2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km

The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.

Let the angle that the golfer has between the spectator and the hole be x

Here, sin 120°/200 =sin x/140

0.8660/200 =sin x/140

0.00433 = sin x/140

sin x=0.866

x=60°

Therefore, option A is the correct answer.

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Hi hi! The answer would be 22.7°, I took the test a while ago.

We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2

An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.

We are given, 4x²+ 12x +k =0, k =Z and x = R

the quadratic equation is 4x²+12x+k =0

we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a

when the quadratic equation is ax²+bx+ c= 0

Hence, roots of the equation given in question will be,

 x = - 12 ±√ (12² - 4×4×k) / 2×4

x = - 12 ± √(144-16k) / 8

as per the condition given in question, one root of this equation is 5 times the other root.

hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5

multiplying both sides by 8

- 12 - √(144-16k) = [-12 + √(144-16k)] ×5

- 12 - √(144-16k) = - 60 + 5√(144-16k)

- 12 + 60 = 6√(144-16k)

48 = 6√(144-16k)

8 = √(144-16k)

64 = 144 -16k

16k = 80

k = 5

the value of k =5

by putting the value of k =5

x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8

x = -1/2 and x = -5/2

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Answer:

There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.

Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.

The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person.      Answer:{2}.

Step-by-step explanation:

The complete statement is f(2) = 8+5√7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=2x²+5√7

Thus f(1) = 2×4+5√7

              = 8+5√7

Hence, The complete statement is f(2) = 8+5√7

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Step-by-step explanation:

false.

3a²b≠3ab².

If a is 3 and b is3 it is not equal

Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.

In geometry, a shape's perimeter, or overall length, is referred to as its perimeter. The lengths of all a shape's sides and edges are added up to determine its perimeter.

Here,

Given :  length = 5 - 1(x) or

=> length = 5-x

Width is twice the length

thus,

=>Width = 2(5-x)

=>Width = 10-2x

So ,To find the perimeter

We use,

=> Perimeter = 2(length + width)

=> Perimeter = 2( 5-x + 10-2x )

=>  Perimeter = 2( 15 -3x)

=>   Perimeter = 30 -6x

Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.

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Answer:4 = -117,3=-212,4+3

Step-by-step explanation:

Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.

The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist.  An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.

given

We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.

Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.

So in this case we can write:

limx → +∞f(x) = 0

limx → - ∞f(x) = 0

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The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.

Given the equation of the parabola;

-x² - 2x + 10 = 0

First, the maximum of a quadratic function occurs at;

x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)

f_max(x) = ax² + bx + c occurs at;

x = -b/2a

Now, find the value of x = -b/2a

Plug in a = -1 and b = -2

x = -( -2/2(-1) )

x = -( -2/-2) )

x = -( 1 )

x = -1

Hence;

f(x) = -x² - 2x + 10

f( -1 ) = -( -1 )² - 2( -1 ) + 10

f( -1 ) = -1 + 2 + 10

f( -1 ) = -1 + 12

f( -1 ) = 11

Therefore, maximum occurs at (-1,11).

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The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).

The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.

First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.

Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).

Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.

Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).

Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:

a + 3b = 0

b = 0

-a = 0

Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.

Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).

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Answer:

chocolate chip 7

walnuts 3.5

Step-by-step explanation:

assume x=chocolate chips

 y=walnuts.

equation

4x + 8y=33

(2x+3y=13)×2

new eq

4x + 8y=33

4x + 6y=26

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

 2y=7

  y=7/2

4x+ 8y = 33

4x + 8(7/2)= 333

4x= 33-28

x=7.00

The rate of growth or decay, r, is equal to 0.10.

Population in math refers to the set of all items of interest in a given context. It is the target or focus of a statistical study, and the objects described by the population's characteristics are known as population elements. It is important to define the population in detail before analyzing data and drawing conclusions. Examples of populations can include all students at a school, all people living in a particular country, or all people who bought a particular product.

So each year the number of residents in the town is 1.10 times the number in the previous year.

There were around 14,641 residents in the town 14 years after 2005.

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A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The line going through the origin equation is also y=2x.

A line that crosses the origin is symbolized by the equation y=mx.

Also, y=2x satisfies the point (0,0)

A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

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Step-by-step explanation:

To find the GCD or GCF of two numbers , you should:

Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.

To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.

To calculate the slope of the line connecting two points, you can use the following formula:

slope = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.

Step-by-step explanation:

Answer:

2 1/3

Step-by-step explanation:

Seperate equation

(3 1/2) - 1

( 3 - 1 ) + 1/2

2 and 1/3

-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.

170° in radian is  17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively

An angle can be converted from degree to radian by multiplying it by π/180.

1. -560°

-560° × π/180 = -28π/9 radian

2. 170°

170° × π/180 = 17π/18 radian

In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.

coterminal of -28π/9:

positive: -28π/9 =  -28π/9 + 2(2π) = 8π/9

negative: -28π/9 =  -28π/9 + 2π = -10π/9

coterminal of 17π/18:

positive: 17π/18 =  17π/18 + 2π = 53π/18

negative: 17π/18 =  17π/18 - 2π = -19π/18

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Answer:

0.16 or 0.2 if rounded

Step-by-step explanation:

4 gallons divided by 25 chairs equals 0.16 gallons for each chair

hope this helps <3

Answer:

18

Step-by-step explanation:

36-10-2-6

26-8

18

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6^2 - 2(5 + 1 + 3)}\\\mathsf{= 6^2 - 2(5) - 2(1) - 2(3)}\\\mathsf{= 6^2 - 10 -2(1) - -2(3)}}\\\mathsf{= 6\times 6 - 10 - 2(1) - 2(3)}\\\mathsf{= 36 - 10 - 2(1) - 2(3)}\\\mathsf{= 26 - 2(1) - 2(3)}\\\mathsf{= 26 - 2 - 2(3)}\\\mathsf{= 24 - 2(3)}\\\mathsf{= 18}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{18}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Having 3 students pick a raffle

Step-by-step explanation:

The solution to the equations are

0 ∈ N is False               7/2 ∈ Q is True

√16 ∈ Q' is False          π ∈ Q' is True

3/2 ∈ I is False              -3 ∈  R is True

0 ∈ I is True                  -1 ∈ I⁺ is False

( 1 - 3 ) ∈ N is False       8/2 ∈ I is True

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the equation will be

a)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is not a natural number

So , the equation is False

b)

Let the number be A = √16

The value of A = 4

The number 4 is a natural number , whole number , rational number and an integer

4 is not an irrational number

So , the equation is False

c)

Let the number be A = 3/2

The number 3/2 is a rational number

3/2 is not an integer

So , the equation is False

d)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is an integer

So , the equation is True

e)

Let the number be A =  ( 1 - 3 )

The value of A = -2

The number -2 is a rational number and an integer

-2 is not a natural number

So , the equation is False

f)

Let the number be A = 7/2

The number 7/2 is a rational number

7/2 is a rational number

So , the equation is True

g)

Let the number be A = π

The number π  is an irrational number

π is an irrational number

So , the equation is True

h)

Let the number be A = -3

The number -3 is a real number

7/2 is a real number

So , the equation is True

i)

Let the number be A = -1

The number -1 is an integer and real number

-1 is a negative integer

So , the equation is False

j)

Let the number be A = 8/2

The value of A = 4

The number 4 is a natural , whole , integer and rational number

4 is an integer

So , the equation is True

Hence , the equations are solved

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Answer: slope=-5 and y-intercept=1

Step-by-step explanation:

The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.

This gives m=-5 and b=1.

Answer:

96

Step-by-step explanation:

24 divided by 1/4 is 96

you turn 24 into a fraction by putting a one under is and then you keep it change it flip it

24/1 Divided by 1/4

24/1 times 4/1

24 times 4= 96

1 times 1= 1

96/1=96

Answer:

Step-by-step explanation:

You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.

An inequality can be written for each of the constraints:

  x + y ≥ 18 . . . . . . . no less than 18 coins

  0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value

  x ≥ 4 . . . . . . . . . . at least 4 dimes

A graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.

One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50

Systems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.

In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.

Let;

x + y ≥ 18

0.1x + 0.05y ≤ 1.50

x ≥4

Using a graphing calculator to solve this,

The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

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Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

The speed of the carts after collision is  3 m/s.

We have to note that in this case, we would need to apply the principle of the conservation of linear momentum. This implies that the momentum before collision would have to be the same as the momentum after collision.

Then we have;

Momentum before collision = Momentum after collision thus;

(3 * 4) + ( 1 * 0) = (3 + 1) v

Note that the two carts are said to stick together and move with a common speed

Hence;

12 = 4v

v = 12/4

v = 3 m/s

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Answer: Gloria will need 14 cups of flour

Step-by-step explanation: 2 1/3 x 6 = 14

Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.

The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.

On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.

When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.

To sum up:

-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.

The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1

-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.

Step-by-step explanation: