Find the value of each variable and the measure of each labeled angle.

The equation of the circle with radius 7 and center at (-4 , -6) is (x + 4)^2 + (y + 6)^2 = 49.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (-4 , -6)

r = 7

(x - -4)^2 + (y - -6)^2 = 7^2

(x + 4)^2 + (y + 6)^2 = 49

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The area of the base of the rectangular prism will be D. 4f² - 6fg + 9g⁴.

it should be noted that from the information given, the cubes have a combined volume that is the same as a rectangular prism of the same height.

The total height of the cubes stacked on top of each other is 2f + 3g²

Therefore, the area will be:

= (2f)² - 2(3fg) + (3g²)²

= 4f² - 6fg + 9g⁴

Therefore, the area of the base of the rectangular prism will be 4f² - 6fg + 9g⁴.

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∠AHF is the exterior angle to the triangle GHI, so m∠AHF = 116°.

What is exterior angle?

When one side of a triangle is stretched, an external angle is generated. An external angle of a triangle is a non-straight angle (one that is not merely an extension of a side) that is outside the triangle but next to an interior angle.

From figure, m∠CIH = 105° (given)

so, m∠GIH = (180° - m∠CIH) = (180° - 105°) = 75° (complementary angles)

And m∠BGD = 41°

So, m∠IGH = M∠BGD = 41° (vertically opposite angles)

Now, m∠AHF = m∠GIH + m∠IGH (exterior angle)

                       = 75° + 41°

                       = 116°

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 The complete expression of the given quadratic function is:

x² + 14x + 49

   An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

   To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:

(a + b)² = a² + 2ab + b²

x² + 14x + ?

where:

Substitute and find b

14x = 2xb

2b = 14

b = 7

   Let's complete the square

x² + 14x + 7²

x² + 14x + 49  

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Answer:

576 feet

Step-by-step explanation:

The bee is at the flowerbed for 11 minutes so we can subtract that form the 15 minutes. The bee travels for 4 minutes.

So now we have that it flew to the flowerbed at 6 feet per second and back at 4 feet per second.

We have a total of 4 minutes or 240 seconds. we now have two speeds where one is 50% faster than the other. We then find the two percents that one is 50% greater than the other percent and both add up to 100. 40% +50% of 40% is 60. 60%+40% is 100%

We know it spent 40% of 240 seconds flying to the flowerbed at 6 feet per second.

40% of 240 is 96

96 seconds at 6 feet per second is 576 feet

The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Given the number is 21,468,127,471.

The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.

The groups of numbers are 3 digit group and which is starting from the right to left.

As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.

From  the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.

Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

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Answer:

The value would be 100

Step-by-step explanation:

Answer:

36 degrees

Step-by-step explanation:

this a complementary angle. This means that both sides add up to 90 degrees. 90-54=36

Answer:

36°

Step-by-step explanation:

These angles are complimentary, meaning they add to 90°. You know this by the little square marking.

a + 54° = 90°

a = 36°

Using a system of equations, the amounts invested in each fund are given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The teacher invested 5000, hence:

x + y + z = 5000.

After a year, the amount was of $5,450, hence, considering the return rates:

1.12x + 1.08y + 1.05z = 5450.

The teacher invested twice as much in the income fund as in the money market fund, hence:

y = 2z.

Then, replacing y = 2z in the first two equations:

Replacing the first equation into the second.

1.12(5000 - 3z) + 3.21z = 5450.

0.15z = 150

z = 150/0.15

z = 1000.

Hence:

The amounts invested in each fund are given as follows:

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Answer:

s = 3 cm

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length )

here V = 27 cm³ , then

s³ = 27 ( take cube root of both sides )

[tex]\sqrt[3]{s^3}[/tex] = [tex]\sqrt[3]{27}[/tex]

s = 3

the length of each edge of the cube is 3 cm

Answer:

2x6x6+7+j

34+67897790+b,xyy

Answer:  20 feet

Step-by-step explanation:

The scale is 3 inches to is to 2 feet

As a ratio, it would be:

The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:

Now to find the missing number, cross multiply the fractions first:

Then solve for x:

The answer is 20 feet

The given sequence  100,10,1,0.1, ........... does not form an AP as the common difference is not same.

In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few key concepts in AP that had been labeled as:

As shown below, the AP can also be referred to in terms of common differences.

Now, the stated sequence is;  100,10,1,0.1, ...........

The series comprises of four defined terms.

Consider the initial term be 'a₁' = 100.

Consider the second term be 'a₂' = 10.

Consider the third term be 'a₃' = 1.

And, consider the fourth term is 'a₄' = 0.1.

The AP must have the equal common difference. So,

d₁ = a₃ - a₂

Substitute the values.

d₁ = 1 - 10

d₁ = -9

Thus, the computed common difference is -9.

or d₂ = a₄ - a₃ (Substitute the values)

d₂ = 0.1 - 1

d₂ = -0.9.

As, for the result it is clear that the value of both common difference is not same. That is,

d₁ ≠ d₂.

Therefore, the given sequence doesn't not form an arithmetic sequence.

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Answer:

Step-by-step explanation:

ur dad

The value of the given expression is -6.93

The expression in the question is given as:

negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths

Rewrite the expression properly

So, we have

-15 - 3.7 + 9.15/5 * 3^2 - 4.7

Evaluate the quotient and the exponent

So, we have

-15 - 3.7 + 1.83 * 9 - 4.7

Evaluate the product

-15 - 3.7 + 16.47 - 4.7

Evaluate the sum and the difference

-6.93

Hence, the value of the given expression is -6.93 (none of the options is correct)

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Answer:

Step-by-step explanation: option b

Using the Fundamental Counting Theorem, the number of pairs are given as follows:

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For matching pairs, we have that:

Hence the number of pairs is:

N = 2 x 20 x 19 = 760.

For the non-matching pair, we have that there are 20 red and 20 blue to choose, hence the number of pairs is:

N = 20 x 20 = 400.

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Answer:

О C  1.494*10⁻⁶

Step-by-step explanation:

1.8*10⁸ = 180000000

8.3*10⁻³ = 0.0083

180000000 * 0.0083 = 1494000

= 1.494*10⁶

Answer:

120 tissues

Step-by-step explanation:

3/5 x 200 tissues

X（´∀｀　）

Answer:

We take 120 tissues

Step-by-step explanation:

[tex]\frac{200}{1} *\frac{3}{5} = \\\\\frac{600}{5} = 120[/tex]

The 20th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 8.246337208 x 10^11.

A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a r^(n-1)

Where:

a(n) = nth term

r = ratio

Given the geometric sequence 3, 12, 48, 192, . . .

Find the ratio,

r = a(n)/a(n-1)

r = a(2)/a(1)

r = 12/3

r = 4

Notice that the ratio between two succeeding terms is always 4.

Use the formula to find the 20th term of the geometric sequence.

a(20) = a r^(20-1)

a(20) = 3[4^(20-1)]

a(20) = 3(4^19)

a(20) = 8.246337208 x 10^11

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Answer:it

Step-by-step explanation:

it should be 10 i think

If Miranda purchased a coat for $101.50 that was regularly priced at $145, not including tax then the percentage Miranda saved by purchasing the coat on sale is equal to 30%.

Percentage in mathematics can be described as a number expressed as a fraction of 100. The symbol % is used to indicate a percent.

The percentage Miranda saved by purchasing the coat on sale can be calculated as follows,

First, subtract the regular price from the price at which she purchased

145 - 101.50 = 43.5

Now, divide this number by the regular price of the coat,

43.5 ÷ 145 = 0.3

Now, the percentage Miranda saved can be calculated by multiplying the result by 100,

0.3 × 100 = 30%

Hence, the percentage Miranda saved by purchasing the coat on sale is calculated to be 30%.

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Answer:

7

Step-by-step explanation:

If he made 6 in the first game and 34 total, then we cant subtract 34 from 6 to find how many he made in the 4 remaining games.

34 - 6 = 28

Now simply divide 28 by 4 to figure out how much he made in each game

28 / 4 = 7

The ladder reaches 24 feet high on the building.

The given parameters are:

Length of ladder (l) = 30 feet

Base of the ladder (b) = 18 feet

The height (h) of the ladder on the wall of the building is calculated as

h^2 =l^2 - b^2

This gives

h^2 = 30^2- 18^2

Evaluate

h^2 = 576

Take the square rots

h = 24

Hence, the ladder reaches 24 feet high on the building.

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The length of the rectangle is 7.875 meters and the width of the rectangle is 5.625 meters.

Perimeter of a rectangle = 2(length + width)

27 = 2(1.4x + x)

27 = 2(2.4x)

27 = 4.8x

x = 27/4.8

x = 5.625

Therefore,

Length of the rectangle = 1.4x

= 1.4(5.625)

= 7.875 meters

Width of the rectangle = x

= 5.625 meters

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The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.

Given the expression in the question;

( 1 + 1/3 )² - 2/9

Add the two terms inside the parenthesis

( (3+1)/3 )² - 2/9

( 4/3 )² - 2/9

Apply product rule to 4/3

4²/3² - 2/9

Raise 4 and 3 to the power of 2

16/9 - 2/9

Combine the numerators over common denominator

( 16 - 2 ) / 9

14/9

Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.

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The pressure inside the container is 81.625 pascals

From the question, we are to determine the pressure applied inside the container

From the Pressure equation, we have that

P = F/A

Where P is the pressure

F is the force

and A is the area

From the given information,

F = 1306 N

A = 16 m²

P = 1306/16

P = 81.625 pascals

Hence, the pressure inside the container is 81.625 pascals

Here is the complete question:

In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied?

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A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain and the outputs are called the range.

The range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain and the outputs are called the range.

We have,

f(x) = |x| + 3

We need to find the range of f(x).

We can have x values of any real numbers.

For x = 0,

f(0) = 0 + 3 = 3

For x = 1,

f(1) = 1 + 3 = 4

For x = 2,

f(2) = 2 + 3 = 5

For x = 3

f(-3) = |-3| + 3 = 6

For x = -1,

f(-1) = |-1| + 3 = 1 + 3 = 4

For x = -2,

f(-2) = |-2| + 3 = 2 + 3 = 5

For x = -3,

f(-3) = |-3| + 3 = 3 + 3 = 6

We see that,

If we take x = 0, 1, 2, 3, 4, .... the f(x) values increases from 3, 4, 5, 6 and so on.

If we take x = 0 , -1, -2, -3, ..... the f(x) values increases from 3, 4, 5, 6 and so on.

This means that f(x) values are from 3 to infinity for x ∈ R

[ R = real numbers ]

Thus the range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.

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Answer:

Step-by-step explanation: i think C is the answer

NO, for such a triangle to exist is impossible.

We are given two angles of 110° and 140°.

We have to find whether Triangle with given angles (110° and 140°) is possible or not.

We will utilize the basic knowledge of triangles and their angles to solve this problem. As we know, the sum of all triangle angles is 180°.

If

let the third angle be x

110° + 140° + x = 180

according to the angle sum property of triangles

then,

x = 180° - 250°

which is not possible.

And if we add 110 and 140, we will get 250° as a resultant, which is much greater than the sum of the three angles.

Therefore, a triangle with 110° and 140° as two of its angles is not possible.

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