What is the solution of the equations 8x +3y 5 and 3x 2y 5?.

Answers

Answer 1

The solution of the given linear equations is (x,y) = (1,-1).

The given linear equations are

8x + 3y = 5 - - - ( 1 )

3x - 2y = 5 - - - ( 2 )

As the RHS of both equations is equal, equating the LHS of both equations, we get,

8x + 3y = 3x - 2y

⇒ 8x - 3x = - 2y - 3y

⇒ 5x = - 5y

⇒ x = - 5y ÷ 5

x = - y

By substituting x = - y in equation ( 1 ), we get,

8x + 3y = 5 - - - ( 1 )

⇒ 8 ( - y ) + 3y = 5

⇒ - 8y + 3y = 5

⇒ - 5y = 5

⇒ y = - 5 ÷ 5

y = - 1

Now,

x = - y

⇒ x = - ( - 1 )

x = 1

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Related Questions

What degree is 3x1?.

Answers

The degree of 3x^1 is 1.

A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.

To find the degree of a polynomial, you can do the following:

→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.

→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.

3x^1 is a monomial with a coefficient of 3 and an exponent of 1. It is also called a linear term. The degree of a monomial is the exponent of the variable. So in this case, the degree of 3x^1 is 1.

Therefore, the degree of 3x^1 is 1.

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What does an increase of 1 on the Richter scale mean?.

Answers

An increase of 1 on the Richter scale means that the scale has increased by approximately 31 units in terms of Richter scale.

A 1.0 increment in the Richter magnitude scale results in a 31-unit difference in the intensity of an earthquake. The Richter scale (ML), a numerical measure of an earthquake's size, was devised by American seismologists Charles F. Richter and Beno Gutenberg in 1935.

The magnitude of an earthquake is determined by taking the height of the largest seismic wave and dividing it by the logarithm of its amplitude. The original Richter scale has been replaced in modern science by newer, more accurate scales, yet it is still routinely misrepresented in news reports of earthquake intensity as the logarithmic scale on which earthquakes are measured.

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Question What is the value of x? Enter your answer in the box. x = Two intersecting lines. The angle formed at the top is labeled 3 x plus 50 degrees. The angle formed at the bottom directly opposite it is labeled 6 x minus 10 degrees.

Answers

The value of x when solving for the alternate angles is; x = 20 degrees

How to solve alternate angles?

Alternate angles are defined as angles that occur on the opposite sides of the transversal line and thus have the same size. There are two different types of alternate angles namely alternate interior angles and alternate exterior angles 3x + 50 degrees and 6x - 10 degrees are alternate angles and as such;

3x + 50 = 6x - 10

Rearrange to collect like terms to get;

6x - 3x = 50 + 10

3x = 60

x = 60/3

x = 20 degrees

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Determine which function(s) are exponential. Select all that apply.
A.
x 0 1 2 3 4
y 0 1 4 9 16
B.
x 0 1 2 3 4
y 13
1 3 9 27
C.
x 0 1 2 3 4
y 5 52
54
58
516
D.
x 0 1 2 3 4
y 4.5 4 3.5 3 2.5

Answers

Only table {1} represents a exponential function.

What is exponential function?The exponential function is a mathematical function denoted by the expression as - f(x) = eˣReal exponential function is commonly defined by the following power series as -

       [tex]$e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }[/tex]

Given are the function tables as shown in the question.

For the table {1}, we have -

       {x} → 0  1  2  3  4

       {y} → 0  1  4  9  16

The value of {y} varies with respect to {x} as : y = x². This is an exponential function.

Therefore, only table {1} represents a exponential function.

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The speed of a ship is given 3/4 where d is the distance the ship travel in 3 hours.if the ship travels 48miles in 3 hours.what was the speed of the ship

Answers

By taking the quotient between the distance and the time, we will see that the speed is 16 miles per hour.

How to find the speed of the ship?

Remember that the speed is defined as the quotient between the distance traveled and the time in which that distance is traveled.

Such that:

speed = (distance)/(time)

Here we know that the ship can travel 48 miles in 3 hours, so:

distance = 48 mi

time = 3 hours

Then the speed is:

S = 48mi/3h

S = 16 mi/h

So the speed of the ship is 16 miles per hour.

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How do you write domain and range examples?.

Answers

The domain and range are described for a relation, and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For example, if the relation is R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then: Domain = {1, 2, 3, 4} and Range  = {2, 3}.

The domain and range of a function are the elements of a function. The domain is the set of all the input elements of a function, and the range is the possible outcome given by the function.

Domain→ Function →Range. If there exists a function f: α → β such that every element of α are mapped to elements in β, then α is the domain, and β is the co-domain.

The image of an element 'p' under a relation R is given by 'q', where (p,q) ∈ R. The function's range is the set of images. The domain and range of a function are denoted in general as follows:

Domain(f) = {x ∈ R} and range(f) = {f(x): x ∈ domain(f)}.

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Mai has picked 1 cup of strawberries for a cake which is enough for 3/4 of the cake. How many cups does she need for the whole cake?

Answers

Answer:

Mai needs 4/3 cups of strawberries in order to make the whole cake.

Step-by-step explanation:

1 cup of strawberries being equal to 3/4 of the cake is also the same as 1 cup of strawberries equaling 75% of the cake. So, what times 0.75 is equal to 1? That is 4/3.

What is the slope and y − intercept of the equation y 2x 4 *?.

Answers

The curve has a y-intercept of -4 and a slope of 2. We will need two points on the line y = 2x - 4 to plot the graph.

Y = 2x + b, where b is the y-intercept, is how the equation y = 2x - 4 can be expressed in slope-intercept form. We must perform the b-solve in order to determine the slope and y-intercept of the equation.

The line's crossing of the y-axis is known as the y-intercept. Setting x equal to 0 in the equation yields y = 2(0) - 4 and the y-intercept, which can be found. As a result, the y-intercept is determined to be y = -4.

The pace at which a line increases is referred to as its slope. Using the coefficient of x, which is 2, we can get the slope. Consequently, the slope of the equation is 2. Y = 2x – 4.

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Full Question = What are the slope and y − intercept of the equation y 2x − 4?

The circumference of a circle is 14π cm. What is the area, in square centimeters? Express your answer in terms of � π.

Answers

A circumference is not, first of all, calculated in square units. Square measurements can only be made for areas.

figuring out the circle's area:

find the circle's radius first

A circle's circumference is determined by

C = 2πr

Given that a circle has a 14π cm circumference

by entering C's value in the formula above, we obtain

14π = 2πr

Divide both sides by 2π

r = 7

Therefore, value of radius ( r ) is 7 cm

The circle's area is defined as :

A = π r^(2)

A = π ( 7 )^2

A = π ( 49 )

Consequently, the circle's area is

49π cm^2

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Triangle def is formed by connecting the midpoints of the sides of triangle abc.

Answers

A triangle def is called a "midsegment triangle" and it is formed by connecting the midpoints of the sides of a triangle ABC.

The midsegment triangle is always parallel to the original triangle and has half the area. The three sides of the midsegment triangle are called the "midsegments" of the original triangle, and they are always parallel to the corresponding sides of the original triangle and have half the length.

A triangle defined by connecting the midpoints of the sides of triangle ABC is called a "midsegment triangle" or "medial triangle." The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. The three sides of the medial triangle are the midsegments of the original triangle, and the three angles of the medial triangle are equal to one-half of the angles of the original triangle.

Triangle

A triangle is a geometric shape that has three sides and three angles. It is a fundamental shape in Euclidean geometry and is one of the basic shapes in geometry. Triangles are classified based on their angles and sides, such as acute, right, and obtuse triangles. The sum of the angles in a triangle is always 180 degrees. Triangles can also be classified as equilateral, isosceles, or scalene based on the lengths of their sides. They are used in a variety of fields such as construction, engineering, and physics.

The triangle's characteristics are:

A triangle's (of all varieties) total sum of angles is 180°.The length of a triangle's two longest sides added together is longer than the third side.Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.The longest of a triangle's three sides is the side that faces the larger angle.A triangle's exterior angle is always equal to the product of its inner and exterior opposing angles. The outer angle attribute of a triangle refers to this characteristic.When the corresponding angles of two triangles match up and the side lengths are proportionate, two triangles are said to be comparable.Triangles have an area equal to one-half of their base and height.A triangle's perimeter is equal to the sum of its three sides.

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Can you please help, I'm offering 30 points!
if a1=5 and an=nan-1+2 then find the value of a4

Answers

Answer:

[tex]a_4 = 154[/tex]

Step-by-step explanation:

In this problem, we are asked to find the fourth term ([tex]\square_4[/tex]) of a sequence [tex]a[/tex] given that [tex]a_1 = 5[/tex] and [tex]a_n = na_{n-1} + 2[/tex].

To solve for this, we can first find the second term in the sequence by inputting [tex]a_2[/tex] into the sequence definition.

[tex]a_2 = 2a_{2-1} + 2[/tex]

Then, we can replace [tex]a_{2-1}[/tex] with the value that we were given: [tex]a_1 = 5[/tex].

[tex]a_2 = 2(5) + 2[/tex]

[tex]a_2 = 10 + 2[/tex]

[tex]a_2 = 12[/tex]

Next, we can solve for the third term in the sequence.

[tex]a_3 = 3a_{3-1} + 2[/tex]

And we can replace [tex]a_{3-1}[/tex] with the value that we just solved for: [tex]a_2 = 12[/tex].

[tex]a_3 = 3(12) + 2[/tex]

[tex]a_3 = 36 + 2[/tex]

[tex]a_3 = 38[/tex]

Finally, we can solve for fourth term in the sequence.

[tex]a_4 = 4a_{4-1} + 2[/tex]

We can again replace [tex]a_{4-1}[/tex] with the value that we just solved for: [tex]a_3 = 38[/tex].

[tex]a_4 = 4(38) + 2[/tex]

[tex]a_4 = 152 + 2[/tex]

[tex]a_4 = 154[/tex]

Answer:

  a₄ = 154

Step-by-step explanation:

You want the value of a₄ given the recursive sequence definition ...

  [tex]\begin{cases}a_1=5\\a_{n}=n\cdot a_{n-1}+2\end{cases}[/tex]

Solution

The easiest way to find the first few terms of a recursively-defined sequence is to use the recursive definition directly:

  [tex]a_2=2\cdot a_1 +2 = 2(5) +2 = 12\\\\a_3=3\cdot a_2+2=3(12)+2 =38\\\\a_4=4\cdot a_3+2=4(38)+2=154[/tex]

The value of a₄ is 154.

__

Additional comment

The terms of this sequence get rapidly larger. The 10th term is 23,357,002. The general term can be defined in terms of the Euler gamma function and the incomplete gamma function:

  [tex]a_n=\Gamma(n+1)+2e\Gamma(n+1,1)[/tex]

In a student council election Kyle receives 120 votes for president. If Kyle receives 60% of the votes, how many students vote in the election?

Answers

Answer:

200 students vote in the election

Step-by-step explanation:

We know

120 votes = 60%

1% = 2 votes

To find how many students vote in the election, we take

2 x 100 = 200 votes

So, 200 students vote in the election

Graph a line that contains the point (-3,-4) and has a slope -5

Answers

Answer:

y = −5x − 19

Step-by-step explanation:

Find the equation using slope-intercept form.

y = −5x − 19

Joseph wants to earn $850 this summer in order to pay for a down payment on a car. His summer break is 6 weeks. He has been offered 3 different jobs.

Which job should he take to earn the $850 quickest? Explain your response.
Working as a cashier in a bookstore that pays $7.50 an hour and he is expected to work 25 hours per week

Working at a summer camp as a camp counselor for a flat rate of $175 per week (the camp is only 4 weeks)

Working as a sales associate at a department store that pays $7.25 an hour with 5% commission on all sales (he is expected to work 20 hours per week and projected to sell $1,350 per week)
B. Which job will not help him get to his goal of $850?

Answers

Answer:

A - Sales associate

B - Summer Camp Counselor

Step-by-step explanation:

First, lets look at how much Joseph would averagely earn from each job.

Cashier in bookstore: in 6 weeks he will earn 900

Summer camp counselor: in 4 weeks 700

Sales associate: in 4 weeks he will earn 850

Overall, becoming a Sales associate will allow Joseph to earn his $850 quicker.

B - the Summer Camp Counselor job will not allow Joseph to make $850 because Summer Camp only lasts 4 weeks.

What is the formula of sum of series?.

Answers

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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Answer:

Step-by-step explanation:

In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.

Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.

Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum   them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.

So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.

If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:

S

3

=2+4+6

S3=12.

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The perimeter of a rectangle i 52 feet. The length of the rectangle i 10 feet longer than the width. Find the dimenion of the rectangle

Answers

The length of the rectangle is 18 feet and width is 8 feet .

What is perimeter of rectangle?

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is

P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.

The perimeter of rectangle is given by  2 ( l + b)

where l is length of rectangle and b is width of the rectangle

given that perimeter of rectangle is 52

so 2 (l+b)= 52

=>  l+b=26  ---(i)

given l = b +10

=> l -b = 10 ---(ii)

adding equation (i) and (ii) we get :

2l = 36

=> l =36/2

so length = 18 and breadth = 18 - 10 =8

so the length is 18 and breadth is 8.

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Ankit visited in a mall with his father. He sees that three shops are situated at P, Q, R as shown in the figure from where they have to purchase things according to their need. Distance between shop P and Q is 8 m, that of between shop Q and R is 10 m and between shop P and R is 6 m.

Answers

The measure of angle PQR is given as follows:

How to obtain the measure of angle PQR?

To obtain the measure of angle PQR, first we verify if the triangle PQR is a right triangle or not.

To verify if the triangle is a right triangle we apply the Pythagorean Theorem, which states that the length of the hypotenuse squared is equals to the sum of the lengths of each side squared, in the case of a right triangle.

Hence, for this problem, considering the side lengths, we have that:

10² = 6² + 8²

100 = 36 + 64

100 = 100.

Which is true, hence this is in fact a right triangle and the measure of angle PQR is of 90º.

Missing Information

The problem asks for the measure of angle PQR.

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What Are sin cos and tan ratios?.

Answers

The three fundamental trigonometric ratios, namely sine, cosine, and tangent, each yield the ratio of the lengths of the two sides of a right-angled triangle.

We are aware that the sides of a right-angled triangle are called the "legs" and the "hypotenuse," respectively. Thus, the longest side of a right-angled triangle is still referred to as the "hypotenuse" in trigonometry, while the other two legs are referred to as the "opposite side" and "adjacent side."

The opposite, adjacent, and hypotenuse sides of a right-angled triangle are used to define the sin, cos, and tan functions in trigonometry. These are the sin, cos, and tan formulae.

sinФ = OppositeHypotenuse

cos Ф = AdjacentHypotenuse

tan Ф = OppositeAdjacent

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Write the relation as a set of ordered pairs. A relation. An arrow goes from 0 to 2, 2 to 6, and 4 to 10. a. ordered pairs: {(0, 2), (2, 6), (4, 10)} b. ordered pairs: {(2, 0), (6, 2), (10, 4)} c. ordered pairs: {(0, 2), (6, 2), (10, 4)} d. ordered pairs: {(2, 0), (2, 6), (4, 10)} Please select the best answer from the choices provided A B C D

Answers

The relation should be written as a set of ordered pairs as follows: A. . ordered pairs: {(0, 2), (2, 6), (4, 10)}.

What is a function?

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (x-value or domain) to an output variable (y-value or range).

What is an ordered pair?

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

Ordered pair = (0, 2)Ordered pair = (2, 6)Ordered pair = (4, 10)

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X and Y are 2 sets such that X has 15 elements, Y has 25 elements and X (union) Y has 40 elements.
Find the number of elements in X (intersection) Y

Answers

The number of elements in the set that represents the intersection of X and Y is given as follows:

Zero.

How to obtain the number of elements in the intersection of X and Y?

The number of elements in the intersection of X and Y is obtained according to the rule presented as follows:

n(X or Y) = n(X) + n(Y) - n(X and Y).

The parameters for this problem have the values given as follows:

n(X) = 15.n(Y) = 25.n(X or Y) = 40.

Hence the number of elements in the intersection set is given as follows:

n(X or Y) = n(X) + n(Y) - n(X and Y).

40 = 15 + 20 - n(X and Y)

n(X and Y) = 0.

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How do you find the domain and range given points on a graph?.

Answers

To find the domain and range from given points on a graph: the set of all x-coordinates is the input and the set of all y-coordinates is the output.

We know that the domain of function is the set of all possible input values for which the function is well defined.

And the range of function is the set of all possible output values for given input.

To find the domain and range of function we can graphical methhod.

We know that the input values of function are shown on the x-axis and the output values of the function are shown on the y-axis.

This means, the domain of a graph shown on the x-axis. Whereas the range is shown on the y-axis.

To find the domain and range when points on a graph are given:

the set of all x-coordinates would be the domain and the set of all y-coodinates is the range of function.

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What is domain and range of a function?.

Answers

Answer: Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

Step-by-step explanation:

Are all triangles 30 60 90?.

Answers

No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.

No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.

A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.

For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.

Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.

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Need help finding the answer to this It doesn't make any since to me.

Answers

Good luck on your assignment!

Help me write a simplified expression for the side length of the square. Please.

Answers

Answer:

Side length of square = -10b³ + 12

Step-by-step explanation:

Forming the equation,

→ P = 4 × side

→ P = 4a

→ [ a = P/4 ]

Now the side length of square is,

→ a = P/4

→ a = (-40b³ + 48)/4

→ a = (-40b³ ÷ 4) + (48 ÷ 4)

→ a = (-10b³) + (12)

→ [ a = -10b³ + 12 ]

Hence, side length is -10b³ + 12.

Answer:

-10b³ + 12

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

As a square has four sides of equal length, the perimeter of a square is four times the length of one side.

Therefore, to find the expression for the side length of a square, simply divide the expression for the perimeter by 4.

[tex]\begin{aligned}\textsf{Side length of a square}&=\dfrac{\textsf{perimeter}}{4}\\\\\implies \textsf{Side length of the square}&=\dfrac{-40b^3+48}{4}\\\\&=\dfrac{-40b^3}{4}+\dfrac{48}{4}\\\\&=-10b^3+12\end{aligned}[/tex]

My brain is broke and I have no brain cells .

THIS IS DUE TODAY HURRYYYY! PLEASEE

Answers

Based on the table of values, the slope and y-intercept include the following:

Slope = 1/2.y-intercept = -1/2.

What is y-intercept?

In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is equal to -1/2.

From the information provided in the table above, the slope and data points on this line include the following:

Points on x-axis (x) = (1, -1).Points on y-axis (y) = (0, 1).

In Mathematics and Geometry, the slope of any straight line can be calculated by using this expression;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have;

Slope (m) = (1 - 0)/(1 + 1)

Slope (m) = 1/2

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How much larger is the amplitude of waves from a 4. 0 earthquake relative to a 3. 0 earthquakes?.

Answers

An earthquake with a Richter scale value of 4.0 is 10 times more powerful than one with a value of 3.0.

On the Richter scale, every whole-number rise in magnitude corresponds to a 10-fold increase in observed amplitude.

In order to evaluate the size of different earthquakes, the Richter scale was initially developed to quantify the magnitude of earthquakes of moderate size (i.e., magnitude 3 to magnitude 7). The scale was created for earthquakes that occurred in southern California, were detected by the Wood-Anderson seismograph, and had epicenters that were less than 600 km (373 miles) away from the seismograph's position.

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pls help i have to do this quickly :')

Answers

Answer:

Circumference = 56.55

Area=254.47

What are the 4 system of equations?.

Answers

There are four systems of equations in mathematics, namely linear equations, quadratic equations, polynomial equations, and exponential equations.

Each has its own unique properties that can be exploited for solving problems. Linear equations are the simplest system of equations and are the basic building blocks of more advanced systems of equations. Quadratic equations use the product of two terms to solve one equation. For example, 5x + 6y = 20 can be rewritten as 2x + 5y = 20. Polynomial equations use the power of a term squared to solve one equation. For example, x^2 + 7x + 12 = 55 can be written as x2 + 9x + 22 = 55. Exponential equations use the power to the base to solve one equation. For example, x^3 + 3x^2 - 10x - 16 = 0 can be written as x^3 + 3x^2 - 10x - 16 = 0e^-3 = e. These systems can be used to represent real world scenarios such as population growth,

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help me calculate the coordinates of points B, D and E​

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Answer:

  B(-π/3, 1/2), D(7π/6, -√3/2), E(11π/12, -1/2)

Step-by-step explanation:

You want the coordinates of various points marked on the graph of the sine and cosine functions.

Graph

The horizontal divisions on the graph are multiples of π/6. That is, there are 6 divisions between 0 and π. This means the x coordinates of interest are ...

  B = -π/3

  D = 7π/6

  E = 11π/6

Points B and D lie on the red curve, which the graph tells you is a plot of cos(x). Then the coordinates are ...

  B = (-π/3, cos(-π/3)) = (-π/3, 1/2)

  D = (7π/6, cos(7π/6) = (7π/6, -√3/2)

Point E lies on the blue curve, which is a plot of sin(x). Its coordinates are ...

  E = (11π/6, sin(11π/6)) = (11π/6, -1/2)

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Additional comment

The attachment shows the coordinates of points on the unit circle as (cos(θ), sin(θ)). On the given graph, θ is on the horizontal axis (x), and sine and cosine are on the vertical axis. To make use of the attachment, you find the angle, then look for the (cos, sin) coordinates at that angle.

Negative angles are clockwise from θ=0. To find the corresponding angle on the attachment, add 2π to any negative angle.

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