write the equation of a circle given the center (2, 9) and radius r = 3

Statements and reasons.

1) ∠1 and ∠3 are supplementary

Reason: This is true because it is stated in the question.

2) ∠1 + ∠3 = 180º

Reason: By statement 1, ∠1 and ∠3 are supplementary, and by definition, supplementary angles sum up 180º.

3) ∠2 = ∠3

Reason: From the picture we see that ∠2 and ∠3 are opposite congruent angles, so they are equal.

4) ∠1 + ∠2 = 180º

Reason: from statement 2 we have ∠1 + ∠3 = 180º, and from statement 3 we have ∠2 = ∠3, so we have ∠1 + ∠2 = 180º.

5) ∠1 and ∠2 are supplementary

Reason: from statement 4 we have that ∠1 sum up ∠2, so by definition ∠1 and ∠2 are supplementary.

6) line m || line n

Reason: from the picture we see that ∠1 and ∠2 are internal collateral angles of the lines m and n, and from statement 5 we know that ∠1 and ∠2 are supplementary, so we have that the angle between line m and line n is 180°, and by definition, they are parallel lines.

Summary of the reasons

1) It is stated in the question

2) By statement 1 and by definition of supplementary angles.

3) Because they are opposite congruent angles, so they are equal.

4) By statement 2 and 3.

5) By statement 4, and by definition of supplementary angles.

6) By picture ∠1 and ∠2 are internal collateral angles of the lines m and n, and by statement 5 they are supplementary so they are parallel lines.

Line's equation is y=(1/5)x + 2.

In elementary geometry, two geometrical objects are perpendicular if they intersect at a right angle. The condition of perpendicularity can be graphically represented using the perpendicular symbol,. Any pair of lines, any pair of planes, or any pair of lines and planes can be used to define it.

The arrow

In slope-intercept form, y=-5x12

y=mx+b

where the slope m is.

Thus, the slope of this line is

m= -5

Slopes on perpendicular lines are reciprocally negative. In other words, modify the sign by taking the slope's reciprocal.

The reciprocal of (-5) in the negative is 1/5.

Plug in the point to determine b in the formula y = (1/5)x + b.

4 = (1/5)(10) + b

4 = 2 + b

b = 2

The perpendicular line passing through the indicated point is y= (1/5)x + 2.

Thus, the equation of the line that is perpendicular to the line y = -5x - 12 and passes through the point is y= (1/5)x + 2.

point (10, 4). (10, 4).

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The equation of the line will be expressed as x = 5.

Slope of a line may be defined as the steepness of a curve plotted on paper. The slope of a line between two points (x₁, y₁) and (x₂, y₂) can be calculated by formula m = (y₂ - y₁)/(x₂ - x₁).

If we have two points and we have to find equation of line through two points (x₁, y₁) then equation will be (y - y₁) = m(x - x₁) where m is the slope of line.

We have two points (5, 3) and slope is undefined.

Undefined slope can be expressed as 1/0. So, the equation of line through (5, 3) will be

(y - 3) = 1/0 (x - 5)

=> x - 5 =0

=> x = 5

This is the equation of line, and this line will be parallel to y-axis.

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Answer: -10 or 9

Step-by-step explanation:

Let the number be x. Then,

[tex]x^2 +x=90\\\\x^2 +x-90=0\\\\(x+10)(x-9)=0\\\\x=-10, 9[/tex]

Answer:

First one is 92

Step-by-step explanation:

Answer:

1. 9/2

2. 7 3/13

3. 3 13/15

4. 3 25/27

5. 2 1/4

6. 3 30/91

7. 2 5/21

8. 6 3/5

Step-by-step explanation:

When I put it like 2 5/21 I mean it's a mixed number.

Now I'll tell you the steps.

1. Find the common denominator (The denominator is the bottom number of the fraction. To find it you have to write out the multiplies of each number and once a number is the same that's the common denominator.)

2. Multiply the numerator by the amount of times it took to find the common denominator. (The numerator is the top number of the fraction. And the amount of times you'll have to multiply the numerator depends. I'll put an example below)

Example:

4/20 ÷ 7/2

2 goes into 20, 10 times so you have to multiply 7 by 10.

Then you'll get

70/20.

Now you can solve it.

4/20÷70/20

(I put random numbers so the answer may turn out funky this is just an example.)

3. Divide the fractions

4. Simplify answer if possible

I hope this helped!

The ratio of the number of students who want waffles to the total number of students is 3 : 26 students

Ratio refers to the number representing a comparison between two named things or quantities.

Number of students who wants waffles = Total number of students - Number of students who wants pancakes

= 26 students - 23 students

= 3 students

Ratio of the number of students who want waffles to the total number of students = 3 students : 26 students

So therefore, the ratio of the number of students who want waffles to the total number of students separated by a colon is 3 : 26

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"Subtract to eliminate x" is correct option that is option C for the given set of equations -3x+2y=-15 and -3x-6y=9. equation defines "A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis".

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

-3x+2y=-15

-3x-6y=9

subtract to eliminate x

8y=-24

For the given set of equations, -3x+2y=-15 and -3x-6y=9, option C, "Subtract to eliminate x," is the correct option. Equation explains "The general equation of a straight line is y = mx + c, where m stands for the gradient and y = c for the point where the line crosses the y-axis. This value c is referred to as the intercept on the y-axis. The equation of a straight line with gradient m and intercept c on the y-axis is represented by Y = mx + c ".

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The inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

So, the inequality can be:

Issac earns:-

Isaac wants to earn $450,

So, the inequality that can be formed here is:

Let, 'x' be the number of times Isaac sell the tickets.

By solving we will get:

Therefore, the inequality to find the number of tickets Isaac needs to sell to earn than $450 is 100 + 3x ≤ 450 and the number of times he will sell the tickets is 117.

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Answer:

y=12

Step-by-step explanation:

1.Took the ratio between x and y value.

18:6 is the same as 3:1 ratio this means that our y value will be 3 times greater than our x value.

Answer:

[tex]1\frac{11}{20}[/tex]

Step-by-step explanation:

155% = 155 / 100 = 1.55

1.55 =155/1 × 100 / 100 = 155 / 100

155 / 100 = 31 / 20

31 / 20 = 1 11/20

Answer:

Step-by-step explanation:

If after one year, she received a total of $620 in interest.  The amount that she invest in each account is 2,000 amount invested at 7% , 8,000 amount invested at 6.

Let x represent the amount invested

Hence,

.07x + .06(10,000-x) =620

.07X+600-.06x = 620

Combine like terms

.01x =620-600

.01x=20

Divide both side by .01x

x=20/.01

x =2,000 amount invested at 7%

So,

10,000-2,000 = 8,000 amount invested at 6%

Check :

.07 × 2,000+.06× 8,000=620

150 + 480 = 620

620 =  620

Therefore we can conclude that $2,000 was invested at 7% and $8,000 was invested at 6%.

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Answer:

It unexpected, but did you know you could live over 40 years on just pizza! Crazy! It's not so good tho because of all the salt in it, so that's not THE HEALTHIEST. I've looked it up and, fish seems to be the top choice when it comes to what's good for you. I've also have come across dark green vegetables too.

Step-by-step explanation:

I didn't notice you were just talking about what tastes good rather than whats healthiest.... eh! YOUR NOW EDUCATED!!!

Hope it helps! =D

The points -5 2/3 and 5 1/3 in the number line attached

An equation shows the relationship between two or more numbers and variables.

Number line a line containing numbers marked at intervals.

The mixed fraction -5 2/3 is equivalent to -[(5 * 3 + 2)/3] = -17/3

The mixed fraction 5 1/3 is equivalent to [(5 * 3 + 1)/3] = 16/3

The points -5 2/3 and 5 1/3 are represented

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Answer:

40

Step-by-step explanation:

why? because there are 5 pieces in each building set so 5×8=40 so the answer is 40

The probability that at least one of them will score a goal if they each play the ball once is 47/48.

Probability is a mathematical and scientific term that describes the possibility or occurrence of an event. Many events are difficult to predict with absolute accuracy. Only the likelihood of an event occurring, i.e. how likely it is, can be predicted using probability.

Given:

The probabilities of Wukong and Nice scoring in the match are 7/8 and 5/6 respectively.

The probability that at least one of them will score a goal is,

=  1 - P(both of them not scoring a goal)

So the probability of Wukong and Nice not scoring a goal in the match is,

(1 - 7/8) (1 - 5/6) =  (1/8)(1/6) = 1/48

Now the required probability is,

=  1 - P(both of them not scoring a goal)

= 1 - 1/48

= 47/48

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Considering the table of f ( x ) and graph of g ( x ), the value of the expression  [tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex] is represented by 3

The table represents the values of f ( x ). Using the table, checking the value of f ( x ) when x = 1 gives f ( x ) = 1

Using the graph, the value of g ( x ) when x = 1 is traced to give a value of -1

substituting the values of f ( x ) = 1 and g ( x ) = -1  into the equation

[tex]\lim_{x \to 1} 2f(x)+g(x)^2[/tex]

[tex]=\lim_{x \to 1} 2f(1)+g(1)^2[/tex]

[tex]=2(1)+(-1)^2[/tex]

= 2 + 1

= 3

This makes the third option the best choice and the value is 3

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We will have the following:

From the problem we will have the following expressions:

Now, from this we determine the value for the bill on september:

Now, since there are 3 people, the payment for each one is:

So, the payment for each one is $26.87 in September.

The slope-intercept form a of the equation of a line is:

Where m is the slope and b is the intercept.

For this exercise m = -1 and b = -1

To find the 'y' values of the table you just have to replace the x values into the equation:

And put these pairs into the graph and join them with a line:

Answer:

10.4

Step-by-step explanation:

explanation in photos

Answer:

Step-by-step explanation:

The largest number of weights Jennifer could own is 798.

Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.

We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.

Given: The collection of weights : 4 , 6 and 9 pounds

The total weight of the weights = 42 pounds

Thus the largest number of weights jennifer could own is 4+6+9 = 19 multiplied  by the total weight of the weights

= 19 × 42

= 798.

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Answer:

discriminant =b^2 -4ac

= (12)^2 -4(-4)(-9)

=0

[tex]3y + 37 + 4y = 9 \\ 3y + 4y = 9 - 37 \\ 7y =- 28 \\ \frac{7y}{7} = \frac{-28}{7} \\ y = -4[/tex]

ATTACHED IS THE SOLUTION

Answer: -20

Step-by-step explanation: 16 x 1/4 - 4x 6

Answer:

x = 29

y = -18

Step-by-step explanation:

5(29) + 6(-18) = 37

145 - 108 = 37

:)