$129 x .80 = $103.20 (80% discount)
$129 (original price) - $103.20 ( 80% discounted amount) = $25.80 (sale price)
Answer: The sale price is $25.80
You want to buy something that costs $129, and it's on sale for 80% off. What is the item's sale price?
First, convert the 80% to a real mathematical number. For percent's, this is always done by dividing the 80% by 100%, or 80% / 100% = 0.800.
Second, find out what 80% of $129 is. This is the amount of the sale discount. This is always found by multiplying 0.800 by the item's cost $129, like this:
0.800 x $129 = $103.20.
So for this sale, you'll save $103.20 on this item.
This means, the cost of the item to you is
$129 - $103.20 = $25.80.
Before Price: $129.00
Discount %: 80%
Answer =====> Sale Price: $25.80 would be the sale price of the bicycle.
Amount Saved: $103.20
Alternatively, you can think about it this way.
The item is 80% off. This means you'll pay 20.000% of the total cost (100% - 80% = 20.000%).
Now what's 20.000% of the total cost?
0.200 x $129 = $25.80.
Just like the result above, the sale price on the item is $25.80.
Hope that helps!!!!!! : )
Adam has been asked to post a parcel for a family member. He has been told that the parcel weighs 12lbs 8oz. How much does the parcel weigh to the nearest whole kilogram
Answer is 6 kg:
Given that Adam was asked to post a parcel. The weight of the parcel was 12 lbs and 8 oz.
To convert the weight in kgs:
Let us convert oz into pounds first to make it uniform.
We have 16 0z. = 1 lb
Hence 8 oz. = 8/16 = 0.5 lbs
Weight of the parcel = 12.5 lbs.
We have the converting factor as
2.2 pounds make 1 kg.
Hence 12.5 pounds = 12.5/2.2 = 5.6818
So weight of the parcel in kg= 6. (after rounding off)
On a number line, the distance from zero to -9 is 9 units.
Which equation demonstrates this concept?
A.
0 + 9 = 9
B.
|-9| = -9
C.
|-9| = 9
D.
92 = 81
Answer:
C. |-9| = 9
Step-by-step explanation:
Distance is always non-negative. Distances in a negative direction are made positive by the use of the absolute value function. The distance from 0 to -9 is one such distance.
You want to estimate the mean weight loss of people one year after using a popular weight-loss program being advertised on TV. How many people on that program must be surveyed if we want to be 95% confident that the sample mean weight loss is within 0.25 lb of the true population mean? Assume that the population standard deviation is known to be 10.6 lb.
Answer:
At least 6907 people.
Step-by-step explanation:
Population std deviation = sigma= 10.6
Since population std deviation is known, we can use normal probability table to get sample size from confidence interval.
The sample mean weight loss is within 0.25 lb of the true population mean.
Hence margin of error < 0.25
Margin of error = z critical (std dev/n) where n = sample size
Z critical for 95% = 1.96
Hence 0.25 >1.96(10.6)/sq rt n
Simplify to get
sq rt n > 1.96(10.6)/0.25 = 83.104
Square both the sides to get
n > 83.104 square = 6906.27
i.e. sample size should be atleast 6907.
Find the Area and Perimeter!
Area of a triangle is 1/2 x base x height.
base = 12
Height = x+6
Area = 1/2 * 12 * x+6
Area = 1/2 * 12x * 72
Area = 6x + 36
Perimeter is the sum of the 3 sides:
x-7 + 12 + 2x+5
3x -2 + 12
3x+10
The last choice is the correct answer.
Each section of a race is 2/5 mile.the race has 44 sections.which expression tells how many miles long the entire race is?
answer is equal to 2X44/5mile=17.6mile
Each section of a race is 25 mile.
The race has 4 sections.
Which expression tells how many miles long the entire race is?
Answer:
4×2/5
please help meeeeeee. image attached
The midpoint between -4 and 8 is answer B) 2
Marissa is an event organizer for a charity group. She is organizing a five-hour dinner event being held to raise funds for the charity. The following list shows the costs for hosting the event. Facility Rental: $150 per hour of event Linens: $2 per attendee Food: $20 per attendee Table Decorations: $3 per attendee Musical Entertainment: $1,800 (flat fee) Cleaning Fee: $250 (flat fee) The total cost of the event, with n attendees, is represented by the given expression. Which statement best describes the constant in this expression?
A constant is a number that stays the same no matter what any outside variables are. In this case, the variables are the number of hours of the event and the number of attendees. However, it states in the problem that the event will be 5 hours so that becomes known; the only thing that might change is the number of attendees so you can eliminate any cost that will be affected by that. You are left with Facility Rental, Musical Entertainment, and Cleaning Fee. Furthermore, you can be sure that Musical Entertainment and Cleaning Fee must be included in the constant because they are described as "flat rates", which means they do not change.
The answer is D) It is the total cost for entertainment, facility rental, and cleaning.
Hope this helps!
The statement that best describes the constant in the expression
25n + 2,800 is:
It is the cost per person for food, linens, and food decorations.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Facility Rental = $150 per hour of the event
Linens = $2 per attendee
Food = $20 per attendee
Table Decorations = $3 per attendee
Musical Entertainment = $1,800
Cleaning Fee = $250
The total cost of the event.
= 25n + 2,800
Where n is the number of attendees.
Now,
25 is the total cost per attendee for food, linens, and table decorations.
Thus,
The constant in the expression is 25 which is the cost per attendee for food, linens, and table decorations.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ3
Mary has two bags of sweets, each of which contains the same number of sweets. She eats four sweets. She then finds that she has 30 sweets left. How many sweets were in each bag to start with?
Given that Mary has 2 bags of sweets. each of which contains same number of sweets.
Let us assume each bag contains x number of sweets.
After eating 4 sweets, total number of sweets left in two bags = x+x-4=2x-4
But given 2x-4 = 30
2x-4+4 = 30+4
2x=34
[tex]x=\frac{34}{2} = 17[/tex]
Hence there are 17 sweets in each bag at starting.
Mary had two bags with an equal number of sweets. After eating 4 sweets, she had 30 left, which means each bag originally contained 17 sweets.
To solve the problem of determining how many sweets were in each bag to start with, we must consider that Mary had two bags with an equal number of sweets and ended up with 30 sweets after eating 4 sweets. We can represent the initial number of sweets in each bag as 'x'. So the equation for the total number of sweets after she eats 4 is 2x - 4 = 30.
Let's solve this equation step by step:
Add 4 to both sides: 2x = 30 + 4
Simplify: 2x = 34
Divide both sides by 2 to solve for x: x = 34 / 2
Therefore, x = 17
This means that initially, there were 17 sweets in each bag.
Which values of P and Q result in an equation with exactly one solution? Px+Q=-19x+18Px+Q=?19x+18
Answer: P = -19, Q = 18
Step-by-step explanation:
Px + Q = -19x + 18
Px = -19x Q = 18
÷x ÷x
P = -19
Which of the following fractions is equivalent to -84/-90 in the least common terms?
14/15
(-)14/15
42/45
(-)42/45
The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.
To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:
-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15
Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.
Tell the numbers that are odd and prime 2,14,23,24,25,31,45
Odd numbers are those numbers that gives a fraction when divided by 2
Prime numbers are those that can be divided only by 1 and the number itself.
Odd numbers are therefore : 23, 25, 31 and 45
Prime numbers are therefore: 2, 23 and 31
Browning, montana, holds the u.S record for the greatest temperature drop in one day. On january 23, 1916, the temperature changed by an average of -4.17°f per hour. To the nearest degree, what was the total temperature change after 24 hours?
Answer:
Total temperature change 104.25 f.
Step-by-step explanation:
Average temperature change is calculated by dividing total temperature change by the total hours it took for the change.
We have been given the average temperature change.
We have to multiply average temperature change by the total number of hours it took for the temperature to change we get the total temperature change.
⇒ Total temperature change = Average temperature change * total hours
= [tex]-4.17*25[/tex]
=104.25 f
A recipe includes 6 cups of flour and three fourths cup of butter butter. Write the ratio of the amount of flour to the amount of butter butter as a fraction in simplest form.
To express the ratio of flour to butter from a recipe as a fraction in simplest form, start by setting it up as a fraction and then multiply by the reciprocal of the denominator. In this case, a recipe with 6 cups of flour and three-fourths cup of butter simplifies to a ratio of 8:1.
Explanation:To find the ratio of the amount of flour to the amount of butter as a fraction in simplest form, we start by writing the amounts given in the recipe as a fraction. There are 6 cups of flour and three-fourths (3/4) cup of butter. The initial ratio is therefore:
6 cups of flour / (3/4) cup of butter
To simplify, we can multiply both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) by the reciprocal of the denominator:
6 / (3/4) = 6 × (4/3) = 24/3 = 8
So, the simplest form of the ratio of flour to butter is 8:1.
what is the base 8 representation of the number 11100111(2)
A) 231(8)
B) 329(8)
C) 347(8)
D) 385(8)
Remark
You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.
Step One
Write the base 2 number in groups of 3 starting from the right and going left
11 100 111
Step Two
Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7
11 = 2*1 + 1 = 2 + 1 = 3
100 = 1*2^2 = 4
111 = 1*2^2 + 1*2 + 1 = 7
Step Three
Read the answer going down.
347 is the answer
Answer
347(8) = C
Answer:
Option C)347(8) is correct. Below is the explanation for changing the base 2 number to the base 8
Step-by-step explanation:
Given:
11100111(2)
To find:
Number with base 8.
Let's convert the given base 2 number to a base 10 number or an integer. Then convert it to a base 8 number.
11100111(2) = 1* [tex]2^{7}[/tex]+1* [tex]2^{6}[/tex]+1*[tex]2^{5}[/tex] + 0*[tex]2^{4}[/tex] +0*[tex]2^{3}[/tex] +1* [tex]2^{2}[/tex]+1*[tex]2^{1}[/tex] +1*[tex]2^{0}[/tex]
Simplify it
=128 +64+32 +0+0+4+1+1
=231
Now, change this integer 231 to a base 8 number ( I have attached a file for this)
We get an answer of 347(8). Option C is correct!
You can learn more:
https://brainly.com/question/11454182.
Alexis received an 85 89 and 92 and three test how many points does she need to score on your next test in order to have an average of at least 90
Lets say Alexis received 85, 89, 92, and x points in her four tests.
Average of a data set or the mean of a data set, we need to add all the values together and divide by the number of values in the set.
So here 85, 89, 92, and x are the values of the data set and the number of values are 4 (since there are 4 tests).
[tex]Avg=\frac{sum}{n}[/tex]
where 'n' represents the number of values and sum represents the total sum of the values.
Here we need to know how much Alexis need to score in her next test so that she can have an average of 90.
So we know the value of average that is 90.
Now,
[tex]90 = \frac{85+89+92+x}{4}[/tex]
Solving for 'x' we get:
[tex]90=\frac{266+x}{4}[/tex]
[tex]266+x=90 \times 4[/tex]
[tex]266+x=360[/tex]
Therefore,
[tex]x=360-266=94[/tex]
So, Alexis need to score at least 94 on her next test in order to have an average of at least 90.
A math teacher gave her students two tests. On the first test, 80% of the class passed the test, but only 30% of the class passed both tests.
What is the probability that a student passes the second test, given that they passed the first one?
0.256
0.375
0.500
0.625
Answer:
0.375 is answer
Step-by-step explanation:
Given that the math teacher gave her students two tests. On the first test, 80% of the class passed the test. But only 30% of the class passed both tests.
Let A - the students pass I test
B = students pass second test
Then P(A) = 80%=0.8 and P(AB) = 30% =0.30
Required probability =probability that a student passes the second test, given that they passed the first one
= P(B/A) = P(AB)/P(A)
= 0.30/0.80
=3/8
=0.375
Right answer is 0.375
The probability that a student passes the second test, given that they passed the first one, is 0.375.
The subject of this question is Mathematics, specifically focusing on the concept of conditional probability. The question asks about the probability that a student passes the second test, given that they passed the first one. Given that 80% of the class passed the first test and 30% passed both tests, we can use the formula for conditional probability P(B|A) = P(A and B) / P(A). Here, A represents passing the first test, and B represents passing the second test.
P(B|A) = P(A and B) / P(A) = 0.30 / 0.80 = 0.375.
Therefore, the probability that a student passes the second test, given that they passed the first one is 0.375.
During 712 months of hibernation, a black bear experienced a weight loss of 64.4 pounds. On average, what was the bear's weight change per month? Round to the nearest tenth. Enter your answer in the box.
Final answer:
To calculate the average monthly weight loss of the black bear, divide the total weight loss by the number of hibernation months. The bear lost 0.1 pound per month during its 712 months of hibernation.
Explanation:
To find the average weight loss per month of the black bear, you need to divide the total weight loss by the number of months of hibernation. The black bear lost 64.4 pounds over 712 months.
First, we write out the calculation needed:
64.4 pounds ÷ 712 months.
When you perform the division, you get approximately 0.0904494382 pounds per month. Rounding to the nearest tenth gives us 0.1 pounds per month.
Therefore, the bear experienced an average weight change of 0.1 pound per month during hibernation.
Factor the expression completely over the complex numbers.
x3−4x2+4x−16
Enter your answer in the box.
Answer:
The factor form of given expression is (x-4)(x-2i)(x+2i).
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+4x-16[/tex]
It can be written as
[tex]f(x)=x^3-4x^2+4x-16[/tex]
According to the rational root theorem, all possible rational roots are in the form of
[tex]\frac{a_0}{a_n}[/tex]
Where, a₀ is constant term and [tex]a_n[/tex] is leading coefficient.
[tex]f(4)=4^3-4(4)^2+4(4)-16=0[/tex]
Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.
Use synthetic method to find the remaining factors.
[tex](x^3-4x^2+4x-16)=(x-4)(x^2+4)[/tex]
[tex](x^3-4x^2+4x-16)=(x-4)(x^2-(2i)^2)[/tex]
[tex](x^3-4x^2+4x-16)=(x-4)(x-2i)(x+2i)[/tex]
Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).
Answer:
(x-4) (x-2i) (x+2i)
Step-by-step explanation:
x^3−4x^2+4x−16
I will factor by grouping
x^3−4x^2+ 4x−16
The first group is the first 2 terms. I can factor out an x^2
x^2 (x-4) + 4x-16
The second group I can factor out a 4
x^2 (x-4) + 4(x-4)
Now I can factor out (x-4)
(x-4) (x^2 +4)
We know that x^2 + 4 factors into +2i and -2i because
(a^2 -b^2) = (a-b) (a+b) but we have (a^2 + b^2) = (a-bi) (a+bi)
(x-4) (x-2i) (x+2i)
-7-(-6)-(-5) using keep, flip, change method
help me pleaseeeee. picture attached.
The answer is B (-6,5) becuase C is located at (-3,4). -3 - 3 is -6... and 4 + 1 is 5
The miniature golf scores for 7 friends are 23, 30, 39, 32, 35, 14, and 23. What is the mean golf score for this group of friends?
a.25
b.30
c.28
d.23
A small company plans to invest in a new advertising campaign. There is a 20% chance that the company will lose $5,000, a 50% chance of a break even, and a 30% chance of a $10,000 profit. Based ONLY on this information, what should the company do? A) The expected value is $2,000.00, so the company should proceed with the campaign. B) The expected value is $4,000.00, so the company should proceed with the campaign. C) The expected value is −$2,000.00, so the company should not proceed with the campaign. D) The expected value is −$3,000.00, so the company should not proceed with the campaign.
A small company plans to invest in a new advertising campaign.
There is a 20% chance that the company will lose $5,000 ,
50% chance of a break even, and a 30% chance of a $10,000 profit
So the expected value from the advertisement campaign is calculated as - 20% of 5000 + 0% of 5000 + 30% of 10,000
= -1000 + 0 + 3000
= 2000
The expected value from the advertisement campaign is $2000.
So the Company must go ahead with the campaign.
Answer : Option A
Hope it helps.
Thank you ..!!
Solve each system using a matrix
4x-12y=-1
6x+4y=4
1 1 | 4
-2 -5 -11
ANSWER
[tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]
EXPLANATION
Given;
[tex]4x-12y=1[/tex]
and
[tex]6x+4y=4[/tex]
The augmented matrix of the two linear equation is given by;
[tex]\left[\begin{array}{ccc}4&-12|&-1\\6\:&\:\:\:4|&4\end{array}\right][/tex]
We now perform row operations;
[tex]\frac{1}{4}\times R_1 \rightarrow R_1 [/tex].
This gives us
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\6\:&\:\:\:4|&4\end{array}\right][/tex]
[tex]R_2-6R_1 \rightarrow R_2[/tex]
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:22|&\frac{11}{2}\end{array}\right][/tex]
[tex]\frac{1}{22}R _2 \rightarrow R_2[/tex]
[tex]\left[\begin{array}{ccc}1&-3|&\frac{-1}{4}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]
[tex]R_1+3R_2 \rightarrow R_1[/tex]
[tex]\left[\begin{array}{ccc}1&0|&\frac{1}{2}\\0\:&\:\:\:1|&\frac{1}{4}\end{array}\right][/tex]
Hence [tex]x=\frac{1}{2}[/tex] and [tex]y=\frac{1}{4}[/tex]
Which ordered pair makes both inequalities true?
y > –3x + 3
y > 2x – 2
(1,0)
(–1,1)
(2,2)
(0,3)
Answer:
All options are wrong.
Step-by-step explanation:
We have y > –3x + 3 and y > 2x – 2
Option A - (1,0)
y > –3 x 1 + 3 = 0
We have y = 0, which is not greater than 0.
Option A is not correct.
Option B - (–1,1)
y > –3 x -1 + 3 = 6
We have y = 1, which is not greater than 6.
Option B is not correct.
Option C - (2,2)
y > –3 x 2 + 3 = -3
We have y = 2, which is greater than -3.
y > 2 x 2 – 2 = 2
We have y = 2, which is not greater than 2.
Option C is not correct.
Option D - (0,3)
y > –3 x 0 + 3 = 3
We have y = 3, which is not greater than 3.
Option D is not correct.
All options are wrong.
F the quadratic formula is used to solve 2x 2 = 8x - 3, what are the solutions?
x = 2 ± [tex]\frac{1}{2}[/tex]√10
express the equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )
then x = ( - b ±√( b² - 4ac) ) / 2a
given 2x² = 8x - 3, then
2x² - 8x + 3 = 0 ( in standard form )
with a = 2, b = - 8, c = 3
x = (8 ±√(64 - 24) )/4 = (8 ±√40) / 4 = (8 ± 2√10) / 4
x = 2 ± [tex]\frac{1}{2}[/tex]√10
Airbags are manufactured by Aces (A), Best (B), and Cool (C) at rates of 57%, 26% and 17%, respectively. Airbags occasionally kill (K) passengers when they deploy in accidents. Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively. One airbag is randomly selected for testing.
If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool. (Round to the nearest ten-thousandth.)
Air bag manufactured by Aces(A)=57%
So, Probability [tex]P(A)=\frac{57}{100}[/tex]
Air bag manufactured by Best (B) =26%
So, Probability [tex]P(B)=\frac{26}{100}[/tex]
Airbag manufactured by Cool(C)=17%
So, Probability [tex]P(C)=\frac{17}{100}[/tex]
Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.
Let K be the event which kill people.
Probability of Air bag made by A which kill people [tex]P(K/A)=\frac{1}{100}[/tex]
Probability of Air bag made by B which kill people [tex]P(K/B)=\frac{4}{100}[/tex]
Probability of Air bag made by C which kill people [tex]P(K/A)=\frac{13}{100}[/tex]
If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool
Using Baye's theorem:
[tex]P(C/K)=\frac{P(K/C)P(C)}{P(K/A)P(A)+P(K/B)P(B)+P(K/C)P(C)}[/tex]
Substitute the values of probabilities into formula
We get,
[tex]P(C/K)=\frac{0.17\times 0.13}{0.57\times 0.01+0.26\times 0.04+0.17\times 0.13}[/tex]
Now we calculate it and get probability
So, [tex]P(C/K)=0.5785[/tex]
So, 57.85% of passenger kills if the airbag was manufactured by Cool.
How is the divisibility rule for 7 more complicated then the rules for 2,3,5 and 10?
Final answer:
The divisibility rule for 7 is more complex than the rules for 2, 3, 5, and 10 due to the lack of a simple pattern or quick digit check, requiring multiple steps and manipulations of the number.
Explanation:
The divisibility rule for 7 is more complicated than the rules for 2, 3, 5, and 10 because it does not follow a simple pattern or involve a quick check of a number's last digit or sum. The rules for divisibility by 2, 3, 5, and 10 are straightforward: a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, by 5 if its last digit is 0 or 5, and by 10 if it ends in 0.
The rule for divisibility by 7 requires more steps and cannot be easily performed in one's head. The process typically involves subtracting or adding multiples of 7 from different segments of the number, which often makes it more difficult for students to use effectively without practice or further understanding of the method. Complicated rules for divisibility by 7 prove the point that while mathematical rules are universally valid, some rules are inherently more complex than others.
Ming took a cab across town. His fare was \$22$22dollar sign, 22, and he leaves an 18\%18%18, percent tip.
Answer:
$25.96
Step-by-step explanation:
We have been given that Ming took a cab across town. His fare was $22, and he leaves an 18% tip.
To find the total amount by Ming for cab ride will be equal to 22 plus 18% of 22.
[tex]\text{Total amount paid by Ming for the cab ride}=22+(\frac{18}{100}*22)[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=22+(0.18*22)[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=22+3.96[/tex]
[tex]\text{Total amount paid by Ming for the cab ride}=25.96[/tex]
Therefore, Ming paid a total amount of $25.96 to the cab driver.
@pinkfloyd @taskmasters PLEASE HELP IM STUCK ONE QUESTION??/
Use the figure to answer the question that follows:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
When written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
Statements Reasons
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
I m∠SQT = 180° Definition of a Straight Angle
II m∠SQV + m∠VQT = 180° Substitution Property of Equality
III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency
Which is the most logical order of statements and reasons I, II, and III to complete the proof?
The correct logical order for the statements I, II, and III in the proof is: I. Definition of a Straight Angle, III. Angle Addition Postulate, and II. Substitution Property of Equality. This order supports the conclusion that corresponding angles, created by the transversal intersecting parallel lines, are congruent.
To complete the two-column proof that demonstrates the congruence of the corresponding angles when segments UV and WZ are parallel and line ST intersects both at points Q and R respectively, we need to place statements and reasons I, II, and III in the most logical order. This should allow us to show
corresponding angles are congruent, which is the ultimate aim of the proof.
The correct order of statements and reasons to complete the proof is:
Definition of a Straight Angle (I): We know that the angle measure of a straight line is 180°, hence m∠SQT = 180°.
Angle Addition Postulate (III): Based on the postulate, we can express m∠SQV + m∠VQT as equal to the measure of angle SQT because the two angles combine to form the straight angle, therefore m∠SQV + m∠VQT = m∠SQT.
Substitution Property of Equality (II): By substituting the equal values established in statements I and III, we get m∠SQV + m∠VQT = 180°.
After arranging the statements and their corresponding reasons, the proof logically demonstrates that the congruent angle pairs are a result of transversal ST intersecting parallel lines UV and WZ.
if a1 = 8 and an =an-1-3 then find the value of a5
Answer:
[tex]a_5=-4[/tex]
Step-by-step explanation:
[tex]a_n=a_{n-1}-3\\\\a_1=8\\\\a_2=a_1-3\to a_2=8-3=5\\\\a_3=a_2-3\to a_3=5-3=2\\\\a_4=a_3-3\to a_4=2-3=-1\\\\a_5=a_4-3\to a_5=-1-3=-4[/tex]
To find the value of a5, we subtract 3 repeatedly from the previous value starting with a1=8. After iterating this process four times, we find that a5 equals -4.
The sequence given is defined by a1 = 8 and an = an-1 - 3. To find a5, we need to apply the formula recursively starting from a1:
a2 = a1 - 3 = 8 - 3 = 5
a3 = a2 - 3 = 5 - 3 = 2
a4 = a3 - 3 = 2 - 3 = -1
a5 = a4 - 3 = -1 - 3 = -4
So, the value of a5 is -4.