In the equation y = 6 - 3x, we can observe that the coefficient of x is -3. This coefficient represents the slope of the line. A positive slope indicates a line that rises as x increases, while a negative slope indicates a line that falls as x increases.
Since the slope is -3, it means that for every increase of 1 unit in the x-coordinate, the corresponding y-coordinate decreases by 3 units. This tells us that the line will move downward as we move from left to right along the x-axis.
We can also determine the direction by considering the signs of the coefficients. The coefficient of x is negative (-3), and there is no coefficient of y, which means it is implicitly 1. In this case, the negative coefficient of x implies that as x increases, y decreases, causing the line to slope downward.
So, to summarize, the line defined by y = 6 - 3x has a negative slope (-3), indicating that the line slopes downward as we move from left to right along the x-axis. Therefore, the statement "the line defined by y = 6 - 3x would slope up and to the right" is false. The line slopes down and to the right.
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Lily i making moothie. Each moothie ue \tfrac{1}{2} 2 1 cup of yogurt. How many cup of yogurt doe he need to make 3 moothie? Expre your anwer in implet form
Lily is making smoothie. Each smoothie 1/2 cup of yogurt. The fraction is [tex]1\frac{1}{2}[/tex] cup of yogurt does he need to make 3 smoothie.
Fraction:
Fractions represent parts of a whole. This whole thing can be a region or a collection. The word break comes from the Latin word "fraction" which means "to divide". The earliest civilization to study fractions, the Egyptians, used fractions to solve mathematical problems such as the division of food, supplies, and the lack of bullion currency.
In ancient Rome, fractions were written to represent parts of a whole using only words. In India, fractions were originally written with the numbers (numerator and denominator) on top of each other, but without lines. Arabs were the only ones who added the dash used to separate the numerator and the denomination.
According to the question:
Lily on the given conditions, formulate: 1/2 × 3
Write as a single fraction: [tex]\frac{1 * 3}{2}[/tex]
Calculate the product or quotient: 3/2
Convert to mixed fraction: [tex]1\frac{1}{2}[/tex]
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Solve the following system of equations graphically on the set of axes below
The solution is the point where the two lines intersect i.e. (-1,-7). The graph for the given system of equations is attached below wherein the blue line represents y=2x-5 and the green line represents y=-x-8.
What is system of equation?
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.
For solving the equations graphically, we need to find points for plotting
So, for y = 2x-5,
The y-intercept is -5, so we need to place a point on the graph at (0,-5). For the another point, put x=1, we get y= -3. So we need to place another point at (1,-3).
Similarly for y = -x-8,
The y-intercept is -8, so we need to place a point on the graph at (0,-8). For the another point, put x=1, we get y= -9. So we need to place another point at (1,-9).
The solution is the point where the two lines intersect.
When the two lines intersect,
2x-5=-x-8
3x=-3
x=-1
So, y=-7
Hence, the two lines intersect at (-1,-7).
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the volume of a cube is 27x9 cubic units. the length of each edge of the cube is (27x9)1/3 units. which of these is equivalent to the length of each edge of the cube?
Length of edge of cube = 6.24 unit
What is cube?A cube is a three-dimensional object that has 6 congruent square faces. Dimensions of all the 6 square faces of the cube are the same. A cube is sometimes also referred to as a regular hexahedron or as a square prism.
Given,
volume of cube = 27×9 cubic units
Length of edge of cube = ∛(27×9)
= ∛243
= 6.24 unit
Hence, 6.24 unit is length of edge of cube.
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4.1 is greater or less than 4.100
How many concepts are there in geometry?
Three fundamental ideas provide the foundation for all basic geometry notions. The three are the plane, line, and point.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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Three basic ideas form the basis of all basic geometry concepts. The three are planes, lines, and points.
Who Named Geometry?Euclid, the father of geometry, was a brilliant mathematician. Learn about the history of Euclid and some of the mathematical ideas we use today, and see how important they have become. The terms ``ge'' and ``metria'', meaning ``measure,'' are of geometric origin. For over 2000 years, the Greek approach to geometry has served as the foundation of geometry.
Geometry is the study of various mathematical or actual forms, figures, and sizes. In geometry, you will discover the concepts of points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.
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In Exercises 21–28, verify that the segment lengths
form a triangle. Is the triangle acute, right, or obtuse?
Acute angles are the angles that measure less than 90 degrees. Right angles measure 90 degrees and Obtuse angles measure more than 90 degrees.
How to explain the angles!By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you can determine whether the triangle is acute, right, or obtuse. The triangle is acute because this sum is higher.
A triangle is said to be acute if the squares of its two shorter sides added together exceed those of its longest side. A triangle is considered obtuse if the sum of the squares of its two shorter sides is less than the square of its longest side.
An overview was given as your information is incomplete.
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Troy had a number cube with the numbers 1-6 on it.Assuming each side is equal king likeley to appear when he rolls the cube,find the following probabilities. a(rolls a 2)
Answer:
P(2)= 1/6
P(odd)= 1/2
P(factor)= 2/3
Suppose that the functions and are defined for all real numbers as follows.
Write the expressions for and and evaluate .
(s+t)(x)=
(s*t)(x)=
(s-t)(-1)=
The expression (s+t)(x) is equal to the sum of the functions s(x) and t(x), the expression (s*t)(x) is equal to the product of the functions s(x) and t(x), and the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1). When evaluating (s+t)(-1) we get the result 0.
(s+t)(x)=s(x)+t(x)
(s*t)(x)=s(x)*t(x)
(s-t)(-1)=s(-1)-t(-1)
(s+t)(-1)=s(-1)+t(-1)=-2+2=0
(s+t)(x) = s(x)+t(x)
This means that the expression (s+t)(x) is equal to the sum of the functions s(x) and t(x).
(s*t)(x) = s(x)*t(x)
This means that the expression (s*t)(x) is equal to the product of the functions s(x) and t(x).
(s-t)(-1) = s(-1)-t(-1)
This means that the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1).
Finally, when we evaluate (s+t)(-1) we get s(-1)+t(-1)=-2+2=0.
The expression (s+t)(x) is equal to the sum of the functions s(x) and t(x), the expression (s*t)(x) is equal to the product of the functions s(x) and t(x), and the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1). When evaluating (s+t)(-1) we get the result 0.
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What is the area of the right triangle with base 5 cm and altitude 4cm?
The area of the said triangle is 10 cm²
Here we have been given the right-angled triangle with base 5 cm and altitude 4 cm.
To find the area of a triangle we can either use Heron's formula or the other formula where area of a triangle = 1/2 X base X height
Since we have been given the base and the height we need to use the latter.
Hence area of the said triangle will be
1/2 X 5 X 4 cm²
= 10 cm²
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A cube, of ide length 6 cm, ha the ame volume a that of a cuboid of height 3 cm and breadth 4 cm. Find the length and the urface area of the cuboid?
As per the given volume of cuboid, the length is 4 cm and the surface area of the cuboid is 5.76cm
The general formula to calculate the surface area of cuboid is written as,
SA = 2[lb + bh + hl]
where l refers the length, w refers width and h refers height.
Here we have given that a cube of side length 6 cm and has the same volume as that of a cuboid of height 3 cm and breadth 4 cm.
Now, we have to find the length and the surface area of the cuboid.
By the given value the Surface Area of Cube is calculated as.
=> 6s sq. = 6 x 4sq.
Then the value is 96 cm square
Then the Surface Area of Cuboid is calculated as,
=> 2(24+10h)=96
When we simplify the equation as
=> 24 + 10h = 48
=> 10h=24
Therefore, the value of h=2.4
Then the volume of Cuboid=6*4*2.4=5.76 cm.
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What are 4 ways to find a midpoint?
The four ways to find the midpoint of a line segment are using the Midpoint Formula, using the Distance Formula, using a Graph, and using a Ruler.
Using the Midpoint Formula:
This method involves using the midpoint formula, which is (x1 + x2)/2, (y1 + y2)/2. This formula gives the coordinates of the midpoint when the coordinates of the two endpoints of the line segment are known.
Using the Distance Formula:
This method involves using the distance formula to find the distance between the two endpoints of the line segment and then dividing the distance by 2. The midpoint will be located at the point that is half the distance from each endpoint.
Using a Graph:
This method involves plotting the two endpoints of the line segment on a graph and then drawing a line segment connecting the two points. The midpoint of the line segment will be located at the point where the line segment is bisected.
Using a Ruler:
This method involves measuring the distance between the two endpoints of the line segment with a ruler or measuring tape, and then marking the point that is halfway between the two endpoints. The midpoint of the line segment will be located at the point that is marked.
All of these methods can be used to find the midpoint of a line segment, it depends on what information is given and what tools are available.
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What is the additive inverse of 8 /- 15?
The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined.
The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined. To find the additive inverse of 8 /- 15, simply change the sign of the number from negative to positive or from positive to negative. In this case, the sign of 15 needs to be changed from negative to positive, giving us 8 /+ 15. This means that when 8 /- 15 is added to 8 /+ 15, the result is 0. The concept of additive inverse is important in mathematics as it helps us to solve equations and understand the properties of numbers. Additive inverse is also referred to as the opposite of a number, as it is the number that needs to be added to the original number to get 0. Therefore, the additive inverse of 8 /- 15 is -8 /+ 15.
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-2x+3y=14 x+2y=7 substitute
The values of x and y are -1 and 4 respectively.
What is substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Given are two equations, -2x+3y=14 and x+2y=7
Solving equations by using substitution method,
-2x+3y=14..........(i)
x+2y=7
x = 7-2y.......(ii)
Using eq(ii) in eq(i)
-2(7-2y) + 3y = 14
-14+4y+3y = 14
7y = 28
y = 4
Put y = 4 in eq(ii)
x = 7-2(4)
x = -1
Hence, the values of x and y are -1 and 4 respectively.
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An art museum installed a large triangular sculpture. One of the sculpture’s exterior angles creates a 158 angle with the ground.
If the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, what is the measure of the interior non-adjacent angle?
The measure of the interior non-adjacent angle as required in the task content is; 95°.
What is the measure of the interior non-adjacent angle?Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.
On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;
x + x - 32.
where, x is the measure of the interior non-adjacent angle.
Hence, x + x - 32 = 158
2x = 158 + 32
2x = 190
x = 95°.
Ultimately, the measure of the interior non-adjacent angle is; 95°.
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what is the opposite value of Owen's score?
Answer:
Davids Score
Step-by-step explanation:
What is the formula of Class 11?
Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations .
what is quadratic equations ?A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.
given
Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations, and mathematical induction can be found in class eleven algebra textbooks.
Students might improve their exam preparation by working through sample papers.
Attempt to answer the test questions from the prior year. Learning about the question format and scoring system will be beneficial.
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Evaluate the following expressions if a=2 , b=6, and c=4 : 7a+b over b+c
Answer:
2 over 1
Step-by-step explanation:
I'm not really sure what you mean in the question but I've substituted the values in
A man weighs 95 kg and starts an exercise and eating programme to lose weight. If he sticks to the programme, he will lose 0,4 kg per week. Calculate how much he will weigh after 36 weeks.
The weight after 36 weeks is 80.6 kg.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, a man weighs 95 kg and starts an exercise and eating programme to lose weight.
Let the number of weeks be x.
Now, the expression is 95-0.4x
Here, x=36
95-0.4×36
= 95-14.4
= 80.6 kg
Therefore, the weight after 36 weeks is 80.6 kg.
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PLEASE HELP ME!! PLEASEE
7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.
what is mean ?The mean of a dataset, often termed as the arithmetic mean, is the amount of all values divided by the overall number of values (as opposed to the geometric mean). This is the most often used indicator of central tendency and is frequently referred to as the "mean." This is obtained by dividing the number of values in the dataset by the sum of all the values. Calculations can be performed using either raw data or data that has been integrated into frequency tables. A number's average is referred to as its average. Simple math can be used to determine: After simply adding all the digits, divide by the number of digits. the sum divided by the number.
given
three obstacles are overcome by three students.
Total Observations / Sum of Observations = Mean
= 21 / 3
= 7
7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.
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The complete question is :- LeveT P × Diane is a camp counselor. She designs a new obstacle course, and tests the course with friends. The dot plot shows the time it takes them to complete the obstacle course. a What is the mean of the times? Obstacle Course Test mean - mean 7 minutes.
Can please tell the answer
Answer:
24
Step-by-step explanation:
120 x 0.20 = 24
Why is replacement or substitution important in math?
The replacement or substitution approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.
The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
This makes it easier to solve by combining two linear equations into one equation with a single variable. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.
By changing the value of another variable in an equation, the variable can be eliminated. Thus, the elimination by substitution method is the name given to this technique.
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Refer to the figure. Name the intersection of lines m and t.
Point B
Point C
Point D
Point H
Answer:
Point C
Step-by-step explanation:
Lines m and t are on the same plane
We can see that they intersect at Point C
Which of the following triplets are Pythagorean? (I)(8, 15,17) (ii) (18, 80,82) (iii)(14,48,51) (iv) (10,24,26) (v)(16,63,65) (vi) (12,35,38)
Only (i), (ii), (iv) and (v) are Pythagorean triplets. A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.
Pythagoras, Gauss, Edison, Hawking. The following are the most noted discoveries of each.
Pythagoras, 500 B.C. School Of Mathematics and Pythagorean theorem.Edison, Year 1879 - Invention of incandescent light bulb.Gauss, Year 1801 - Therom of Alegbraic Solution. Stephen Hawking Year1980 - Studies in cosmology particularly contributing to the context of black holes.
you can check by taking largest side square
and adding square of rest two sides
17^2= 15^2+ 8^2
82^2= 18^2+80^2
26^2= 24^2+10^2
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Given the function f(x) = 3x - 1, find x when f (x) = 20
The function f(a+1) is equal to option C. 3a + 4.
What is meant by mathematical function?A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed. A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more. The expression y=f(x) defines the function f. You should interpret this as "y is a function of x." The input value, also known as an independent variable, is symbolized by the letter x.Given function:
f(x) = 3x + 1
We have to find f(a+1).
For this purpose, we will take x = a+1 and
substitute it in the function f(x) = 3x+1:
f(x) = 3x + 1
f(a+1) = 3(a+1) +1
f(a+1) = 3(a) + 3(1) +1
f(a+1) = 3a+3+1
f(a+1) = 3a + 4
So the function f(a+1) is equal to option C. 3a + 4.
The complete question is,
Given the function f(x) = 3x + 1, evaluate f(a + 1).
A. 3a + 1
B. a + 2
C. 3a + 4
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0.1x − 5 = −11
Show work
Answer:
x = -60
Step-by-step explanation:
Given the equation:
[tex] \displaystyle{0.1x - 5 = - 11}[/tex]
Add both sides by 5
[tex] \displaystyle{0.1x - 5 + 5= - 11 + 5} \\ \\ \displaystyle{0.1x = - 6}[/tex]
Multiply both sides by 10 to get rid of the decimal
[tex] \displaystyle{0.1x \times 10 = - 6 \times 10} \\ \\ \displaystyle{x= - 60}[/tex]
Therefore, x = -60
Answer:
x = -60
Step-by-step explanation:
0.1x − 5 = −11
0.1x = -11 + 5
0.1x = -6 multiply by 10 both sides
x = -60
--------------------------
check0.1 x (- 60) - 5 = -11
-6 - 5 = -11
-11 = -11
the answer is goodWhat are solutions 3 properties?
The particle size of a solution is 0 point 1 nm – 1 nm, and it is a homogeneous mixture of two or more substances called solution.
Explain the term solutions and its 3 properties?When one or more solutes are dissolved in a solvent, the result is a homogeneous mixture known as a solution.Solvent and Solute are the components of solutions.Solute:The term "solute" refers to the material that is dissolving in the solvent to create a solution. It is less prevalent in the solution than the solvent.
Solvent:A solvent is a substance found in solutions that helps a solute dissolve. It is more prevalent than the solute in the solution.
A solution has the following characteristics:
An homogeneous mixture is a solution.The diameter of the component particles in a solution is less than 10-9 meters.A solution's constituent particles are invisible to the unaided eye.To know more about the solutions, here
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During a sale, the price of a sweater was changed from $20 to $16. What was the percent of decrease in the price of the sweater?
Answer: 20%
Step-by-step explanation: You can evenly divide 20 by 5, which is four, which makes four 20% of 20. You can subtract 4 from 20 to get 16 to prove this, and keep going all the way back to 0 5 times.
What is the value of x in the equation: 2^(3^x) = 10^(6^x) ?
____________________
False answer will be REPORTED immediately. Do not waste your time if you do not have sufficient knowledge.
Answer:
[tex]log\ (log\ 2)/\ log\ 2[/tex] or ≈ - 1.73------------------------------
Solve in below steps, using log and exponent rules:
[tex]2^{3^x}=10^{6^x}[/tex] Given[tex]log\ 2^{3^x}=log\ 10^{6^x}[/tex] Log both sides[tex]3^x\ log\ 2=6^x\ log\ 10[/tex] Log of power rule[tex]3^x\ log\ 2=6^x[/tex] log 10 = 1[tex]3^x\ log\ 2=(3*2)^x[/tex] Power of the product rule[tex]3^x\ log\ 2=3^x*2^x[/tex] Cancel 3ˣ on both sides[tex]log\ 2=2^x[/tex] Log both sides[tex]log\ (log\ 2)=x\ log\ 2[/tex] Divide both sides by log 2[tex]x=log\ (log\ 2)/\ log\ 2[/tex] AnswerWhen a scaled copy is bigger than the original The scale factor is greater than 1?
The scaled copy is bigger that means each side is bigger than the original one or the factor is grater tan 1 as final length(bigger)/ original > 1
What is dilation ?In mathematics, a dilation is the enlargement or contraction of a figure by a predetermined scale factor, k, at or around a center of dilation. It is a transformation style that yields comparable figures.
Depending on the scale factor, the original figure will either enlarge or decrease in size. Scaling, also known as dilations, has no impact on how angles are measured.
The original and updated figures' angles will not change because the size has not changed but the shape has. Preimage and image are two terms that can be used to describe the first and new figures, respectively.
The original figure's vertices are identified with capital letters, such as B, to make it easier to identify between two similar figures.
The scaled copy is bigger that means each side is bigger than the original one or the factor is grater tan 1 as final length(bigger)/ original > 1
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I have to use a bar diagram or a scale factor how do I do it
In order to respond to the query ,of bar graph we must first comprehend what a compound Tim received 4 emails on Thursday and 8 SMS on Monday, making up 0.52 of all communications.
What exactly is a bar graph?A blended bar chart is used to display the rates of two connected sets of data. In this investigation, two forms of data—emails and emails used, but they are both grouped together under the term "messages" and are shown as vertical bars in the graph.
Here,
14+16+14+15+14=73 messages in total.
A total of 38 emails were sent: 6 + 10 + 10 + 4 + 8
Email to message ratio is 38/73, or 0.52.
Emails therefore made up 0.52 of the messages.
Tim received 4 emails on Thursday, 8 texts on Monday, and 0.52 of the messages were emails, as shown by an examination of the composite bar chart that we used to come up with the answers to the three questions.
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