Consider the numbers z = StartRoot 2 EndRoot (cos 45o + i sin 45o )and w = 2(cos 90o + i sin 90o).
Fill in the blanks to complete the statements.
In rectangular form, z − w = 1 − ____ i
In polar form z – w = StartRoot 2 EndRoot (cos
^o + i sin ___ ^o)
Answers
Answer:
In rectangular form, z - w = 1 - 1i
Step-by-step explanation:
Got it correct on Edge 2020
In rectangular form, (z − w = 1 - i) and in polar form \(\rm z-w = \sqrt{2} (cos135^\circ+isin135^\circ)\) and this can be determined by using the given data.
Given :
\(\rm z=\sqrt{2} (cos45^\circ+i\;sin45^\circ)\)\(\rm w={2} (cos90^\circ+i\;sin90^\circ)\)First, evaluate the value of 'z' by using the below calculation.
\(\rm z=\sqrt{2} (cos45^\circ+i\;sin45^\circ)\)
\(\rm z=\sqrt{2} (\dfrac{1}{\sqrt{2} }+i\dfrac{1}{\sqrt{2} })\)
z = 1 + i --- (1)
Now, evaluate the value of 'w' by using the below calculation.
\(\rm w={2} (cos90^\circ+i\;sin90^\circ)\)
\(\rm w={2} (0+i)\)
w = 2i ---- (2)
Now, the difference (z - w) is given by:
z - w = 1 + i - 2i
z - w = 1 - i
The rectangular form of (z - w) is given by:
z - w = 1 - i
Now, the modulus of (z - w) is given by:
\(\rm |z - w| = \sqrt{1^2+(-1)^2}\)
\(\rm |z-w| = \sqrt{2}\)
Now, the argument is given by:
\(\rm \theta = tan^{-1}\dfrac{y}{x}\\\)
\(\rm \theta = -45^\circ\)
\(\theta = 180-45 = 135^\circ\)
The polar form of (z - w) is given by:
\(\rm z-w=|z-w|(cos\theta-i \; sin\theta)\)
\(\rm z-w = \sqrt{2} (cos135^\circ+isin135^\circ)\)
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Related Questions
The cost of 3 quarts of milk is $6.75. How many quarts can you buy with $20.25?
Answers
Explanation: 20.25/6.75 = 3 x 3 = 9
Fipress each of the following numbers in scientific notation with correct significart figures, finter your ansaer uning ane of the following formats: 1.2e−3 for 0.0012 and 1.20e+2 for 120.) (a) 723.6 배은 (a) 0.249 (c) 5048.3 (d) 155.7 (e) 0.00646 ) 릭 (t) 600000 (9) Express each of the following numbers in exponential notation with correct significant figures. IEnter your answer using one of the following formats: 1.2e−3 for 0.0012 and 1.20e+2 for 120.) (a) 656 (b) 6.03391 (c) 5655.7 (d) 23086 बन्] (e) 2000.0000 배은 (f) 0.0000000645 (จ) 0.007843 बन (d) 9.83159×10
−5
] e) 0.06627 cm
3
f) 67.00 kg (a) 0.06960 g/mL Dw many significant fiv (a) 131 cm b) 5.530×10
9
m (c) 7300041 d) 5.960×10
5
m s
s
e) 100.01 m
3
Round off each of the following numbers to two significant, figures. (a) 0.318 ] 피 (b) 7.000 II (c) 26.1 बV] (d) 1 Es (e) 1.53×10
−3
ब. (1) 0.515 Perform the following calculations and report each answer with the correct number of significant figures. (a) 607×383 (b) (5.44×10
2
)×(5.4×10
3
) ब. (c)
13.465
22.9
(d) 8133×0.000049 (e) 14.56+27370+84.6859 (f) 44.1+0.293
Answers
(a) 723.6: The number 723.6 can be written in scientific notation as 7.236 × 10².
(b) 0.249: The number 0.249 can be written in scientific notation as 2.49 × 10⁻¹.
(c) 5048.3: The number 5048.3 can be written in scientific notation as 5.0483 × 10³.
(d) 155.7: The number 155.7 can be written in scientific notation as 1.557 × 10².
(e) 0.00646: The number 0.00646 can be written in scientific notation as 6.46 × 10⁻³.
(f) 600000: The number 600000 can be written in scientific notation as 6 × 10⁵.
(g) 656: The number 656 can be written in scientific notation as 6.56 × 10².
(h) 6.03391: The number 6.03391 can be written in scientific notation as 6.03391 × 10⁰.
(i) 5655.7: The number 5655.7 can be written in scientific notation as 5.6557 × 10³.
(j) 23086: The number 23086 can be written in scientific notation as 2.3086 × 10⁴.
(k) 2000.0000: The number 2000.0000 can be written in scientific notation as 2 × 10³.
(l) 0.0000000645: The number 0.0000000645 can be written in scientific notation as 6.45 × 10⁻⁸.
(m) 0.007843: The number 0.007843 can be written in scientific notation as 7.843 × 10⁻³.
(n) 9.83159×10³: The number 9.83159 × 10³ can be written in standard notation as 9,831.59.
(o) 22.9: The number 22.9 can be written in scientific notation as 2.29 × 10¹.
(p) 8133 × 0.000049: The product of 8133 and 0.000049 is equal to 0.398217. This can be written in scientific notation as 3.98217 × 10⁻¹.
(q) 14.56+27370+84.6859: The sum of 14.56, 27370, and 84.6859 is equal to 27469.2459. This can be written in scientific notation as 2.74692459 × 10⁴.
(r) 44.1+0.293: The sum of 44.1 and 0.293 is equal to 44.393. This can be written in scientific notation as 4.4393 × 10¹.
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TIME REMAINING
55:06
A city’s bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized.
The population of City A, in Texas, is 29,455 and covers an area of 19.42 mi2.
The population of City B, in Alabama, is 34,890 and covers an area of 25.4 mi2.
Which city’s residents are more likely to use public buses? Explain.
The residents of City B are more likely to use public transportation because the city has the lowest population density.
The residents of City B are more likely to use public transportation because the city has the highest population density.
The residents of City A are more likely to use public transportation because the city has the lowest population density.
The residents of City A are more likely to use public transportation because the city has the highest population density.
Answers
Answer:
d
Step-by-step explanation:
i just took the test
The residents of City A are more likely to use public transportation because the city has the highest population density. Therefore, the correct option is A.
What is Population density?Population density is the amount of people living in a specific area. In this example, City A has 29,455 residents in an area of 19.42 square miles, while City B has 34,890 residents in an area of 25.4 square miles.
Due to the large number of people living in the small space, the population density is high in City A. Greater demand for public transport services, such buses, is often brought about by higher population density as residents find these services more practical and cost effective to use for commuting and travel. As a result of their increased population density, people in City A are more inclined to use public transport.
Therefore, the correct option is A.
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The table below shows all of the possible outcomes for rolling two six-sided number cubes. A table with 36 possible outcomes. How many possible outcomes are there? 6 12 21 36
Answers
There are 36 possible outcomes.
The correct option is D.
What is the probability?Probability in mathematics is the possibility of an event in time. In simple words, how many times does that incident is happening in any given time interval?
Given:
The table below shows all the possible outcomes for rolling two six-sided number cubes.
A table with 36 possible outcomes.
The number of possible outcomes,
= 6 x 6
= 36
Therefore, 36 possible outcomes are there.
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2. Find the slope of each line.
Answers
Answer:
6/2 or 3
Step-by-step explanation:
count the amount it rises and put that over the amount it moves on x axis or the run.
Answer: The equation would be written as Y=3/1x, and your slope would be 3/1
Step-by-step explanation:
The area of a rectangle is x^2 + 4x - 5. If we factored this out, we would get the lengths and widths of the sides of the rectangle. For what value(s) of x would these side lengths not make any sense? Why?
Answers
Answer:
If X ≤ 1, these side lengths has no sense.
Step-by-step explanation:
We can factored the expression X² + 4X - 5 in a expression in the form:
(X+a) (X+b)
Where a*b = -5 and a+b = 4
That means a could be 5 and b = -1:
(X+5) (X-1)
The side lenghts of the rectangle will not have any sense if ≤ 0. With the factored expression:
(X+5) ≤ 0 ; If X ≤ -5, these side lengths has no sense.
Also:
(X-1) ≤ 0; If X ≤ 1, these side lengths has no sense.
Both expressions are resumed in:
If X ≤ 1, these side lengths has no sense.to estimate the true mean speed of vehicles traveling on a particular section of roadway, a speed-detection device is programmed to measure the speed of the first 100 vehicles that pass it. are the conditions for constructing a t confidence interval met? no, the random condition is not met. no, the 10% condition is not met. no, the normal/large sample condition is not met. yes, the conditions for inference are met.
Answers
It's difficult to say whether the conditions for constructing a t-confidence interval are met based on the information provided. To construct a t-confidence interval, three conditions must be met:
The sampling method must be random. It's not specified in the problem whether the method of selecting the vehicles was random or not, so it's impossible to say whether this condition is met.
The sample size must be large enough. A sample size of 100 vehicles is considered to be large enough for the normal/large sample condition to be met.
The population must be approximately normally distributed or the sample size must be large. Since the problem does not specify anything about the distribution of the population, it is not clear if this condition is met.
Given that the information provided does not give enough details to state whether the conditions for constructing a t-confidence interval are met or not.
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Area=
Help me please thanks
Answers
The area of the shaded region shown in the figure is 80π unit²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Area of the shaded region = area of semicircle IL - area of semicircle JK + area of semicircle IJ + area of semicircle KL
Area of the shaded region = area of semicircle IL + area of semicircle IJ = (0.5 * π * 12²) + (0.5 * π * (12/3)²) = 80π
The area of the shaded region shown in the figure is 80π unit²
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The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as?
Answers
The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.
What is inferential statistics?Statistical inference is the method of using data analysis to infer characteristics of a probability distribution. Inferential statistical analysis deduces population properties, for example, by testing hypotheses and generating estimates. The observed data set is assumed to be a sample from a larger population. Inferential statistics is the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter.Descriptive statistics is only concerned with the properties of the observed data and does not assume that the data come from a larger population. Inferential statistics differ from descriptive statistics.Therefore, the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.
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in the citation 319 n.w. 2d 459, the number 459 represents the
Answers
The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.
In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.
To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.
In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.
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Mrs. Brown's class has 28 students. She is going to have students pick balls out of a bag. The bag contains 6 red balls, 2 blue balls, 1 green ball, and 1 gold ball. Each student in class pulls out a ball. The teacher records the result, and then the teacher replaces the ball. This process is repeated until each student has picked a ball. The results are in the table below. Ball Color Frequency Red 15 Blue 6 Green 4 Gold 3 Can you determine if Mrs. Browns probability is accurate by multiplying the ratio of red balls by the number of students in class? No, there is no way to predict the relative frequency. No, because replacing the balls does not provide an accurate representation of probability. Yes, the the result is 16.8 which is close to the frequency in the table of 15. Yes, the result is 15 exactly, which is the same as what the table is showing us.
Answers
Answer:
Step-by-step explanation:
70x 28 IF YOU SEE SUM LIKE THATS ITS DA ANSWER
Given: ∆MNP, PM = 8 m∠P = 90°, m∠N = 58° Find: Perimeter of ∆MNP
(Not 22.4 or 22.43)
Please answer ASAP, brainly awarded.
Answers
Answer:
Step-by-step explanation:
Triangle MNP is a right triangle with the following values:
m∠P = 90°m∠N = 58°PM = 8Interior angles of a triangle sum to 180°. Therefore:
m∠M + m∠N + m∠P = 180°
m∠M + 58° + 90° = 180°
m∠M + 148° = 180°
m∠M = 32°
To find the measures of sides MN and NP, use the Law of Sines:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Substitute the values into the formula:
\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)
\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)
Therefore:
\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)
\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)
To find the perimeter of triangle MNP, sum the lengths of the sides.
\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)
Minh spent $3.50 on 25 stickers.
How much did each sticker cost?
answer and i'll give brainliest.
Answers
Answer:
each sticker cost $0.14.
Step-by-step explanation:
To find the cost of each sticker, you can divide the total cost by the number of stickers.
In this case, Minh spent $3.50 on 25 stickers, so the cost of each sticker is:
3.50 / 25 stickers = $0.14/sticker
Therefore, each sticker cost $0.14.
Answer:
Each sticker = $\(0.14\)
Step-by-step explanation:
\(25\) stickers \(=$3.50\)
\(1\) sticker = \(\frac{3.50}{25}\)
\(1\) sticker= \($0.14\)
according to a recent survey, 85% of high school sutdents own a personal media player. what is the probability that 6 out of 10 random high school students own a personal media player?
Answers
As per the binomial distribution, the probability that 6 out of 10 random high school students own a personal media player is 4%.
Binomial distribution:
The general formula to calculate the binomial distribution is written as,
P = aCx pˣ (1 - p)ᵃ⁻ˣ
Where,
x = Total number of successful trails
a = Total number of events
p = Probability of success
1 – p = Probability of failure
nCr = [n!/r!(n−r)]!
Given,
According to a recent survey, 85% of high school students own a personal media player.
Here we need to find the probability that 6 out of 10 random high school students own a personal media player.
While we looking into the given question,
Total number of student = 10
Success rate = 6
Probability percentage = 85%
When we convert this into decimal then we get the probability as 0.85.
Now, according to the binomial distribution, Substituting in values for this problem, n=10, p=0.85, and X=6 on the formula, then we get,
=> P = [10!/6!4!] x (0.85)⁶ x(1- 0.85)¹⁰⁻⁶
When we simplify this one then we get the probability as,
=> P = 0.04
When we convert this into percentage, then we get the probability as 4%.
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Andy wants to buy a used car that cost $8,500. He has
saved $1,300 and can save an additional $225 each month.
How many months will it take for Andy to have enough
money for the car?
Answers
Answer:
32 months.
Step-by-step explanation:
Andy wants a car that costs $8,500.
He already saved $1,300.
$8500 - $1300 = $7200
Andy can save an additional $255 each month.
7200 ÷ 255 = 32
So, it would take Andy 32 months to have enough money to buy the car.
When being dealt two cards from a standard deck of fifty-two playing cards, find the probability that both cards are an ace.
Answers
We have:
Total number of cards in a pack = 52
Total number of aces in a pack = 4
The probability of drawing an ace is:
\(P(one\text{ }ace)=\frac{4}{52}\)The probability that both are aces is:
\(P(both\text{ aces\rparen=}\frac{4}{52}\cdot\frac{3}{51}=\frac{4\cdot3}{52\cdot51}=\frac{12}{2652}=\frac{1}{221}\)Answer: the probability is 1/221
Which sample size would give the
best estimate of the population
mean?
Answer choices:
18
30
45
60
Answers
Betty has 42 butterfly stickers, as shown below.
She puts an equal number of stickers on each of 6 pages in her sticker book.
How many stickers does Betty put on each page in her sticker book?
Answers
Answer:
7
Step-by-step explanation:
42/6=7
Please help me solve this
Answers
Answer:
1st pic:
x = 49
top angle = 45
bottom angle = 108
far right angle = 27 degrees
2nd pic:
angle 1 = 88 degrees
angle 2 = 57 degrees
angle 3 = 35 degrees
angle 4 = 145 degrees
Step-by-step explanation:
1st pic:
you can find the far right angle by taking 153 and subtracting it from 180:
⇒ 180 - 153 = 27 degrees
you can find x by the following equation ⇒ x - 4 + 2x + 10 + 27 = 180
combine like terms ⇒ 3x + 33 = 180
subtract 33 from each side ⇒ 3x + 33 - 33 = 180 - 33 ⇒ 3x = 147
divide 3 on each side: ⇒ \(\frac{3x}{3} = \frac{147}{3}\)
x = 49
to find the top and bottom angles, substitute 49 for x:
top angle : x - 4
49 - 4 = 45 degrees
bottom angle: 2x + 10
2 x 49 + 10 = 108 degrees
2nd pic:
angle 1:
⇒ 180 - 92 = 88 degrees
angle 2:
⇒ 180 - 123 = 57 degrees
angle 3:
⇒ 180 - (88 + 57) = 35 degrees
angle 4:
⇒ 180 - 35 = 145 dgerees
Leonardo da Vinci wrote, "When each of two squares touch the same circle at four points, one is double the other." Explain why the statement is true.
Answers
To understand why the statement is true, let's consider a circle with a radius r, a smaller square with side length a, and a larger square with side length 2a. We'll examine the geometric relationships between these three shapes.
The smaller square is inscribed in the circle, meaning that the circle passes through all four vertices of the square. Thus, the diameter of the circle is equal to the diagonal of the smaller square. Using the Pythagorean theorem for the smaller square, we can derive the diameter (d) of the circle:
a^2 + a^2 = (d/2)^2
2a^2 = (d/2)^2
d = 2 * √(2a^2) = 2a√2
Now, let's consider the larger square. In this case, the circle is inscribed within the larger square, meaning that the diameter of the circle is equal to the side length of the larger square. Thus:
d = 2a
By equating the two expressions for d, we can confirm that the side length of the larger square is indeed double the side length of the smaller square:
2a√2 = 2a
2a = a√2
Therefore, when each of two squares touches the same circle at four points, one square is indeed double the other, as Leonardo da Vinci's statement suggests.
True or False : The environmental lapse rate is usually the same as the dry adiabatic rate
Answers
False. The environmental lapse rate, which changes based on various variables like humidity and atmospheric stability, is the real rate at which temperature decreases with increasing altitude in the atmosphere.
The pace at which a parcel of dry air cools as it ascends in the atmosphere, on the other hand, is known as the dry adiabatic rate and is set at around 9.8 degrees Celsius per 1000 meters of ascension.
Although it is not often the same, the environmental lapse rate can occasionally be comparable to the dry adiabatic rate. The environmental lapse rate can differ from the dry adiabatic rate due to things like the presence of moisture or atmospheric instability.
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A hospital can increase the dollar amount budgeted for nurses' overtime wages during the
next year by only 3%. The nurses union has just won a 5% hourly rate increase for the next
year. By what percentage must the hospital cut the number of overtime hours in order to
stay within budget?
Answers
The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.
To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.
Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.
With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.
To calculate the required percentage reduction in overtime hours, we can set up the following equation:
(1.05R) * (1 - x) * H = 1.03B
where x represents the required percentage reduction in overtime hours.
Simplifying the equation, we have:
(1 - x) * H = (1.03B) / (1.05R)
Now, let's solve for x:
1 - x = (1.03B) / (1.05R * H)
x = 1 - [(1.03B) / (1.05R * H)]
Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.
It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.
By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.
Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.
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A researcher is interested in estimating the average commute time of people in a city: Assume that the commute time follows a normal distribution with a standard deviation of 9.4 minutes. The researcher takes a sample of 10 people and obtains the average commute time of 26.3 minutes. Estimate a 99% confidence interval for the population mean: What is the error term? A researcher is interested in estimating the average commute time of people in a city: Assume that the commute time follows normal distribution with a standard deviation of 9.4 minutes. How many people do they need to sample to obtain a 98% confidence interval for the population mean that extends at most +/- 3 mins?
Answers
For problem 1: confidence interval is (17.28, 35.32) & the margin of error is 9.02
For problem 2: The researcher need to sample at least 125 people to estimate the average commute time with a 98% confidence interval.
problem 1:
According to the sample size of 10 and assuming a normal distribution, we can use a t-distribution to calculate the confidence interval.
To calculate the 99% confidence interval,
We have to find the t-value with 9 degrees of freedom.
Using a t-table, we find that the t-value is 3.2508.
Now, we can use the following formula to calculate the confidence interval,
⇒ CI = X ± t(s/√n)
Where,
X = sample mean = 26.3
t = t-value = 3.2508
s = sample standard deviation = 9.4
n = sample size = 10
Put the values, we get,
⇒ CI = 26.3 ± 3.2508(9.4/√10)
⇒ CI = 26.3 ± 9.02
Therefore,
The 99% confidence interval for the population mean commute time is (17.28, 35.32).
The error term in this calculation is the margin of error,
which is the value we add and subtract from the sample mean to get the confidence interval. In this case, the margin of error is 9.02.
problem 2:
To determine the sample size necessary to estimate the population mean commute time with a 98% confidence interval that extends at most +/- 3 mins,
Use the following formula,
n = [(z-value x standard deviation) / margin of error]²
where z-value represents the critical value from the standard normal distribution corresponding to the desired confidence level, standard deviation is the known population standard deviation, and the margin of error is the desired maximum distance between the sample mean and population mean.
For a 98% confidence interval, the z-value would be 2.33.
Using the given standard deviation of 9.4 minutes and a maximum margin of error of 3 minutes,
Put these values to get,
⇒ n = [(2.33 x 9.4) / 3]² = 124.6
Therefore,
The researcher would need to sample at least 125 people to estimate the average commute time with a 98% confidence interval that extends at most +/- 3 mins.
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math related pls help
Answers
Answer:
(a) (f +g)(x) = √(x-2) +√(x)
Step-by-step explanation:
The sum of two functions is the sum of their definitions.
Application(f +g)(x) = f(x) +g(x)
(f +g)(x) = √(x -2) +√(x)
Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.
Simplify the expression below:
14^2 - 24 / 3(2)
--------------------- (divided by)
|-3 + 2(6)|
Answers
Answer:
I got 20 when calculating this
Consider the equations y= |x-1 | and y = 3x + 2. The approxirate solution of this system of equations is
Answers
Answer:
Point Form: (- 1/4, 5/4)
Equation Form: x = - 1/4, y = 5/4
Step-by-step explanation:
Select the correct answer. Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -62 -30 -14 -6 -2 Function g is represented by the equation. Which statement correctly compares the two functions on the interval [-2, 1]? A. Only function f is increasing, and only function f is negative. B. Only function f is increasing, and both functions are negative. C. Both functions are increasing, but function g increases at a faster average rate. D. Both functions are increasing, but function f increases at a faster average rate.
Answers
based on the given exponential functions, we can tell that C. Both functions are increasing, but function g increases at a faster average rate.
what function is increasing faster?function g is represented by the model:
g(x) = -18 x (1/3)^x + 2
g(x)=-18(1/3)^x In(1/3)
In1/3 < 0
this means that:
g (x) > 0
for any interval, g(x) > f(x)
this means that g is increasing at a faster rate than f which is increasing as shown by the table given in the question.
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1. Find the Perimeter AND the Area of the following objects with the given coordinate
pairs:
(7,-5) (-5, 4) (-8, 0) (4, -9)
Answers
The value of perimeter of figure is,
⇒ 40 units
And, Area of figure is,
⇒ A = 75 units²
We have to given that,
The given coordinates pairs are,
⇒ A (7,-5), B (-5, 4), C (-8, 0) , D(4, -9)
Now, We know that,
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, We get;
AB = √(- 5 - 7)² + (- 5 - 4)²
AB = √ 144 + 81
AB = √225
AB = 15
BC = √(- 8 + 5)² + (0 - 4)²
BC = √9 + 16
BC = √25
BC = 5
CD = √(4 + 8)² + (- 9 - 0)²
CD = √144 + 81
CD = √225
CD = 15
DA = √(4 - 7)² + (- 9 + 5)²
DA = √9 + 16
DA = √25
DA = 5
Hence, The value of perimeter of figure is,
⇒ 15 + 5 + 15 + 5
⇒ 40 units
And, Area of figure is,
A = Lenght x Width
A = 15 x 5
A = 75 units²
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0.0084 scientific notation
Answers
Answer:
8.4*10^-3
Step-by-step explanation:
Move the decimal point 3 places in order to get a number in the one's place.
Identify the initial amount and the growth rate of the following:
Y = 9.8 (1.35)^t
Answers
The initial amount is when t = 0, so it is 9.8 * 1 = 9.8. The growth rate is how much the amount goes up by for every increase of 1 in t. This is 1.35 because that is the part being affected by t. we plug in 0 for t to get 9.8 as the initial amount. The growth rate is just 135% factor, or 35% more each time, because 1.35 is the base of the exponent.