the graph of the equation below is a circle. what is the length of the radius of the cirlce? (x+5)2+(y+7)2=21^2

s^2 means we're squaring the number s

For example, if s = 3, then s^2 = 3^2 = 3*3 = 9

This is likely a formula to find the area of a square. In the example above, the square would have a side length of 3 leading to an area of 9.

The statement 'The experimental procedure is to bet on one object. Then, roll three Lucky Dice and count the number of matches. The number of matches will decide your profit.' is an example of empirical probability. Empirical probability is calculated by dividing the number of times an event occurs by the total number of opportunities for the event to occur.

The statement 'The experimental procedure is to bet on one object. Then, roll three Lucky Dice and count the number of matches. The number of matches will decide your profit.' is an example of empirical probability.

Empirical probability is calculated by dividing the number of times an event occurs by the total number of opportunities for the event to occur. In this case, the student is rolling three dice and counting the number of matches, which is an observation-based approach to determining the probability.

An example of empirical probability in action is conducting an experiment to see how many times a specific outcome occurs, such as rolling dice or flipping coins, and then using that data to calculate the probability of that outcome happening.

The statement that represents an example of empirical probability is:

"In order to find the percentage of bass that he had in his pond this spring, Matt decided to spend 5 days catching a total of 15 fish each day and counting how many of those were bass." Option 4 is correct.

What is empirical probability ?

Actual observations or data gathered from studies or observations serve as the foundation for empirical probability.

In this instance, Matt is gathering information by counting the quantity of bass he catches relative to the total amount of fish he catches over time.

The surface area of a cylinder with a radius of 6.8 inches and a height of 14.2 inches can be estimated by using the formula including both the curved surface area and the area of the bases, then rounding to compare with provided options.

The surface area of a cylinder can be calculated using the formula S = 2πr(height) + 2πr². Substituting the given radius r = 6.8 inches and height L = 14.2 inches, and using π = 3.14, we estimate the surface area as follows:

S = 2πrL + 2πr² = 2(3.14)(6.8)(14.2) + 2(3.14)(6.8)²

The first term accounts for the curved surface area of the cylinder and the second term accounts for the two circular bases. Calculate each part and sum them to estimate the total surface area. To compare to the provided options, we can round to the nearest whole number.

.1 Option D) Surface area of cylinder 923 in².2 Option (B)√41 3.Option (D) 5/13 4.Option (D) 4. 5Option (c)y = 2x + 1.  6 Option (c)53/72

To find the surface area of a cylinder with radius r = 6.8 inches and height h = 14.2 inches, we use the formula for the surface area of a cylinder:

Surface Area = 2πr(h + r)

First, calculate the lateral surface area:

Lateral Surface Area = 2πrh = 2 * 3.14 * 6.8 * 14.2

Lateral Surface Area ≈ 607.04 square inches

Next, calculate the area of the two circular bases:

Area of bases = 2πr² = 2 * 3.14 * (6.8)^2

Area of bases ≈ 290.66 square inches

Now, add the lateral surface area and the area of the bases to get the total surface area:

Total Surface Area ≈ 607.04 + 290.66 ≈ 897.7 square inches

Comparing this with the given options, the closest estimate is:

D) 923 in²

Using the Pythagorean Theorem

To find the distance between points A and B, assuming a right triangle with legs of length 2 and 3:

Distance = √(2² + 3²) = √(4 + 9) = √13

Thus, the best estimate for the distance is:

B) √41

Fraction between 5/12 and 5/11

To find a fraction between 5/12 and 5/11, first convert these fractions to a common denominator:

Common denominator is 132:

5/12 = 55/132

5/11 = 60/132

Between 55/132 and 60/132, the fraction closest to these is:

D) 5/13

Probability of picking an orange marble

If you pick a marble at random and replace it each time over 4 attempts, the best prediction for the number of times you will pick an orange marble will depend on the probability of picking an orange marble once. If the probability is uniform, then:

D) 4

Choosing the correct rule for the graph

Based on given options and typical linear functions, if a graph shows a line increasing with a slope of 2 and a y-intercept of 1:

C) y = 2x + 1

Rational number between 7/8 and 6/9

Convert to a common denominator to find a fraction that fits:

7/8 = 21/24, 6/9 = 16/24

The fraction closest to these is:

C) 53/72

Combine like terms

4y-2y=24-6

2y=18

y=9

Answer-

Set of constraints to model the problem are,

[tex]12x+9y\geq 510[/tex]

[tex]y \leq 2x[/tex]

[tex]y \geq 25[/tex]

Solution-

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

[tex]\text{Earnings of Gwen} = 12x[/tex]

[tex]\text{Earnings of Fabio} = 9y[/tex]

[tex]\text{Total earning} = 12x+9y[/tex]

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

[tex]12x+9y\geq 510[/tex]

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

[tex]y \leq 2x[/tex]

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

[tex]y \geq 25[/tex]

Explanation:

Lets break the problem into steps and observe the constraints:

So Fabio and Gwen they are trying to save money and altogether they need at least $510.00.

Gwen charges $12.00 each time she weeds a yard.

Fabio charges $9.00 each time he walks a dog.

Fabio will walk at least 25 dogs. Here, 'x' represents the number of lawns weeded and 'y' represents the number of dogs walked.

Now talking about constraints:

Fabio will walk at least 25 dogs, so that implies:

[tex]y>25[/tex]

Also, the number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, that implies:

[tex]y<2x[/tex]

The total money that they need after doing all the work should be at least $510.00.

[tex]12x+9y>510[/tex]

Answer:

20 students do NOT prefer math over lunch.

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

If nine out of ten students ([tex]\frac{9}{10}[/tex]) prefer math class over lunch, then we can infer that one out of ten students ([tex]\frac{1}{10}[/tex]) do not.

[tex]\frac{1}{10} = 0.10[/tex] or 10%

As we can see, this equals a 10% of the students that were asked. If 200 students were asked, we would need to find what 10% of 200 would be. We can do this by multiplying 200 by the decimal form of 10% like so,

[tex]200 * 0.10 = 20 students[/tex]

So we can see that 20 students do NOT prefer math over lunch.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

larger amount = 630

the smaller amount, that is 5 parts is 450

divide 450 by 5 to find 1 part of the ratio

[tex]\frac{450}{5}[/tex] = 90 ← 1 part

7 parts, the larger amount = 7 × 90 = 630

Answer:

The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).

D=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

D=(x2−x1)2+(y2−y1)2

Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

D=(3−(−1))2+(4−1)2−−−−−−−−−−−−−−−−−√=

D=(3−(−1))2+(4−1)2=

=16+9−−−−−√=25−−√=5

=16+9=25=5

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates:

(x1+x22,y1+y22)

(x1+x22,y1+y22)

Step-by-step explanation:

To find the endpoint B given midpoint M and endpoint A, we use the coordinates of the midpoint formula and solve for the unknown values. Plugging the given values into the formula, we solve for B and find that the coordinates of B are (-5, 7).

In this particular instance, we are working with the concept of midpoints on a coordinate plane. Given that the point M(-3,5) is the midpoint of the segment AB and A(-1,3) is one endpoint, we are tasked to find the coordinates of point B, the other endpoint.

The formula for the coordinates of the midpoint is [(x1+x2)/2 , (y1+y2)/2]. This finds the average of the x-coordinates and y-coordinates of the two endpoints to find the point exactly in between, or the midpoint.

Since we are given one endpoint A(-1,3) and the midpoint M(-3,5) and are asked to find the other endpoint B, we should set up the equation using the known values and solve for the unknown values. We know that (-3,5) should equal [(-1+x2)/2 , (3+y2)/2]. Solving for x2 (x-coordinate of B) gives us x2 = -3*2 + 1 = -5. Solving for y2 (y-coordinate of B) gives us y2 = 5*2 - 3 = 7. Therefore, the coordinates of B are (-5, 7).

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since there are two bags and theyre equal in weight, you have to subtract 3 then divide by 2.

Answer: Hello!

There are two bags:

you write: "the weight of bag B is 3 pounds more than twice the weight of both bags of potatoes is 27 pounds."

this has no sense, I think you want to write something like:

"The weight of bag B is 3 pounds more than the weight of bag A, and twice the weight of both bags of potatoes is 27 pounds.

If we define B as the wheight of bag B, and A as the wight of bag A; we know that:

B - A = 3lb

2( B + A) = 27lb

in the first equation we can isolate B as: B = 3lb + A, and then replace it in the second equation:

2(B+ A) =27lb

2( (3lb + A) + A) = 27lb

6lb + 3A = 27lb

3A = 27lb - 6lb = 21lb

A= 21lb/3 = 7lb

now we can replace it in the first equation and get:

B - A = 3lb

B - 7lb = 3lb

B = 3lb + 7lb = 10lb

Then Bag A weights 7lb and bag B weights 10lb.

Lets go through the steps

1) 1.22 + .89 = 2.11

2) 2.34 - 2.11 = .23

Jenny's frog jumped .23 meters further than Christina's frog.

I hope this helped!

Have a fantastic day!

Jenny's: 2.34

Chistina's: 1.22+0.89

The first thing you want to do is add 1.22 and 0.89 which is 2.11

Then too find how much further Jenny's frog jumped you subtract 2.34 and 2.11 which is 0.23.

Therefore your answer would be:0.23

Remember the formula for time is distance/speed

So 60 would be the distance, or 60m.

Answer:

60 represents the distance

Step-by-step explanation:

Given : y is the time in hours that it takes Micheal to travel to his grandparents house,

            x is his average speed in miles per hour.

To Find: What does the number 60 represents

Solution :

Time= y

x = speed

So, To find distance we will use formula :

[tex]Time = \frac{Distance}{Speed}[/tex]

[tex]y = \frac{Distance}{x}[/tex]  -- A

Given function: [tex]y = \frac{60}{x}[/tex] --B

On comparing A and B

Distance = 60 miles

So, 60 represents the distance .

(a) Let x be the cost of one of Brian's items, then cost of all 4 items bought by Brian will be 4x.

We have been given that Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. The price of each item bought by Chris will be x+2.5. Therefore, the cost of all 3 items bought by Chris will be [tex]3(x+2.5)[/tex].

(b) We are told that Brian and Chris both paid the same amount of money, so we can equate costs of Brian's 4 items and Chris's 3 items as:

[tex]4x=3(x+2.5)[/tex]

Now let us solve for x by distributing 3.

[tex]4x=3x+7.5[/tex]

[tex]4x-3x=7.5[/tex]

[tex]x=7.5[/tex]

Therefore, cost of Brian's each item is $7.5.

Now let us find price of Chris's each item.

[tex]\text{Cost of Chris's each item}=x+2.5=7.5+2.5=10[/tex]

Therefore, cost of Chris's each item is $10.

(c) Now let us check our solution by substituting x=7.5 in [tex]4x=3(x+2.5)[/tex].

[tex]4(7.5)=3(7.5+2.5)[/tex]

[tex]4(7.5)=3(10)[/tex]

[tex]30=30[/tex]

We can see that both Brian and Chris spent equal amount of money that is $30, therefore, our solution is correct.

Answer:

Duration of the tour he planned first is 8 days.

Step-by-step explanation:

Given that a person has 12000 rupees for his daily expenses.

Let x be the number of days.

Then daily expenses per day [tex]=\frac{12000}{x}[/tex]

Given that number of day is increased by 2 more days, that is number of days is x+2.

New daily expense per day [tex]\frac{12000}{x+2}[/tex]

Given that this new daily expenses are 300 less than original.

That is [tex]\frac{12000}{x}-\frac{12000}{x+2}=300[/tex]

              [tex]\frac{12000(x+2)-12000x}{x(x+2)}=300[/tex]

                  [tex]\frac{24000}{x(x+2)}=300[/tex]

                  [tex]x(x+2)=\frac{24000}{300}[/tex]

                    [tex]x^{2}+2x-80=0[/tex]

                    (x-8)(x+10)=0

                     x=8 or -10.

Since number of days cannot be negative, duration of the tour planned=8.

The ratio of soccer balls to footballs is 3/5.

To write the ratio of soccer balls to footballs as a fraction in simplest form, you need to divide the number of soccer balls by the number of footballs. In this case, there are six soccer balls and ten footballs. So the ratio can be written as 6/10. To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor, which in this case is 2. Thus, the ratio of soccer balls to footballs as a fraction in simplest form is 3/5.

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For this case we have the following equation, in a linear way:

[tex]y + 2 = 3 (x-1)[/tex]

This expression can be written in the form [tex]y = mx + b[/tex]

Where "m" is the slope and "b" is the cut point with the y axis.

Rewriting the given expression we have:

[tex]y + 2 = 3x-3\\y = 3x-3-2\\y = 3x-5[/tex]

Thus, the slope is 3 and the cut point is -5.

To graph, we must find two points through which the line passes, so, we perform the following steps:

Step 1:

We do [tex]x = 0[/tex]

[tex]y = 3 (0) -5\\y = 0-5\\y = -5[/tex]

Thus, the point [tex](x1, y1) = (0, -5)[/tex]

Step 2:

We do[tex]y = 0[/tex]

[tex]0 = 3x-5\\5 = 3x[/tex]

[tex]x =\frac{5}{3}[/tex]

Thus, the point [tex](x2, y2) = (\frac{5}{3},0)[/tex]

Answer:

See attached image

Answer:

AND THE NUMBERS ARE (0,3)IS UP AND (1,1) ARE DOWN

WISH THAT HELP

سبحان الله ,الحمدالله ,الله اكبر

The greatest common factor for these two numbers is 6 because if you divide 24 by 6 you get 4 and if you divide 84 by 6 you get 14.

22, 76, 238, 724, 2182

to generate the terms substitute n = 0, 1, 2, 3, 4 into the recursive function

[tex]a_{1}[/tex] = 3[tex]a_{0}[/tex] + 10 = ( 3 × 4 ) + 10 = 22

[tex]a_{2}[/tex] = 3[tex]a_{1}[/tex] + 10 = (3 × 22)+ 10 = 76

[tex]a_{3}[/tex] = 3[tex]a_{2}[/tex] + 10 = ( 3× 76) + 10 = 238

[tex]a_{4}[/tex] = 3[tex]a_{3}[/tex] + 10 = ( 3 × 238) + 10 = 724

[tex]a_{5}[/tex] = 3[tex]a_{4}[/tex] + 10 = (3 × 724) + 10 = 2182

The answer is $8, sense 12÷3×2=4×2=8.

To find the cost of the store brand cough medicine, which is 2/3 the cost of the national brand priced at $12, you multiply $12 by 2/3, resulting in the store brand costing $8.

The question asks: If one bottle of the national brand of cough medicine costs $12, what is the cost of a bottle of the store brand if it's 2/3 of the national brand? To find the answer, you multiply the cost of the national brand by 2/3, since the store brand costs 2/3 of the national brand's price.

Here's the calculation:

Therefore, the cost of a bottle of the store brand cough medicine is $8.

1) 36

2)8

3)14

4a) 21 4b) 42 4c) 56

5a)22 5b)40 5c)52

6a) 15.5 6b) 17 6c)18

7a)9 7b)18 7c)24

8) 3x +5

3  x 4 +5

=17

Answer:

Step-by-step explanation:

TO prove this we have to prove one of following.

SSS ( all three sides are equal )

SAS ( two sides and their middle angle is equal )

ASA ( two angles and their middle side are equal )

I am proving both triangles equal by ASA method.

The complete proof and explanation is given in attachment below.

Answer : option B

This graph shows the solutions to the inequalities

system of inequalities y>3x+14 and y<3x+2

the system of inequalities have solutions only when the shaded part satisfies the given inequalities

We are given with the graph of inequalities . The given inequalities have 'and' in between.

so we look at the graph where both inequalities intersects

From the graph we can see that there is no intersection part of both  shaded portions

So , we conclude that there is no solution.

Answer:

Step-by-step explanation:

There is no solution

(0,6)

y=-2x(0)+6

y=6

(5,4)

y=-2(5)+6

y=-10+6

y=-4

(-7,20)

20=-2x+6

20-6=-2x+6-6

14=-2x

14/-2=-2x/-2

-7=x

4.3 you can't expand a number, only an equation

The expanded form of a number shows the value of each digit. Meaning you must separate each digit by its placement.

4 is in the ones, therefore it just remains as 4

.3 is in the tenths, and therefore turns into 0.3

Now combine the two terms. The expression would be the answer:

4 + 0.3

Answer:

468

Step-by-step explanation:

If the first term of a geometric series and the common ratio are known, then the sum of the infinite series is

                a

s      = --------------

               1 - r

In this particular case we have:

               156

s      = -------------- = 156/(1/3) = 468

               1 - 2/3

The sum of an infinite geometric series with a first term of 156 and a common ratio of 2⁄3 is 468. This is computed using the formula [tex]S = a / (1 - r).[/tex]

The sum of an infinite geometric series can be found by using the formula [tex]S = a / (1 - r)[/tex], where 'S' is the sum of the series, 'a' is the first term of the series, and 'r' is the common ratio. In this case, the first term 'a' is 156 and the common ratio 'r' is 2⁄3.

Substituting these numbers into the formula, we get: S = 156 / (1 - 2/3) . After calculating this expression, we find the sum of the series to be 468. Therefore, the sum of the infinite geometric series with a first term of 156 and a common ratio of 2⁄3 is 468.

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The system of equations satisfied by the solution shown in the graph are:

x + y = 6 and x − y = -10.

Option D is the correct answer.

We have,

To check which system of equations is satisfied by the solution (-2, 8), we substitute the values x = -2 and y = 8 into each equation of the given systems.

A.

x + 2y = 6

(-2) + 2(8) = 6

-2 + 16 = 6

14 ≠ 6

B.

x + y = 6

(-2) + 8 = 6

6 = 6

x − 2y = 10

(-2) − 2(8) = 10

-2 - 16 = 10

-18 ≠ 10

C.

x + 2y = 10

(-2) + 2(8) = 10

-2 + 16 = 10

14 ≠ 10

x − y = 6

(-2) − 8 = 6

-10 ≠ 6

D.

x + y = 6

(-2) + 8 = 6

6 = 6

x − y = -10

(-2) − 8 = -10

-10 = -10

From the above calculations, we can see that the solution (-2, 8) satisfies the equations in x + y = 6 and x − y = -10.

Therefore,

The system of equations satisfied by the solution shown in the graph are:

x + y = 6 and x − y = -10.

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