Which lines can you conclude are parallel given that m14 + m2 = 180? Justify your conclusion with a theorem.
Answers
because m<14 and m<2 are in lines a and b and they aren't corresponding angles
Answer:
Option 2 is correct.
Step-by-step explanation:
Given the diagram and also the condition m∠14 + m∠2 = 180°
we have to tell which lines are parallel.
By the theorem of exterior angles
Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.
The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.
∴ Lines a and b are are parallel by converse of same side exterior angle theorem.
Related Questions
Lola takes the train from Paris to Nice. The distance between the two cities is about 921,000 meters. If the train travels at a speed of 307 kilometers per hour, how long will it take Lola to travel from Paris to Nice
Answers
Answer:
First,you need to convert 307km/hr into 85.2 meter per second.The formula for finding time is the distance divided by the speed.So,the answer is 10809 second,about 3 hours.
What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.
Answers
Consider the equation [tex] x^6+6x^3+5=0 [/tex].
First, you can use the substitution [tex] t=x^3 [/tex], then [tex] x^6=(x^3)^2=t^2 [/tex] and equation becomes [tex] t^2+6t+5=0 [/tex]. This equation is quadratic, so
[tex] D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1 [/tex].
Then you can factor this equation:
[tex] (t+5)(t+1)=0 [/tex].
Use the made substitution again:
[tex] (x^3+5)(x^3+1)=0 [/tex].
You have in each brackets the expression like [tex] a^3+b^3 [/tex] that is equal to [tex] (a+b)(a^2-ab+b^2) [/tex]. Thus,
[tex] x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1) [/tex]
and the equation is
[tex] (x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0 [/tex].
Here [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex] and you can sheck whether quadratic trinomials have real roots:
1. [tex] D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25} <0 [/tex].
2. [tex] D_2=(-1)^2-4\cdot 1=1-4=-3<0 [/tex].
This means that quadratic trinomials don't have real roots.
Answer: [tex] x_1=-\sqrt[3]{5} , x_2=-1 [/tex]
If you need complex roots, then
[tex] x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2} [/tex].
Directions: Describe the transformation. (x,y) -> (5x,5y)
Answers
The transformation (x, y) -> (5x, 5y) is a scaling transformation that dilates a point by a factor of 5 in both the x and y directions, making the entire figure five times larger while preserving its shape.
Explanation:The transformation described by (x, y) -> (5x, 5y) is a scaling transformation or dilation in both the x and y directions by a factor of 5. What this means is that any point on the plane, when subjected to this transformation, will move five times further away from the origin along both axes. For example, if you begin with the point (1, 1), applying this transformation will result in the point (5, 5). This dilation affects all points equally, meaning that the relative distances between points are preserved, but the entire figure is made larger by a factor of 5. Therefore, if you have a figure with dimensions of length and width, after the transformation, both dimensions will be increased by five times their original measure.
Final answer:
The transformation (x, y) -> (5x, 5y) represents a dilation, enlarging a figure by a factor of 5 along both the x-axis and y-axis, which alters size but not shape.
Explanation:
The transformation described by the rule (x, y) -> (5x, 5y) is a geometric transformation known as a dilation or scaling. This type of transformation alters the size of a figure without changing its shape. Specifically, the coordinates of each point in the figure are multiplied by 5, which means that the figure is enlarged by a factor of 5 in both the x-axis (east-west direction) and the y-axis (north-south direction). If, for example, we apply this transformation to a point (1, 2), the resulting coordinates will be (5, 10), and similarly, applying it to (3, 7) would yield (15, 35). This illustrates the dependence of y on x as each x-coordinate and y-coordinate are scaled by the same factor, maintaining the shape but increasing the size.
In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.
Answers
Consecutive angles are next to each other. squares and rectangles are the only to that has angles with the same values that are next to each other
Answer:
Rectangle and Square.
Step-by-step explanation:
To know if the angles of a quadrilateral is congruent you must overlap these angles one over the other, if all elements of the angles coincide, the angles are congruent; if the elements do not match, the angles are not congruent. In quadrilateral rectangle and square consecutive angles are always congruent.
In other words, two or more angles are said congruent if and only if they have the same measurement.
HELP might fail class
Answers
The password pattern is <letter><letter><digit><digit><digit><digit>. Use the Multiplication Principle:
25 x 25 x 9 x 9 x 9 x 9 = 4,100,625
Sandy can assemble a particular type of light fixture in 3/8 hour. it takes her 2/3 hour to hang the fixture and another 1/6 hour to wire the fixture once it is hung. how many fixtures could sandy install in 29 hours?
Answers
Sandy can install a maximum of 24 fixtures in 29 hours.
Explanation:To calculate the number of fixtures Sandy can install in 29 hours, we need to determine the amount of time it takes for Sandy to complete one installation process (excluding assembly time).
Sandy takes 2/3 hour to hang the fixture and another 1/6 hour to wire it, totaling
2/3 + 1/6 = 7/6 hour.
Therefore, Sandy takes 7/6 hour per fixture.
Next, we can calculate the number of fixtures by dividing the total time available (29 hours) by the time it takes for one installation process.
Number of fixtures = Total time available / Time per fixture
Number of fixtures = 29 / (7/6) = 29 * (6/7) = 174/7 = 24.86
Since we can't have a fraction of a fixture, Sandy can install a maximum of 24 fixtures in 29 hours.
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On his birthday newton was 14 years old and his father was 41 newton noticed that his age was his fathers age with the digits reversed how many years later with their ages next have their digits reversed
Answers
When the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
It is given that when Newton was 14 years old , his fathers age was 41 yrs.
We have to find out that at what age of Newton his fathers age will be reversed again ?
Solve for the value of x ; 10 x - 14 = 12x - 28 ?
The value of x will be 7.
Let's assume the tens place as x and one's place as y.
The actual number will be ; 10 x + y.
Reverse numbers pairs can be written as (10x+y) and (10y+x).
As the age of Newton's father is 41 yrs when he is 14 yrs old , so we have ;
(10x+y) - (10y+x) = 41–14 = 27
Hence , we can say that the age difference between Newton and his father is 27 years. This age difference will be same forever.
So ;
(10x+y) - (10y+x) = 27
and we have to find all values of x and y that will satisfy this equation.
⇒ (10x+y) - (10y+x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3
For all x’s and y’s who have their difference as 3 will answer the question. For example , (4,1) (5,2) (6,3) (7,4) (8,5) …. and so on.
Since Newton's father age today is 41 yrs.
The next age to satisfy the condition is 52 yrs.
This makes Newton’s age to be 52 - 27 = 25 which is the reverse of 52.
So , the answer of the question is that Newton should be of 25yrs , for his age to be the reverse of his father’s age.
Thus , when the age of Newton will be 25 years , the age of his father will be reversed i.e., 52 yrs.
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Simplify.
Square root of 121m^8n^4
A. 11mn
B. 11m^2n^2
C. 11m^4n^2
Answers
Answer:
B
Step-by-step explanation:
no
The equation of the straight line of slope 3 passing through the point (2, 5) may be written as
Answers
m=(y-y1)/(x-x1)
therefore the formula for our graph will be:
3=(y-5)/(x-2)
3(x-2)=y-5
y-5=3x-6
y=3x-6+5
y=3x-1
the answer is y=3x-1
Write a conditional that multiplies the value of the variable pay by one-and-a-half
Answers
What is the slope of the line below
Answers
The formula for slope can be found by finding the difference in y between two values divided by the difference in x between the same two values. In this case, you would subtract 4 from 8 and 2 from 4, to get 4/2, or 2. The slope is represented by the variable m, so m = 2.
Need help geometry ^^^
Answers
What is i^16 simplified
Answers
and fairly sure you know how much that is.
How much dirt is there in a hole 3 feet deep, 6 ft long and 4 ft wide?
Answers
the volume of the hole would be 3 * 6 * 4 =72 cubic feet.
However, since it is a hole, there would be no dirt in it.
the sum of 3 numbers is 26. the second number is twice the first and the third number is 6 more than the second. find the number
Answers
Answer:
the numbers are 4, 8, 14
Step-by-step explanation:
If we subtract 6 from the third number and from the total, we find that we now have 5 times the first number for a total of 20.
The first number is 4.
The second number is 2×4 = 8.
The third number is 8 + 6 = 14.
1. What is 3/8x < -6 or 5x>2 solved and graphed?
2. What is 2<10 -4d< 6 solved and graphed?
I appreciate your help!
Answers
[tex]3x\ \textless \ -48[/tex] and divide to get x<-16. Now the second one, just divide both sides by 5 to get
[tex]x\ \textgreater \ \frac{2}{5} [/tex]
On a single number line, make 0 your center, put -16 where it belongs in reference to the 0 and put 2/5 where it belongs in reference to the 0. The numbers to the left of -16 are those that are less than -16, and the circle above the -16 is an open one, not including the -16. The numbers to the right of 2/5 are those numbers that are greater than 2/5, so put an open circle above the 2/5 and go to the right with that line. And you can see that you have a big open space between the -16 and the 2/5 where the solution set is not the same at all. For b, solve this one simultaneously. It is a conjunction, an "and", where there will be a solution set that is shared by both values for x. Solve it like this...start by subtracting 10 from both sides:
-8< -4d < -4 Now, when you divide by the negative 4, you have to change the signs to greater than: 2 > d > 1. That means, in words, that "d is less than 2 and greater than 1". On a single number line you will have open circles above the 1 and the 2 and the numbers in between 1 and 2 are shared solutions.
Need help with math problem
Multiply
(3x – 7)(3x – 5)
A.
9x 2 + 6x + 35
B.
9x 2 + 36x + 35
C.
9x 2 – 36x – 35
D.
9x 2 – 36x + 35
Answers
1 step: 3x term
3x*3x - 3x*5 the minus comes as you multiply by -2
2 step: -7 term
-7*3x + 7*5 the second plus comes from -*-=+
add these together
3x*3x-3x*5-7*3x+7*5 and do the multiplications:
9x^2 -15x-21x+35=9x^2-36x+35
I don't understand how we do this PLEASE help me!!!
Answers
28 = (45 + KL)/2
56 = 45+ KL
KL = 56-45
KL = 11
The student came to the conclusion that the system has infinitely many solutions, which is not correct. Describe the error was the student work being shown.
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1. Given f(x)=3x+8f(x)=3x+8 and g(x)=6x+6g(x)=6x+6 then what is (f+g)(−1))(f+g)(−1)) ?
2. Given f(x)=6x+4f(x)=6x+4 and g(x)=3x+7g(x)=3x+7 then what is (f−g)(1)) ?
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In a survey, the planning value for the population proportion is p*=.35. how large a sample should be taken to provide a 95% confidence interval with a margin of error of .05 (to the nearest whole number)?
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p* = 0.35, the populatin proportion.
Sp = 0.05, the margin of error
Let n = the size of the sample.
Because the standard error is 0.05, therefore
[tex] \sqrt{ \frac{p(1-p)}{n} } =0.05[/tex]
[tex] \sqrt{ \frac{0.35(1-0.35)}{n} } =0.05[/tex]
[tex] \frac{0.2275}{n} =0.05^{2} =0.0025[/tex]
n = 0.2275/0.0025 = 91
Answer: The sample size is 91.
WILL GIVE A BRAINLIEST PLEASE HELP!!!
Use the formula below to find the 6th term in the geometric sequence.
a(n)=(5)x(3/2)n-1
A.
5
B.
15/2
C.
1,215/32
D.
3,645/64
Answers
In the formula given a₁ = 5, r = 3/2 and n = 6 (we have to find the 6th term value).
a₆ = 5.(3/2)⁶⁻¹ = 5.(3/2)⁵ = 1215/32 (answer C)
In 1980, the United States' national debt exceeded $9 billion dollars. Express the exact dollar amount in scientific notation.
Answers
One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.
Answers
2y = x
If z is 7 less than x then that equation would look like
X = z +7
The perimeter is the sum of all the sides
P = x + y + z = 43
Now by using all three equations, we can find the value of each variable by plugging into the equations.
First, let's start by changing the first two equations to compare the values of z and y to x.
Y = x/2
Z = x - 7
Now we can use these new equations to plug into the perimeter equation and find the value of x.
43 = x + y + z Plug in your variables
43 = x + x/2 + x-7 Add 7 to both sides
50 = x + x/2 + x Multiply both sides by 2 to get rid of the fraction
100 = 2x + x + 2x Add all your x's together
100 = 5x Divide both sides by 5
X = 20
No we can use the value of x to find the values of y and z by plugging into the two equations before.
2y = 20
Y = 10
Z = 20 - 7
Z = 13
Therefore, the lengths of the sides are 20, 10, and 13
Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. If /,/, /, and /, solve for x.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
Answers
Find the surface area of the sphere.
Round to the nearest hundredth.
Answers
The average wind speeds for one year at 44 climatic data centers around the United States are as follows:
9.0, 6.9, 9.1, 9.2, 10.2, 12.5, 12.0, 11.2, 12.9, 10.3, 10.6, 10.9, 8.7, 10.3, 10.6, 10.9, 8.7, 10.3, 11.0, 7.7, 11.4, 7.9, 9.6, 8.0, 10.7, 9.3, 7.9, 6.2, 8.3, 8.9, 9.3, 11.6, 10.6, 9.0, 8.2, 9.4, 10.6, 9.5, 6.3, 9.1, 7.9, 9.7, 8.8, 6.9, 8.7, 9.0, 8.9, 9.3
a) Make a stem plot of the average wind speeds data. The frequency in the stem for 9 to 9.9 is?
b) The first quartile for the wind speed data set is?
Answers
There are a total of 48 data
Question a:
The frequency in the stem for 9 to 9.9 is 13 data
Question b:
The location of the first quartile is given by [tex] \frac{n+1}{4} [/tex], where 'n' is the number of data
We have n = 48
Location of the first quartile is at [tex] \frac{48+1}{4}= \frac{49}{4}= 12.25[/tex] rounded down to 12
The value of the lower quartile is on the [tex] 12^{th} [/tex] on the diagram which is 8.7
Explain how you would use trig ratios to find the height of the tree if you know you are standing 30 feet from the base of the tree when you measure the 37-degree angle.
Answers
make sure your calculator is in Degree mode.
From use of trigonometric ratios, it is seen that the height of the tree is; 22.61 feet
How to work with trigonometric ratios?We are told that you are standing 30 ft from the base of a tree.
Now, the distance from where you are standing to the top of the tree will be the hypotenuse of the triangle formed by you and the tree.
Thus, if the height of the tree is h and the angle the hypotenuse makes with the 30 ft base is 37°, then we have;
h/30 = tan 37
h = = 30 * tan 37
h = 22.61 ft
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HELP ME PLEASE!
Peter walks 30 feet away from his house and places a mirror on the ground. He backs 6 feet away from the mirror so that he can see the tip of the roof. Peter's eyes are 5 feet above the ground. Peter and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Peter's eyes, the mirror, and the ground are congruent as shown in the image below:
Image depicts a mirror on the ground between a person and a house. The mirror is 6 feet away from the person and 30 feet away from the house.
What is the height of the house?
Answers
By setting up a proportion based on the similar triangles formed by Peter's line of sight and the analogous line from the top of the house to the mirror, we find that the house is 25 feet tall.
According to the Law of Reflection and the information provided, we have two similar triangles: one formed by Peter's eyes, the mirror, and the point on the ground directly below his eyes, and the other formed by the top of the house, the mirror, and the point on the ground directly below the top of the house.
The first triangle has a height of 5 feet (Peter's eye level) and a base of 6 feet (the distance from Peter to the mirror). The second triangle's height is what we are trying to find (height of the house), and its base is 30 feet (distance from the house to the mirror).
Because the triangles are similar, the ratios of their corresponding sides are equal. So, we can set up the following proportion:
Height of Peter's eyes / Distance to mirror = Height of the house / Distance to mirror from house
5 feet / 6 feet = Height of the house / 30 feet
Now, cross-multiply to solve for the height of the house:
5 feet * 30 feet = Height of the house * 6 feet
Height of the house = (5 * 30) / 6
Height of the house = 150 / 6
Height of the house = 25 feet
Therefore, the height of the house is 25 feet.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. x2 + 4x + 3 = 0