Find the distance from point B to point C.
Enter as a decimal rounded to the nearest tenth.
58°
6 mi
B
BC = [?]

Trigonometric ratios depend only on angles as they remain constant no matter what.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides relate to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trigonometric ratios, cosec, sec, and cot.

Even if the sides of the triangle increases or decreases in a specific ratio, the angles of the triangle will always remain the same no matter what.

Trigonometric ratios in right triangles are therefore independent of the side lengths  and solely depend on the magnitude of the angles.

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The second step required to solve the given system of equations using elimination method is to add or subtract the modified system of equations.

As given in the question,

Steps required to solve the given system of equations by elimination method :

Let us consider two system of equations are :

2x + 3y = 1  __(1)

3x + 2y = 1  __(2)

1. Multiply 3 to (1) and 2 to (2)  to eliminate the x-term.

6x + 9y = 3  __(3)

6x + 4y = 2   __(4)

2. Now in second step subtract (4) from (3) to get the value of y.

6x + 9y = 3  

6x + 4y = 2

0x + 5y = 1

⇒ y = 1/5

3.  Multiply 2 to (1) and 3 to (2)  to eliminate the x-term

4x + 6y = 2 __(5)

9x + 6y = 3  __(6)

4. Now in subtract (5) from (6) to get the value of x.

9x + 6y = 3

4x + 6y = 2

5x = 1

⇒ x = 1/5

Therefore, the second step in the given system of equation using elimination method is add or subtract the modified equations.

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The equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0

The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.

Given the center of the circle is (-2,3) and the radius is 3cm.

Substituting the given values we get (x + 2)^2 + (y - 3)^2 = 3^2

Expanding and simplifying we get x^2 + 4x + 4 + y^2 - 6y + 9 = 9

x^2 + 4x + y^2 - 6y + 5 = 0 is the equation of the circle in the form of x^2 + y^2 + Px + qy + c = 0

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Part A: percent of 70 is 10.

x% of 70 = 10

70x / 100 = 10

x = 1000 / 70

x = 14.28 %.

Part B: percent of 2.8 is 20.

x% of 2.8 = 20

2.8x/ 100 = 20

x = 2000/ 2.8

x = 714.28%

Part C: percent of 90 is 18.

x% of 90 = 18

90x/100 = 18

x = 1800 / 90

x = 2 %

Part D: percent of 10 is 55.

x% of 10 = 55

10x / 100 = 55

x = 5500/ 10

x = 550%.

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In a perfect square trinomial, two of your terms will be perfect squares. If you do not have two perfect square terms, then this trinomial is not a perfect square trinomial.

The general shape of a really perfect rectangular trinomial is (x + y)^2, in which x and y are the roots of the trinomial. to check if a trinomial is perfectly rectangular, we will try to the component it into the rectangular binomial. We also can whole the square technique, which involves adding and subtracting the rectangular of 1/2 of the x-coefficient of the linear time period after which grouping the resulting phrases.

It's far essential to note that for a trinomial to be a super rectangular trinomial, the regular time period has to be a square of an integer and the linear time period should be an excellent variety.

Perfect rectangular trinomials are used in fixing quadratic equations and expertise their solutions, they also have programs in algebra, geometry, and trigonometry. Factoring them is an essential talent in algebra and is utilized in solving exceptional types of mathematical troubles.

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A 20 degree angle called an acute angle.

Any angle which is less than 90 degree but greater than 0 degree is called an acute angle. For example - 20, 30, 40 , 50 etc are acute angles.

Polygons with at least one acute angle include triangles, parallelograms, trapezoids, and so on.The acute angle that are present in the triangle they are known as acute angle triangle.

Properties of acute angle triangles:

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Answer:

8:00

Step-by-step explanation:

This is probably extremely late

distance between their ends greater at 8.00

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Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.

A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.

In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.

On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.

In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.

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Step-by-step explanation:

22 pounds for $11.

we could now calculate how many pounds we can buy for $1.

that would be 22/11 = 2 pounds.

or we can calculate as requested how much (how many $) he needed to pay for 1 pound.

that would be 11/22 = 1/2 = $0.50

and as you can see, both answers work prefectly together. they are just different views of the same basic problem.

we have to pay $0.50 per pound, and so we can buy 2 pounds with $1.

The measure of Supplementary angles is ∠1 is 59° and ∠2 is 121°.

The word "supplementary" refers to two angles coming together to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles. If two angles complement one another.

It has an acute angle on one side and an obtuse angle on the other.

The angles are both right angles.

Given ∠1 and ∠2 are supplementary angles,

let ∠ 1 = x°

∠1 + ∠2 = 180°

so ∠2 = 180 - x

angle 2 is 3° more than twice the measure of angle 1,

and ∠2 = 3 + 2x

substitute the values

∠2 = 180 - x

3 + 2x = 180 - x

2x  + x = 180 - 3

3x = 177

x = 177/3

x = 59°

∠2 = 180 - x

∠2 = 180 - 59

∠2 = 121°

Hence the value of ∠1 is 59° and ∠2 is 121°.

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$12034 is the worth of the car after 4 years.

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

Given that we purchased a  car for $22,000

Every year your car depreciates by 14%

We have to find the worth of the car after 4 years.

[tex]A=P(1-r)^{t}[/tex]

P is the principal amount=$12000

r is rate of interest =14%=0.14

t is time =4 years

A=22000(1-0.14)⁴

A=22000(0.86)⁴

A=22000×0.547

A=$12034

Hence, $12034 is the worth of the car after 4 years.

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The equivalent fractions of 3/4 are 6/8, 9/12, 12/16, and 15/20.

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions.

To find the equivalent fractions for any given fraction, multiply the numerator and the denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say, 2. Thus, 6/8 is an equivalent fraction of 3/4. We can find some other equivalent fractions by multiplying the numerator and the denominator of the given fraction by the same number.

3/4= 3×3/4×3

=9/12.

3/4=

3/4= 3×4/4×4

=12/16

3/4= 3×5/4×5

=15/20

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We can demonstrate the solution set in a number of different ways. Number line, interval notation, and set notation are all options for accomplishing this.

Depending on the question, these methods may or may not be used.

There are two ways to write the interval notation solution set.

The closed interval is the first. The solution is enclosed by square brackets and includes the endpoints in a closed interval.

The form [a, b] is used to indicate this. The set notation, on the other hand, is x a x b. This indicates that the solution set runs from a to b, with the second interval being open. The endpoints are not included in the solution when an open interval is enclosed by round brackets ().

The format used for this is (a, b). The set notation, on the other hand, is x a x b. The solution set is therefore situated between a and b.

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A system of equations is an arrangement of one or more equations with many variables.

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The one example of absolute value function is x =|y| , and the graph is sketched below .

What is Absolut value Function ?

The absolute value function is defined as a function in algebra that consists of the variable in the absolute value bars. The general form of absolute value function is written as f(y) = a |y - h| + k .

let the absolute value function be : x = |y|  ;

we put y = -1 , we get ⇒ x = 1  ;

we put y = 1 , we get ⇒ x = 1 ;

we put y = 0 , we get ⇒ x = 0 ;

from the above points we observe that , what ever we put in the function , the result "x" is always positive .

Therefore , the graph of the function x = |y| , is a V shaped graph that faces Right .

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A 45-45-90 triangle is an isosceles right triangle, meaning that it has two congruent sides and one right angle. To find the area and perimeter of a 45-45-90 triangle, use the following formulas:

Area:

(1/2) * (side length)^2

Perimeter:

2 * (side length) + (side length) * √2

Note that the perimeter of a 45-45-90 triangle is equal to twice the length of one of its sides plus the length of the hypotenuse.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

Where is the triangle?

Step-by-step explanation:

Beatrice made 11 sales this week. The solution has been obtained using linear equations.

What is linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.

Let the sales of Beatrice be 'x'.

Since, Marshall made 5 more sales than Beatrice, we get

Sales of Marshall= x+5

Thus, Earnings of Beatrice = $276 + $11x

Earnings of Marshall = $29 + $23(x+5)

We are given that Beatrice and Marshall have earned the same amount this week, therefore,

⇒$276 + $11x = $29 + $23(x+5)

⇒$276 + $11x = $29 + $23x + $115

⇒$12x = $132

⇒x = $132/$12

⇒x = 11

Hence, Beatrice made 11 sales this week.

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Answer:

If you're looking for the equivalent of m then it is -390

Step-by-step explanation:

-30 = m divided by 13 is the same as -30 times 13 = m

Finally m is equal to -390

Answer:

m = -390

Step-by-step explanation:

Given statement,

→ -30 = m divided by 13.

Forming the equation,

→ -30 = m/13

Now the value of m will be,

→ -30 = m/13

→ m/13 = -30

→ m = -30 × 13

→ [ m = -390 ]

Hence, value of m is -390.

The value of x for the two expressions will be 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are (-x+2y= 6) and 6y =x+18. The equations can be solved as below,

-x+2y= 6 or x = 2y - 6

6y = x + 18

Substitute the value of x in the second equation,

6y = 2y - 6 + 18

4y = 12

y = 3

x = 2y - 6

x = ( 2 x 3 ) - 6

x = 0

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  The mathematical function known as a logarithm expresses the degree to which a base number must be raised in order to obtain a specific value. The symbol logb(x), where b is the logarithm's base and x is the value being evaluated, stands for the logarithm of a number. The natural logarithm, which has a base of e, is the most widely used logarithm (approximately 2.71828). The inverse function of exponentiation is the logarithm, according to this definition. The exponent to which we must raise b in order to obtain a number x is its logarithm to base b.

       It reads log2(3x + 8) = 5.

logb(a^n) = n * logb(a) where b is the base of the logarithm, is a property of logarithms that can be used to rewrite expressions. Since the base in this instance is 2, we obtain log2(3x + 8) = 5.

 corresponding to 2^5 = 3x + 8

Now that x is on one side of the equation, we can solve for it.

32 = 3x + 8

After deducting 8 from both sides, we arrive at 24 = 3x, which we then multiply both sides by to get 8

 Thus, x = 8 is the corresponding equation.

and the solution is 8.

     Therefore, the x=8 is the solution of this problem .

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Answer:

1. a 2. 8

Step-by-step explanation:

Find the x and y-intercepts of the line. Let y and solve for x. Let x and solve for y. Find a third solution to the equation. Plot these three coordinates and check that they line up. Draw the line.

Let the equation be y = Px + Qz. P and Q are constants, and x and z are 2 variables.

Firstly, make one variable 0, z = 0. This implies that you are dealing with only two variables, so you can make a graph(1) on X and Y axis. A simple line passes through the origin. Now take z = 1, and plot on the same plane, i.e., Plot y = Px + Q (this will be graph 2). Similarly, for all z. You will get a set of parallel lines separated by B.

Then you realize that only Graph(1) belongs to the z = 0 plane. and Graph(2) belongs to z = 1 plane and so on for z = 2, 3, 4….

So all you get is a Plane with slope P with respect to the x-axis and slope Q with respect to slope Q.

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Answer:74 blue beads and 90 purple beads

Step-by-step explanation:

first you need to take the total number of beads 164 divide by the 2 colors so 164÷2=86 then you subtract the 8 more purple from 1/2 of 86 and you get 74 then you add 8 more to the other half of 82 and get 90 purple and 74 blue.

Answer:

Obtuse

Step-by-step explanation:

An angle that is measured more than 90 degrees is an obtuse angle. Although an angle that measures 180 degrees is a straight angle or a half angle, and an angle that measures 360 degrees is a straight angle or a complete angle. However, when it's 360 degrees it's a full circle because a circle measures 360 degrees. If you want to measure an angle to determine which one it is, you must use a protractor.

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Answer:

Step-by-step solution:

Let's first familiarize ourselves with the basic types of angles out there.

The simplest angles are:

In a nutshell, acute angles are angles whose measure is less than 90 degrees, right angles are the ones whose measure is exactly 90 degrees, and obtuse angles are the ones whose measure is greater than 90 degrees.

Here's what an obtuse angle looks like.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{.4mm}\qbezier(1,1)(1,1)(5.5,1)\qbezier(1,1)(1,1)( -1,4)\qbezier(0.65,1.55)(1.5,1.8)(2,1)\put(3,3){\rm Obtuse Angle :}\put(3,2.5){\it measures more than}\put(3,2){\sf 90 degrees}\end{picture}[/tex]

--

Now, since 140 measures more than 90 degrees, it's an obtuse angle.

[tex]\therefore\quad\underline{\boxed{\sf{The~angle~is~obtuse}}}[/tex]

The y-intercept of y =- 2/3x + 7 is 7.

The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

Thus, The y-intercept of y =- 2/3x + 7 is 7.

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36 feet of fencing will be needed

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square metres serving as the standard unit (m2).

Area of a Square = Side × Side

Therefore, the area of square = Side2  square units

and the perimeter of a square = 4 ×  side units

Area of square field = 81 hectare

1 hectare = 10000 sq.m.

So, 81 hectare = 810000 sq.m.

So, Area of square field = 810000 sq.m.

Area of square=Side²

side²=810000

side =√810000

side=900

So,

Perimeter of square = 4×  side

Perimeter of square field = 4 × 900 =3600m

Therefore 36 feet of fencing will be needed

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Due to its peculiar ratio of 1:2:3  , the  30-60-90 triangle is referred to as a special right triangle. Any triangle with a ° angle is considered to be a right triangle in this context.

A unique type of right triangle known as  30-60-90 a  triangle always has angles of

30-60 and -90 ,

The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √ times the length of the shortest side in a  30-60-90  Triangle.

The above theorem can be written mathematically as the 30-60-90  Triangle Formula as

√  which is the ratio of the three sides of the  30-60-90 Triangle.

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Answer:

24 children

Step-by-step explanation:

Given ratios:

Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:

Therefore the combined ratio is:

So the ratio of Adult Males to Adult Females is 22 : 15.

If the difference between the number of Adult Males and Adult Females is 28 then:

[tex]\implies \dfrac{22}{22+15}x-\dfrac{15}{22+15}x=28[/tex]

[tex]\implies \dfrac{22}{37}x-\dfrac{15}{37}x=28[/tex]

[tex]\implies \dfrac{7}{37}x=28[/tex]

[tex]\implies 7x=1036[/tex]

[tex]\implies x=148[/tex]

Therefore:

[tex]\implies \textsf{Adult Males}=\dfrac{22}{37} \times 148=88[/tex]

[tex]\implies \textsf{Adult Females}=\dfrac{15}{37} \times 148=60[/tex]

If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:

[tex]\implies 11:3=88:c[/tex]

[tex]\implies \dfrac{11}{3}=\dfrac{88}{c}[/tex]

[tex]\implies 11c=264[/tex]

[tex]\implies c=24[/tex]

Therefore, the number of children in the village is 24.

The results for X = -5 and y = 2 yield one solution.

An equation is an expression that states the equality of two values using mathematical operators. It is a mathematical statement consisting of an expression involving variables and constants, connected by an equal sign. Equations are used to solve problems in a wide range of fields, such as science, engineering, and economics.

This is because a system of equations will always have either one solution, no solutions, or infinitely many solutions. Since the equations are equal to a single value, the solution is unique, yielding one solution.

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Answer:

1296

Step-by-step explanation:

(6+30)²=36²=1296

Answer:

1296

Step-by-step explanation:

(6+30)^2

(36)^2

1296