Answers
Answer:
Let me know if there is anything you don't get
∠3 = 102 because ∠1 and ∠3 are supplementary and 102 + 78 = 180
∠4 = 102 because ∠1 and ∠4 are consecutive interior angles
∠5 = 78 because ∠1 and ∠5 are corresponding angles
∠6 = 133 because ∠2 and ∠6 are supplementary angles
∠7 = 47 because ∠2 and ∠7 are vertical angles
∠8 = 47 because ∠2 and ∠8 are opposite interior angles
∠9 = 133 because ∠8 and ∠9 are supplementary, and we just saw ∠2=∠8
∠10 = 102 because ∠1 and ∠10 are supplementary
You could have used a whole bunch of different relations, but I wanted to focus on ∠1 and ∠2 since those were told to us
Step-by-step explanation:
For this question you need to know several parts of geometry. Let me know if anything doesn't make sense.
First, parallel lines are two or more lines which are angles in such a way that no matter how long they are they will not cross. In other words they are slanted at the same angle. you can see this with lines a and b in this picture.
Second, a transversal is a line that crosses through two or more parallel lines. A transversal creates a number of angles that have special properties. I would like you to look specifically at line c as I describe these angles. line c is a transversal to Ines a and b. Also line d is also a transversal.
There are seven special angles to know.
The easiest is supplementary angles. This you don't need parallel lines, but if any two lines ever cross this creates 4 angles. you can actually look at where lines c and b intersect in your problem. Angles 2. 6 and 7 are labeled but there is one more unlabeled one. Now, 180 degrees is a straight line. With angles you can see angles 6 and 7 add together to be a straight line. Similarly 2 and 6 do as well. These are two sets of supplementary angles.
To list off the supplementary angles here 9 and 8 are supplementary, as are 2 and 6, 6 and 7, 1 and 3, 1 and 10, and finally 4 and 5.
From supplementary angles comes vertical angles. Again, if you look at angles 2, 6 and 7 we already know ∠2 + ∠6 = 180 and ∠6 + ∠7 = 180. Well lets say ∠6 = 133. Well then, we could use algebra to see that both ∠2 AND ∠7 are 47 degrees. This is the property of vertical angles. if you have two lines intersecting, any two angles that have a third in between the are called vertical angles, and are equal.
some examples of vertical angles are ∠2 and ∠7as well as ∠3 and ∠10,
Finally we go into parallel line specific angles. If you have two or more parallel lines with a transversal, so in particular look at a and b as the parallel lines and c as the transversal. The transversal creates some special angles. in particular, the transversal crosses a and b at the same angle, so angles 8 and 7 have the same value. These are known as corresponding angles, since they correspond tot he same position with a transversal crossing through parallel lines.
the corresponding angles in the picture are ∠8 and ∠7, ∠3 and ∠4 and finally ∠1 and ∠5. the last two using line d as a transversal.
After corresponding angles opposite interior angles I think are the next logically to look at. Opposite means they are on two different parallel lines and on different sides of the transversal, while interior means they are between the parallel lines. so if you look at the parallel lines a and b there are angles 8 and 2 that are interior angles. Since 8 is against line a and 2 is against line b, and ∠8 is above transversal c while ∠2 is below it, they are opposite angles. so 8 and 2 are opposite interior angles. Now, if you look at ∠8 and ∠7 you know these are corresponding angles, then ∠7 and ∠2 are vertical angles. This means opposite interior angles are equal.
A list of opposite interior angles are ∠8 and ∠2, and ∠10 and ∠4.
Alongside opposite interior, there are opposite exterior angles. opposite means on different parallel Ines and on opposite sides of the transversal, while this time exterior means not between the parallel lines. Now just like we figured with opposite interior angles
The only labeled pair of opposite exterior angles are ∠9 and ∠6. Now just like we figured with opposite interior angles, let's start with ∠8 and ∠9, which are supplementary. then ∠8 and ∠7 are corresponding angles so ∠9 and ∠7 are supplementary. We can also see ∠7 and ∠6 are supplementary. well, since ∠9 + ∠7 = 180 = ∠6 + ∠7 then ∠9 = 180 - ∠7 = ∠6 so ∠9 = ∠6. This shows opposite exterior angles are equal.
So we did two kinds of opposite angles, it might make sense there are non opposite angles. And there are. these are called consecutive angles. There are consecutive exterior and consecutive interior angles. An example of each are ∠1 and ∠4 for consecutive interior, consecutive because they are on the same side of the transversal, and interior because they are between the two parallel lines. ∠3 and ∠5 are consecutive exterior angles.
You can use similar reasoning we have been so far to conclude all consecutive angles are supplementary
Related Questions
Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if if the sample mean weight is significantly different than 68g. She takes a random sample of 100 eggs and finds a mean weight of 67g and a sample standard deviation of 1g.
Required:
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?
Answers
Answer:
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Step-by-step explanation:
To solve this question, we use the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 67g and a sample standard deviation of 1g.
This means that [tex]\mu = 67, \sigma = 1[/tex]
Sample of 4
This means that [tex]n = 4, s = \frac{1}{\sqrt{4}} = 0.5[/tex]
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?
This is the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 67}{0.5}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
0.9987 = 99.87% probability that the mean weight of 4 eggs in a package is less than 68.5g
Answer:
-10
Step-by-step explanation:
Khan
I need help please.
Answers
Answer:
B
Step-by-step explanation:
Put "Volume of a Cone" in your browser and all you have to do is type the height and radius.
a soccer game started at 2:15p.m. and ended at 3:35p.m. how long did the game last
Answers
Which equation is equivalent to 3-4x=12
Answers
We have a linear equation here.
3 - 4x = 12
Subtract 3 from both sides.
3 - 3 - 4x = 12 - 3
-4x = 9
Divide both sides by -4 to find x.
-4x/-4 = 9/-4
x = -9/4
The value of solution of expression is,
⇒ x = - 9 / 14
WE have to given that;
A mathematical expression is,
⇒ 3 - 4x = 12
Now, WE can simplify as;
⇒ 3 - 4x = 12
Add 4x both side,
⇒ 3 - 4x + 4x = 12 + 4x
⇒ 3 = 12 + 4x
Subtract 12 both side, we get;
⇒ 3 - 12 = 14x
⇒ - 9 = 14x
⇒ x = - 9 / 14
Thus, The value of solution of expression is,
⇒ x = - 9 / 14
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Hey guys can you guys help me thanks :)
Answers
Explanation
Answer:
d
Step-by-step explanation:
60x9 =540
Please help!!!!!!!!!!
Answers
Answer:
104 ft^2
Step-by-step explanation:
Before we start, one thing to notice is the 90 degrees symbol at the corners. This lets you know a rectangle has four 90 degrees angle, which will help in the next step.
First, separate the shape to become three rectangles.
After you've done that, start with the first recantgle on the left.
The edges are 8 and 5. To find the area, you must multiple 8 by 5.
8 * 5 =40
The area is 40 for the first rectangle.
Next, we do the second rectangle to the right of the first one.
oThe edges are 6 and 4. We know it is four because the full length on the rectangle on the left is 8 and below the 6 ft is the place that says 4 ft. The 6ft line cuts to rectangle in half so the other edge will be 4 ft. (Hope that made sense )
Now we find the area of the second rectangle by multiplying 6 and 4
6 *4 = 24
Now we conclude with the third rectangle. We know one edge which is 5 and the other edge will be 8 because, at the opposite end, it tells us the length is 8.
Now we multiply 8 and 5.
8 * 5 = 40.
Now, the three numbers we have found are 40, 24, and 40. Our final step is to add up these three numbers from the rectangles we made to find the area.
40 + 24 + 40 = 104
The area will be 104 ft^2
I hope this explanation helped and have a good day!
An elementary school held a fundraiser. Students sold candles and plants. The plants sold for $12.50 each and the
candles sold for $3.75 each. The school raised $3,987.50 and sold 410 candles and plants altogether. How many
CANDLES did they sell?
Answers
Answer:
The school sold 130 candles
Step-by-step explanation:
Given that the plants sold for $12.50 each and the candles sold for $3.75 each. If the school raised raised $3,987.50 and sold 410 candles and plants altogether then the number of candles and plants sold may be computed simultaneously as follows:
Let the number of candles sold be c and the number of plants sold be p. If the school sold 410 candles and plants altogether
p + c = 410
p = 410 - c
if the plants sold for $12.50 each and the candles sold for $3.75 each and the school raised raised $3,987.50
12.5p + 3.75c = 3,987.50
12.5(410 - c) + 3.75c = 3,987.50
5125 -12.5c +3.75c = 3,987.50
-8.75c = 3,987.50 - 5125
-8.75c = -1137.5
c = -1137.5/-8.75
= 130
Mrs. Stephens bought 3 pounds of tomatoes.How many ounces are equal to 3 pounds?
Answers
Answer:
48 ounces
Step-by-step explanation:
16 ounces per pound
3 x 16 = 48 ounces
classify the triangle base on angles and sides
Answers
Answer:
C. Acute; isosceles
Step-by-step explanation:
As you can see 2 sides of the triangle are equal to 10 which means they are congruent. It's an isosceles triangle because it has two congruent sides.
You can also see that none of the angles form 90 degrees or more which means they are acute angles.
Hope that helps
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level. What would be the appropriate alternative hypothesis if he wanted to substantiate his suspicion
Answers
Answer:
The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be [tex]H_{a}: \mu > 238[/tex]
Step-by-step explanation:
At the null hypothesis, we test that the mean is equal to a certain value.
At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 238[/tex]
A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.
This means that the alternate hypothesis is:
[tex]H_{a}: \mu > 238[/tex]
The school debate team sold candy bars as fundraiser. The earnings are graphed below. What is the rate the debate team charged for each candy bar ?
Answers
Answer:
were is the graph lol
Which math term is it for this one ?
Answers
Answer:
option D
the set of all points that are a fixed distance from a given point
hope it helps
really need help! anything would be appreciated
Answers
Jk, the answer is 6x + 16y + 8 :)
HELP ME WITH A MATH PROBKEM Type a number that has a value less than 4.7|
Answers
Answer:
i think
all the numbers between
0 to 4.6
A carpenter needs to cut a 3.9 meter long piece of wood into 3 equal lengths. How long should each piece be in millimeters?
Answers
Answer:
1300
Step-by-step explanation:
Answer:
1300
Step-by-step explanation:
ITS AN EMERGENCY PLEASE HELP
Answers
Answer:
$9.80
Step-by-step explanation:
Remember that the way to find the mean of a data set is by adding together all the values, and dividing by the number of the values. So, in this case, you add the 5 values together and get 49. Since there are 5 values, you divide 49 by 5 and get 9.8, or in a real world-money situation $9.80.
How do I start this problem? I don't need help with the graphing part.
Answers
Answer:
x = 6 , y = 0 (x , y) = (6 , 0)
x = 12, y = 3 (x , y) = (12 , 3)
x = 24, y = 9 (x , y) = (24 , 9)
Step-by-step explanation:
Simply plug in a x, and find a y that would make the equation true:
When x = 6:
6 - 2y = 6
6 (-6) - 2y = 6 (-6)
-2y = 0
(-2y)/-2 = (0)/-2
y = 0
When x = 6, y = 0 (x , y) = (6 , 0)
When x = 12:
12 - 2y = 6
12 (-12) -2y = 6 (-12)
-2y = -6
(-2y)/-2 = (-6)/-2
y = 3
When x = 12, y = 3 (x , y) = (12 , 3)
When x = 24:
24 - 2y = 6
24 (-24) - 2y = 6 (-24)
-2y = -18
(-2y)/-2 = (-18)/-2
y = 9
When x = 24, y = 9 (x , y) = (24 , 9)
~
Show your work: 1/2x = 10
Answers
think of it as 1/2 • x = 10
then multiple both sides by 2
1 • x = 20
so x=20
A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 46 cables and apply weights to each of them until they break. The 46 cables have a mean breaking weight of 779 lb. The standard deviation of the breaking weight for the sample is 15.4 lb. Find the 99% confidence interval to estimate the mean breaking weight for this type cable.
Answers
Answer:
The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 46 - 1 = 45
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 45 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.69
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.69\frac{15.4}{\sqrt{46}} = 6.1[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 779 - 6.1 = 772.9 lb
The upper end of the interval is the sample mean added to M. So it is 779 + 6.1 = 785.1 lb
The 99% confidence interval to estimate the mean breaking weight for this type cable is between 772.9 lb and 785.1 lb.
A triangular fence is built with sides each of length 15 m, 14 m, and 24 m, respectively. To the
nearest degree, what is the measure of the smallest angle made by the fence?
Answers
9514 1404 393
Answer:
33°
Step-by-step explanation:
The law of cosines tells you ...
a² = b² +c² -2bc·cos(A)
Solving for A, we get ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((15² +24² -14²)/(2·15·24)) = arccos(605/720)
A ≈ 32.8305°
The smallest angle is about 33°.
What are the fourth, seventh, and tenth terms of the
sequence A(n) = 7 + (n - 1)(-3)?
Answers
Answer:
B
Step-by-step explanation:
fourth term
A(4)= 7 - ( 4-1)(-3)
=-2
seventh term
A(7)= 7 - (7-1)(-3)
=-11
tenth term
A(10) = 7 - (10-1)(-3)
= -20
Help math eh at t were rhehh
Answers
Helpppppppppp fasttttttttttttttttttt
Answers
Answer:
first 2 , second 50, third 8
Step-by-step explanation:
What about the rational equation causes asymptotes?
Answers
Answer:Some functions have asymptotes because the denominator equals zero for a particular value of x or because the denominator increases faster than the numerator as x increases.
Step-by-step explanation:
solving and graphing inequalities
Answers
Answer:
wssp i can help
Step-by-step explanation:
help for 10 points plsssss
Answers
Answer:
on math way you can take a picture of your problem. hope those helps
Step-by-step explanation:
In a town, 65% of people had high speed internet in their homes. If the population of the town is 80,000, how many
people do not have access to high speed internet in their homes?
Show work
Answers
please help me for brqinliest im imed
Answers
Answer:
77°
Step-by-step explanation:
As we can see ABCD is a cyclic quadrilateral so opposite angles of a cyclic quadrilateral is supplementary.
< A + <B = 180° { being opposite angles of cyclic quadrilateral }
2x + 9° + 3x + 1° = 180°
5x + 10° = 180°
5x = 180° - 10°
5x = 170°
x = 170° / 5
x = 34°
Now
< A = 2x + 9°
= 2 * 34° + 9°
= 77°
Hope it will help :)❤
8. Misty created the number pattern below. 32, 28, 24, 20, ... If n represents a number in this pattern, which rule could be used to find the next number in the pattern?
Answers
Answer:
An = 32 - (4*(n-1))
Step-by-step explanation:
the starting term for this pattern is 32 (which you will need to include in the "rule")
you also know that the next term is the previous term - 4
so!
we can write this pattern as
An = 32 - (4*(n-1))
An = any number of term in the pattern
- ex). A2 = 28, A3 = 24, etc
n = the nth term
- the 3rd term = 24, the fourth term = 20, etc
HELP WILL GIBE BRAINLIEST.
HOW MUCH IS IT FOR 1
Answers
Answer:
small is 0.018
medium is 0.016
large is 0.010