In a small section of a stadium there are 40 spectators watching a game between the Cook Islands and Fiji. They all support at least one of the two teams.
25 spectators support the Cook Islands and 16 of these support both teams. How many support only Fiji?

Answer:

90° counter clockwise rotation of point 0(x, y) about origin = (-y, x)

Step-by-step explanation:

Following are the rules for a counter clockwise rotation of 90 degrees about the origin for a point O(x,y):

1. Invert the sign of the value of y.

2. Switch x and y with each other.

For example, a point A(5,2) after rotation gives a point B(-2,5) using the rules given above. The points on the x-y plane are shown in the image attached.

Answer:

64

Step-by-step explanation:

Volume of a cube is:

V = s³

When s = 8 in:

V = (8 in)³ = 512 in³

When s is doubled (s = 16 in):

V = (16 in)³ = 4096 in³

Now we can write a proportion:

8 mugs / 512 in³ = x mugs / 4096 in³

x = 64

The maximum number of mugs that the larger box can hold is:

                                     64

The edge length of box is:  8 inches.

This means that the volume of box is: 8×8×8=512 cubic inches.

Also, the number of mugs a box of edge length 8 in. can hold is: 8

Hence, volume of 1 mug= Volume of box/Number of mugs

Volume of 1 mug= 512/8=64 cubic inches

Now, if the dimension of the box is doubled.

This means that the Volume of new box= 8×Volume of old box

Volume of new  box=8×512=4096 cubic inches

Let n be the number of mugs that the new box can hold.

Volume of new box=n×Volume of  1 mug

⇒   4096=n×64

⇒   n=4096/64

⇒  n=64

               Hence, the answer is:

                            64

Answer:

The solution set is {1, -2/3, 2/3}.

Step-by-step explanation:

81m^3-81m^2-36m+36=0

9(9m^3 - 9m^2 - 4m + 4) = 0

Looks  like 1 might be  one root:

f(1) = = 9*1 - 9*1 - 4*1  + 4 = 0  so one factor is (x - 1).

Divide the function  by x - 1:

        9m^2 - 4  <------------------Quotient

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

m - 1 ) 9m^3 - 9m^2  - 4m + 4

         9m^3-9m^2

         -----------------------

                       -4m + 4

                        -4m + 2

                         ..............

Now :

9m^2 - 4 = (3m - 2)(3m + 2).

so  m - 1 = 0  or 3m - 2 = 0 or 3m + 2 = 0

m = 1 , 2/3,  -2/3.

Answer:

(4x -3yi) (4x+3yi)

Step-by-step explanation:

We have a^2 + b^2

Over  the complex number, this is equal to

(a-bi) (a+bi)

(4x -3yi) (4x+3yi)

Answer:

(4x -3yi) (4x+3yi)

Step-by-step explanation:

The expression 16x^2 + 9y^2 is a sum of squares, and it can be factored over the complex numbers using the difference of squares formula:

a^2 + b^2 = (a + bi)(a - bi)

In your expression:

a = 4x

b = 3y

So, applying the difference of squares formula:

16x^2 + 9y^2 = (4x + 3yi)(4x - 3yi)

This is the factored form of the expression 16x^2 + 9y^2 over the complex numbers.

Answer:

25.8°

Step-by-step explanation:

The wall is vertical so it makes 90°  with the ground.

The ladder forms a right triangle of base = 45 ft and hypotenuse = 50 ft

To find the angle (x) the ladder makes with the ground:

Cos x = [tex]\frac{45}{50}[/tex] = 0.9

[tex]Cos^{-1}[/tex] 0.9 = 25.8° (answer rounded up to nearest tenth)

The angle that the bottom of the ladder makes with the ground in a scenario where a 50ft ladder is leaning against a wall, with the base of the ladder being 45ft from the base of the wall, can be found using basic trigonometry. By using the cosine law, we find that the angle is approximately 25.84 degrees.

To find the angle the bottom of the ladder makes with the ground, we can use basic trigonometry. In this situation, we have a right-angled triangle formed by the wall, the ground, and the ladder, and we are given that the adjacent side (base of the ladder in relation to the vertical wall) is 45 feet and the hypotenuse (the ladder) is 50 feet.

Using the cosine law, the cosine of the angle is equal to the adjacent side divided by the hypotenuse, so:

cosine(Angle) = Adjacent/hypotenuse = 45ft/50ft = 0.9.

Now, we just need to find the inverse cosine (or acos) of 0.9 to find our angle:

Angle = acos(0.9) = 25.84 degrees approximately.

So, the angle that the bottom of the ladder makes with the ground is approximately 25.84 degrees. This result is independent of the length of the ladder.

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Answer:

D

Step-by-step explanation:

The ratio of corresponding sides are equal, that is

[tex]\frac{4}{8}[/tex] = [tex]\frac{y}{14}[/tex]

Answer:

k = 10

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

∠ZYM is an exterior angle and

∠YZX and ∠ZXY are the 2 opposite interior angles, hence

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

The cost of one ticket is $9

Step-by-step explanation:

we have

4x+12=48

where

x represents the cost of a ticket

Solve for x

Subtract 12 both sides

4x=48-12

4x=36

Divide by 4 both sides

x=36/4=9

therefore

The cost of one ticket is $9

Your answer is going to be: 979,660

Answer:

If your equation is (2+2)x489829 then the answer is 1959316

hiwever if your equation is 2+2*489829 then your answer is 979,660

Step-by-step explanation:

Answer:

[tex]\frac{(k+5)}{12(k+2)}[/tex]

Step-by-step explanation:

We need to perform the folowing operation:

[tex]\frac{k^{2} + 3k - 10 }{36}[/tex] × [tex]\frac{3}{k^{2} -4 }[/tex]

Factorizing we have:

[tex]\frac{(k-2)(k+5)}{36}[/tex]  × [tex]\frac{3}{(k+2)(k-2)}[/tex]

Simplifying, we get:

[tex]\frac{(k+5)}{12(k+2)}[/tex]

Answer:

x<48.83778966 :) have a great day!

Step-by-step explanation:

Answer:  The required solution is x < 48.837.

Step-by-step explanation:  We are given to solve the following inequality for the value of x :

[tex]11.22x-200<347.96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the above inequality, we need to take all the constant terms on one side and the term involving unknown variable on the other.

The solution of inequality (i) is as follows :

[tex]11.22x-200<347.96\\\\\Rightarrow 11.22x<347.96+200\\\\\Rightarrow 11.22x<547.96\\\\\Rightarrow x<\dfrac{547.96}{11.22}\\\\\Rightarrow 48.837.[/tex]

Thus, the required solution is x < 48.837.

Answer:

A  viable solution is the ordered pair (0,0)

Step-by-step explanation:

we know that

The number of books cannot be a negative number

The number of books is a positive integer

The weight cannot be a negative number

therefore

A  viable solution is the ordered pair (0,0)

Answer:

The third option

Step-by-step explanation:

Trust me ;) I got it right

For the sake of showing work I will replace the empty space with an x like so...

[tex]\frac{9}{10} =\frac{90}{x}[/tex]

To find out what x is you must cross multiply (aka butterfly)

***Image of this step is attached below

9*x = 10*90

9x = 900

Next divide 9 to both sides to finish isolating x. Since 9 is being multiplied by x, division (the opposite of multiplication) will cancel 9 out (in this case it will make 9 one) from the left side and bring it over to the right side.

9x ÷ 9 = 900 ÷ 9

1x = 100

x = 100

To make these fractions equivalent the empty spot must be 100

[tex]\frac{9}{10} = \frac{90}{100}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Exponential

Step-by-step explanation:

As the x value is increasing by 1, the Y value is multiplying by 3. Since the value is increasing rapidly from 3 to 9 to 27 to 81 to 243, this is an exponential function.

The type of function which  is represented by the table of values below is:

                               B. Exponential

We are given a table of values as:

              x                 y

              1                  3

              2                 9

              3                 27

              4                 81

              5                 243  

We can model this equation by the formula:

[tex]y=3^x[/tex]

Since, when x=1 we have:

[tex]y=3^1\\\\i.e.\\\\y=3[/tex]

when x=2 we have:

[tex]y=3^2\\\\i.e.\\\\y=9[/tex]

when x=3 we have:

[tex]y=3^3\\\\i.e.\\\\y=27[/tex]

and so on.

Hence, the function is exponential.

          i.e.  [tex]y=3^x[/tex]

Answer:

2x^2 - 7x - 2

Step-by-step explanation:

Write 2x2 - 11 first.  Please use " ^ " to indicate exponentiation:

 2x^2 - 11

Now change both signs of 7x - 9 and combine the result with 2x^2 - 11:

2x^2 - 11

   -7x  + 9

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

2x^2 - 7x - 2   (answer)

Answer:

b on edge 2021

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

√(9×16) =√9×√16 = 3 ×4 = 12

Answer:

RAGE

Step-by-step explanation:

Answer:

There are 13 different ways to finish the race

Step-by-step explanation:

To identify the number of different ways to finish the race we should categorized the types of win:

1. Without tie: the ways that are possible in this option are defined by the rule of multiplicación. There are 3 participants and 3 places, there are 3 possibles participant that can occupy the first place, then 2 possibles participants that can occupy the second place and one participant that can occupy the last place.

       3               x          2                x          1                  =   6

first place              second place           third place

So, there are 6 different ways to win without tie.

2. Double tie in the second place: This time there are 3 participant that can occupy the first place and the other participant are going to occupy the second place. So there are only 3 ways in this option, every option is defined by the winner. that's mean: the winner is Alfred, or is Brandon or  is Charles.

3. Double tie in the first place: This option is like option 2, there are only 3 ways because every option is defined by the person that is in the second place. That's mean: the second place is occupy by Alfred, or by Brandon or by Charles.

4. All the participants end in tie: There are just one possibility in this option, all are the winners.

Finally there are 13 ways to end this race, 6 ways without tie, 3 ways with double tie in second place, 3 ways with double tie in first place and 1 way with all the participants in the same place.

Final answer:

Alfred, Brandon, and Charles can finish the race in 13 different ways, considering the possibilities of no ties, two-way ties, and a three-way tie. This is calculated by adding 6 permutations for no ties, 6 combinations for two-way ties, and 1 possibility for a three-way tie.

Explanation:

We need to calculate in how many different ways Alfred, Brandon, and Charles can finish a race given that there is the possibility of a tie. There are three scenarios to consider for the finishes: no ties, two-way ties, and a three-way tie.

No ties: This is a simple permutation of 3 participants, which gives us 3! (3 factorial) ways to finish, or 3 x 2 x 1 = 6 ways.

Two-way ties: For the two-way tie, we have 3 possible pairs (Alfred & Brandon, Alfred & Charles, Brandon & Charles), and for each pair, there is one person who does not tie, resulting in 2 finishing orders per pair, so 3 pairs x 2 orders = 6 ways.

Three-way tie: There is only 1 way that all three can tie.

Adding up the possibilities from each scenario, we get 6 (no ties) + 6 (two-way ties) + 1 (three-way tie) = 13 different ways they can finish the race.

Answer:

2 1/24

Step-by-step explanation:

2/3 =    16/24

3/4=      18/24

5/8=       15/24

16+18+15=49

49-24=  25-24=1

2 1/24

Answer: 75

Step-by-step explanation:

The area formula for a trapzoid is area= 1/2 (a+b) h

In this equasion, the substitution would be area=1/2 (10+15) 6

Following PEMDAS, enter the numbers within the parenthases (10+15)

Divide the 25 in half, then multiply by 6. This comes out to 75.

For this case we have that by definition, the area of a trapezoid is given by:

[tex]A = \frac {1} {2} (B + b) * h[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

According to the figure we have the following data:

[tex]B = 15ft\\b = 10ft\\h = 6ft[/tex]

Substituting in the formula:

[tex]A = \frac {1} {2} (15 + 10) * 6\\A = \frac {1} {2} (25) * 6\\A = \frac {1} {2} 150\\A = 75[/tex]

Finally, the area of the trapezoid is[tex]75ft ^ 2[/tex]

Answer:

[tex]75ft ^ 2[/tex]

The key aspect of a function's graph in Mathematics is its ability to visually illustrate relationships, patterns, and comparisons. Different types of graphs, like line, bar, and pie, provide different ways to interpret the data. Understanding these graphs helps in mathematical analysis and solving problems.

The question involves analyzing functions' graphs and matching them with their meanings. In Mathematics, a function's graph can represent different types of information based on its structure. For example, a line graph signifies a linear relationship between two variables denoted on the horizontal and vertical axis. The height of the curve at any point on the graph represents the value of the function at that point.

Three distinct types of graphs are the line, bar, and pie graph. A line graph shows the relationship between two variables with one variable being represented on the horizontal axis and the other on the vertical axis. A bar graph utilises the height of the bars to signify a relationship, with each bar representing a distinct entity like a group of people or a country. A pie graph is used to show how something is distributed, with each slice representing the corresponding percentage of the whole.

Deciphering this information from a graph includes recognizing patterns, comparisons, and trends, providing an intuitive sense of relationships in the data.

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Here are the matches: f(x) > 0: Intervals of the domain where the graph is above the x-axis. f(x) < 0: Intervals of the domain where the graph is below the x-axis. Y-intercept: Location on the graph where the output is zero. X-intercept: Location on the graph where the input is zero.

In a function f(x), when f(x) > 0, it indicates the intervals on the domain where the function's values are positive, corresponding to regions above the x-axis. Conversely, when f(x) < 0, it denotes intervals where the function's values are negative, representing areas below the x-axis.

The y-intercept is the point where the graph intersects the y-axis, highlighting where the output (function value) is zero. On the other hand, the x-intercept is where the graph crosses the x-axis, signifying the point where the input (x-value) is zero, resulting in a zero output. These aspects provide valuable insights into a function's behavior and characteristics.

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Answer:

Diameter: 4

Radius: 2

Equation: ( x-3 ) + ( y + 2) = 4

Final answer:

The length of the diameter is 4 units, the radius of the circle is 2 units, and the equation of the circle, with its center at (3,-2), is (x - 3)² + (y + 2)² = 4.

Explanation:

The diameter of a circle is the distance between two points on the circumference of the circle which pass through the center of the circle. The two points given are (5,-2) and (1,-2), which both lie on a horizontal line since their y-coordinates are the same. To find the length of the diameter, you calculate the distance between these two points using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

For these points, it becomes:

d = √((1 - 5)² + (-2 - (-2))²) = √((-4)² + (0)²) = √(16) = 4

Therefore, the length of the diameter of the circle is 4 units.

To find the radius of the circle, which is half the diameter, divide the diameter by 2:

r = d / 2 = 4 / 2 = 2 units

The equation of a circle in the standard form is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Given that the center is the midpoint between (5,-2) and (1,-2), which is (3,-2), the equation of the circle with a radius of 2 would be:

(x - 3)² + (y + 2)² = 2²

(x - 3)² + (y + 2)² = 4

Answer:

x = 1

y = 3

Step-by-step explanation:

We can solve this problem by inputting the second equation into the first equation by replacing the y variable with the second equation.

x + 3y = 10

y = x + 2

x + 3(x + 2) = 10

Now, distribute three with x and 2

3 * x = 3x

3 * 2 - 6

x + 3x + 6 = 10

4x + 6 = 10

Subtract 6 from both sides

4x = 4

So, x = 1

Solve for y by replacing x in the second equation with 1.

y = 1 + 2

y = 3

The solution to the system of equations is x = 1 and y = 3.

To solve the system of equations using the substitution method, we can start by substituting the value of y from the second equation into the first equation. Let's proceed step by step:

Step 1: Given equations:

1) x + 3y = 10

2) y = x + 2

Step 2: Substitute the value of y from equation (2) into equation (1):

x + 3(x + 2) = 10

Step 3: Distribute the 3 on the left side of the equation:

x + 3x + 6 = 10

Step 4: Combine like terms:

4x + 6 = 10

Step 5: Move the constant term to the other side of the equation:

4x = 10 - 6

Step 6: Simplify the right side:

4x = 4

Step 7: Divide both sides by 4 to solve for x:

x = 4/4

x = 1

Step 8: Now that we have the value of x, substitute it back into equation (2) to find y:

y = x + 2

y = 1 + 2

y = 3

Step 9: Check the solution by substituting the values of x and y into the original equations:

Equation 1: 1 + 3(3) = 10

1 + 9 = 10 (True)

Equation 2: 3 = 1 + 2

3 = 3 (True)

The solution to the system of equations is x = 1 and y = 3.

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There are approximately 157.48 inches in 4 meters

Begin with the number 4 meters. We understand that 1 meter is the same as 39. 37 This is a number that helps convert one measurement to another measurement.

Take the number 4 (which stand for 4 meters) and multiply it by 39. 37 (which represents the number of inches in 1 meter). The unit of meters is removed, so we are left with inches as the unit we want.

4 meters * 39.37 inches/meter = 157.48 inches

So, when one convert 4 meters to inches using the conversion factor, we get about 157.48 inches.

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4 meters is equal to 157.48 inches, calculated by multiplying 4 by the conversion factor of 39.37 inches per meter.

The question asks for the conversion of 4 meters to inches. Using the conversion factor that 1 meter is equivalent to approximately 39.37 inches, we can calculate the equivalent number of inches in 4 meters by multiplying 4 by 39.37. Therefore, to convert from meters to inches, you would follow this calculation:

Thus, 4 meters is equal to 157.48 inches.

Answer:

16

Step-by-step explanation:

We use the completing square method to find make the expression a perfect square.

(b/2)²=ac where a and b are coefficients of x² and x respectively while c is a constant.

= (-8/2)²=16

We add 16 to both sides and the expression becomes a perfect square.

Answer:

a = k / (4 + 9b)

Step-by-step explanation:

k = 4a + 9ab

Factor out a:

k = a (4 + 9b)

Divide by 4 + 9b:

k / (4 + 9b) = a

Answer:

radius is perpendicular to the chord

The radius of a circle that bisects a chord is perpendicular to that chord.

If a radius of a circle bisects a chord, then it is perpendicular to that chord. By definition, the radius that bisects the chord also bisects the angle at the center of the circle which subtends the chord. This is a direct consequence of a theorem in geometry which states that in a circle, the radius that bisects an angle at the centre is perpendicular to the chord which subtends the angle and bisects the chord itself. This perpendicularity is an important property as it asserts that the bisector of the chord is the shortest path from the circle's center to the chord and it cuts the chord into two equal segments, thus verifying the right angle formed between the radius and the chord.

Answer:

11 in each box with 30 left over

Step-by-step explanation:

1702/152: 11.1973684211

about 11 in each box

11 x 152 = 1672

1702 - 1672 = 30

11 in each box with 30 left over

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{5x^2+8x+7}{4x}[/tex]

Divide each term on the numerator by 4x

= [tex]\frac{5x^2}{4x}[/tex] + [tex]\frac{8x}{4x}[/tex] + [tex]\frac{7}{4x}[/tex]

= [tex]\frac{5x}{4}[/tex] + 2 + [tex]\frac{7}{4x}[/tex]