys purchased 2, 4 and 5 boxes respectively.

If you've still not understood, you can ask me for more detailed answer :)