Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. <1 and <3 <3 and <7 <8 and <10<4 and <14<6 and <14<2 and <3
Answers
EXPLANATION:
To make a correct classification we must do the following:
First we must know the following terms:
-Corresponding angles:
They are on the same side of the parallels and on the same side of the transversal.
For example: <1 <3 ; <6 and <14
-Alternate interior:
They are found within the parallel lines and on the opposite sides to the transversal
For example: <3 and <7 ; <8 and <10
-Alternate Exterior:
they lie outside the parallel lines and on the opposite sides to the transversal.
For example: <4 and <14
-Consecutive interior angles:
They are the pairs of angles on one side of the transversal that are between the lines.
For example: <2 and <3
Related Questions
A line passes through the point (-3, -9) and has a slope of -2.
Write an equation in slope-intercept form for this line.
Answers
have a great day!
how many solutions does 2(x+4)=4(x+2)
Answers
lets solve the equation!
[tex]\begin{gathered} 2(x+4)=4(x+2) \\ x+4=\frac{4}{2}(x+2) \\ x+4=2(x+2) \\ x+4=2x+4 \\ 4-4=2x-x \\ x=0 \\ \\ \text{Thus there is only ONE solution, and it is x=0} \end{gathered}[/tex]Solve the equation: 3x - 6 = 2(x - 2)no solution0all real numbers0.752
Answers
Problem
Solve the equation: 3x - 6 = 2(x - 2)
Solution
For this case we can do the following:
3x -6= 2x -4
And now we can subtract in both sides 2x and we got:
3x- 2x = 6-4
x = 2
And the final solution for this case would be x=2
find the unit price of 16 oz of candy with sells for $4.82
Answers
The price of 16 oz candy is $4.82.
Determine the unit price of candy.
[tex]\begin{gathered} s=\frac{4.82}{16} \\ =0.30125 \end{gathered}[/tex]I need the answer right now please someone help.Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB. AB||RTRCTC
Answers
From the diagram provided, line AB is parallel to line RT
AB | | RT
using the elimination method, find x and y: please explain to me, I want an explanation because I don't get this a 100% yet 4x - 3y = 25-3x + 8y = 10
Answers
Given the system of equations :
[tex]\begin{gathered} 4x-3y=25 \\ -3x+8y=10 \end{gathered}[/tex]To eliminate y :
multiply the first equation by 8 and the second equation by 3
[tex]\begin{gathered} 8\cdot4x-8\cdot3y=8\cdot25 \\ 3\cdot-3x+3\cdot8y=3\cdot10 \\ ================ \\ 32x-24y=200 \\ -9x+24y=30 \end{gathered}[/tex]Add the equation , we will find the sum of y = 0
[tex]\begin{gathered} (32x-24y)+(-9x+24y)=200+30 \\ 32x-24y-9x+24y=230 \\ (32x-9x)+(-24y+24y)=230 \\ (23x)+(0)=230 \end{gathered}[/tex]So, solve the the result for x
[tex]\begin{gathered} 32x-9x=200+30 \\ 23x=230 \\ \\ x=\frac{230}{23}=10 \end{gathered}[/tex]Then substitute with x at the first equation to find y
[tex]\begin{gathered} 4\cdot10-3y=25 \\ 40-3y=25 \\ -3y=25-40 \\ -3y=-15 \\ \\ y=\frac{-15}{-3}=5 \end{gathered}[/tex]So, the answer of the system of equations :
[tex]\begin{gathered} x=10 \\ y=5 \\ (x,y)=(10,5) \end{gathered}[/tex]
help pleaseeeeee!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. No
2. Yes
3. No
4. No
Step-by-step explanation:
helpp pleasee List the domain of the following function.(0,1),(9,0), (2,7),(4,3)
Answers
Problem
Solution
For this case we want to determine the domain from the following relation:
(0,1), (9,0), (2,7), (4,3)
And if we see the first cooridnate for all the points we have the domain and then the answer we have:
0,2,4,9
Show your work (no explanation just the answer and how you got it) DUE TODAY
Answers
The solutions to the absolute value equations are given as follows:
1. k = -8 or k = 8.
2. x = -7 or x = 7.
3. a = -10 or a = 6.
4. a = -2.5 or a = 2.5.
5. m = -4 or m = 22.
6. x = -4 or x = 6.8.
7. x = -16 or x = 9.
8. a = -2.4 or a = 1.2.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.This means that there are two possible solutions for the equation |x| = a, which are:
x = a or x = -a.
Item 1The equation is:
|k| = 8.
Applying the definition of the absolute value function, we have that the possible solutions are:
k = -8 or k = 8.
Item 2The equation is:
|x| = 7.
Applying the definition of the absolute value function, we have that the possible solutions are:
x = -7 or x = 7.
Item 3The equation is:
|a + 2| = 8.
The possible solutions are that the inside term can be equals to either -8 or 8, hence:
a + 2 = -8 -> a = -10.a + 2 = 8 -> a = 6.Item 4The equation is:
|8a|/10 = 2
In standard format, the equation is:
|8a| = 20
Then the solutions are:
8a = -20 -> a = -20/8 = -2.5.8a = 20 -> a = 20/8 = 2.5.Item 5The possible solutions are:
-m + 9 = -13 -> m = 22.-m + 9 = 13 -> m = -4.Item 6The possible solutions are:
7 - 5x = -27 -> 5x = 34 -> x = 6.8.7 - 5x = 27 -> 5x = -20 -> x = -4.Item 7Applying cross multiplication, the expression is:
|2x + 7| = 25
The possible solutions are:
2x + 7 = -25 -> 2x = -32 -> x = -16.2x + 7 = 25 -> 2x = 18 -> x = 9.Item 8Applying cross multiplication, the expression is:
|-3 -5a| = 9.
The possible solutions are:
-3 - 5a = -9 -> 5a = 6 -> a = 1.2.-3 - 5a = 9 -> 5a = -12 -> a = -2.4.More can be learned about absolute value equations at https://brainly.com/question/5012769
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6)26 A 4 R2 (B) 2 R4 © 4 DE
Answers
On red step we multiply 6 by 4 to obtan 24, and subtract with 26, the solution is 2
O green step we add a comma to 4 do add a zero on the last solution (2), now the number is 20 and multiply 6 by 3 to obtan 18 and the solution is 2
As we can see the number two will be repeated forever since 20 divided by 6 is not exact, then the 3 will repeat infinitely
A hot air balloon descended 3240 feet in an hour. Find the change in altitude per minute?
Answers
3,240 / 60 = 54
Therefore, the change in altitude per minute is 54 feet.
Unit analysis is a tool that we can use to convert units. It involves multiplying the original number by a fraction to cancel out units.
Solving the QuestionWe're given:
[tex]\dfrac{3240\hspace{4}feet}{hour}[/tex]
We also know that:
[tex]\dfrac{hour}{60\hspace{4}minutes}[/tex]
Multiply the two to cancel out the hour:
[tex]\dfrac{3240\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{3240\hspace{4}feet}{60 minutes}[/tex]
Simplify:
[tex]=\dfrac{54\hspace{4}feet}{minute}[/tex]
Answer[tex]\dfrac{54\hspace{4}feet}{minute}[/tex]
Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 28 and 36 miles per gallon is?
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The probability that a random vehicle gets between 28 and 36 miles per gallon is 0.3333.
What's probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Given that,
a = 23
b = 47
P(c < x < d) = (d - c) / (b - a)
P(28 < x < 36) = (36 - 28) / (47 - 23) = 0.3333
Probability = 0.3333
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help or I die,... HELP
Answers
Regarding the points on the given line, it is found that:
a) The midpoint is: (3,4.5).
b) The coordinates of C are: C(4,5).
c) The coordinates of the other end of the line are: (4,3).
MidpointThe midpoint between two points is given by the mean of the coordinates of these points.
In this problem, the coordinates of points A and B are given as follows:
A(0,3) and B(6,6).
Hence the coordinates of the midpoint are given as follows:
x-coordinate: (0 + 6)/2 = 3.y-coordinate: (3 + 6)/2 = 4.5.As for point C, we have that C is closer to B then A, hence:
The x-coordinate is greater than 3.The y-coordinate is greater than 4.5.The coordinates are integers, hence it is given as follows:
C(4,5).
As for line AB, it is found that:
The other line is parallel, hence the slope is also of 0.5. (change in y divided by change in x is of 0.5).For the x-coordinate, on line AB, they change by 6, hence in the new line they increase by 2/3 x 6 = 4.For the y-coordinate, on line AB, they change by 3, hence in the new line they increase by 2/3 x 3 = 3.Thus the other endpoint is:
(4,3).
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The diagram shows a field.
66 m
140m
102 m
Work out the area of the field.
4
Answers
Answer:
The area of the field will be 60504 Sq. m
Step by Step calculation:
Area of the cuboidal field
A cuboid is a three-dimensional figure bounded by six rectangular planes that have different lengths, widths, and heights. If you look around and see a box, brick, or anything in the shape of a rectangle, it might be a cuboid. A cuboid ([tex]3[/tex]-dimensional) can be seen as composed of rectangles ([tex]2[/tex]-dimensional) of different dimensions when viewed from either end
Total area of block = lh + lh + lb+ lb+ hb+ hb=[tex]2[/tex](lb+bh+hl).......(1)
where l means length h means height and b means the breadth of the cuboid
Put the value of length, breadth, and height in (1)
We get TSA of field as= 2(66*140+140*102+102*66 ) = 60504 m^2
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a parabola can be drawn given a focus of (4, -7) and a directrix of y=-1
Answers
The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
What is Parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Any point on the parabola is equidistant from the focus an directrix.
Distance of a point (x,y) from y=-1 is (y+1)
Distance of a point (x,y) from (4,-7) say L, then
L² = (x - 4)² + (y+7)²
since, L = y + 1
(y + 1)² = (x - 4)² + (y+7)²
y² + 1 + 2y = (x - 4)² + y² + 49 + 14y
-12y - 48 = (x-4)²
-12(y + 4) = (x-4)²
Therefore, The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
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Tamera is using rice paper to make Japanese Lanterns. The expression 2s^2 + 40s represents the surface area of a lantern where the base edges are s inches long. What is the surface area of a lantern when is 9 in?
2s^2 = 2s to the power of two
Answers
The surface area of the Japanese Lanterns Tamera made when the sides are 9 inches long will be 522 sq inches.
What is surface area?The Surace area of any 2D or 3D figure is the outer area of the given figure.
Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.
Given that Tamera is using rice paper to make Japanese Lanterns.
The expression 2s² + 40s represents the surface area of a lantern where the base edges are 's' inches long.
Therefore to find The surface area of the Japanese Lanterns when the sides are 9 inches in length we have to substitute 9 into the variable s.
So, 2(9)² + 40(9).
= 2×81 + 360.
= 162 + 360.
= 522 sq inches.
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heyyyy i need help with jumber 2
Answers
We are asked to determine whether the given two polygons are similar or not.
Recall that the two polygons are said to be similar if the ratio of their corresponding sides is equal.
The corresponding sides of the two polygons are
side 3 = side 6
side 4 = side 8
side 5.5 = side 11
Let us check if they are in the same ratio
[tex]\begin{gathered} \frac{3}{6}=\frac{4}{8}=\frac{5.5}{11} \\ \frac{1}{2}=\frac{1}{2}=\frac{1}{2} \end{gathered}[/tex]As you can see, the ratio of the corresponding sides is equal.
Therefore, the given pair of polygons is similar.
Evaluate. 0⁵= equal
Answers
The most important concept to solve this questio
Answer:
0
Step-by-step explanation:
o^5 = 0 x 0 x 0 x 0 x 0 = 0
A circle has a radius of 4 in find the length s of the arc
Answers
The rule of the length of an arc is
[tex]s=r\theta[/tex]r is the radius of the circle
Cita is the central angle subtended by this arc in radian measure
Since the radius of the circle is 4 inches, then
[tex]r=4[/tex]Since the measure of the central angle is 1.9 radian, then
[tex]\theta=1.9[/tex]Substitute them in the rule above
[tex]\begin{gathered} s=4\times1.9 \\ s=7.6\text{ inches} \end{gathered}[/tex]The length of the arc is 7.6 inches
Substitution method. show work.7.) y=x+2 10.) 2x+y=3 y=3x+4 3x-y=2elimination method. show work.11.) 5x+y=9 12.) -7x+y=-19 10x-7y=18 -2+3y=-19
Answers
Solution
7) y= x+2
replacing this in the second equation we got:
x +2 = 3x +4
-2 = 2x
x= -1
And solving for y we got:
y = -1 +2 = 1
10) 2x +y = 3
If we solve for y we got:
y = 3-2x
And replacing into the second equation we got:
3x - 3+2x = 2
5x = 5
x= 1
And solving for y we got:
y = 3 -2*1 = 3-2= 1
11) If we multiply the first equation by -2 and we add to the second one we got:
-10 x -2y = -18
10x -7y = 18
___________
-9y = 0
y=0
x= (9-0)/5 = 9/5
12) If we multiply the first equation by -3 we got:
21x -3y = 57
-2x +3y =-19
_______________
19x = 38
x= 2
y= (-19 + 4)/3= -5
The drama club is selling tickets to their play to raise money for the show's expenses.Each student ticket sells for $5 and each adult ticket sells for $7.50. The auditoriumcan hold at most 125 people. The drama club must make no less than $790 fromticket sales to cover the show's costs. If 73 adult tickets were sold, determine allpossible values for the number of student tickets that the drama club must sell inorder to meet the show's expenses. Your answer should be a comma separated list ofvalues. If there are no possible solutions, submit an empty answer.
Answers
Let
x ------> number of student tickets that the drama club must sell
so
we have
[tex]x+73\leq125[/tex][tex]\begin{gathered} x\leq125-73 \\ x\leq52 \end{gathered}[/tex]and
[tex]5x+7.50\cdot73\ge790[/tex][tex]\begin{gathered} 5x\ge790-547.5 \\ 5x\ge242.5 \\ x\ge48.5 \end{gathered}[/tex]the values of x lie on the interval [48.5,52]
therefore
all possible values for the number of student tickets are on the interval
[49,52]
Integers greater than or equal to 49 and less than or equal to 52possibles values are 49,50,51,52Solve the equation below.
3(x−9)−6=16x−72
Answers
3x-27-6=16x-72
3x-33=16x-72
3x-16x= -72+33
-13x=39
x= -3
Work out the value of (-8)2
Answers
Answer:
-16
Step-by-step explanation:
2x(-8)=16
Hey there!
Assuming you meant:
(-8)^2
= (-8)(-8)
= 64
Therefore, your answer should be:
64
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is the solution to this equation?4x - 6 + 2x = 18OA. x = 6OB. X= 4OC. X = 2OD. x = 12
Answers
In order to solve this equation, we can do the following steps:
[tex]\begin{gathered} 4x-6+2x=18\\ \\ 6x-6=18\\ \\ 6x=18+6\\ \\ 6x=24\\ \\ x=\frac{24}{6}\\ \\ x=4 \end{gathered}[/tex]Therefore the correct option is B.
Solve the triangle. (Do not round until the final answer. Round angles to the nearest degree and side lengths to the nearest tenth of a unit.)C=___∠A=___∠B=___
Answers
Explanation
to solve this we need to use the cosine law
Law of cosines says
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ b^2=a^2+c^2-2ac\cdot\cos (B) \\ c^2=a^2+b^2-2ab\cdot\cos (C) \end{gathered}[/tex]then
Step 1
find c
Let
[tex]\begin{gathered} b=8 \\ a=5 \\ \angle C=67 \end{gathered}[/tex]now, let's find c
[tex]\begin{gathered} c^2=a^2+b^2-2bc\cdot\cos (C) \\ \text{replace} \\ c^2=5^2+8^2-2\cdot5\cdot8\cdot\cos (67) \\ c^2=25+64-31.25849028 \\ c^2=57.74 \\ \text{square root in both sides} \\ \sqrt{c^2}=\sqrt{57.74} \\ c=7.598 \\ \text{rounded} \\ c=7.6 \end{gathered}[/tex]Step 2
now,let's find the angle A
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cdot\cos (A) \\ replace \\ 5^2=8^2+7.6^2-2\cdot8\cdot7.6\cdot\cos (A) \\ 25=64+57.76-121.6\text{ cos(A)} \\ 25=121.76-121.6(\cos A) \\ \text{subtract 121.76 in both sides} \\ 25-121.76=121.76-121.6(\cos A)-121.76 \\ -96.76=-121.6(\cos A) \\ \text{divide both sides by -121.6} \\ \frac{-96.76}{-121.6}=\frac{-121.6(\cos A)}{-121.6} \\ 0.795=\cos \text{ (A)} \\ Inverse\text{ cosine} \\ \cos ^{-1}(0.795)=\cos ^{-1}(\cos \text{ (A))} \\ 37.276=\text{ A} \\ \text{rounded} \\ A=37\~\text{ =A} \end{gathered}[/tex]Step 3
Finally,let's find angle B
we can use the formula as we did in step 2 to find angle A, but also we can use this fact:
the sum of the internal angles in a triangle equals 180 ,so
[tex]\angle A+\angle B+\angle C=180[/tex]replace and solve for angle C
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ 37+\angle B+67=180 \\ 104+\angle B=180 \\ \text{subtract 104 in both sides} \\ 104+\angle B-104=180-104 \\ \angle B=76 \end{gathered}[/tex]I keep getting the wrong answer for some reason, help please
Answers
In order to find the measure of angle A we have the next equation. Remember that the sum of the interior angles of a triangle is 180°
[tex](3x-6)+(8x+4)+(180-130)=180[/tex]Then we sum like terms
[tex]11x+48=180[/tex]Then we isolate the x
[tex]11x=180-48[/tex][tex]11x=132[/tex][tex]x=\frac{132}{11}[/tex][tex]x=12[/tex]For angle A
angle A= 3x-6=3(12)-6=30°
angle A=30°
4.) Rotate 90° counterclockwise about the origin.Original NewCoordinates: Coordinates:A: (___) A: ()YAON+COB:(_)B': ()2D2CC: (-)C':(___)D: (___)D:(__)
Answers
The Solution:
Rule:
When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
The original coordinates of the given points are as follows:
[tex]\begin{gathered} A(-4,3)_{} \\ B(2,3) \\ C(2,-1) \\ D(-4,-1) \end{gathered}[/tex]So, the new coordinates of the given points are below:
[tex]A^{\prime}(-3,-4)[/tex][tex]B^{\prime}(-3,2)[/tex][tex]C^{\prime}(1,2)[/tex][tex]D^{\prime}(1,-4)[/tex]Each side of a square is lengthened by 5 inches. The area of this new, larger square is 49 square inches. Find the length of
a side of the original square.
Answers
Answer:
2 inches
Step-by-step explanation:
Since the area of the larger square is 49 inches, each side of this square is 7 inches, which is 5 inches longer than the original square. So each side of the original square is 2 inches.
the baseball stadium the price for popcorn is $16.20 for 6 bags. If youwanted to buy 5 bags of popcorn, how much would it cost?
Answers
It is given that the cost of 6 bags of popcorn is $16.20
So the cost of 1 bag is:
[tex]\frac{16.20}{6}=2.7\text{ dollars}[/tex]So the cost of 5 bags at $2.70 per bag is:
[tex]2.7\times5=13.5\text{ dollars}[/tex]So the cost of 5 bags of popcorn is $13.5.
When you add 12 to a number and then divide the sum by 13, you get the same result as when you subtract 13 from the number and then divide the difference by 12. What is the number?
Answers
144 + 169 = X
313 = x
