The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.
How do you find the linear inequality of a graph?The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.
To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.
When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.
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Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.
1. -560°
2. 170°
-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
How to convert the degree measure of angle to radians?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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summarize how you can find the slope of a perpendicular line.
Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.
Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.
In mathematics, slope is the proportion of the change in the y value to the change in the x value.
Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.
The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.
Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.
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Checkpoint 4 is -117 and checkpoint 3 is -212 how much higher is checkpoint 4 than 3
Answer:4 = -117,3=-212,4+3
Step-by-step explanation:
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.
Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees
If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
60.0°
59.6°
37.3°
22.7°
The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.
What is sine rule?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.
PLEASE FAST WILL GIVE BRANILY
A 12-foot tall tent pole is secured to the ground using a piece of rope 15 feet long from the top of the tent pole to the ground. If the tent pole makes a 90-degree angle with the ground, determine the number of feet along the ground from the tent pole to the rope.
3 feet
9 feet
19 feet
81 feet
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.
There is a raffle for the class of 30
students. There are 3 prizes that are gift
cards for the value of $5, $10 and $25.
How many ways can there be 3 winners of
this raffle?
Answer:
Having 3 students pick a raffle
Step-by-step explanation:
DIRECTIONS: Use this information to answer Parts A and B. The width of a rectangle is shown. The length is twice the width. Part A 5-1x Write an expression for the perimeter listing each side separately.
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
Define perimeter.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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Using the paths shown, how long is the shortest route from Lexington to Somerville?
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
Two cards are drawn at random from a well shuffled pack of cards. What is the probability that
i)both are spades or both are diamonds?
ii)both are queens or both are red coloured?
iii)both are diamonds or neither is a king?
Answer:
Step-by-step explanation:
1 in a tenth of a million. I did the math with all the cards and how many are kinds diamonds or red or queens yk.
what is 3 1/3 minus -1
Answer:
2 1/3
Step-by-step explanation:
Seperate equation
(3 1/2) - 1
( 3 - 1 ) + 1/2
2 and 1/3
A 3kg cart moving with a speed of 4m/s collides with a 1 kg cart at rest
The speed of the carts after collision is 3 m/s.
What is the velocity after collision?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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Rashaad has
x
x dimes and
y
y nickels, having no less than 18 coins worth at most $1.50 combined. At least 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Answer:
see attached for a graph4 dimes, 22 nickelsStep-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.
InequalitiesAn 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
GraphA 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
What is System of Linear InequalitySystems 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 = dimesy = nickelx + 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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Show 24÷1/4 step by step
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
Greatest common factor
Step-by-step explanation:
To find the GCD or GCF of two numbers , you should:
List the prime factors of each one of them(the 2 numbers)choose the common number+least exponent multiply them3. Function G is defined by the equation G(x) = [x].
Function R is defined by the equation R(x) = x/+2.
Describe how the graph of function R relates to the graph of G, or sketch the graphs
of the two functions to show their relationship.
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:
If f(x)=2(x)^2+5square root (5+2) complete the following statement f(2)= blank
The complete statement is f(2) = 8+5√7
What are functions?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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Consider whether it's wrong or right.
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
What is an Equation?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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Five people each working eight hours a day can assemble 400 toys in a five day work week. What is the average number of toys assembled per hour per person?
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:
evaluate 6²-2(5+1+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]
A store is having a sale on chocolate chips and walnuts. For 4 pounds of chocolate chips and 8 pounds of walnuts, the total cost is $33. For 2 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $13.
Find the cost for each pound of chocolate chips and each pound of walnuts.
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
Select the correct answer from each drop-down menu.
A town's population was 10,000 in 2005. The population has increased by 10% per year since 2005.
This situation represents
The rate of growth or decay, r, is equal to ____. So each year the number of residents in the town is ___ times the number in the previous year.
There were around 14,641 residents in the town ___ years after 2005.
The rate of growth or decay, r, is equal to 0.10.
What is population?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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PLEASE Help. The answers I got so far are A. 72. B. 301. C 90 and D 252. I am having the most trouble with B and D.
The correct solutions for this question are as:
(A) Bearing of B from A = 72°
(B) Bearing of B from C = 342°
(C) Bearing of A from B = 252°
(D) Bearing of A from C = 293°
Step by step solution:
(A) Bearing of B from A:
= 72° (Given in question)
(B) Bearing of B from C: = 342°
Solution:
As sum of co-interior angles is 180° , i.e. ∠NBC +∠NCB =180°
so, 162° + ∠NCB = 180°
∠NCB = 180°-162°
∠NCB = 18°
reflexive angle NCB =360° - ∠NCB
reflexive angle NCB = 360° - 18°
reflexive angle NCB = 342°
So, bearing of B from C: = 342°
(C) Bearing of A from B: = 252°
Solution:
First extend the line AB to any point (let's say "X")
So, ∠NBX = 72° [BY USING CORRESPONDING ANGLES]
Bearing of A from B = ∠NBX + 180°
Bearing of A from B =72° + 180°
Bearing of A from B =252°
(D) Bearing of A from C: = 293°
Solution:
Bearing of A from C= 360° - (∠BCA + ∠BCN)
Bearing of A from C= 360° - (49° + 18°)
Bearing of A from C= 360° - (67°)
Bearing of A from C= 293°
Important Points for "Bearing of Angles":
A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.
The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.
Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.
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8.326 rounded to the nearest tenth
Answer:
8.3
Step-by-step explanation:
The number after three is below 5 so it stays as 8.3
-3/5(1+5n) =102
Solve for n
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
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:
1. Let
U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},
and let
V = span {(1, 0, -1), (3, 1, 2)}.
Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.
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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Four gallons of paint are used to paint 25 chairs. If each chair used the same amount of paint, how many gallons are used to paint each?
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
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3a²b and 3ab² are like terms true or false
Step-by-step explanation:
false.
3a²b≠3ab².
If a is 3 and b is3 it is not equal
One root of the equation 4x² + 12x + k = 0, k = Z and x = R, is five times the other root.
Find the value of k.
We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2
What is quadratic equation?An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.
How to determine the value of k in the question?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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Mrs. Sarto told her son that if he babysat his baby sister, she would pay him $5.80 per hour. If Mrs. Sarto’s son babysits his sister for 5.2 hours, how much money will he be paid?