Answers
Answer:
The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )
Step-by-step explanation:
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of the midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
The slope of a line segment with coordinates of the ends
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
~~~~~~~~~~~~~
Point D is the midpoint of a segment AB
A ( 4 , 12 )
B ( - 6 , - 8 )
( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )
D ( - 1 , 2 )
C ( 8 , - 6 )
[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]
Related Questions
Triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
A′(−4.5, 2)
A′(3, 3)
A′(4.5, 2)
A′(4.5, 3)
Answers
Answer:
vertex of point A′ is A′(4.5, 3)
Step-by-step explanation:
To determine the vertex of point A′ after dilation, we need to know the coordinates of point A and the scale factor of the dilation.
In this problem, point A has the coordinates (3, 2) and the scale factor of the dilation is 1.5.
To find the coordinates of the dilated point, we multiply each of the original coordinates by the scale factor:
A'(x,y) = (1.5* x, 1.5*y)
So the coordinates of the point A' are:
A'(1.53, 1.52) = (4.5, 3)
Therefore, vertex of point A′ is A′(4.5, 3)
The vertex of point A after the dilation is A′(4.5, 3)
What is dilation?Dilation is a transformation that changes the size of a figure or an object without changing its shape.
The figure or object and its image after dilation are similar.
The size of the figure or object may increase or decrease based on a number called the scale factor.
Dilation is defined by a point called the center of dilation and the scale factor.
Given that, a triangle ABC, has been dilated by a scale factor of 1.5.
We need to determine the vertex of A',
The rule of dilation by a scale factor of k,
(x, y) → (kx, ky)
Therefore,
A'(x,y) = (1.5·x, 1.5·y)
So the coordinates of the point A' are:
A'(1.5·3, 1.5·2) = (4.5, 3)
Therefore, vertex of point A′ is A′(4.5, 3)
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Q. You’re on a reidential contruction team doing roofing. The pitch of a roof i 13 rie over run. Find the rie if the horizontal run of the roof i 15 feet 34 inche
Answers
The rise is 231 feet 10 inches if the horizontal run of the roof is 15 feet 34 inches.
Let us assume that x represents the rise and y represents the run,
According to the given problem,
x= 15 feet 34 inches
Converting feet into inches,
we know, 1 feet = 12 inches
so, 15 feet 34 inches = 15*12+34 = 214 inches
Now finding the rise in terms of x and y,
13 = y/x
substituting the value of x and solving for y:
13 = y/214
y = 13*214
y = 2782 inches
Converting inches into feet,
2782 inches = 2782/12 = 231 feet 10 inches
Thus, The rise is 231 feet 10 inches if the horizontal run of the roof is 15 feet 34 inches.
Correct question: You’re on a residential construction team doing roofing. The pitch of a roof is 13 rise over run. Find the rise if the horizontal run of the roof is 15 feet 34 inches.
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in a school 21% of teachers were trained in britain and 26% of teachers were trained in usa and 15% were trained in both Britain and USA what percentage of teachers were neither trained in usa nor Britain represent using a venn diagram
Answers
A Venn diagram to represent the given information of a school and attached
The percentage of the teachers neither trained in USA or Britain is 68%
How to find the percentage of the teachers neither trained in USA or BritainSince the problem is stated in percentage, the total number of teachers in the school which is the universal set is 100
15% were trained in both Britain and USA.
The number of teachers trained in Britain only
= 21% - 15% = 6%
The number of teachers trained in USA only
= 26% - 15% = 11%
The total number of teachers trained in Britain and USA
= number of teachers trained in Britain only + number of teachers trained in USA only + number of teachers trained both Britain and USA
= 6% + 11% + 15%
= 32%
percentage of the teachers neither trained in USA or Britain
= universal set - number of teachers trained in Britain and USA
= 100% - 32%
= 68%
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Becca needs to find the volume of the following composite figure formed by stacking a triangular prism on top of a cube.She finds the volume of the cube by multiplying 10 by 10 by 10 to get 1,000 cubic cm. Then, she multiples by 1.5 to get the total volume of the figure. Is Becca's solution correct? Why or why not?
Answers
Becca's solution is not correct. Multiplying the volume of the cube (10 x 10 x 10 = 1,000 cubic cm) by 1.5 will not give the correct total volume of the composite figure.
Is this solution of Bella correct?From the information, Becca needs to find the volume of the following composite figure formed by stacking a triangular prism on top of a cube.She finds the volume of the cube by multiplying 10 by 10 by 10 to get 1,000 cubic cm. Then, she multiples by 1.5 to get the total volume of the figure.
The solution is incorrect is because the triangular prism and the cube are separate shapes and their volumes need to be added together to find the total volume of the composite figure. Becca needs to calculate the volume of the triangular prism separately and add it to the volume of the cube to find the total volume of the composite figure.
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How to Study Math: Algebra
Answers
Answer:
I like to take out my work (review guide, homework, etc.) and cover my answers with a piece of paper so that only the question is showing and answer the problem. Repeat for as many problems as you'd like. I hope this helps!
Step-by-step explanation:
Use a line of fit through (9, 80) and (15, 50) to find the equation of the line in slope-intercept form.
Answers
what is the difference between 880 and 580
Rhonda' job i to drive a car for a company. Each month he i paid the ame alary. She i alo paid extra money for the number of mile he drive the car each month. • In July Rhonda drove 640 mile and wa paid a total of $3,502. 0. • In Augut Rhonda drove 820 mile and wa paid a total of $3,601. 0. Which function can be ued to find y, the total amount he i paid in a month if he drive × mile?
Answers
If Rhonda drives x miles in a month, she will be paid a total of $2,352 + ($0.55 * x).
We can use the information given to set up a system of equations to find the function that relates the number of miles driven (x) to the total amount paid (y).
Let's call the fixed salary that Rhonda receives each month "s" and the extra money she receives per mile driven "m".
Based on the information given, we know that in July, Rhonda drove 640 miles and was paid a total of $3,502. So, we can set up the following equation:
y = s + (m * 640) = $3,502
And in August, Rhonda drove 820 miles and was paid a total of $3,601. So, we can set up the following equation:
y = s + (m * 820) = $3,601
We can use these equations to solve for "s" and "m".
Subtracting the first equation from the second equation:
$3,601 - $3,502 = s + (m * 820) - s - (m * 640)
$99 = (m * 820) - (m * 640)
$99 = m * 180
m = $0.55
Now we can substitute this value of m back into one of the equations to solve for s
$3,502 = s + (0.55 * 640)
s = $2,352
So the function that relates the number of miles driven (x) to the total amount paid (y) is:
y = $2,352 + ($0.55 * x)
Thus, This means that if Rhonda drives x miles in a month, she will be paid a total of $2,352 + ($0.55 * x).
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practice 5-3 concurrent lines medians and altitudes
Answers
Concurrent lines are lines intersecting a common point. Medians are lines connecting the vertex to the midpoint. Altitudes are lines perpendicular to the base of the triangle and pass through the vertex opposite the base.
Concurrent lines in a triangle refer to lines that pass through a common point, such as the centroid, which is the point where the medians of a triangle intersect. Medians are lines that connect a vertex of a triangle to the midpoint of the opposite side. Altitudes are lines that are perpendicular to the base of a triangle and pass through the vertex opposite the base. They also intersect at another point called the orthocenter. The concurrent lines, medians, and altitudes of a triangle are important concepts in geometry that are used in various proofs and problem-solving tasks.
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Your question seems to be incomplete, but I assume the question was:
"What are concurrent lines, medians, and altitudes in a triangle?"
in 6-7 explain whether each graph represents a functions
Answers
A graph is a visual representation of data, showing relationships between different variables or values.
What is graph?Graphs are often used to represent a function, which is a set of inputs and outputs. A function is a relationship between two variables, where the output of the function depends on the input. In a graph, the input is represented on the x-axis, and the output is represented on the y-axis.
The first graph pictured is a linear function, which is a function that can be expressed as a straight line. This linear graph has a positive slope, meaning that as the input increases, so does the output. This graph represents a linear function because the output can be determined by the input, which is expressed as an equation in the form of y = mx + b.
The second graph pictured is a quadratic function, which is a function that can be expressed as a parabola.
This graph also has a positive slope, meaning that as the input increases, so does the output. This graph represents a quadratic function because the output can be determined by the input, which is expressed as an equation in the form of y = ax2 + bx + c.
Both of these graphs represent functions because they show a relationship between the input and output of a given data set. The input values are shown on the x-axis and the output values are shown on the y-axis, and these values can be used to determine the equation for the function.
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What is the x -intercept?
What is the y -intercept?
Answers
Answer: (4, 0) and (0, -18)
Step-by-step explanation:
Drag the points to create a graph that satisfies the following requirements:
Answers
Graph for Domain : 1 ≤ x ≤ 3 ; Range : 2 ≤ y ≤ 7 is attached below:
What is graph?A graph is a kind of a chart where data are plotted as variables across the coordinate.
Given,
Domain : 1 ≤ x ≤ 3
Range : 2 ≤ y ≤ 7
value of y should be 2 to 7.
value of x should be 1 to 3.
Hence, following is the graph that satisfy
Domain : 1 ≤ x ≤ 3
Range : 2 ≤ y ≤ 7
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What do you call the triangle that have the same shape but not the same size?
Answers
The triangle that have the same shape but not the same size are similar triangles
What are Similar triangles ?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same form but may not be the exact same size.
Two triangles are said to be similar if their corresponding angles are equal. Equiangular triangles are what they are called. Two equiangular triangles were the subject of a significant finding made by the well-known Greek mathematician Thales. He applied the Basic Proportionality Theorem, sometimes known as the Thales Theorem, as a conclusion.
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How do you write the symbol for greater than 1?
Answers
The symbol for greater than 1 is written as " >1".
Greater than ">" means that one number or value is larger than the other. number or value The symbol is made by your right-hand thumb and index finger, just like ">", which is known to be a "greater than" symbol. If you use this symbol to write some value is greater than 1 then you need to write 1 towards the right side of this symbol.
For example, 9 > 1. The open end of the greater than symbol is pointed at the one and it is read as '9 is greater than 1. So the symbol for any value greater than 1 is written as " >1".
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What is the coefficient of y² in the expression 3y² 4x *?
Answers
3 is the coefficient of y² in the expression 3y²+4x
What is the term for coefficient?A coefficient is an integer that is either printed alongside or multiplied by a variable. A coefficient, in other terms, is the numerical component of a phrase including constants and variables. For example, the coefficient in the expression 2x is 2. A coefficient is a number that has been multiplied by a variable. Coefficient examples: The coefficient in the expression 14 c 14c 14c is 14. The coefficient in the phrase g is 1.
In an expression, it is generally a number, although it may also be a letter. In the phrase ax2 + bx + c, for example, x is the variable and ‘a’ and ‘b’ are the coefficients.
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Evaluate. [2−∣∣−14−2(−35)∣∣]÷(−6)
Answers
Answer:
Step-by-step explanation:
5 I think
What is 1 in exponential form?
Answers
Answer: The exponential form of 1 is 1.
In simple words, the exponents can said to be the powers of the base. For example, in 2³, the exponent will be 3. If a number is given without any power then its power is 1. The exponential form is simply the number with exponents.
Answer:
I think 0a
Step-by-step explanation:
What is the standard form of equation y 3x 10?
Answers
The standard form of the equation y = 3x + 10 is -3x +y = 10.
To accomplish the given equation and bring it in the standard form for our problem, we first arrange it in standard form and then apply a little algebra to subtract 3x from both sides of the equation.
Given,
y = 3x + 10
Subtract 3x from each side.
Simplify: y - 3x = 3x + 10 - 3x.
y - 3x = 10
The x word should be placed first in the left-hand side arrangement.
-3x + y = 10
We discover that y = 3x + 10 is written as -3x + y = 10.
Ax + By = C is the equation of a line in its standard form, where A, B, and C are constants. There are several possible ways to express a line's equation, and if we are given a line that isn't in standard form, we can apply a little algebra to change the equation.
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Analyze the function: f(x)=-x/x+2
Answers
Answer:
f (x) = -x over x+2
Step-by-step explanation: if you want to find the inverse you do f and the exponent of negative 1 (x) = - 2x over 1+x .
Find the value.
3 x 5²
30
225
45
75
Answers
Answer:
75
Step-by-step explanation:
3 × 5²
= 3 × 5 × 5
= 15 × 5
= 75
Answer:
75
Step-by-step explanation:
This is testing Order of Operations
PEMDAS
In this equation we see E (exponents) and M (Multiplication)
The E comes first so doing the exponent of 5^2 we get 25, because that's the same as 5 * 5
After the E is the M, so we multiple the 25 by the 3, giving you 75.
What are the three types of coordinates?
Answers
The three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
Which coordinate system is used?Three digits are used to indicate distances in the three-dimensional flat space of the Cartesian coordinate system, often known as the "rectangular coordinate system." The East/West direction, North/South direction, and Elevation are represented by the first two digits, respectively.
The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.
So, three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
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What are the 5 types of math?
Answers
Algebra
Geometry
Trigonometry
Calculus
Statistics and Probability
Hope it Helps!
Suppose a binomial trial has a probability of success of 0.2, and 500 trials are performed. What is the standard deviation of the possible outcomes? Round your answer to two decimal places.
Answers
10 is the standard deviation of the possible outcomes.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given a a binomial trial has a probability of success of 0.2, and 500 trials are performed
We need to find the standard deviation of the possible outcomes
To find the standard deviation of this binomial distribution, first find the variance by the formula:
= Number of trials x probability of success x ( 1 - probability of success )
= ( 500 x 0. 2 x ( 1 - 0. 2))
= 100
The standard deviation would be:
= √(Variance )
= √(100)
= 10
Hence, 10 is the standard deviation of the possible outcomes.
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12.) There are 12 cats and 13 dogs in math class. What percent of the class are cats?
Answers
Answer:
48%
Step-by-step explanation:
You want to know the percent of the class that is cats if there are 12 cats and 13 dogs in the class.
PercentThe percent can be found by multiplying the fraction by 100%.
cats/class = 12/(12+13) × 100% = 12/25 × 100% = 48%
48% of the class are cats.
<95141404393>
(-3v)^5
simplify the expression
Answers
Explanation: What you need to know is that since (-3v) is in parentheses, the exponent applies to to all of it, not just the variable v. (-3)^5 = -243, (v)^5= v^5 => -243v^5
Determine whether the pair of sets is equal, equivalent, both, or neither.
A={computer science, calculus, algebra}
B={calculus, chemistry, computer science}
Are set A and set B equal, equivalent, both, or neither?
OA. Equivalent
OB. Both
OC. Equal
OD. Neither
Answers
The given are equivalent sets because the number of elements in the sets are equal. So sets A and B are equivalent.
What is equivalent, equal and unequal sets?Equivalent sets are sets that contain the same number of elements. For example, if set A has three elements, and set B also has three elements, then set A and set B are equivalent sets. Equal sets are sets that contain the same elements. For example, if set A has the elements {1, 2, 3}, and set B also has the elements {1, 2, 3}, then set A and set B are equal sets.Unequal sets are sets that contain different elements. For example, if set A has the elements {1, 2, 3}, and set B has the elements {4, 5, 6}, then set A and set B are unequal sets. Unequal sets may still be equivalent sets. For example, if set A has the elements {1, 2, 3}, and set B has the elements {4, 5, 7}, then set A and set B are both still equivalent sets (as they both contain three elements), but they are unequal sets (as they contain different elements).To learn more about sets refer to:
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An air cannon
launches a T-shirt upward toward basketball
fans. It reaches a maximum height and then
descends for a couple of seconds until a fan
grabs it. Sketch the graph that represents this
situation.
Distance (ft)
Answers
When an air cannon fires a T-shirt upward toward the basketball, the highest height it can reach is 50 and the time until a fan snatches it is 5 seconds.
what is graph ?Using visual charts or representations, mathematicians utilize graphs to logically communicate facts or values. A graph point often illustrates the relationship between two or more objects. In a graph, a non-linear data structure, nodes, or vertices, and edges come together. The nodes, also known as vertices, should be adhered together. The edges of this graph, E=1, 2, 1, 3, 2, 4, and (2.5), have the following values: V=1, 2, 3, 5, (3.5). (4.5). Visual depictions of exponential development in statistics include bar charts, pie charts, line charts, and more. a triangle-shaped logarithmic graph
given
y = x( 0.4 - 0.008x)
x=0
0.4 - 0.008x =0
0.4 - 0.008x
50 = x
y = 5
When an air cannon fires a T-shirt upward toward the basketball, the highest height it can reach is 50 and the time until a fan snatches it is 5 seconds.
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How to do a dilation of 1.5 about the origin?
Answers
Remember that to dilate something in the coordinate plane, multiply each coordinate by the scale factor. For this dilation, the mapping will be ( x , y ) → ( 1.5 x , 1.5 y )
How do dilate from the origin?If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the imageIf you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.The time between dilating to 1 cm and giving birth varies from woman to woman. One woman may go from having a closed cervix to giving birth in a matter of hours, while another is 1–2 cm dilated for days or weeks. Some women do not experience any dilation until they go into active laborTo learn more about dilate refers to:
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Solve the equation with explanation
0.4 (20 - 10m) = 2.5 - 2m - 12.5
Answers
Answer
The answer is (m = 9)
Step-by-step explanation:
Rearrange terms = Step 1
0.4(20-10m) = 2.5 - 2m-12.5
0.4(-10m+20) = 2.5 - 2m - 12.5
Step 2 = Combine multiplied terms into a single fraction
Step 3 = Distribute
Step 4 = Subtract the numbers
Step 5 = Rearrange terms
Step 6 = Add 2m to both sides
Step 7 = Simplify
Step 8 = Multiply all terms by the same value to eliminate fraction denominators
Step 9 = Cancel multiplied terms that are in the denominator
Step 10 = Multiply the numbers
Step 11 =Subtract 40 from both sides
Step 12 = Simplify
Step 13= Divide both sides by the same factor
Last but not least is Simplify
Hope it helped:)
What is the angle measure of x? (numbers only)
Answers
Answer:30 degrees
Step-by-step explanation:
S = O/H
sin-1(6/12) = 30
Given: AD // BC, AB // CD
Prove: △DBC ≅ △BDA
Answers
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
Define pentagonal.Pentagons is that are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."
Here, we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.
Pentagonal prisms are pentagon-shaped if we look at them from the bottom.
When viewed from the side, a pentagonal prism would have a rectangular shape.
If we were to look at the pentagonal prism from the front, it would appear rectangular.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
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On solving the provided question, we can say that In triangle DBC and BDA, So, By SSS, △DBC ≅ △BDA
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
In triangle DBC and BDA
BD = BD ( common base)
AB = CD
AD = BC
So, By SSS,
△DBC ≅ △BDA
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