A circle is inscribed in quadrilateral , tangent to at and to at . Given that , , , and , find the square of the radius of the circle.

By using the fact that the two images are similar, we can write and solve a linear equation to get x = 3/2.

We know that the two figures are similar, then, if we take the quotient between the adjacent sides for both figures, these quotients should give the same value.

Thus, we can write the equation:

14/10 = (x + 9)/(x + 6)

Now we can solve that equation for x, if we multiply both sides by (x + 6) we will get:

(14/10)*(x + 6) = x + 9

Now we can multiply both sides by 10 to get:

14*(x + 6) = 10*(x + 9)

14x + 84 = 10x + 90

Now we can solve this linear equation for x.

14x - 10x = 90 - 84

4x = 6

x = 6/4

x = 3/2

That is the value of x.

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Answer:

Yes

Step-by-step explanation:

y = x has the inverse x = y

The measure of the angle ∠PQS will be 53°. Then the correct option is C.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

If angle ∠PQR measures 75°. And angle ∠PQS measures 22°.

Angle ∠SQR and angle ∠PQS are the adjacent angles. Then we have

∠PQS + ∠SQR = ∠PQR

∠PQS + 22° = 75°

∠PQS = 53°

The measure of the angle ∠PQS will be 53°. Then the correct option is C.

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Complete question is attached below.

When these equations are solved, the value of x is 4 and the value of y is 3. Therefore, the value of x + y = 7.

To solve the system of equations, we will use the elimination method.

First, we multiply the first equation by 3 and the second equation by 5.

3(3x + 5y = 9)

5(5x + 3y = 7)

Then, we add the equations together:

9x + 15y = 27

25x + 15y = 35

Now, we subtract the second equation from the first to eliminate the x terms:

-16y = -8

y = 0.5

Next, we plug this value for y into one of the original equations and solve for x:

3x + 5(0.5) = 9

3x = 8.5

x = 2.83

Finally, we plug the values of x and y into the original equation to verify that they are correct:

3(2.83) + 5(0.5) = 9

So, the value of x is 2.83 and the value of y is 0.5. Therefore, the value of x + y = 2.83 + 0.5 = 3.33.

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Answer: 11, 23, 166

Step-by-step explanation:

Hiya! From the drawings, I'm assuming all of the triangles are right-angled triangles. If they aren't though, tell me and I'll tell you how to solve them.

Anyways, assuming they are right angled-triangles, you can use Pythagoras' Theorem (aka a² + b² = c²)

c is the hypotenuse or the side opposite the right angle.

a and b are just the other two sides (doesn't really matter which is which)

Question 7:

c² = a² + b²

12² = a² + 5²

144 = a² + 25

144 - 25 = a²

119 = a²

a = 10.908712114635714411502154487373

(To the nearest whole number: 11)

Question 8:

c² = a² + b²

24² = 7² + b²

576 = 49 + b²

576 - 49 = b²

527 = b²

b = 22.956480566497992703585747092065

(To the nearest whole number: 23)

Question 9:

c² = a² + b²

c² = 90² + 140²

c² = 8,100 + 19,600

c² = 27,700

c = 166.43316977093238068928214785346

(To the nearest whole number: 166)

Hoped this helped! Tell me if there's something you don't understand. :)

The player who goes first will win.

This is because the chocolate bar can be broken up into 6*8=48 squares, and the player who goes first can always ensure that the second player is left with one square on their turn (by breaking the bar into two pieces that leave one square for the second player to take). This means that the second player will always be the one who cannot make a break, and thus loses the game.

Therefore, The player who goes first will win.

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The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.

1. It has a definite starting point and a definite ending point.

2. It has a definite length.

3. It has a definite direction.

4. It has a slope and equation.

5. It divides the plane into two parts.

6. It is symmetric about its mid-point.

7. It is two-dimensional.

A directed line segment is a line segment that has a definite starting point and a definite ending point. Its length is the distance between the two points and it has a direction, given by the vector from the starting point to the ending point. The line segment divides the plane into two parts. It is symmetric about its mid-point, which is the point halfway between the two endpoints. It has a slope and an equation. The slope is the ratio of the change in y-coordinates to the change in x-coordinates. The equation of the line segment is written in the form y = mx + b, where m is the slope and b is the y-intercept. Finally, a directed line segment is two-dimensional.

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On solving the provided question, we can say that the sequence what we tell on day 3 = he sold 5; on day 4 = he sold 7; on day 5 = he sold 9

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.

here,

on day 1 = he sold 1

on day 2 = he sold 3

on day 3 = he sold 5

on day 4 = he sold 7

on day 5 = he sold 9

.

.

.

.

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Let's start by using the provided information to formulate an equation.

Kelly starts with $800 in her savings account, so this is the initial amount. She makes $340 per week, 15% of which is invested into her savings account for 8 weeks, so this information will form a rate. Kelly also withdrew (subtracted) 45 dollars 3 times. Now, let's form the equation.

y=8(.15·340)+800-45(3), where y=remaining balance after 8 weeks. Now, lets simplify the equation using Orders of Operations.

Simplify parenthesis first:

y=8(.15·340)+800-45(3)

y=8(51)+800-45(3)

Complete any multiplication:

y=8(51)+800-45(3)

y=408+800-135

Add and subtract from left to right; addition and subtraction are not separate steps and must be done in the same step, so we work left to right as to whichever comes first:

y=408+800-135

y=1208-135

y=1,073

Remember that y is the remaining balance after 8 weeks. This means that $1,073 dollars is the balance after 8 weeks.

Hope that helps, and feel free to give Brainliest!

The account balance at the end of 8 weeks is $1073.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Kelly has a savings account with a beginning balance of $800 and she earns $340 per week.

Therefore, 15% of her weekly earnings for 8 weeks is,

= (15/100)×340×8.

= $408.

Again, She made $45 withdrawals 3 times, which is,

= 3×45.

= $135.

Therefore, The final amount in her account after 8 weeks is,

= $(800 + 408 - 135).

= $1073.

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Answer: Nonresponse, voluntary, and convenience.

Step-by-step explanation:

For the first question, it should be noted that everyone cannot respond as only the people who have strong opinions will respond. Therefore, it's a nonresponse error.

For the second question, the people will have to volunteer. Therefore, it's a voluntary bias while the third one is a convenience sample as it's an easily available sample.

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The distance traveled after 2 hours will be 324 miles.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

The table shows the average speed of the winner of a car race for different

years.

year      average speed

2005     135.17

2010      137.28

2015      161.94

2020     141.11

In order to find out how many miles the winner of the car race in 2015 traveled after 2 hours, we need to know the average speed at which they were traveling, which is given as 161.94 miles per hour. To find out how far they traveled in 2 hours, we can multiply this speed by the time, measured in hours.

So, if the average speed was 161.94 miles per hour, then the distance traveled in 2 hours is:

161.94 miles/hour × 2 hours = 323.88 miles.

Rounding up to the nearest whole number, the distance traveled after 2 hours is 324 miles.

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The question seems to be incomplete the missing table has been attached below

Answer:

0.16 btw thanks for the points

Answer: 0.16

Step-by-step explanation:

put 16 over 100 and divide it. Then you get your answer 0.16.

7 students failed the examination out of 28 students who appeared for the examination.

What is the Proportion?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls)

When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.

For instance, 5/10 equals 1/2.

If 3/4 of the students passed the exam, this means that 1 - 3/4 = 1/4 of the students failed the exam.

We can use this information to find the number of students who failed the exam by multiplying the total number of students who appeared for the exam by the proportion of students who failed:

Number of students who failed = Total number of students * Proportion of students who failed

Number of students who failed = 28 students * 1/4 = 28 students * 0.25 = 7 students

Hence, 7 students failed the examination out of 28 students who appeared for the examination.

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Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.

Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for  creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

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Answer:

Yes, Tamara is correct that the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y).

The Distributive Property states that for any real numbers a, b, and c, we have:

a(b + c) = ab + ac

This property allows us to distribute a factor to each term within a set of parentheses.

In this case, Tamara used the Distributive Property to rewrite the expression 21x + 56xy as an equivalent expression. She did this by taking the factor of 7 and distributing it to each term within the parentheses:

7(3x + 8y) = (73x) + (78y) = 21x + 56xy

Therefore, the correct expression is 7(3x + 8y).

Step-by-step explanation:

Each video game = $19 and each DVD = $ 32

An equation is a mathematical statement that represent that two expressions are equal. An equation can be formed by one or more variables along with numerical terms.

let, x denotes the cost of each video games.

y denotes the cost of each DVD

Katie bought 2 games and 3 DVD and total spent $134.

the equation can be written as 2x + 3y = $134 .......equation 1

Emily bought 1 less video game than Katie that means she bought 1 game.

 and    2 more DVD than Katie that means 5 DVD bought by Emily.

total spent of Emily = $179

The equation will be x + 5y = $179...... equation 2

in order to solve the two equations by addition method

we multiply by 2 to the second equation.

2x + 10y = 358

the first equation 2x +3y = 134

                             2x + 10y = 358

                            -       -          -

                    by subtracting we get,

                         - 7y = -224

                         y = 32

from the 2nd equation we get x = -5×32 + 179

                                       x = 19

each video game cost $ 19 and each DVD cost $ 32

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The sum of the two polynomials 6s²t – 2st² and  4s²t – 3st² is 5(2s²t – st²) in factorized from.

One or more algebraic terms (monomials) are combined mathematically to form a polynomial. Poly- (many) and -nomial (terms) are the roots of the word "polynomial".

A polynomial can have exponents (powers), constants (numbers), and variables (letters), but never negative exponents or division by a variable.

In standard form, polynomials prefer to be expressed. In addition, the exponents are arranged in descending order because they don't contain any similar terms (largest to smallest).

The sum of two polynomial is

⇒6s²t – 2st² + 4s²t – 3st²

= 6s²t + 4s²t – 3st²– 2st²

= 10s²t – 5st²

= 5(2s²t – st²)

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Full question

What is true about the sum of the two polynomials?

6s²t – 2st² and  4s²t – 3st²

Answer:

y=1/2x-3

Step-by-step explanation:

y=mx+b

y=1/2x-3

The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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ans Is here i) 1/9

ii) 3

tq brainlest?

To find the inverse of a function, you can follow these steps:

Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.

Solve the equation for y. In this case, you would get:

x = √y + 8

y = x - 8

Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:

f^-1(x) = x - 8

This is the inverse function of y = √x + 8.

Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.

Therefore, the solution of the given problem of function comes out to be [tex]f^{-1}[/tex] =  x+ 6 /7.

Mathematics includes the study of numbers, equations and associated structures, forms and the environments in which they occur, quantities and their changes, and spatial relationships. A function is an association between such a set of inputs, each of which has an output. Simply described, a function is an association between the inputs and outputs in which each input results in a single, distinct result. Each operation has a domain and a scope, which are also referred to as codomains.

Here ,

In our case, f(x) = y = 7x-6.

The following procedures must be taken in order to determine the inverse function of the given function:

First, x and y must be switched, thus

x= 7y-6

We must add 6 to both sides in order to solve for y in the following step.

x+6=7y

7 divided by both sides, that is

y = x+ 6 /7

Therefore, the solution of the given problem of function comes out to be

[tex]f^{-1}[/tex] =  x+ 6 /7.

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The answer is yes, she does and she still has 10 minutes free.

What is time ?

Time can be defined as the sequence on which particular event exists and time can measured in minutes , seconds, and hours.

Given,

The film started at 14 30. The film is 105 minutes long.

When the film ends, Liz takes 20 minutes to get to the bus stop.

105min=1h 45min

14h 30min + 1h 45min= 16h 15min

16h 15min + 0h 20min=16h 35min

16h 45min - 16h 35min= 10min

Hence, the answer is yes, she does and she still has 10 minutes free.

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A triangle is a polygon with 3 sides, and the sum of its interior angles is 180 degrees.

The properties of a triangle are:

There are several types of triangles, including:

Equilateral triangle: This is a triangle with three sides of equal length and three angles of 60 degrees.

Isosceles triangle: This is a triangle with two sides of equal length and two angles of equal measure.

Scalene triangle: This is a triangle with three sides of different lengths and three angles of different measure.

Right triangle: This is a triangle with one 90-degree angle.

Acute triangle: This is a triangle with three angles that are all less than 90 degrees.

Obtuse triangle: This is a triangle with one angle that is greater than 90 degrees.

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draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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$1862  is Devi red from his biweekly paycheck for medical insurance

percentage, a relative value indicating hundredth parts of any quantity.

The annual cost of Randall coverage is 4900.

The college pays 62% of the cost.

We need to find How much is Devi red from his biweekly paycheck for medical insurance

Let us convert 62% to decimal value by dividing with 100

62/100=0.62

Now multiply 0.62 with 4900

0.62×4900

3038

Now subtract 3038 from 4900

4900-3038

1862

Hence, $1862  is Devi red from his biweekly paycheck for medical insurance

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