Can triangles AAJB and ACBJ be proven congruent by SAS?
OA) No, the triangles AAJB and ACBJ are congruent only through SSS.
B) No, because only two pairs of congruent sides are known.
OC) Yes, because BC
JA. JB
JB, and AB - CJ
-
.
D)
Yes, because BC JA. JB JB, and their included angles CBJ and AJB are congruent
because they're alternate interior angles.
Answers
Answer:
A.
Step-by-step explanation:
SAS:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
ASA:
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.
SSS:
if we can determine that the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
You can also apply the ASA postulate in this triangle but not the SAS.
Related Questions
Which of the following sets of sides does not form a right triangle?
6.8.10
8.15, 17
7.24.26
5, 12, 13?
Answers
Answer:
7, 24, 26
Step-by-step explanation:
6 squared is 36 and 8 squared is 64. Add them together and you get 100, which is 10 squared. Do the same for the other ones and you'll notice that 7 squared and 24 squared added together is 625, which is not 26 squared. In my head 25 squared is 625(check if you don't believe me) so I know that the answer is the third one. The basic formula for a right triangle is a^2 + b^2 = c^2, and that's how you find if three numbers form a right triangle or not. Hope this helps :)
Solve the math problem
Answers
Answer:
73.09 ,3.09,9.04,7.43 im in 6th grade...
Step-by-step explanation:
Answer:
this is your answer.
0 to -300-300 to -9003 to 9-300 to -900MARK ME AS A BRAINLIST PLZ
for the function : f(x) = -(x-2)^2+9 name all transformations, intercepts and the vertex
Answers
Given:
The given function is:
\(f(x)=-(x-2)^2+9\)
To find:
The transformations, intercepts and the vertex.
Solution:
The vertex form of a parabola is:
\(y=a(x-h)^2+k\) ...(i)
Where, a is a constant and (h,k) is vertex.
If a<0, then the graph of parent quadratic function \(y=x^2\) reflect across the x-axis.
If h<0, then the graph of parent function shifts h units left and if h>0, then the graph of parent function shifts h units right.
If k<0, then the graph of parent function shifts k units down and if k>0, then the graph of parent function shifts k units up.
We have,
\(f(x)=-(x-2)^2+9\) ...(ii)
On comparing (i) and (ii), we get
\(a=-1,h=2,k=9\)
So, the graph of the parent function reflected across the x-axis, and shifts 2 units right and 9 units up.
Putting x=0 in (ii), we get
\(f(0)=-(0-2)^2+9\)
\(f(0)=-4+9\)
\(f(0)=5\)
The y-intercept is 5.
Putting f(x)=0 in (ii), we get
\(0=-(x-2)^2+9\)
\((x-2)^2=9\)
Taking square root on both sides, we get
\((x-2)=\pm \sqrt{9}\)
\(x=\pm 3+2\)
\(x=3+2\text{ and }x=-3+2\)
\(x=5\text{ and }x=-1\)
Therefore, the x-intercepts are -1 and 5.
The values of h and k are 2 and 9 respectively and (h,k) is the vertex of the parabola.
Therefore, the vertex of the parabola is (2,9).
The grocery store is having a candy sale. Originally, a candy bar was $1.50. The
sale price is $0.50. What is the markdown rate? Round to the nearest whole
percent.
Answers
The markdown rate is 66.7%.
Markdown rateUsing this formula
Markdown rate= Change in price/original price×100
Let plug in the formula
Markdown rate=$1.50-$0.50/$1.50
Markdown rate=$1.00/$1.50×100
Markdown rate=66.66%
Markdown rate=66.7% (Approximately)
Inconclusion the markdown rate is 66.7%.
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336,765=3,14×0.55×(l+0.55) please help
Answers
Answer:
l = 194999.45
Step-by-step explanation:
I'm going to assume that you meant 3.14 by 3,14.
336,765 = 3.14 × 0.55 × (l + 0.55)
336,765 ÷ (3.14 × 0.55) = l + 0.55
(336,765 ÷ (3.14 × 0.55)) - 0.55 = l
l = 194999.45
a kitten's weight increase by 12% each week for 4 mouths the little currently weighs 2.6 pounds which will not calculate how much the kitten will weigh in 1 week?
a. 2.6(0.12)
b. 2.6(1.12)
c. 2.6 + 2.6(0.12
d 2.6 + 0.312
Answers
Answer:
a. 2.6(0.12)
Step-by-step explanation:
Check all of the other answers: b. c. and d. are variations of equations that equal to 2.912. 2.6(0.12) is not the correct equation because it equals to 0.312. The kitten‘s weight must increase, so that is the incorrect equation.
I need help now or i fail my class :( .Will give an extreme amount of points of points.
Answers
Step-by-step explanation:
-2>x+3
-2-3>x
-5>x
For the first one, draw an open circle above -5 and draw an arrow from it to the right
x-3<-3
x< -3+3
x<0
For the second one, draw an open circle above 0 and draw an arrow from it to the left
For the last one, divide both sides by 8... so x would be greater than or equal to -3. Draw a closed/shaded circle above -3 and draw an arrow to the right
Hope this helps:)
Under her cell phone plan, Avery pays a flat cost of $58.50 per month and $5 per gigabyte. She wants to keep her bill at $64.50 per month. Write and solve an equation which can be used to determine x, the number of gigabytes of data Avery can use while staying within her budget.
Answers
Answer:
x=1
Step-by-step explanation:
64.50=5x+58.50
64.50=5(1)+58.50
64.50=63.50 CORRECT
It can't be 2 because it will be over 64.50
5(2)+58.50
10+58.50
68.50 WRONG
Avery can use up to 1.2 gigabytes of data while staying within her budget of $64.50 per month.
The equation to determine the number of gigabytes of data Avery can use while staying within her budget can be written as:
$58.50 + $5x = $64.50
Where:
$58.50 represents the flat cost per month
$5x represents the cost based on the number of gigabytes used (x gigabytes)
$64.50 is the total budget she wants to stay within
To solve for x, we can subtract $58.50 from both sides of the equation:
$5x = $6.00
Then, divide both sides by $5:
x = 1.2
So, Avery can use up to 1.2 gigabytes of data while staying within her budget of $64.50 per month.
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a. It is impossible for LCLX in an Xbar chart to be > an Upper Specification Limit. T_ F b. Statistical Tolerancing offers lower FTY over Worst Case Tolerancing. T /F
c. In Worst Case analysis, the probability of interference is > 0%. T F d. For sample sizes >> 30, o may be considered -s in SPC. T/F
e. For Cpk> 2, C charts are preferred for Statistical Process Control. T_ F f. If Cpk < 0, the process mean is still within the specification limits. T /f
g. Reducing assembly parts counts through DFM reduces OFD's. T/F
h. Defects are additive in a multi-step manufacturing process. T /F
i. FTY=1-DPU is valid for DPU's >0.5. T /F
j. Reducing the o of a process always increases the Cpk. T/F
Answers
Cpk measures the relationship between the process variability and the specification limits. If the process mean is not centered within the specification limits, reducing the standard deviation alone may not improve the Cpk.
a. False. It is possible for the Lower Control Limit (LCL) in an Xbar chart to be greater than the Upper Specification Limit (USL). The control limits in statistical process control (SPC) are based on the process variability, while specification limits are determined by customer requirements. If the process is in control but does not meet the customer's specifications, it is possible for the LCL to be greater than the USL.
b. False. Statistical Tolerancing generally offers higher First Time Yield (FTY) compared to Worst Case Tolerancing. Statistical Tolerancing takes into account the statistical distribution of the process and allows for better utilization of the allowable tolerance range, resulting in higher FTY. Worst Case Tolerancing, on the other hand, assumes extreme values for all variables, leading to lower FTY.
c. False. In Worst Case analysis, the probability of interference can be zero or non-zero, depending on the specific scenario. It is possible to have cases where the tolerances do not overlap and there is no interference, resulting in a probability of interference of 0%.
d. True. For sample sizes that are significantly larger than 30, the standard deviation (o) of the process can be approximated by the sample standard deviation (s) in Statistical Process Control (SPC). This approximation holds under the assumption of a normal distribution and large sample sizes where the Central Limit Theorem applies.
e. False. C charts are control charts used for monitoring the count or number of defects per unit. Cpk, on the other hand, is a capability index that measures the process capability to meet specifications. C charts and Cpk serve different purposes in Statistical Process Control (SPC) and are not directly comparable.
f. False. If Cpk < 0, it indicates that the process is not capable of meeting the specification limits. In this case, the process mean is not within the specification limits.
g. True. Design for Manufacturability (DFM) aims to reduce the number of assembly parts, which can help reduce opportunities for defects or occurrences of failure modes. By simplifying the design and reducing the number of parts, the overall Failure Detections (OFDs) can be reduced.
h. True. Defects in a multi-step manufacturing process are generally additive. Each step in the process has its own probability of generating defects, and as the product moves through the various steps, the defects can accumulate.
i. False. FTY (First Time Yield) is calculated as 1 minus DPU (Defects Per Unit). It is valid for DPU values ranging from 0 to 1. DPU values greater than 0.5 indicate a high defect rate, but the formula FTY = 1 - DPU is still applicable.
j. False. Reducing the standard deviation (o) of a process does not always increase the Cpk (Process Capability Index). Cpk measures the relationship between the process variability and the specification limits. If the process mean is not centered within the specification limits, reducing the standard deviation alone may not improve the Cpk. The process mean also needs to be adjusted to ensure that it falls within the specification limits to increase the Cpk value.
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PLS HELP!!! REALLY REALLY IMPORTANT!!!
Answers
Answer:
uwu daddy san its called addition just add up the prices
Step-by-step explanation:
add the prices up
Which function is equivalent to g of x = x squared + 6x + 8?
A.g(x)=(x+2)(x+4)
B. g(x)=(x-2)(x--4)
C. g(x)=(x+2)(x-4)
D.g(x)=(x-2)(x+4)
Answers
HELP ASAP DUE LAST WEEK (EASY MATH)
Answers
Answer:
136sq feet
Step-by-step explanation:
Two of its surfaces are 35ft in surface area, the bottom is 42ft in surface area and the front and back are both 12ft in surface area.
Answer:
SURFACE AREA OF TRIANGULAR PRISM IS---
area of two triangles:
h = 4, b = 6
A = 1/2(b)(h) = 1/2(6)(4) = 12 sq. ft (area of one triangle)
two triangles, so 12 sq. ft + 12 sq. ft = 24 sq. ft
area of two equal rectangles:
l = 7, w = 5
A = (l)(w) = (7)(5) = 35 sq. ft (area of one rectangle)
two rectangles, so 35 sq. ft + 35 sq. ft = 70 sq. ft
area of one (bottom) rectangle:
l = 7, w = 6
A = (l)(w) = (7)(6) = 42 sq. ft
24 + 70 + 42 = 136 sq. ft
Answer: 136 sq. ftWhich of the following algebraic represents shows a dilation that is an enlargement ?
Answers
The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)
A dilation is a type of transformation that changes the size of the shape or object. It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.
A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).
For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.
Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)
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Joshua plans to buy x pencils and one notebook at the schoolstore. A pencil costs $0.10 and a notebook costs $1.25. Joshua
has $7.00
Iln
Answers
Hope this helps :)
1) Find the domain of the function f(x) = 1 / |x ^2- 4|
2) Find the domain of the function f(x) = 1 / (x^ 2 + 4x + 3)
Answers
Answer:
x<-3 or -3<x<-1 or x>-1
Step-by-step explanation:
Domain - The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
\mathrm{Domain\:of\:}\:\frac{1}{x^2+4x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:-3<x<-1\quad \mathrm{or}\quad \:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:-1\right)\cup \left(-1,\:\infty \:\right)\end{bmatrix}
Janice has these times recorded on her time sheet for the week.
How many hours did she work?
47 hours
44 hours
37 hours
34 hours
Time in Time out
7:05 2:58
7:30 5:01
8:01 4:32
7:22 4:46
6:55 3:31
Answers
9 hrs 31 min
8 hrs 31 min
9 hrs 24 min
8 hrs 36 min
43 hrs and 55 min… so I guess 44 hrs is your answer(?)
The number of hours Janice worked in a week is 44 hours.
Given that, Janice has recorded on her time sheet for the week.
What is a clock?A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the year.
Now,
Time in Time out
7:05 2:58
7:30 5:01
8:01 4:32
7:22 4:46
6:55 3:31
Between 7:05 and 2:58 the number of hours is 7 hours 53 minutes
Between 7:30 and 5:01 the number of hours is 9 hours 31 minutes
Between 8:01 and 4:32 the number of hours is 8 hours 31 minutes
Between 7:22 and 4:46 the number of hours is 9 hours 24 minutes
Between 6:55 and 3:31 the number of hours is 8 hours 36 minutes
Now, (7+9+8+8+8)+(53+31+31+24+36)
= 40 hours + 175 minutes
= 40 hours + 2 hours 55 minutes
= 43 hours 55 minutes
= 44 hours
Therefore, the number of hours Janice worked in a week is 44 hours.
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Which statement illustrates the distributive property?
O A. 13i + 2i = 2i + 13i
O B. (13 + 2i)i = 13(i) + 2i(i)
O C. (13 + 2) + i = (13 + 2) + (2 + i)
OD. 13i + 2i = (13 + 2) (i+i)
Answers
Explanation: you multiply one number/letter by an equation in parentheses
PLEASE ANSWER THIS I NEED HELP RNNN!!
SHOW WORK PLEASE AND EXPLANATIONS SO I CAN UNDERSTAND!!! :)
Answers
Answer:
Every five minutes, the shuttle loses 1.6km in altitude. This can be written in the equation y = \(\frac{1.4}{-5}\)x + 100.It would have been 100.56 km above the earth. You can do this by plugging in -2 into the equation above. You have to use -2 because it is 2 minutes before tracking started.It will take around 357 minutes for it to reach the ground. Set the equation equal to 0 and solve for x which represents the time taken.Step-by-step explanation:
1. change in y over change in x.
\(\frac{100-98.6}{0-5}\) = \(\frac{1.4}{-5}\)
This becomes your slope.
the y-intercept is 100 because at x = 0, y= 100.
So plug these values into y = mx + b and you get y = \(\frac{1.4}{-5}\)x + 100.
2. If the line starts at x = 0, then if you want to get a value for 2 minutes prior you have to use -2 because 0 - 2 = -2.
y = \(\frac{1.4}{-5}\)(-2) + 100
Set it equal to zero and solve algebraically. The answer should be 100.56.
3. If we want to see how many minutes it takes to get to an altitude of 0, we have to make y = 0 and solve for x. This is because we know that y will be 0 but we don't know how long it takes.
0 = \(\frac{1.4}{-5}\)x + 100
Solve algebraically and you should get an answer around 357.
What's the slope of this chart?
Answers
Answer:
y= -2/7x +4
Step-by-step explanation:
Answer: -2/7
Step-by-step explanation:
1. Use the slope equation (y2-y1)/(x2-x1) you take 2 coordinates in the chart and use the second coordinates y output minus the first corrdinates y output and the same for the x inputs and whatever you get is your slope
1. Plug the first two coordinates into the slope formula:
(6-8)/(-7-(-14))
2. Solve:
-2/7!
I hope this helped :)
Question 15(Multiple Choice Worth 5 points)
(03.03 LC)
What is the approximate distance between points A and B?
4-3-2-10
1
03.74
07.95
08.56
Help please
Answers
Answer:
1 is the answer you needed
In a chocolate chip cookie recipe flour,brown sugar, and chocolate chips are mixed in the ratio 5:3:4 if the total volume of the three ingredients is 720 ML how many mL of Chocolate chips are in the mix
Answers
Answer:
240 mL.
Step-by-step explanation:
The following data were obtained from the question:
Ratio of Flour = 5
Ratio of brown sugar = 3
Ratio of chocolate = 4
Total volume = 720 mL
Next, we shall determine the total ratio. This can be obtained as follow:
Total ratio = ratio of flour + ratio of brown sugar + ratio of chocolate
Total ratio = 5 + 3 + 4
Total ratio = 12
Finally, we shall determine the volume of the chocolate chips in the mixture as shown below:
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Ratio of chocolate = 4
Total ratio = 12
Total volume = 720 mL
Volume of chocolate chips =..?
Volume of chocolate chips = ratio of chocolate /total ratio x total volume
Volume of chocolate chip = 4/12 x 720
Volume of chocolate chip = 240 mL
Therefore, the volume of the chocolate chips in the mixture is 240 mL.
How do we calculate using the column method
\( 274561 + 367238\)
![How do we calculate using the column method[tex] 274561 + 367238[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/T8yWyQ6ylPkZC9T0lXpDFm1Lgn6XiprH.jpeg)
Answers
Answer:
641799
Step-by-step explanation:
274561
+367238
641799
a random variable from an experiment where outcomes are normally distributed a. can have any value between -infinity and infinity. b. can have only a few discrete values c. can have positive values d. can have no values
Answers
a random variable can have any value that is possible within the range of -infinity and infinity.So a. can have any value between -infinity and infinity.
A random variable from an experiment with outcomes that are normally distributed can take on any value between -infinity and infinity. This means that it can take on any real number, including fractions and decimals. It is not limited to only a few discrete values, nor does it have to be positive.
A random variable from an experiment with outcomes that are normally distributed can take on any real value between -infinity and infinity. This means that the variable is not limited to a few discrete values, nor does it have to be positive. Instead, it can have any value, no matter how small or large, and including fractions and decimals. Such a random variable can have any value that is possible within the range of -infinity and infinity.
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Let x be a discrete random variable. if pr(x<6) = 1/7, and pr(x>6) = 1/4, then what is pr(x=6)?
Answers
Answer:
\(pr(x=6)=\frac{17}{28}\)
Step-by-step explanation:
Well the probabilities should all up to 1. This means pr(x<6) + pr(x=6) + pr(x>6) = 1.
So plugging in the known values we get: \(\frac{1}{7} + pr(x=6) + \frac{1}{4}=1\)
To make things easier, let's multiply the 1/7 by 4/4 and 1/4 by 7/7
\(\frac{4}{28}+pr(x=6)+\frac{7}{28}=1\)
Now combine like terms: \(pr(x=6)+\frac{11}{28}=1\)
Subtract 11/28 from both sides
\(pr(x=6)=\frac{17}{28}\)
what is the measure of angle TSU?
Answers
Answer:
m<TSU = 65
Step-by-step explanation:
As one can see, the measure of angle (RST) is (90) degrees. This is indicated by the box around the angle. As a general rule, when there is a box around an angle, the angle measure if (90) degrees. It is also given that the measure of angle (RSU) is (25) degrees. As per the given diagram, the sum of the measures of angles (RSU) and (UST) is (RST). Therefore, one can form an equation and solve for the measure of angle (UST).
(RSU) + (UST) + (RST)
Substitute,
25 + (UST) = 90
Inverse operations,
25 + (UST) = 90
UST = 65
(<UST) is another way of naming angle (TSU).
Answer:
∠ TSU = 65°
Step-by-step explanation:
∠ RST = 90°
∠ RSU + ∠TSU = ∠ RST , that is
25° + ∠ TSU = 90° ( subtract 25° from both sides )
∠ TSU = 65°
Which of the following expressions is equivalent to b x b? A. 2b B.) b^2 C.)2^b D.)2b^2
Answers
Answer:
B
Step-by-step explanation:
because b x b is equals to b raised to the power of 2
The expression that is equivalent to b x b will be b².
For this question to be solved, you simply have to multiply the values given. In this case, you're multiplying the same value twice and this will simply be raised to the power of 2.
Therefore, based on the question asked, b × b will be:
= b × b
= b²
Therefore, the value of b × b is b².
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Select the correct answer from each drop-down menu. A system of linear equations is given by the tables. x y -5 10 -1 2 0 0 11 -22 x y -8 -11 -2 -5 1 -2 7 4 The first equation of this system is y = x. The second equation of this system is y = x − . The solution to the system is ( , ).
Answers
For the linear equations provided by the coordinates in the table;
The first equation of this system is y = -2x.
The second equation of this system is y = x - 3.
The solution to the system is (1, -2).
How do we solve for the system of linear equation?We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.
The slope (m) is given by the formula (y2 - y1) / (x2 - x1).
For the first line, we can use the points (-5,10) and (-1,2)
m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.
the first equation is y = -2x
the second line, we can use the points (-8,-11) and (-2,-5)
m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.
the second line has a slope of 1,
the equation should have the form y = x + c.
To find c, we can use one of the points, for instance (-2,-5):
-5 = -2 + c => c = -5 + 2 = -3.
So, the second equation is y = x - 3.
the solution to the system, we need to find where the two lines intersect.
y = -2x
y = x - 3
Setting both equation equally
-2x = x - 3
=> 3x = 3
=> x = 1.
Substituting x = 1 into the first equation
y = -2(1) = -2.
the solution to the system of linear equation would be (1, -2).
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Convert the decimal number 431 to binary in two ways: (a) convert directly to binary; (b) convert first to hexadecimal and then from hexadecimal to binary. which method is faster?
Answers
The conversion of decimal number directly to binary number will be faster.
What is a conversion of the number system?The number conversion deals with the operation to change the base of the number.
Binary number - It contains only 2 numbers that are 1 and 0.
Decimal number - It contains 10 numbers that are from 0 to 9.
Hexadecimal number - It contains 16 numbers that are from 0 to F.
Convert the decimal number 431 to binary will be
431 / 2 = 215 with 1 remainder
215 / 2 = 107 with 1 remainder
107 / 2 = 53 with 1 remainder
53 / 2 = 26 with 1 remainder
26 / 2 = 13 with 0 remainder
13 / 2 = 6 with 1 remainder
6 / 2 = 3 with 0 remainder
3 / 2 = 1 with 1 remainder
1 / 2 = 0 with 1 remainder
The decimal number 431 to binary number will be 110101111.
Convert first to hexadecimal and then from hexadecimal to binary. Then we have
(431)₁₀ = (1AF)₁₆ = (110101111)₂
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find the value of 64°
Answers
Answer:
The number 64 has 4 in the ones place and 6 in the tens place. Explore different numbers with your children. Discuss how many tens and how many ones (units) there are in each number.
\
Step-by-step explanation:
Answer:
I cannot complete this without an image but the answer you might be looking for is 16/25 that is the number simplified when put into decimal form.
Step-by-step explanation:
I did the best I could with what you gave me Vote Brainiest!!
the taylor series for a fuction about x=0 is given by 2^k/3kx^k a) find f5(0) Show the work that leads to your answer.
Answers
The Taylor series for a function about x=0 is given by 2^k/3kx^k. We are supposed to find f5(0).The given Taylor series can be written as follows'(x) = ∑_k=0^∞▒(2^k)/(3k)x^k``f5(x) = (2^5)/(3×5)x^5``f5(0) = (2^5)/(3×5)×0^5 = 0`Therefore, f5(0) = 0. The work leading to this answer has been shown above.
To find f^(5)(0), we need to identify the term in the Taylor series that corresponds to the 5th derivative of the function evaluated at x=0. The general term in the Taylor series is given by:
(2^k / 3k) * x^k
We need to find the term where k = 5:
(2^5 / 3*5) * x^5 = (32 / 15) * x^5
Now, to find f^ (5)(0), we evaluate this term at x = 0:
(32 / 15) * 0^5 = 0
So, f^ (5)(0) = 0.
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