Answer:
(k + 7) • (k - 6)
Step-by-step explanation:
Final result :
(k + 7) • (k - 6)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "k2" was replaced by "k^2".
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring k2+k-42
The first term is, k2 its coefficient is 1 .
The middle term is, +k its coefficient is 1 .
The last term, "the constant", is -42
Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is 1 .
-42 + 1 = -41
-21 + 2 = -19
-14 + 3 = -11
-7 + 6 = -1
-6 + 7 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 7
k2 - 6k + 7k - 42
Step-4 : Add up the first 2 terms, pulling out like factors :
k • (k-6)
Add up the last 2 terms, pulling out common factors :
7 • (k-6)
Step-5 : Add up the four terms of step 4 :
(k+7) • (k-6)
Which is the desired factorization
Final result :
(k + 7) • (k - 6)
Donte simplified the expression below.
4 (1 + 3 i) minus (8 minus 5 i). 4 + 3 i minus 8 + 5 i. Negative 4 + 8 i.
What mistake did Donte make?
He did not apply the distributive property correctly for 4(1 + 3i).
He did not distribute the subtraction sign correctly for 8 – 5i.
He added the real number and coefficient of i in 4(1 + 3i).
He added the two complex numbers instead of subtracted.
Answer:
He did not apply the distributive property correctly for 4(1 + 3i).
Step-by-step explanation:
4 (1 + 3 i) minus (8 minus 5 i)
4 + 12i - 8 + 5i
-4 + 17i
Answer:
A. He did not apply the distributive property correctly for 4(1 + 3i).
Step-by-step explanation:
edg 2020
Write one digit on each side of 73 to make a four digit multiple of 36. How many different solutions does this problem have?
Answer: an option is 2736
and we only have two possible solutions, the other is 6732
Step-by-step explanation:
we want to write a number:
a73b, where a and b are one digit numbers (0 to 9) in such way that the number is divisible by 36.
Now, we know that 36 is multiple of 6, so 6*6 = 36
The multiples of 36 are always even numbers, so we can discard all the odd options for b.
We also can discard the option a = 0, because we want a 4 digit number.
now, let's do it by brute force.
if a = 1, we have:
173b, now you can give b different values (only even values) and see if some of them is divisible by 36. You will find that none is.
if a = 2
273b
when b = 6, we have:
N = 2736, that is divisible by 36 as:
2736/36 = 79, so this is a multiple of 36.
now, you can keep changing the value of a and find all the different possible solutions.
if a = 3,
373b is not divisible by 36 for any value of b
if a = 4
473b is not divisible by 36 for any value of b
if a = 5
573b is not divisible by 36 for any value of b
if a= 6
673b it is divisible by 36 when b = 2.
6732/36 = 187
if a = 7
773b is not divisible by 36 for any value of b
if a = 8
873b is not divisible by 36 for any value of b
if a = 9
973b is not divisible by 36 for any value of b
So we only have two possible solutions
The different solutions this problem have are 2736 and 6732.
What is a Digit?This is a part of a number which consists of numerals from 0 to 9.
a73b is the first number where a and b are one digit numbers (0 to 9) which is divisible by 36.
All multiples of 36 are always even numbers, so odd number options for b isn't considered.
If a = 2 when b = 6, we have: it is divisible by 36 when b = 2.
N = 2736, which is divisible by 36 to give 76 hence it is a multiple of 36.
673b is divisible by 36 when b = 2.
N = 6732 which is divisible by 36 to give 187 hence it is a multiple of 36.
Hence, the two values are 2736 and 6732.
Read more about Digits here https://brainly.com/question/13124157
help help help please
Answer:
to add to the table, continue the arithmetic sequence in each columnto use the table, extend the third column to 45, or multiply the first row by 9Step-by-step explanation:
The numbers in the first column are an arithmetic sequence with a common difference of 2. The next few numbers will be 6, 8, 10, ...
The numbers in the second column are an arithmetic sequence with a common difference of 3. The next few numbers will be 9, 12, 15, ...
The numbers in the third column are an arithmetic sequence with a common difference of 5. The next few numbers will be 15, 20, 25, ...
To use the table, Mark can extend each sequence until he has a row with 45 in the third column, or he can multiply or add rows to give a result of 45 in the third column. For example, multiplying the first row by 9 gives 18:27:45 meaning that Mark needs 18 liters of blue and 27 liters of yellow to make 45 liters of green paint.
Not sure on how to do these questions
Answer:f(8)=g(8)
Step-by-step explanation:
So in these problems f(8) means that you look at the f(x) function (function 1) and plug in 8 for x. Then since it says g(8), you look at the g(x) function and substitute x for 8. If we do that, f(x)=2(8)-3 which is 13. g(x)=3/2x+1=13. The two of them are equal when x=8. So the answer is the third choice
Answer:
f(8)=g(8)
Step-by-step explanation:
Just put the values of given functions in the equation
Consider the polynomial: StartFraction x Over 4 EndFraction – 2x5 + StartFraction x cubed Over 2 EndFraction + 1 Which polynomial represents the standard form of the original polynomial? StartFraction x cubed Over 2 EndFraction – 2x5 + StartFraction x Over 4 EndFraction + 1 –2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1 –2x5 + StartFraction x Over 4 EndFraction + StartFraction x cubed Over 2 EndFraction + 1 1 – 2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction
Answer:
(B)[tex]-2x^5+\dfrac{x^3}{2}+\dfrac{x}{4}+1[/tex]
–2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1
Step-by-step explanation:
Given the polynomial: [tex]\dfrac{x}{4}-2x^5+\dfrac{x^3}{2}+1[/tex]
We are required to pick an equivalent polynomial which is in standard form.
A polynomial is in standard form when it is written in descending powers of x.
Therefore, rearranging the polynomial above, we have:
[tex]-2x^5+\dfrac{x^3}{2}+\dfrac{x}{4}+1[/tex]
The correct option is B.
The correct answer is B. –2x5 + StartFraction x cubed Over 2 EndFraction + StartFraction x Over 4 EndFraction + 1
hope you have a great day :D
Find the area of the shape
what is the result of 3×3/5×(-8×1/3)
Answer:
-4.8
Step-by-step explanation:
Answer:
−24/5
Step-by-step explanation:
3x3/5x(-8x1/3)
Use the order of operations method, PEMDAS, in order to solve this expression.
اذا كانت س زاويه حاده و كان جاس= ٣/٥ فان ظا س=؟؟
PLEASE HELP IJLFEGNSKEURILAYGKUERU
Answer:
No. See below.
Step-by-step explanation:
No, Seth lost the plot at the end.
At x = 3,
y = 4x + 1 = 12 + 1 = 13
At x = -2,
y = 4x + 1 = -8 + 1 = -7
Therefore, the curves intersect at (3,13) and (-2,-7)
What is the length of AC?
Answer:
2.96
Step-by-step explanation:
The cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. In this case:
[tex]\cos 65=\dfrac{x}{7}[/tex]
[tex]x=7\cdot \cos 65\approx 2.96[/tex]
Hope this helps!
Pls help with this one I will give brainliest thank you!
Answer:
B. 10 in.
Step-by-step explanation:
When you do length times width times height 10*10*10 equals 1000
10*10=100 and 100*10=1000
Answer:10 feet
Step-by-step explanation:
edge=[tex]\sqrt[3]{1000}[/tex]= 10 so the answer is B
Lana's little sister needs to take a bubble bath. The package says to put in a drop of bubble bath for every half gallon of water in the bathtub. Lana doesn't know how many half-gallons there are, but she knows that their bathtub can hold 12 gallons of water. How many drops can she put into the bath for her sister? *
24 drops of bubble bath
Step-by-step explanation:
this is because the ratio is .5 gallon:1 drop, so 12 gallons would be 24 drops. I hope this helps!
A circle has a circumference that is greater than 8 meters. The inequality 3.14 d greater-than 8 can be used to determine the possible lengths of the diameter of the circle. What are the possible values of d, the length of the diameter in meters?
d less-than 25.1
d greater-than 25.1
d less-than 2.5
d greater-than 2.5
Answer:
It is the last one
Step-by-step explanation:
Answer:
it is d
Step-by-step explanation:
Math Help!!! Can someone solve this?? I will give you Brainliest!!!!!!
Answer:first one is false, second is true and third is true
Step-by-step explanation:
HELP ME PLEASE , ALOT OF POINTS, CHECK DOCUMENT! Show work
Answer:
x = 25
Step-by-step explanation:
Log10 ( x - 21 ) + Log10 ( x ) = 2,
Log10 ( ( x - 21 )x ) = 2,
( x - 21 )x = 100,
Simplify:
x^2 - 21x = 100,
x^2 - 21x - 100 = 0,
x = - ( -21 ) + √ ( -21 )^2 - 4 * 1 ( -100 )/2 * 1 : 25
and
x = - ( -21 ) + √ ( -21 )^2 - 4 * 1 ( -100 )/2 * 1 : -4
( x = 25 ) ⇒ true
( x = - 4 ) ⇒ false
Answer: x = 25
Graphs of what functions are shown below?
Answer:
y = -√(x -5) +2
Step-by-step explanation:
This looks like a square root function reflected vertically, and translated up 2 and right 5.
y = -√(x -5) +2
_____
g(x) = a·f(x -h) +k represents a translation of f(x) by (h, k) and a vertical scaling by a factor of "a". If "a" is negative, the function is reflected across the x-axis.
Find the ratio a:b, if it is given that ...
7a=3b
Answer:
a:b
3:7
Step-by-step explanation:
a:b also means a/b
Taking the equation
7a = 3b
Dividing each side by b
7a/b = 3b/b
7 a/b = 3
Divide each side by 7
a/b = 3/7
The ratio is 3/7
a:b
3:7
Answer:
a:b = 3/7
Step-by-step explanation:
we need to find the ratio a:b which is the same as a/b.
7a=3b
Devide left and right of the = sign by b gives
7a/b = 3 * b/b
7a/b = 3 * 1
7a/b = 3
Multiply left and right of the = sign by 1/7 gives
1/7 * 7a/b = 1/7 * 3
7/7 * a/b = 3/7
1 * a/b = 3/7
a/b = 3/7
Since a/b is the same as a:b, we now have the answer.
a:b = 3/7
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
In this case, you should check the x-intercept (y = 0).
=> (x-3)(x+4) = 0
=> Two x-intercept at x = 3 and x = -4
C, D are not right, because there is no two x-intercepts.
A is not correct, because both of x-intercepts are less than 0.
=> Option B is correct.
Hope this helps!
:)
What is the value of –112.84 – 54.14 – (–29.18)?
A) –137.8
B)–29.52
C)87.88
D)196.16
Answer:A
Step-by-step explanation:
-112.84-54.14-(-29.18)
-112.84-54.14+29.18=-137.8
Answer:
Option A is correct.
Two datasets arranged in descending order are; {8, x, 4,1} and {9, y, 5,2}. If the medians of
the two given datasets are equal, what is the value of (y − x)
2
?
Answer:
1Step-by-step explanation:
A data arranged in descending order is a data arranged from the biggest to the smallest. The medisn of the data sets is the value at the middle of the dataset after rearrangment.
For the dataset {8, x, 4,1}, the median will be x and 4. Since we have two median values, we will take their average as shown
Median(1) = [tex]\frac{x+4}{2}[/tex]... 1
Simialrly for dataset {9, y, 5,2}, the median will be y and 5.
Median(2) = [tex]\frac{y+5}{2}[/tex] ...2
Since the medians of the two given datasets are equal, we will equate equation 1 and 2 and calculate for y-x as shown;
[tex]\frac{x+4}{2} = \frac{y+5}{2}[/tex]
[tex]x+4 = y+5\\x-y = 5-4\\x-y = 1\\y-x = -1[/tex]
Therefore y-x = -1
(y-x)² = (-1)²
= 1
U
14 poi
At the college football game there were 48,000 people. If 77% of the
people at the game were supporters for the home team, how many
people were supporting the home team? *
Answer:
36960 people
Step-by-step explanation:
Answer:
36,960 people
Step-by-step explanation:
[tex]\frac{is}{of}=\frac{percent}{100}[/tex] is the formula to solve for this equation, here plugging in all our numbers gives us [tex]\frac{x}{480,000} = \frac{77}{100}[/tex].
We do not know our "is" so we replace it for x and solve → [tex]x=(480,000)(\frac{77}{100} )[/tex] = 36,960 people
The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the population standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.
Construct a 95% confidence interval estimate for the popu- lation mean life of compact fluorescent light bulbs in this shipment.
Answer:
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.95[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1000}{\sqrt{64}} = 245[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.
The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
A means of the estimate numerical, the variation in that estimate is referred to as the confidence interval, therefore its value is "[tex][7255, 7745][/tex]".
Confidence interval:[tex]95\%[/tex] C.I. for a mean lifetime is given by
[tex]= [ \overline{X} - \tau_{0.975} \frac{\sigma}{\sqrt{n}} , \overline{X} + \tau_{0.975} \frac{\sigma}{\sqrt{n}} ][/tex], where
[tex]\bar{X}[/tex] (sample mean) [tex]= 7500[/tex]
[tex]\sigma[/tex] (standard deviation)[tex]= 1000[/tex]
[tex]n = 64[/tex]
by putting the value into the above-given formula we get the value that is [tex]= [7255, 7745].[/tex]
Find out more information about the confidence interval here:
brainly.com/question/2396419
Which equation represents a line that has a slope of 1/3 and passes through point -2, one
Answer: y= 1/3 x + 5/3
Step-by-step explanation:
1= 1/3(-2) + b where b is the y intercept
1= -2/3 + B
+2/3 +2/3
B = 5/3
so we know the slope and the y- intercept
y= 1/3x + 5/3 check: 1=1/3(-2) +5/3
1 =1
Slope intercept form: y = mx + b
m = slope
b = y-intercept
Since we know the slope and one point, we can solve for the y-intercept.
y = 1/3x + b
1 = 1/3(2) + b
1 = 2/3 + b
1 - 2/3 = 2/3 - 2/3 + b
1/3 = b
Now, put the final equation together.
y = 1/3x + 1/3
Best of Luck!
If a coin is flipped three times, how many possible outcomes will include exactly 2 tails?
Answer:
If a coin is flipped three times, possible outcomes would be:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
=> possible outcomes that will include exactly 2 tails:
HTT
THT
TTH
TTT
Hope this helps!
:)
Answer:
The answer is 3 or option B.
Step-by-step explanation:
I just answered the question.
simplify- 5^23 x 5^15
Answer:5^38
Step-by-step explanation:
5^23 x 5^15
5^(23+15)
5^38
In order to evaluate the performance of the artificial pancreas, a researcher randomly draw 5 rats as a control group, and draw other 5 rats as a treatment group. The control group did not receive the artificial pancreas, the treatment group did. The research wanted to compare the blood-sugar readings for the treatment group with those of the control group. The treatment group has a sample mean blood-sugar reading Y = 400 unit and a standard deviation Si = 80 unit. The control group has a sample mean blood-sugar reading Y, = 200 unit and a standard deviation S2 = 50 unit. Assume the population variances are not equal, calculate the standard error for the difference of the sample means Ý -Y (Round to three decimal places)
Answer: 42.190
Step-by-step explanation:
From the question, the population variances are not equal. The calculation has been attached in the picture below.
The answer is 42.190 to 3 decimal places.
Calculate the area for the shape above. Round answer to the nearest hundredths
Answer:
400
Step-by-step explanation:
20 x 20= 400
Answer:
I'd say that if it is the total area square and half of the circle. the answer could be 557.08
Step-by-step explanation:
area of the square 20*20= 400
area of the circle= Pi*radio to the square divided by two cause its only the half of a circle so it is like 3.1416*10^2=100*3.1416=714.16/2=157.08
now we can sum up the square area and the circle
400+157.08= 557.08
I'm not actually sure itll depend if the wide and height of the square is the same. here im guessing that its 20 both. and another thing I didnt round the answer it was just that
A ladder is leaning against a building. Match the values with their descriptions.
(K is up Above the G )
Answer:
The height of the building: g
Distance from the building to the base of the ladder: 57
The length of the ladder: m
Angle the ladder makes with the building: k
Angle the ladder makes with the ground: 55
Step-by-step explanation:
Based off the location of the variables and numbers, the descriptions match where they are.
Hope that helps!
A 95% confidence interval of 17.6 months to 49.2 months has been found for the mean duration of imprisonment, mu, of political prisoners of a certain country with chronic PTSD. a. Determine the margin of error, E. b. Explain the meaning of E in this context in terms of the accuracy of the estimate. c. Find the sample size required to have a margin of error of 11 months and a 99% confidence level. (Use sigmaequals45 months.) d. Find a 99% confidence interval for the mean duration of imprisonment, mu, if a sample of the size determined in part (c) has a mean of 36.5 months.
Answer:
a) [tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]
b) For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.
c) [tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]
So the answer for this case would be n=112
d) [tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]
[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]
Step-by-step explanation:
Part a
For this case we know that the cinfidence interval for the true mean is given by:
[tex] \bar X \pm E[/tex]
Where E represent the margin of error. For this case we have the confidence interval at 95% of confidence and we can estimate the margin of error like this:
[tex] E = \frac{49.2-17.6}{2}= 15.8[/tex]
Part b
For this case we have 95% of confidence that the true mean would be between [tex]\pm 15.8[/tex] units respect the true mean.
Part c
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =11 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The critical value would be [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(45)}{11})^2 =111.39 \approx 112[/tex]
So the answer for this case would be n=112
Part d
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Replcaing the info given we got:
[tex]36.5-2.58\frac{45}{\sqrt{112}}=25.53[/tex]
[tex]36.5+2.58\frac{45}{\sqrt{112}}=47.47[/tex]
НА
.
-
НА
N
1 point
Which has a value 10 times greater than 0.008?
о 0.8
o0.08
ов
а
3
80
????????????????????
