Sector of a circle has arc length 11cm and central angle. Find its radius and area.

An acute triangle is a triangle with all angles measuring less than 90°.

To solve an acute triangle using trigonometry, we need to know the length of at least one side and at least one angle of the triangle.

For example, let's assume the triangle has side lengths a = 6, b = 8, and we know the angle A = 30°.

First, we can use the Law of Cosines to calculate the length of the third side, c:

c² = a² + b² - 2abcos(A)

c² = 6² + 8² - 2(6)(8)cos(30°)

c² = 64 - 96cos(30°)

c² = 64 - 48

c² = 16

c = 4

Now we can calculate the other two angles, B and C, using the Law of Sines:

sin(B) = sin(A) * c/a

sin(B) = sin(30°) * 4/6

sin(B) = 0.5 * 2/3

sin(B) = 0.3333

B ≈ 19.47°

sin(C) = sin(A) * c/b

sin(C) = sin(30°) * 4/8

sin(C) = 0.5 * 0.5

sin(C) = 0.25

C ≈ 14.04°

Therefore, the three angles of the triangle are A = 30°, B = 19.47°, and C = 14.04°, and the three sides are a = 6, b = 8, and c = 4.

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we can use the Triangle inequality Theorem a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side

It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

1 . Triangle Inequality Theorem

smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.

In this case, a, b, and c are each equal to seven.

2. Check to see if the sum of the first two sides is greater than the third

Check to see if the sum of the first two sides is greater than the third adding the sides a and b yields 17, which is larger than 5, or 7 plus 10. It can alternatively be considered as 17 > 5.

3. Check to see if the sum of the next combination of two sides is greater than the remaining side

just see if the sum of sides a and c are greater than the side b.[4] This means you should see if 7 + 5, or 12, is greater than 10. 12 > 10,

4. Check to see if the sum of the last combination of two sides is greater than the remaining side.

Check to see if side b and side c added together are greater than side a. To accomplish this, you must determine whether 10 Plus 5 is greater than 7. The triangle is complete on all sides since 10 + 5 = 15 and 15 > 7.

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Answer:

x = $25,400 [the original price of the Junko car]

Step-by-step explanation:

The price Ben paid, $23,622, is after the 7% discount.  Let x be the original price of the Jinko car.   Ben's prices reflect a 7% discount:

 x*(1-0.07) = $23,622  [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]

(0.93)x = $23,622

x = $25,400

The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

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[tex] \longmapsto \: side = \frac{16}{4} = 4 \\ \longmapsto volume = 4 {}^{3} = 64[/tex]

The graph of the line y = 4x + 3 is shown below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 4x + 3

When x = 0, y = 3

When x = 1, y = 4 + 3 = 7

When x = 2, y = 11

Similarly for negative x values, we get,

x = -1, y = -4 + 3 = -1

x = -2, y = -8 + 3 = -5

So on......

So we must get the following coordinates:

(-1, -1), (-2, -5), (0, 3), (1, 7), (2, 11),, ........

Thus,

The graph is shown below.

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Answer:

2.35 + 0.55 × 15 = 10.6

Therefore, she can go 10.6 miles.

Answer:

10.6

Step-by-step explanation:

2.35 + 0.55 x 15 = 10.6

Answer:

X=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

17x−30+7x+18=180

17x+−30+7x+18=180

(17x+7x)+(−30+18)=180(Combine Like Terms)

24x+−12=180

24x−12=180

Step 2: Add 12 to both sides.

24x−12+12=180+12

24x=192

Step 3: Divide both sides by 24.

X=8

In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.

The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.

Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.

Using the law of ins we can state that:

Sin 8°/x = sin 15°/90

90 (Sin 8°) /x = Sin 15°

90 Sin 8° = x Sin 15°

90 Sin 8° / Sin 15° = x

90 (0.13917310096)/ 0.2588190451 = x

Thus,

x = 48.3951213156

x [tex]\approx[/tex] 48.4

Thus, the distance of the flight is approximately 48.4 miles.

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The ordered pairs that are in the solution set of the system of linear inequalities are (2 ,2), (3 , 1) and (4 , 2).

A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system.

Given the system of linear inequalities:

y > -3x + 2

y< 2x + 3

Substitute the value of x and y for each given ordered pair.

For (2, 2) x=2 and y =2:

y > -3x + 2

2 > -3(2) +2

2> -4 True.

y< 2x + 3

2 < 2(2) +3

2< 7 True

For (3, 1) x=3 and y=1:

1 > -3(3) + 2

1 > -7 True

y< 2x + 3

1 < 2(3) + 3

1< 9 True

For (4 , 2) x=4 and y =2

y > -3x + 2

2 > -3(4) +2

2 > -10 True.

y< 2x + 3

2 < 2(4) + 3

2 < 11 True.

Hence the ordered pairs (2 ,2), (3 , 1) and (4 , 2) are in the solution set of the system of linear inequalities.  

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The vertex of the equation is (0, -1), the line of symmetry is x = 0 and the y-intercept is (0,-1).

For the equation f(x) = [tex]-3x^7[/tex] + 2x - 1, the vertex is the highest or lowest point on the parabola and it can be found by completing the square method.

To find the line of symmetry, we can set the function equal to zero and solve for x. The x-coordinate of the vertex is the same as the line of symmetry.

The y-intercept is the point at which the parabola crosses the y-axis, and it can be found by setting x equal to zero and solving for y.

The vertex of the parabola:

The line of symmetry:

The y-intercept:

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Answer:

N = Pd - 2

Step-by-step explanation:

P = N + 2/d

Pd = N + 2

Pd - 2 = N

N = Pd - 2

The missing sides of the triangle can be found by applying the Pythagoras Theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that square of  hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex]  ;

let missing side of the Right triangle be hypotnuse ;

So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .

For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .

let , the length of side "base" be unknown.

So ,  in order to find length of side b  (base) , we substitute the  known values into Pythagoras theorem:

[tex]10^{2} =6^{2} +Base^{2}[/tex] ;

[tex]Base = 100-36[/tex] ;

So , missing side "base" is = 8 ;

Therefore , the missing side can be found by using  the Pythagoras Theorem .

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Answer:

analysis (i got to put a bunch of random stuff here cs the limit)

Answer:

Step-by-step explanation:

The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.

To solve a system of equations, you can use substitution or elimination.

One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.

Solving for y in the first equation:

y = 3x - 7

Then substitute the result in the second equation:

6x - 2(3x - 7) = 12

6x - 6x + 14 = 12

14 = 12

That clearly is not true and this system of equations has no solution.

--The question is incomplete, answering to the question below--

"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?

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The unit rate of flavor A is; $0.2245 per ounce

The unit rate of flavor B is; $0.20 per ounce

An equation to help Ray determine how many red balloons are needed compared to the the total number of balloons used is; y = ²/₅x

A unit rate is also called unit ratio and it describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

We are given that Flavor A is 20 ounces and costs $4.49. Thus;

Unit rate of flavour A = $4.49/20 = $0.2245 per ounce

For Flavor B, the equation y = 0.20x represents the cost (y) per ounce (x) in each box. Thus, the unit rate is $0.20 per ounce

Since ray is making bouquets of balloons. In each bouquet 2 out of every 5 balloons are red.

If x is the number of ounces, then the unit rate is 2/5 . Thus, the equation is; y = ²/₅x

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Answer:

(2) y = -2x² + 6x - 6

Step-by-step explanation:

Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.

The size roll which is the better value is $1.17 per ounce.

To determine which size roll is the better value, we need to compare the price per ounce of each roll.

To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.

To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.

Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.

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Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

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Answer:

15a

Step-by-step explanation:

5a + 10a = 15a

Answer:

Step-by-step explanation:

SHOW HIGH CLARITY IMAGE, BUT USE CONGRUENCE OF TRINALGES AND FIND X BY EQUATING THE GIVEN SIDE I GUESS

IF YES MARK ME BRAINLIEST

Using the centroid P on the triangle, the value of QN is 25.5 and PN is 8.5

The centroid of a triangle is a point located at the intersection of the three medians (the lines that connect the vertices to the midpoints of the opposite sides). The centroid divides each median in two segments that have the same length. It is the center of gravity of the triangle and is the point at which the triangle's three medians intersect.

The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

In this triangle, the centroid is at P and the QP is 17.

a) QN

The distance between QP is two-thirds the length of QN

The length of QP = 17

QP = 2/3 QN

17 = 2/3 QN

QN = (3 * 17) / 2

QN = 25.5

b) PN

The distance between PN is calculated as;

PN = QN - QP

PN = 25.5 - 17

PN = 8.5

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The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ x⁶ - 64x⁴ + x² - 7x - 51

If the value of the polynomial is zero at x = 8. Then (x - 8) will be the factor of the polynomial.

At x = 8, the value of the polynomial is given as,

⇒ (8)⁶ - 64(8)⁴ + (8)² - 7(8) - 51

⇒ 262,144 - 262,141 + 64 - 56 - 51

⇒ - 43

The expression (x - 8) is not the factor of the polynomial x⁶ - 64x⁴ + x² - 7x - 51.

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The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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The examples for each of the quadrant is explained below.

Quadrant in math is defined as one of the four regions or sections of the coordinate system and the quadrants are separated by the x-axis and the y-axis and these axes are perpendicular to each other.

Here we have to know the value that must be placed on each quadrant.

Here the first quadrant has both x and y-coordinates are positive.

The second quadrant has the value of the x-coordinate is negative and the y-coordinate is positive.

The third quadrant has both x and y-coordinates are negative.

The fourth quadrant has the value of the x-coordinate is positive and the y-coordinate is negative.

Therefore, the example for each of them are written as

=> Quadrant I = (1, 1)

=> Quadrant II = (-1, 1)

=> Quadrant III = (-1, -1)

=> Quadrant IV = (1, -1)

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The number √2 is called an irrational number because the value of √2 = 1.41421356... and the the value is non terminating and non repeating .

What are Irrational Numbers ?

The Numbers whose vales are Non Repeating and Non Terminating are called as Irrational Numbers ,

also the numbers that cannot be expressed on the form of [tex]\frac{p}{q}[/tex] are called as Irrational Numbers .

the number is given as √2 ;

we know that the values of √2 is = 1.41421356... ,

we see that the the value is non terminating and the numbers after decimal point are non repeating ,

Therefore  , the number √2 is an irrational number .

The given question is incomplete , the complete question is

Why the number √2 is called a Irrational Number ?

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