Answers
The special angles pairs that are formed are identified below.
What are the Special Angle Pairs?Special angle pairs are formed by a transversal and the parallel lines it cuts across.
Based on the image given, the special angle pairs are given as follows:
Corresponding angles:
∠1 and ∠5
∠4 and ∠8
∠2 and ∠6
∠3 and ∠7
Alternate interior angles:
∠3 and ∠5
∠4 and ∠6
Consecutive interior angles:
∠4 and ∠5
∠3 and ∠6
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Related Questions
x+y=5
x×y=6
Solve simultaneously with steps
Answers
Answer:
(3, 2), (2, 3)
Step-by-step explanation:
x + y = 5
xy = 6
Solve the first equation for x.
x = 5 - y
Substitute 5 - y for x in the second equation.
xy = 6
(5 - y)y = 6
5y - y² = 6
y² - 5y + 6 = 0
Factor.
(y - 2)(y - 3) = 0
y - 2 = 0 or y - 3 = 0
y = 2 or y = 3
Now substitute 2 for y in the first equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
One solution is x = 3; y = 2, or (3, 2).
Now substitute 3 for y in the first equation and solve for x.
x + y = 5
x + 3 = 5
x = 2
Another solution is x = 2; y = 3, or (3, 2).
Answer: (3, 2), (2, 3)
ST=
Help me please thank u
Answers
Step-by-step explanation:
RS + ST = 8
(RS + ST)×RS = (4 + 2)×4
8 × RS = (4 + 2) × 4 = 6 × 4 = 24
RS = 24/8 = 3
RS + ST = 8
3 + ST = 8
ST = 5
Triangle XYZ was reflected across m and then dilated to form a similar triangle. Which triangle represents the image?
Triangle X Y Z is reflected across line m. It is rotated about point X prime and then is dilated to form a smaller triangle.
Triangle X Y Z is reflected across line m and then is dilated to form smaller triangle X prime Y prime Z prime.
Triangle X Y Z is reflected across line m to form triangle Z prime Y prime X prime.
Answers
The triangle that represents the image is; Option B; Triangle X Y Z is reflected across line m and then is dilated to form smaller triangle X prime Y prime Z prime.
How to carry out Transformations?From the given transformation as seen in the attached image, we can say that;
In Option A, the triangle is first reflected across m and then reflected across the vertical line. Then, it is dilated.
In Option C, the triangle is reflected across m but the angles are not preserved.
In Option B, the triangle is reflected across m and then dilated and as such is a correct image similar to the original triangle.
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It's Option B.
(You can also call it the middle one, up to you <3)
Question 1 of 10
A triangle has two sides of lengths 7 and 9. What value could the length of
the third side be? Check all that apply.
A. 5
B. 13
C. 2
D. 22
E. 10
F. 8
Answers
Answer:
A, B, E and F.
Step-by-step explanation:
A triangles side must be larger than the difference of the other sides, and smaller than the sum of the other sides. So in this case we could create an equation such as, 9-7<x<9+7. From this equation we can conclude that this side can be between 2 and 16. So, A, B, E and F all work.
An encryption machine uses a formula to encrypt words, by taking each letter and changing it to the letter that is just before it in the alphabet. If the letter is ‘a’, it changes it to ‘z’. If you put the word STAR into the machine, what would the output be?
A) TARS
B) RSZQ
C) TUBS
D) RSTA
Answers
The output of the word STAR is RSZQ
How to determine the output?The encryption rule is given as:
Change a letter to the previous letter
This means that:
S -> R
T -> S
A -> Z
R -> Q
So, we have:
STAR -> RSZQ
Hence, the output of the word STAR is RSZQ
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A survey conducted by a reputed Business School in Texas among 400 students showed that students spend on an average $500 for textbooks in a year. The sample standard deviation was $80. What is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%
Answers
[489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
n=400
sample mean (x)=500
sample standard deviation (s)=80
99% confidence interval for mean
α=0.01
critical value [tex]Z_{\frac{a}{z} }[/tex] =2.58
Standard error of sample mean Sx = [tex]\frac{s}{\sqrt[]{n} }[/tex] = [tex]\frac{80}{\sqrt[]{400} }[/tex] = [tex]\frac{80}{20}[/tex] = [tex]4[/tex]
∴ Sx = 4
Confidence interval (μ)
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] [tex]\frac{s}{\sqrt[]{n} }\\[/tex]
μ= [tex]x[/tex] ± [tex]Z_{\frac{a}{z} }[/tex] (Sx)
=500 ± 2.58(4)
=500 ± 10.32
lower limit = 500 - 10.32 = 489.68
upper limit= 500 + 10.32= 510.32
Hence, [489.68, 510.32] is the confidence interval for the average amount spent on textbooks in a year if the desired level of confidence is 99%.
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write an exponential function that includes the following given pair of points.
(1,-2) and (2,-4)
Answers
Answer:
[tex]f(x)=-2^x[/tex]
Step-by-step explanation:
So generally an exponential equation is expressed in the form: [tex]f(x)=a(b)^x[/tex] and: [tex]b=1+r\text{ or }b=1-r \text{ depending on whether it's decaying or growing}[/tex]. In this case we see that as x increased by 1, the y-decreases, BUT the absolute value is increasing, so it's really just reflected.
Plug in known values:
[tex]-2=a(b)^1[/tex]
[tex]-4=a(b)^2[/tex]
So if you think about it. you really have
-2 = a * b
-4 = a * b * b
since ab = -2, then we can substitute this into the second equation
-4 = -2 * b
-4 = -2b
Divide both sides by -2
b = 2
You can also deduce that b=2, by realizing to go from -2 to -4, you have to subtract 100% of -2 from -2. This means r=1, so b=1+1, b=2
Anyways, now it's time to solve for a, by plugging in a point as well as b.
-4 = a(2)^2
-4 = 4a
-1 = a
You can verify this by using the other point
-2 = -(2)^1
-2 = -(2)
-2 = -2
So the equation is: [tex]f(x)=-2^x[/tex]
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 6 millimeters. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by less than 0.5 millimeters
Answers
The probability that the sample mean would differ from the population mean by less than 0.5 millimeters is 0.3970.
Given mean diameter of 145 millimeters, standard deviation of 6 millimeters.
We have to find out the probability that the sample mean would differ from the population mean by less than 0.5 millimeters.
μ=145 and ,σ=60 ,n=39 then
s=60/[tex]\sqrt{39}[/tex]=0.96
By finding the probability that the sample mean would differ by less than 0.5 mm equal to p value of Z when X=145+0.5=145.5 mm subtracted by the p value of Z when X==145-0.5=144.5 mm.
When X=145.5 mm
Z=(X-μ)/σ
By central limit theorem
Z=(145.5-145)/5
=0.5/0.96
=0.52
p value of 0.52=0.6985.
When X=144.5
Z=(144.5-145)/0.96
=-0.5/0.96
=-0.52
p value of -0.52=0.5-0.1985=0.3015
Required probability=0.6985-0.3015=0.3970.
Hence the probability that the sample mean would differ from the population mean by less than 0.5 mm is 0.3970.
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An island has three villages and the total number of males is 75. The first village has 20 males and 25 females. The second village has 50 people of whom 30 are males. The third village has 30 females.
Answers
There are 25 males in village 3
The number of males in the third village?The given parameters are:
Total males = 75
Male Female Total
Village 1 20 25
Village 2 30 50
Village 3 30
Total 75
The number of male in village 3 is calculated using:
Male = Total Male - Male in villages 1 and 2
So, we have:
Male = 75- (20 + 30)
Evaluate
Male = 25
Hence, there are 25 males in village 3
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Complete question
An island has three villages and the total number of males is 75. The first village has 20 males and 25 females. The second village has 50 people of whom 30 are males. The third village has 30 females.
Calculate the number of male in third village
A state health department was considering a new policy that would require all school-age children to receive the varicella (Chicken Pox) vaccine. In order to evaluate the need for such a requirement, health department epidemiologists were asked to determine the incidence of varicella in a randomly-selected fifth-grade class. During the previous school year, the class had 20 students, 5 of whom had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade. What was the incidence of varicella during the fifth grade
Answers
The incidence rate of varicella is 13 per 100 if there were 20 students and 5 of whom got vaccinated before fifth grade.
Given Total students of 100 in which 5 had varicella before entering fifth grade and 2 of whom developed varicella during fifth grade.
We have to find the incidence rate of varicella means requirement of vaccine in proportion form.
So we want the incidence rate, which is the number of people who caught the disease who were at risk to it. So we have 20 people in the class in total. But we said that five of them already had it and they were told that they are immune. So we have 15 people in the class who are at risk, then two people caught it. and so the incidence rate is going to be two divided by 15, which you can check is Not .13 recurring. And so as a percentage We just times by 100 this is going to be 13/ 100.
Hence the incidence of varicella during the fifth grade is 13/100.
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PLEASE HELP ASAP!!! Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
dot plot titled Number of Golfers for Week 1 with number line labeled Age of Golfer, 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
dot plot titled Number of Golfers for Week 2 with number line labeled Age of Golfer, 3 dots at 62, 4 dots at 63, 2 dots at 64, 1 dot at 66, 1 dot at 67, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
A) The range for Week 1 equals the range for Week 2.
B) The range for Week 1 is greater than the range for Week 2.
C) The median for Week 1 is less than the median for Week 2.
D) The mean for Week 1 is greater than the mean for Week 2.
Answers
The true statement is the range for Week 1 equals the range for Week 2.
What is the true statement?A dot plot is a graph that is used to show the frequency of a data set using dots. Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
Range of the first dot plot : 89 - 62 = 27
Range of the second dot plot : 89 - 62 = 27
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Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each restaurant owner and sets of 20 blue flyers to each clothing store owner. At the end of the day, Tayli realizes that she gave out the same number of red and blue flyers. What is the minimum number of flyers of each color she distributed?
Answers
The minimum number of flyers of each color distributed is 1.
What is the minimum flyer distributed?
In order to determine the minimum number of flyers of each color distributed, the common factor of 13 and 20 has to be determined. The factor of a number is a number that divides another number perfectly without any remainder.
Factors of 13 = 1, 13
Factors of 20 = 1, 2, 4, 5, 10, 20
Common factor = 1
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Show you work for full credit Use the SUBSITUTION method or ELIMINATION method to solve this system of equations. y = 4x and 8x + y = 18
Answers
Answer:
A. (3/2, 6)
Step-by-step explanation:
Use the substitution method:
8x + y = 18 and y = 4x
8x +4x = 18
12x = 18
x = 18/12 = 3/2
y = 4x
= 4(3/2)
= 12/2
= 6
What is DF? Help me please :)
Answers
The value of DF = 20.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given:
Using theorem
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
ΔSDF/Δ RTY = (SD/RT)= (DF/TY)= (FS/ YR)
ar ΔSDF² / ar ΔRTY² = 16/81
SD/ RT = 4/9
SD = 4x, RT= 9x
SD= 8
4x = 8
x = 2
So,
RT= 9*2 = 18
SF = RT -2
SF = 16
(SD/RT)= (FS/ YR)
8 / 18 = 16/ YR
YR= 36
TY= 9 +RY = 45
(DF/TY)= (FS/ YR)
DF / 45= 16/ 36
DF=20
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4. Write the trinomial represented by each rectangle of algebra tiles. Then, determine the
dimensions of each rectangle.
Answers
Answer:
Trinomial: [tex]\boldsymbol{\text{x}^2 + 3\text{x} - 4}[/tex]
Dimensions: [tex]\boldsymbol{\text{x}+4} \text{ by } \boldsymbol{\text{x}-1}[/tex]
=======================================================
Explanation:
The big green square is x units by x units. Its area is [tex]\text{x} * \text{x} = \text{x}^2[/tex] which represents x squared.
The long vertical green rectangles are x units tall and 1 unit across. The area of one such rectangle is x times 1 = x. Since we have four of these green rectangles, so far we have x+x+x+x = 4x in additional area.
So far the area is [tex]\text{x}^2+4\text{x}[/tex]
---------------
All of the green areas mentioned so far are positive areas so to speak.
In contrast, the red areas are negative areas. They take away from the positive. You can think of it like a bank balance.
If a single green rectangle is x square units in area, then a red rectangle is negative x or -x
So we go from 4x to 4x-x = 3x
Then we subtract off 4 due to the 4 small squares
This gives a total area of [tex]\text{x}^2 + 3\text{x} - 4[/tex] and this represents the standard form of the polynomial area. It is a trinomial since it has 3 terms.
---------------
Now onto the dimensions.
Check out the diagram below. The overall figure is x+4 units across the horizontal dimension, and x-1 units tall along the vertical dimension.
If you were to use the FOIL rule, then you would find that [tex](\text{x}+4)(\text{x}-1) = \text{x}^2 + 3\text{x} - 4[/tex] which helps show how the two forms connect to one another.
This also helps show that area = length*width which is what we'd expect from any rectangular area.
(-3x2 + x + 5) − (4x2 − 2x)
Answers
Answer:
-7x^2 + 3x + 5
Step-by-step explanation:
-3x^2 + x + 5 - 4x^2 + 2x
-1+x-8+2x
-9 + 3x
If 3x-9=0
Then x =3
The graph represents the heights of two climbers on a climbing wall over a 12-minute time period.
A graph titled The Climbing Wall where the horizontal axis shows time (minutes), numbered 1 to 12, and the vertical axis shows height (feet) numbered 2 to 24. The line labeled Brynn's climb begins at 0 feet in 0 minutes, to 15 feet from 5 to 7 minutes, to 0 feet in 10 minutes. The line labeled Abby's climb begins at 4 feet in 0 minutes, to 14 feet from 4 to 6 minutes, to 22 feet in 8 minutes, to 0 feet in 12 minutes.
Which statement is true about the climbers’ heights?
Brynn was resting at a constant climbing height when Abby’s climbing height was decreasing.
Abby’s climbing height was decreasing when Brynn’s climbing height was increasing.
The heights of both climbers increased, then decreased, with no rest at a constant height.
Both climbers rested on the wall at a constant height for 2 minutes.
Answers
Both climbers rested on the wall at a constant height for 2 minutes.
How to determine the true statement?The complete question is added as an attachment
From the attached graph, we have the following highlights
Abby's movement stopped from 4 minutes to 6 minutes i.e. 2 minutesBrynn's movement stopped from 5 minutes to 7 minutes i.e. 2 minutesThe above means that both climbers stopped for 2 minutes
Hence, the true statement about the climber's height is that (d) Both climbers rested on the wall at a constant height for 2 minutes.
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Answer: D: Both climbers rested on the wall at a constant height for 2 minutes.
Step-by-step explanation: i did the quiz edge 2022
An opinion poll survey based on a sample of ____________________ people is likely to provide the most accurate results.
Answers
An opinion poll survey based on a sample of a small section of people is likely to provide the most accurate results.
What is an opinion poll?An opinion poll, often known as a poll or survey, is a human research survey of the general public from a specific sample. By asking a series of questions and extending generalizations into ratios or confidence intervals, opinion polls are often created to represent the opinions of a population. A person who conducts polls is referred to as a pollster.
An opinion poll is a survey that samples a tiny portion of the population in an effort to forecast election outcomes or gauge popular sentiment toward various concerns.
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Please help ill appreciate it best answer gets the brainliest answer!
Answers
Answer:
Linear
Step-by-step explanation:
Notice that x values increase by 1 each row and that the y values increase by 5 each row. By definition, in linear functions, x and y values both increase by constant values. Going down each row, the y value increases by 5 as the x value increases by 1, so we know that the graph must be a linear function.
Function Type: linear
Equation: y = 5x + 7
Which question is a biased question?
(1) How old are you?
(2) What is your favorite color out of red, blue, and green?
(3) Do you prefer a beautiful sunny day or a depressing rainy day?
(4) How many siblings do you have?
Answers
Answer:
3!
Explanation:
By calling a sunny weather "beautiful" and rainy weather "depressing", you're inserting your own opinion into the question- which makes it biased!
What is the gradient of the graph shown?
Answers
Answer:
Step-by-step explanation:
Answer:
gradient= change in y intercept ÷change in x intercept
gradient=-2-0 ÷3-0
gradient=
In the monthly rate payment formula M= Pr(1+r)^n/(1+r)^n-1, what value do you give r if the interest rate is 7.3%?
Answers
Answer:
r = 0.073/12 ≈ 0.0060833...
Step-by-step explanation:
In the given amortization formula, the interest rate (r) is the rate for one payment period.
Period interest rateThe given 7.3% interest rate is presumed to be a nominal annual interest rate. Since there are 12 months in a year, the corresponding monthly interest rate is ...
7.3%/12 = 0.073/12 ≈ 0.00608333...(repeating)
The value of r that goes in this formula is 0.0608333...(repeating).
Answer:
0.61
Step-by-step explanation:
Question 9 Eight wooden spheres with radii of 3 inches are packed snuggly into a cube-shaped box 12 inches on one side. The remaining space is filled with packing beads. What is the volume occupied by the packing beads
Answers
Reason
For the sphere
We know V=4/3 TT r^3
Radius is 3
V=4/3 (3.14) 3^3
V= 4/3 (3.14) 27
V= 113.1 for each sphere
8 spheres x 113.1 = 904.8 cu.in.
For the cubed shaped box
We know v= length x width x height
V= 12 x 12 x 12
V = 1728 cu.in.
Now we take volume of box and subtract volume of spheres to get space filled by packing beads
1728 - 904.8 = 823.2 cu.in.
f(x) = (x-2)(x+1)
————-
x+1
Which statements describe the end behavior of the graph of the function shown? Check all that apply.
• As x to infinity, y to 1.
•As x to infinity, y to infinity
•As x to infinity, y to negative infinity
•As x to negative infinity, y to - 1
•As x to negative infinity, y to infinity
•As x to negative infinity, y to negative infinity
Answers
Answer:
As x to negative infinity, y to negative infinity
Step-by-step explanation:
A six sided die is rolled three times. Find the probability that the result is an even number for every roll.
A. 1/9
B. 3/8
C. 1/3
D. 1/8
Answers
[tex]|\Omega|=6^3\\|A|=3^3\\\\P(A)=\dfrac{3^3}{6^3}=\left(\dfrac{3}{6}\right)^3=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}=12.5\%[/tex]
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
Solve the equation for x.
2
3
x −1
9
x + 5 = 20
x =
Answers
The number of hours it will take Brigid to fill 5 bushels of strawberries is; 5³/₅ hours
How to simplify algebraic equations?
We are told that the scenario that Brigid represents is;
⁵/₈x + 1¹/₂ = 5
where x is is the number of hours she picks
Now, let us solve for x by converting the mixed fraction to improper fraction to get;
⁵/₈x + ³/₂ = 5
Multiply through by 8 to get;
5x + 12 = 40
Subtract 12 from both sides to get;
5x = 28
x = 28/5
x = 5³/₅ hours
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1.You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
2. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
3.After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
SHOW ALL WORK!!!!
Answers
When you win 25% of the time based on the probability, this illustrates that the number of products picked will be 7 products.
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
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[tex]\sqrt(1-2)+\sqrt(1+2)\\[/tex]
Answers
please help me!!
20 points
Answers
Answer:
182 [tex]yd^{2}[/tex]
Step-by-step explanation:
Area of a parallelogram: bh
bh
= 13(14)
= 182 sq. yds
Figure A Figure B 3 ft 10 ft 2 ft 4 ft V= 120 cu ft Find the volume of Figure B.
Answers
The volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
As we have given the volume of the larger cube is 120
Let v is the volume of the small shape.
[tex]\rm \dfrac{120}{v} =\left( \dfrac{4}{2} \right)^3[/tex]
After simplifying:
v = 120/8 cubic ft
or
v = 1.5 cubic ft
Thus, the volume of the small figure is v = 120/8 cubic ft or v = 1.5 cubic ft if the volume of the larger cube is 120.
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