Answer:
square meters.
Step-by-step explanation:
Area = lengthxwidth for any rectangle.
If length and width are in meters area will be in square meters.
Here length = 105 m and width = 67 m
Area = 105x67 =7035sqm
Answer:
square meters
Step-by-step explanation:
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]
What are two straight lines that cross each other at a right angle? A. Curved B. Parallel C. Broken D. Perpendicular
1.Consider the average speed of a runner who jogs around a track four times. The distance (400m) remains constant for each lap. However, each lap is run 5 seconds slower than the first. The time for each lap increases. The average speed for each lap ______________. This is an example of a(n) _____________ relationship.
A) increases, direct
B) decreases, direct
C) increases, inverse
D) decreases, inverse
Larry and Balky set up an experiment to analyze the motion of a marble as it rolled down an incline. They started the marble at the top of the ramp and set up photogates to collect data as the marble rolled down the ramp.
Which graph format will allow Larry and Balky to calculate instantaneous accleration from the slope of the graph?
A) Velocity on the y-axis, time on the x-axis
B) Distance on the y-axis, time on the x-axis
C) Time on the x-axis, distance on the y-axis
D) Velocity on the y-axis, distance on the x-axis
Tim drives to his brother Casey's house. Given the distance travelled and the time spent, what can Tim calculate about his trip?
A) acceleration
B) density
C) force
D) velocity
Car A travels from New York to Miami at 25 m/s. Car B travels from New York to Chicago, also at 25 m/s.
Car A and Car B have ___________ speeds and ____________ velocities.
A) equal, equal
B) equal, different
C) different, equal
D) different, different
28)
While Bob is demonstrating the gravitational force on falling objects to his class, he drops an 1.0 lb bag of feathers from the top of the science building. Determine the distance the bag has traveled after falling for 1.5 seconds assuming it has reach free fall and given the gravitational acceleration of 9.8 m/sec2.
A) 7.4 m
B) 11 m
C) 15 m
D) 22 m
29)
A boat is travelling down stream in a river at 20 m/s south. A passenger on the boat walks toward the back of the boat at 10 m/s north. Relative to the ground, at what velocity is the passenger moving?
A) 10 m/s north
B) 10 m/s south
C) 30 m/s north
D) 30 m/s south
Sarah wanted to know the velocity of an airplane traveling from Houston to Dallas. After recording the distance (in miles) and time (in hours) it took to travel to Dallas, what other measurement does Sarah need to determine the airplanes velocity?
A) acceleration
B) direction
C) force
D) inertia
33)
If an object is said to be moving at 10 m/s due north. The measurement 10 m/s north would be best described as
A) a speed.
B) a velocity.
C) neither a speed or velocity.
D) either a speed or a velocity.
While performing an experiment, the student creating the data table is not sure if a measurement from the experiment is a vector or scalar. Which question should she ask to determine if a measurement is a vector or a scalar?
A) Is the measurement a rate?
B) Is the measurement in metric units?
C) Does the measurement include direction?
d) Does the measurement include magnitude?
1. D) decreases, inverse
The average speed for each lap is given by:
[tex]v=\frac{S}{t}[/tex]
where S is the length of the lap (400 m) while t is the time taken to complete the lap. Since the time t increases at each lap, we see from the formula that v, the speed, decreases at each lap. This is an example of inverse relationship: when one of the two quantities increases (the time), the other one decreases (the speed).
2. A) Velocity on the y-axis, time on the x-axis
Acceleration is defined as the change in velocity divided by the time taken:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
In a graph, the slope of a line is given by the increment in y divided by the increment in x:
[tex]s=\frac{\Delta y}{\Delta x}[/tex]
Therefore, if we put velocity on the y-axis and time on the x-axis, we immediately see that the acceleration corresponds to the slope of the curve.
3. D) velocity
In fact, velocity consists of 1) speed and 2) direction. The speed can be calculated as:
[tex]v=\frac{S}{t}[/tex]
where S is the distance covered and t the time taken. So, by knowing these two quantities, Tim can calculate the speed of the trip. Tim also knows the direction of motion, so he can determine the velocity of the trip.
4. B) equal, different
The difference between speed and velocity is simple: speed is a scalar, and it is just the magnitude of the velocity, so "how fast" is the object moving, while velocity takes also into account the direction of motion, so it is a vector.
Therefore: the two cars have same speed (25 m/s), but they have different velocities, since they are moving into different directions (car A is moving from NY to Miami, while car B is moving from NY to Chicago).
28. B) 11 m
The distance travelled by the bag in free fall is given by:
[tex]S=\frac{1}{2}at^2[/tex]
where [tex]a=9.8 m/s^2[/tex] is the acceleration of gravity and t=1.5 s is the time. Replacing these numbers into the formula, we find
[tex]S=\frac{1}{2}(9.8 m/s^2)(1.5 s)^2 =11 m[/tex]
29. B) 10 m/s south
The boat is moving 20 m/s south, relative to the ground. The passenger is moving 10 m/s north, relative to the boat. Considering south as positive direction, the passenger's velocity relative to the ground is
[tex]v' = v_b + v_p = 20 m/s + (-10 m/s) = 10 m/s[/tex]
and the positive sign means it is due south.
30. B) direction
In fact, velocity is a vector, so it consists of a magnitude (the speed) and a direction. The speed can be determined by the distance and the time, in fact speed is defined as
[tex]v=\frac{d}{t}[/tex]
where d=distance and t=time; however, in order to determine velocity, we also need to know the direction of motion.
33. B) a velocity.
In fact, velocity is a vector, and it consists of a magnitude (the speed) and a direction. In this case, 10 m/s is the speed, while north is the direction.
34. C) Does the measurement include direction?
As stated in the previous question, a vector includes both magnitude and direction, while a scalar includes only a magnitude. Therefore, by asking if the measurement includes a direction, we are able to determine if the quantity is a vector or not.
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.
In one year, a company has a profit of −$2 million. In the next year, the company has a profit of $7 million. How much more profit did the company make the second year?
Can you please find the sum of 599and 326.
please help meeeeeee. image attached
The midpoint between -4 and 8 is answer B) 2
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
-7-(-6)-(-5) using keep, flip, change method
PLEASE HURRY IM TIMED!!!
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L=10log l/l0, wherel0 =10^-12 and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10-10. Ahmad, Brandon’s neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10-4. How does Brandon’s sound intensity level compare to Ahmad’s?
Answer-
A. Brandon’s sound intensity level is 1/4th as compared to Ahmad’s.
Solution-
Given that, loudness measured in dB is
[tex]L=10\log \frac{I}{I_0}[/tex]
Where,
I = Sound intensity,
I₀ = 10⁻¹² and is the least intense sound a human ear can hear
Given in the question,
I₁ = Intensity at Brandon's = 10⁻¹⁰
I₂ = Intensity at Ahmad's = 10⁻⁴
Then,
[tex]L_1=10\log \frac{I_1}{I_0}=10\log \frac{10^{-10}}{10^{-12}}=10\log \frac{1}{10^{-2}}=10\log 10^{2}=2\times10\log 10=20[/tex]
[tex]L_2=10\log \frac{I_2}{I_0}=10\log \frac{10^{-4}}{10^{-12}}=10\log \frac{1}{10^{-8}}=10\log 10^{8}=8\times10\log 10=80[/tex]
[tex]\therefore \frac{L_1}{L_2} =\frac{20}{80} =\frac{1}{4}[/tex]
Answer:
a
Step-by-step explanation:
Suppose the function, g(x), is used to model the height ,y, of a soccer ball, x seconds after the ball is kicked up in the air. The ball starts on the ground and travels in a parabolic shape as it reaches a maximum height and then returns to the ground. Suppose further that the ball reaches its maximum height of 15 feet in 2.2 seconds. What would be an appropriate domain for g(x)?
A. 0<=x<=2.2
B. -2.2<=x<=2.2
C. 0<=x<=4.4
D. 0<=x<=15
Answer:
The correct option is C.
Step-by-step explanation:
The height of the ball is defined by a parabolic function.
Let the equation of the parabola is
[tex]f(x)=a(x-h)^2+k[/tex]
Where, (h,k) is the vertex and a is stretch factor.
The maximum height of the ball is 15 feet in 2.2 seconds. So, the vertex is (2.2, 15).
The equation of the parabola is
[tex]f(x)=a(x-2.2)^2+15[/tex]
The initial height of the ball is 0.
[tex]f(0)=a(0-2.2)^2+15[/tex]
[tex]0=a(-2.2)^2+15[/tex]
[tex]a=-\frac{15}{(2.2)^2}[/tex]
[tex]a=-3.1[/tex]
The equation of the parabola is
[tex]f(x)=-3.1(x-2.2)^2+15[/tex]
The function takes 2.2 seconds to reach at maximum height, so after that it will take 2.2 seconds to reach at growth again.
[tex]2.2+2.2=4.4[/tex]
The ball will reach the growth at x=4.4.
The height can not be negative, therefore the value of x lies between 0 to 4.4. The domain of the function is
[tex]0\leq x\leq 4.4[/tex]
Therefore option C is correct.
Elise has budgeted $800 in her checking account to spend during the summer for entertainment. She would like to have at least $200 available at the end of summer. If Elise withdraws $50 per week, which inequality could she use to determine the greatest number of weekly withdrawals (w) she can make without exceeding her budget?
A) 200 + 50w > 800
B) 800 − 50w ≥ 200
C) 800 + 50w ≥ 200
D) 800 − 50w > 200
The answer is B because you are takin away $50 a week. $200 is what she wants to have at the end off the summer. So that automaticly means it is ≥ 200. She is TAKING AWAY $50 a week. Meaning - 50w ≥ 200. Finally she has $800 to begin with. So, 800 - 50w ≥ 200.
Sorry if l am not very well at explaining this kind of stuff. Let me know if you need anymore help!!
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
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.
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.
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.
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)
the perimeter of a rectangle is 150 cm. the length is 4 cm greater than the width find the width and length
(please explain how you did this or show) (thank you)
Let's call the width of our rectangle [tex]w[/tex] and the length [tex]l[/tex]. We can say [tex]l = w + 4[/tex], since the length is equal to 4 cm greater than the width.
Also remember that the perimeter of a rectangle is the sum of two times the width and two times the length, or [tex]P = 2l + 2w[/tex]. To solve this problem, we can substitute in the information we know, as shown below:
[tex]150 = 2(w + 4) + 2w[/tex]
[tex]150 = 4w + 8[/tex]
[tex]142 = 4w[/tex]
[tex]w = \frac{71}{2}[/tex]
Now, we can substitute in the width we found into the formula for length, which is [tex]l = w + 4[/tex]:
[tex]l = \frac{71}{2} + 4[/tex]
[tex]l = \frac{79}{2}[/tex]
The width of our rectangle is [tex]\boxed{\frac{71}{2} \,\, \textrm{cm}}[/tex] cm and the length of our rectangle is [tex]\boxed{\frac{79}{2} \,\, \textrm{cm}}[/tex]
Help will mark brainlyst
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.
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.
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.
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.
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.
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.
Can you help with this questions: 95% of what is 57?
3 1/5 x 7 1/4 in simplest form
a.22
b.10 1/9
c.21 1/20
d.23 1/5
Answer:
We have
(16/5)x(29/4) = (16x29)/(5x4) = 464/20 = 116/5 = 23 1/5;
The correct answer is d. 23 1/5;
Step-by-step explanation:
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)
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
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