The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by \[\frac{1}{r}

Zero is the middle point of a number line.

On the number line, all positive (natural numbers) numbers are on the right side of zero, while all negative numbers are on the left. A number's value lowers as we turn to the left. As an illustration, 1 is greater than -2.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. [1]

The integers are frequently represented as specially designated, uniformly spaced dots on a line. It is frequently employed as a teaching tool for basic addition and subtraction, particularly when negative numbers are involved.

The number line may also be referred to as a real line or real number line in advanced mathematics.

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Answer:

8.66 years

Step-by-step explanation:

F = Pe^(rt)

2 = e^(0.08t)

ln 2 = ln [e^(0.08t)]

ln 2 = 0.08t

t = (ln 2)/0.08

t = 8.66

Answer: 8.66 years

Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{35}{m}=\cfrac{m}{7}\implies 245=m^2\implies \sqrt{245}=m\implies \sqrt{7^2\cdot 5}=m\implies 7\sqrt{5}=m[/tex]

Answer:

24.90 pound

1 dollar equivalent to 0.8301 pound

so 30 dollar will be 30 multiply by 0.8301

which equals 24.903 pounds

Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

The value of the shortest of the four side lengths of the quadrilateral is 30 cm

The perimeter of a quadrilateral is the sum of all the sides.

Perimeter of the Quadrilateral = 132 centimeters

Let

The shortest side = x

Since, the sides are consecutive even integers;

Second side = (x + 2)

Third side = (x + 4)

Fourth side = (x + 6)

Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side

132 = x + (x + 2) + (x + 4) + (x + 6)

132 = x + x + 2 + x + 4 + x + 6

132 = 4x + 12

132 - 12 = 4x

120 = 4x

divide both sides by 4

x = 120/4

x = 30 centimeters

Therefore,

Second side = (x + 2)

= 30 + 2

= 32 cm

Third side = (x + 4)

= 30 + 4

= 34 cm

Fourth side = (x + 6)

= 30 + 6

=36 cm

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Answer:

  (a)  (5, 9)

Step-by-step explanation:

You want the solution to the system ...

The value of x is already given, so no work is required to find that.

The value of y is found by using that value of x in the equation for y:

  y = 2x -1

  y = 2·5 -1 = 10 -1 = 9

The solution is (x, y) = (5, 9).

Answer:

[tex]x = \sqrt{87}[/tex]

Step-by-step explanation:

So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's  [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:

[tex]13^{2} + x^{2} = 16^{2}[/tex]

Now, we will simplify the equations:

[tex]169 + x^{2} = 256[/tex]

Then, we will subtract 169 from both sides, giving us:

[tex]x^{2} = 87[/tex]

Square rooting both sides gives us:

[tex]x = \sqrt{87}[/tex]

And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.  

Hope this helped

The average tuition for two randomly chosen in-state and out-of-state students is around $1,508 less than the mean of $6,348.75.

Mean Deviation

The average deviation from the mean value of the provided data set is determined using the mean deviation, which is defined as a statistical metric.

Given

μS = $6,348.75

σS = $1508.48

The average sum of the tuition fees is $6348.75

As a result, it follows:

The standard deviation of the tuition for in-state students is measured as a difference from 6348.75.

The standard deviation for out-of-state students gauges how their tuition is different from 1508 in total.

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Answer:

[tex]80^{\circ}[/tex]

Step-by-Step Explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Answer: The slope is the cost per hour (in this case $20 per hour).

=========================================================

Further Explanation:

Recall that,

[tex]\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}[/tex]

The rise tells us how much to go up or down, depending if the rise is positive or negative. The run tells us how much to go to the right. Always move to the right.

In this problem, the change in y is the change in price. The change in x is the change in hours. Dividing the two items gives cost per hour, aka unit cost.

-----------------------

Example:

Let's pick two points from this line and use the slope formula. I'll pick (1,60) and (3,100) as they are the only two points with coordinate labels.

So,

[tex](x_1,y_1) = (1,60) \text{ and } (x_2,y_2) = (3,100)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{100 - 60}{3 - 1}\\\\m = \frac{40}{2}\\\\m = 20\\\\[/tex]

The slope is 20, or 20/1

It says that each time the number of hours x goes up by 1, the cost variable y goes up by 20.

Put simply: The hourly fee is $20 per hour.

This matches what it says in the instructions when your teacher wrote "A roofer charges $60 for the first hour and $20 per hour for each additional hour".

Answer:x=5

Step-by-step explanation:

f(x) = g(x)

[tex]\frac{1}{2}(3x-1)=7\\\\ \frac{3}{2}x-\frac{1}{2} =7\\\frac{3}{2}x-\frac{1}{2}+\frac{1}{2} =7+\frac{1}{2} \\\\\frac{3}{2}x=\frac{15}{2} \\\frac{3}{2}x*\frac{2}{3} =\frac{15}{2}*\frac{2}{3} \\\\x=5[/tex]

Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables

If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.

When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.

To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:

Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)

So if tt represents the number of tables Zachary waits on, then he can expect to earn:

Earnings = $40 + $7 x tt

For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.

Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.

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The linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

What is a system of linear equations?

A system of linear equations is a set of two or more linear equations that describe a relationship between multiple variables. The variables in each equation are related to each other, and the solution of a system of linear equations is the set of values that satisfy all of the equations in the system.

In this case, since Kent and Rew each bought the same amount of boondins and hopts, we can use the same variable names (x for boondins and y for hopts) for both of them. We can use this information to write two equations to model the relationship between the amounts of boondins and hopts that Kent and Rew bought:

4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

This system of linear equations is called a system of two equations in two variables.

Hence, the linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)

6x + 2y = 60 (the equation representing the total cost of Rew)

and the solution would be x = 8, y = 6.

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The missing term of the arithmetic sequence is 2 1/2

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the equation will be

A = 1 3/8 , 1 3/4 , 2 1/8 , x , 2 7/8

The first term a₁ = 1 3/8

The second term a₂ = 1 3/4

The common difference d of the arithmetic sequence d = second term - first term

Common difference d = 1 3/8 - 1 3/4 = 3/8

Now , the fourth term of the arithmetic sequence is given by

Tn = a + (n - 1) d

Substitute the values in the equation , we get

a₄ = 1 3/8 + ( 4 - 1 ) ( 3/8 )

a₄ = 11/8 + 9/8

a₄ = 20/8

a₄ = 2 4/8

a₄ = 2 1/2

Therefore , the fourth term is 2 1/2

Hence , it is an arithmetic sequence and the fourth term is 2 1/2

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Answer: -37

Step-by-step explanation: -11-26

Answer: The answer is $1,317.50

Step-by-step explanation:

First, Find how much they earn in the goods sale.

Make $1,700, their goal to earn, into 1,700/1 and set it to multiply that by 2/5, the fractional amount of money earnt at the goods sale proportional to how much they have to earn.

Simplify that by crossing 1,700 and 5 into a 340 and 1.

Multiply 340/1 by 2/1 to get 680/1.

Make that into a whole number ($680) to show how much money earnt from the goods sale.

Secondly, find how much money they earn by the Bingo Night

Make 1,700, like last time, into 1,700/1 and set it to multiply 3/8, the fractional amount of money earnt from the Bingo Night proportional to how much they have to earn

You can't simplify, so just multiply the amount.

If you multiply, you will get 5,100/8.

Divide 5,100 by 8 (the divisor by the dividend).

Make sure to also add the 0 after the tenths place after you get your quotient, which is supposed to be 637.5 (or $637.50)

Lastly, You have to add them up.

Add $637.50+$680.

You shall get $1,317.50

The modulus of 2 - 3i is √13. So, the correct option is d.

Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.

It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.

Let z = -2 - 3i

z = (-2) + (-3)i

Modulus of z = √((-2)² + (-3)²)

√(4 + 9) = √13

Modulus of z = √13

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A student needs to receive 20 out of a possible 50 points on the test in order to receive a passing grade of 40%.

The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value. When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.

given

test score to 50 points

test score of 40 %

= 50/100 * 40

= 20

A student needs to receive 20 out of a possible 50 points on the test in order to receive a passing grade of 40%.

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Answer: 0.8 what?

Step-by-step explanation:

prolly likely

The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The triangle ABC and PDF are concurrent by AAS,

The AAS concurrency required two angles and one side to be equal,

Here,

AB = PD,

∠ ABC = ∠ PDF

Now one more angle is required to be equal,

∠ ACB = ∠ PFD  

Thus, the missing angle is ∠ ACB and ∠ PFD.

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Answer:

yes, it uses the Commutative Property

Step-by-step explanation:

Answer: 54 inches squared

Step-by-step explanation:

Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.

In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.

The base and height of an isosceles triangle can be found by using the Pythagorean theorem.The hypotenuse is also the base of the triangle.

First, you need to determine the length of the two sides that are equal, which are referred to as the "legs" of the triangle. Then, use the Pythagorean theorem to find the length of the hypotenuse, which is the longest side of the triangle.

Once you have determined the length of the hypotenuse, the height of the triangle can be found using the formula, h = √(b^2 - (l/2)^2). In this formula, b is the length of the hypotenuse, and l is the length of the legs.

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The == operator determines if two operands are equivalent in terms of value. The === operator determines if two operands are equivalent in terms of value and datatype.

The assignment operator = is straightforward. The left side operand receives values from the right side operands.

On the other hand, == determines whether or not the values of two operands are equal.

The Python is operator determines if two variables point to the same memory item as opposed to the == operator, which compares the value or equality of two objects. This implies that you should almost always employ the equality operators == and != Difference between == and = in Python.

A single equal sign is used to assign a value to a variable in Python and many other programming languages, whereas two successive equal signs are used to determine if two expressions provide the same result.

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Check the picture below.

The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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The equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

Option (D) is correct.

What is a linear equation?

A linear equation is an equation that can be written in the form of

y = mx + b

Where x and y are variables and m and b are constants. This is also known as the slope-intercept form of a linear equation. The slope of the line (m) represents the steepness of the line and the y-intercept (b) represents the point where the line crosses the y-axis.

Luciana is adding water to the pool at a constant rate of 9 gallons per minute. So, for every minute that passes, the number of gallons in the pool increases by 9. This relationship can be represented by the equation W = 12,000 + 9m, where W is the total number of gallons in the pool and m is the number of minutes that have passed.

Hence, the equation that represents the total number of gallons of water in the pool, w, after Luciana adds water for m number of minutes is W = 12,000 + 9m.

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The given series is convergent and the sum S∞ is 5.555

Think about 10 - 8 - 6.4 - 5.12

If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.

the average ratio,

r = -8/10

⇒ r = -0.8

This equals 1 - 0.8 - 1.

The presented series is hence convergent.

Sum of series = S∞ = a/(1 - r)

Here, first term(a) = 10,

common ratio(r) = -0.8,

S∞ = a/(1 - r)

⇒ S∞ = 10/(1 - (-0.8))

⇒ S∞ = 10/(1 + 0.8)

⇒ S∞ = 10/1.8

⇒ S∞ = 5.555

Therefore, the given series is convergent and the sum S∞ is 5.555

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