The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If v_1, ......, v_4 are in R^4 and v_3 = 2v_1 + v_2, then {v_1, v_2, v_3, v_4} is linearly dependent. Choose the correct choice below and, if necessary, fill in the answer boxes to complete your choice. a. True Because v_3 = 2v_1 +v_2, v_4 must be the zero vector. Thus, the set of vectors is linearly dependent. b. True. The vector v_3 is a linear combination of v_1 and v_2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. c. True. If c_1 =2, c_2 = 1, c_3 = 1, and c_4 = 0, then c_1v_1 + middot middot middot + c_4v_4 =0. The set of vectors is linearly dependent. d. False. If v_1 =, v_2 =, v_3 =, and v_4 = [1 2 1 2], then v_3 = 2v_1 + v_2 and {v_1, v_2, v_3, v_4} is linearly independent.
Answers
Answer: The correct option is (B).
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
Step-by-step explanation:
Given that;
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
Lets {V₁, V₂, V₃, V₄} are linearly dependent
Then there exist a scalars C₁, C₂, C₃, C₄
So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Take C₃ ≠ 0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂ and V₄}
that is
Given V₃ = 2V₁ + V₂
⇒ 2V₁ + V₂ - V₃ = 0
⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
So that {V₁, V₂, V₃, V₄} is linearly dependent.
therefore option B id the right answer.
- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
B is the correct option. True, The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and the set is linearly dependent.
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
What is meant by linearly dependent?A set of vectors is linearly dependent if some vector can be expressed as a linear combination of the others.
Let's consider {V₁, V₂, V₃, V₄} are linearly dependent
then there exist a scalars C₁, C₂, C₃, C₄
therefore, C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Lets C₃ ≠ 0 then we will get
V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂, and V₄
which means V₃ = 2V₁ + V₂
2V₁ + V₂ - V₃ = 0
2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
therefore, {V₁, V₂, V₃, V₄} is linearly dependent.
So, option B is correct here.
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others, and the set is linearly dependent.
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Related Questions
Read paragraphs 4-5 from the passage.
(4) Springing to my feet I received my first Martian surprise, for the effort, which on Earth would have brought me standing upright, carried me into the Martian
air to the height of about three yards. I alighted softly upon the ground, however, without appreciable shock or jar. Now commenced a series of evolutions
which even then seemed ludicrous in the extreme. I found that I must learn to walk all over again, as the muscular exertion which carried me easily and safely
upon Earth played strange antics with me upon Mars.
(5) Instead of progressing in a sane and dignified manner, my attempts to walk resulted in a variety of hops which took me clear of the ground a couple of feet
at each step and landed me sprawling upon my face or back at the end of each second or third hop. My muscles, perfectly attuned and accustomed to the
force of gravity on Earth, played the mischief with me in attempting for the first time to cope with the lesser gravitation and lower air pressure on Mars.
How do the underlined words help establish a sense of place and circumstance?
A. They suggest that the narrator is clumsy and careless, making him unable to explore Mars because he is unable to walk properly.
B. They demonstrate how frustrated the narrator is becoming due to his inability to stay on the ground without gravity.
C. They create vivid imagery, which reinforces that the narrator has landed somewhere that is extremely different from Earth.
D. They help establish a mood of joy and lightness as the narrator begins to enjoy the weightlessness of being on Mars.
Answers
Answer: C
Step-by-step explanation:
I recognize this as coming from an old 1912 novel published as "A Princess of Mars", by Edgar Rice Burroughs. I read the book as a teenage boy. A 2012 movie, called "John Carter", was based on this same book.
Answer A - No, because the character (Carter) says, "My muscles, perfectly attuned and accustomed to the force of gravity on Earth". Perfectly attuned is an athlete, not a clumsy person.
Answer B - No, because the character just doesn't sound all that frustrated. The experience is strange and inconvenient, yet he is handling his emotions pretty well for how weird it must be. It is more like he is writing about an amazing experience, not just complaining.
Answer D - No, because he never says that the experience was making him happy. He does not say that he was laughing or smiling or that it reminded him of some pleasant time he had as a boy.
Answer C - Yes. - Creation of vivid imagery. In a novel, the author must paint pictures with their words. Part of how the author does this is by giving you the picture of a man who feels very comfortable with his coordination on Earth, but keeps winding up about 9 feet off the ground without trying. He doesn't just "I kept falling". He tells you in vivid detail - "... landed me sprawling on my face or back ..."
Hope this helps!
A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $5, 0.3 for $25, 0.2 for $50, and 0.004 for $75. What
are the odds that the ticket is worth at least $25?
Answers
Answer:
0.7
Step-by-step explanation:
Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7
We saw that about 34% of
all students received at least one referral. Suppose we have concerns about the number of
disciplines in one particular school - it seems very high, and we've had concerns from parents at the school. In one particular year, 162 out of the 340 students at that school had a referral.
a. If we selected a random sample of 340 students, would the sample proportion that are
disciplined be approximately normally distributed? Why or why not?
b.
Use the normal distribution to find the probability of randomly selecting a sample of 340
students and finding that 162 of them or more have received a referral during that
particular year.
C. Would we think that is unusual? Explain your reasoning.
Answers
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
what is probability ?It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.
given
The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.
Calculating the sample proportion is necessary:
The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:
P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031
Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:
\(z = (0.476 - 0.34) / 0.031 = 4.39\)
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
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7x + 4y = 2
7x + 2y = 8
Answers
Answer:
x = 2 , y = − 3
Step-by-step explanation
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form: ( 2 , − 3 )
Equation Form: x = 2 , y = − 3
What is the probability of rolling two 6’s in a row on a dice?
Answers
Each die has 6 sides, and there are 2 dice, each having 1 side with a 6. Therefore, the chance is 2/12, which is 1666666667%, which rounds to 17%.
The National Assessment of Educational Progress interviewed a random sample of 1917 people 21 to 25 years old. The sample contained 840 men, of whom 775 were fully employed. Of the 1077 women 680 were fully employed. Is there sufficient evidence to support the claim that the employment levels for men compared to woman were different
Answers
Answer:
\(z=\frac{0.923-0.631}{\sqrt{0.759(1-0.759)(\frac{1}{840}+\frac{1}{1077})}}=14.83\)
The p value for this case would be:
\(p_v =2*P(Z>14.83)\approx 0\)
For this case the p value is very low so we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of employment levels for men compared to woman were different
Step-by-step explanation:
Information given
\(X_{1}=775\) represent the number of people fully employed men
\(X_{2}=680\) represent the number of people fully employed women
\(n_{1}=840\) sample 1 selected
\(n_{2}=1077\) sample 2 selected
\(p_{1}=\frac{775}{840}=0.923\) represent the proportion estimated for male employed
\(p_{2}=\frac{680}{1077}=0.631\) represent the proportion estimated for women employed
\(\hat p\) represent the pooled estimate of p
z would represent the statistic
\(p_v\) represent the value for the test
System of hypothesis
We want to test the claim that the employment levels for men compared to woman were different, the system of hypothesis would be:
Null hypothesis:\(p_{1} = p_{2}\)
Alternative hypothesis:\(p_{1} \neq p_{2}\)
For this case the statistic is given by:
\(z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}\) (1)
Where \(\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{775+680}{840+1077}=0.759\)
Replacing the info given we got:
\(z=\frac{0.923-0.631}{\sqrt{0.759(1-0.759)(\frac{1}{840}+\frac{1}{1077})}}=14.83\)
The p value for this case would be:
\(p_v =2*P(Z>14.83)\approx 0\)
For this case the p value is very low so we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of employment levels for men compared to woman were different.
17.
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) Compute P(all four are red).
(b) Compute P(exactly two are red and exactly two are green).
(c) Compute P(exactly two are red or exactly two are green).
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
Answers
A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answers
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
70+20=90
90+20=110
110+20=130
so i have 1,521,588 poker chips how much do i need to get 2 million (poker chips on a game called pokerstars vr)
Answers
Answer: 478,412
Step-by-step explanation:
In order to do this just take 2 million and subtract the number of chips you wanted to take away. For example, it'd be 2,000,00 - 1,521,588 which leaves you with 478,412.
Jun-seo notices that there are 13 right-handed players on his baseball team and 2left-handed players.
What is the ratio of right-handed players to left-handed players?
Answers
Step-by-step explanation:
ratio of the right handed to left handed is 13 to 2
PLSSS HELP ME 14 POINTS
Answers
The transformation of f(x) to g(x) is :
Vertically compressed by a factor of 9Shifted down by 2 Describing the transformation of the functionsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = x
g(x) = 1/9x - 2
The graph of the functions f(x) and g(x) are added as an attachment
And we have the transformations to be:
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Kacie has a bag of
pretzels. She eats 1/3 of
the bag and gives 1/2 of
the bag to her brother.
How much of the bag
does she have left?
Answers
Answer: .
Step-by-step explanation:
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-unit production run in the following situations.
(a) The process standard deviation is 0.25, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.75 or greater than 10.25 ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number.
Probability of a defect:
Number of defects:
Answers
The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.
To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.
First, we need to standardize the weight limits as follows -
\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4
\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4
Next, we will find the area under the standard normal curve that lies outside of these limits as follows -
P(Defect) = P(Z < -4) + P(Z > 4)
Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x \(10^{-5}\) and P(Z > 4) = 2.8665 x \(10^{-5}\) .
So, the total probability of a defect is -
P(Defect) = 2.8665 x \(10^{-5}\) + 2.8665 x \(10^{-5}\) = 5.7330 x \(10^{-5}\)
Finally, we will find the number of defects for a 1,000-unit production run as follows -
The number of defects = 1000 * 5.7330 x \(10^{-5}\) = 5.73 (rounded to the nearest whole number).
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3x + 2y - x + 3x - y^2
please explain
100 POINTS
Answers
Answer:
-y^2 +2y + 5x
Step-by-step explanation:
add/subtract the numbers with the same letters
3x -x + 3x = +5x
2y
-y^2
-y^2 +2y + 5x
Answer:
7x + 2y - y^2.
Step-by-step explanation:
I guess you want to simplify this expression.
3x + 2y - x + 3x - y^2
First bring like terms together:
= 3x + 3x - x + 2y - y^2
= 6x - x + 2y - y^2
= 5x + 2y - y^2.
A car travels 125 miles in 2 hours. At the same rate, how far would it travel in 5 hours?
Answers
Answer: 312.5 miles
Step-by-step explanation:
125/2 = 62.5 per hour x 5 hours = 312.5 miles
Use proportional reasoning to determine the value of a in the proportion shown below.
25
a=1
a=25
a=10
a=15
it’s c
Answers
Answer:
c
Step-by-step explanation:
Look at the picture and solve it guys!!!!!! Right answers only!
Answers
Answer:x=7,1
Step-by-step explanation:
A cell phone company is considering using a new manufacturer to produce batteries for their phones. The company distributes a random sample of cell phones with the new batteries to 13 of their employees to record how long the battery will last with typical usage. The length of time each battery lasts is recorded (in hours) in the set below.
{32.3, 28.8, 29.1, 29.5, 30.8, 31.0, 17.5, 34.5, 23.5, 33.0, 31.7, 28.6, 27.4}
On a blank sheet of paper, find the following information. You may use a calculator, and you may discuss this assignment with your classmates, but you must show all your work (including any formulas or calculations you use), and the work must be your own. Be neat and clearly mark your answer.
1. The range.
2. The mean.
3. The median.
4.Q1 and Q3.
5. The IQR.
6. The variance.
7. The standard deviation.
8. Identify any outliers.
Answers
Answer:
1. The range = 17
2. The mean = 29.053846153846
3. The median = 29.5
4.i) Q1 = 28
ii) Q3 = 32
5. The IQR = 4
6. The variance = 19.7626923
7. The standard deviation = 4.445524975
8. Identify any outliers = 17.5
Step-by-step explanation:
We are given this random samples of data
{32.3, 28.8, 29.1, 29.5, 30.8, 31.0, 17.5, 34.5, 23.5, 33.0, 31.7, 28.6, 27.4}
First step before solving any of the question is we rearrange the numbers from lowest to highest
17.5, 23.5, 27.4, 28.6, 28.8, 29.1, 29.5, 30.8, 31.0, 31.7, 32.3, 33.0, 34.5
1. The range
This is the difference between the Maximum value and the Minimum value in a given data set.
Maximum value = 34.5
Minimum value = 17.5
Range = 34.5 - 17.5
= 17
2. The mean
Mean = Sum of terms/Number of terms
= 17.5 + 23.5 + 27.4 + 28.6 + 28.8 + 29.1 +29.5 + 30.8 + 31.0 +31.7 +32.3 +33.0 +34.5/13
= 377.7/13
= 29.053846153846
3. The median
The formula for Median = 1/2(n + 1)th value
n = 13
= 1/2(13 + 1)th value
= 1/2(14)th value
= 7th value.
The 7th value for the data set = 29.5
4.i) Q1 means the First Quartile
The formula for First Quartile
= 1/4(n + 1)th value
= 1/4(13 + 1)th value
= 14/4 th value
= 3.5 th value
This means, the first quartile is between the 3rd and 4th value
3rd value = 27.4
4th value = 28.6
Q1 = 27.4 +28.6/2
= 56/2
= 28
ii) Q3
The Formula for Third Quartile
= 3/4(n + 1)th value
= 3/4(13 + 1)th value
= 42/4 th value
= 10.5th value
This means, the first quartile is between the 10th and 11th value
10th value = 31.7
11th value = 32.3
Q1 = 31.7 +32.3/2
= 64/2
= 32
5. The IQR
IQR = Interquartile range. It is the difference between Q3 and Q1
= 32 - 28
= 4
6. The sample variance
The formula = (x -mean)²/n - 1
= [(17.5 -29.053846153846)² + (23.5 -29.053846153846)² + (27.4 -29.053846153846)² + (28.6 -29.053846153846)² + (28.8 -29.053846153846)² + (29.1 -29.053846153846)² + (29.5 -29.053846153846)² +(30.8 -29.053846153846)² + (31.0 -29.053846153846)² + (31.7 -29.053846153846)² +(32.3 -29.053846153846)² +(33.0 -29.053846153846)² +(34.5 -29.053846153846)² ] /13 - 1
= [133.4913609+ 30.8452071 +2.735207101 +0.2059763313 + 0.0644378698 + 0.002130177514 + 0.1990532545 + 3.049053254 + 3.787514792 + 7.002130177 + 10.53751479 + 15.57213018 +29.66059171] /12
= 237.1523076/12
= 19.7626923
7. The standard deviation =
= √Variance
= √ 19.7626923
= 4.445524975
8. Identify any outliers
Outliers are number in a data set that varies different from the other data. It can be a extremely large or extremely small.
The outliers in the data set = 17.5
Round 4,929 to the place value of the underlined digit. 9
Answers
Answer:
4,900
Step-by-step explanation:
if it is 4 or less it stays the same
if it 5 or more add 1 more
Somebody please help meee
Answers
3√2/(√3 - √2) . (√3 - √2)/(√3 - √2)
3√2(√3 - √2)/(3 - 2)
3√2(√3 - √2)
3√6 - 6
3(√6 - 2)
Answer: 3(√6 - 2)
Can someone tell me what the evaluated answer is?
Answers
Answer:
16) 7⁻²
17) -1⁻²
Step-by-step explanation:
plug in the x=, y=, and n= into the equation.
6430789 rounded to the ten-thousands is
Answers
Answer:
6430789 rounded to the ten-thousands = 6400000
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
A media personality argues that global temperatures are not rising because every year an increase is reported such as 0.09 degrees Celsius. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
Answers
The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:
1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.
2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.
3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.
In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.
the rational numbers that are equivalent to 6/9 ?
Answers
What values of b satisfy 3(2b + 3)² = 36?
Answers
Answer:
The values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
Step-by-step explanation:
To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:
1. Divide both sides of the equation by 3:
(2b + 3)² = 12
2. Take the square root of both sides:
√[(2b + 3)²] = √12
Simplifying further:
2b + 3 = ±√12
3. Subtract 3 from both sides:
2b = ±√12 - 3
4. Divide both sides by 2:
b = (±√12 - 3) / 2
Simplifying further:
b = (±√4 * √3 - 3) / 2
b = (±2√3 - 3) / 2
Therefore, the values of b that satisfy the equation are:
b = (2√3 - 3) / 2
b = (-2√3 - 3) / 2
In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.
The perimeter of the rectangle below is 166 units. Find the value of y.
4y + 2
Sy
Answers
The value of y is 9.
Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.
Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or
( l + l + b + b), here l and b represent the length and breadth of the given rectangle.
Perimeter of the given rectangle = 166 units ( given )
Length of the given rectangle = 5y ( given )
Breadth of the given rectangle = (4y + 2) ( given )
By putting values in the formula, we get
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
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The value of y is 9.
The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.
A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or
(l + l + b + b), where l and b stand for the provided rectangle's length and width
The rectangle's perimeter is 166 units ( given )
The rectangle's length is 5y ( given )
Given rectangle's width equals (4y + 2) ( given )
When we enter values into the formula, we obtain
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
Simplify the fraction 14/50
Answers
14/50 to its simplest form is 7/25
Answer:
\(\frac{7}{25}\)
Step-by-step explanation:
Find the common factor for both the numerator and the denominator, which is 2:
\(\frac{14}{50} =\frac{7}{25}\)
What is the equation of the line that passes through the point (7,6) and has a slope of 0
Answers
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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Thandi is 1,23 m tall and Peter is 0,45 m taller than Thandi.What is Peter's height
Answers
Peter is 1.68 meters tall.
What is height?
Height is a measure of the distance between the base and the top of an object, or the distance between the bottom and the top of a vertical structure. It is often used to describe the vertical dimension of an object or structure, such as the height of a building, the height of a person, or the height of a mountain. In mathematics, height can also refer to the vertical distance between two points on a coordinate plane or the vertical dimension of a three-dimensional shape. The height of a triangle, for example, is the perpendicular distance from the base to the highest point of the triangle.
Peter's height is Thandi's height plus the additional 0.45 m. Therefore:
Peter's height = Thandi's height + 0.45 m
Peter's height = 1.23 m + 0.45 m
Peter's height = 1.68 m
Therefore, Peter is 1.68 meters tall.
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If each term in a geometric sequence is defined as
an = -6. (-1)"-1
what's the sum of the first 20 terms of
the sequence?
A. 0
B. 6
C. 120
D. 15
Answers
Answer:
A
Step-by-step explanation:
\(a_n=-6(-1)^{n-1} \)
The first term is -6 and the common ratio is -1.
The sum is thus
\(\frac{6(1-(-1)^{20})}{1-(-1)}=0\)
