The simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
f'(x) = xIn(2x)
To find the simplified expression for the rate of change of f'(x) integrate the function:
∫f'(x) dx = ∫xIn(2x) dx
Using integration by parts:
∫uv dx = uv - ∫u'v
After solving:
∫xIn(2x) dx = x²(2 ln(2x) - 1)/4 + c
Thus, the simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.
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Do the values in this table represent a proportional relationship?
X
y
2
O I don't know.
1
O Yes, and the constant of proportionality is 1/2.
O Yes, and the constant of proportionality is 2.
O No.
4
Creative Section - B
7. a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300
in the last week. If he earned Rs 2,000 on Saturday, find
income of the week.
7 - (-3) = 7+ blank* equals blank*
Answer: 7 -(-3)=7+3=10
Step-by-step explanation:
If you multiply a negative sign be a negative number in parenthesis, then it becomes positive. So, -(-3) = 3
Can also be seen as -1*-3 = 3
angle M measures 13°.
(a) Find the supplement of angle M.
(b) Find the complement of angle M.
(a) The supplement of angle M is ?
As a result, angle M's supplement is 167 degrees, while angle M's complement is 77 degrees.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees. If the two additional angles are combined, they create a straight line and an angle.
What are complementary angles?Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.
So as per the given information:
we know that
a). 180-angle M=supplement of angle M
180-13=167 degree
b). 90-angle M=compliment of angle M
=77 degree
Therefore, the supplement of the angle M is 167 degree and the complement of angle m is 77 degree.
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At a local sandwich shop, 55% of customers preferred white bread over whole wheat bread. Of those who chose whole wheat bread, 58% preferred ham for the protein, and 46% of those who chose white bread also preferred turkey. What percentage of customers chose whole wheat bread with turkey? Round your answer to the nearest whole percentage.
19%
25%
46%
58%
The percentage of customers who chose whole wheat bread with turkey are 19 %.
Given that:-
Percentage of customers who preferred white bread = 55 %
Percentage of customers who preferred turkey with white bread = 46 % of those who like white bread.
Percentage of customers who preferred ham with whole wheat bread = 55 %
We have to find the percentage of customers who chose whole wheat bread with turkey.
Let the total number of customers at the local sandwich shop be 100x.
Percentage of customers who preferred whole wheat bread = (100-55) % = 45 %
45 % of 100x = 45x.
Percentage of customers who preferred turkey with whole wheat bread = (100-58) % of 45x = 42 % of 45x.
42 % of 45x = 18.9x ≈ 19x.
19x is 19 % of 100x.
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Answer: The answer is A, 19%
Step-by-step explanation: I had the same question.
4. Find the value of x.
6x + 14
8x + 12
The answer is x = 1, assuming that the space is meant to be an equal sign.
Find the values of x,y, and z.
guys please help me. I missed a class and can't find the video to help me solve this
Answer:
x = 7.2 , y = 57 , z = 10.8
Step-by-step explanation:
the sum of the 3 angles in the outer triangle = 180° , that is
y + 88 + 35 = 180
y + 123 = 180 ( subtract 123 from both sides )
y = 57
------------
the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{12}[/tex] = [tex]\frac{9}{9+6}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15x = 108 ( divide both sides by 15 )
x = 7.2
and
[tex]\frac{z}{18}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15z = 162 ( divide both sides by 15 )
z = 10.8
I need help and I appreciate anyone who helps
use the quadratic formula to find the solutions to the equation 3x^2-10+5=0
what is the answer for 8x - 4
Answer:
Step-by-step explanation:
Laura Russo lost her earnings statement from Siler's Lawn
and Garden. She recalls paying $43.00 in federal income taxes and
knows she deposited $306.36 in her checking account. Each week she
had deductions for Social Security and Medicare taxes; $22.35 for
medical insurance; 1.5% state tax; 1.5% local tax; and $25.00 for the
credit union. What is her gross weekly pay?
Employee's gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.
Her goss weekly pay is $409.13.
How to find her gross weekly pay?
Before taxes, benefits, and other payroll deductions are deducted, an employee's gross pay is what they are paid.
Net pay, often known as take-home pay, is the sum that is left over after all deductions have been taken into consideration.
Federal income tax:
306.36+ 43 = 349.36
Medical insurance:
349.36 + 22.35 = 371.71
Credit union:
371.71 + 25 = 396.71
State tax:
396.71 increased by 1.5% is 396.71 * (1.015) = 402.66
Local tax:
402.66 increased by 1.5% is 402.66 * (1.015)= 409.13
Her goss weekly pay is $409.13.
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A rock climber throws a first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero. How far apart are the two climbers (horizontally)?
A rock climber throws a first aid kit to the another climber who is higher up the mountain, the initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal, at the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero, height difference between climbers is 0.85 m.
What is velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by specific unit of time (for example, 60 km/h northbound). In kinematics, area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.
Vertical motion of the first aid kit:
The Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s
Acceleration, g = -9.81 m/s²
When climber who is higher up the mountain catches the kit it's vertical speed is zero.
Final vertical velocity, v = 0 m/s
We have the equation of motion, v² = u² + 2as
Substituting
0² = 4.08² + 2 x -9.81 x s
s = 0.85 m
So kit travels 0.85 m vertically.
Height difference between the climbers = 0.85 m.
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Please answer the question in the photo for a Brainliest
A lifeguard spots a swimmer in the lake at an angle of depression
of 32°. He spots a sailboat, further out, at an angle of depression of 13°. If the lifeguard is 36.5 dm away from the swimmer and 84.7 dm away from the sailboat, how far is the swimmer from the sailboat? Round your answer to the nearest tenth of a dm
Help me please! thank you
Swimmer is 47 dm away from the sailboat.
The mentioned problem will use cosine trigonometric functions to find the distance between swimmer and sailboat. Assuming the distance between lifeguard and swimmer be x and the distance between lifeguard and sailboat be y.
Taking the triangle between swimmer and lifeguard -
cos theta = base/hypotenuse
cos 32 = x/36.5
x = 0.8×36.5
x = 29.2 dm
Taking the triangle between lifeguard and sailboat -
cos 13 = y/84.7
y = 0.9×84.7
y = 76.23 dm
Therefore, the distance between sailboat and swimmer is y - x
Distance = 76.23 - 29.2
Performing subtraction
Distance = 47.03 dm
Round to nearest tenth
Distance = 47 dm
Thus, the sailboat and swimmer are 47 dm apart.
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Evaluate this expression:
| b + 1 | + 8
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\pm b + 9 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given expression is :
[tex]\qquad \tt \rightarrow \: |b + 1| + 8[/tex]
[tex]\qquad \tt \rightarrow \: |b| + 1 + 8[/tex]
[ as 1 is a positive number, it can come out of modulus function as it is ]
[tex]\qquad \tt \rightarrow \: |b| + 9[/tex]
Now, there are two cases possible.
Case 1 :
[tex]\qquad \tt \rightarrow \: b + 9[/tex]
[ if b is a positive number, it will come out of modulus as it is ]
Case 2 :
[tex]\qquad \tt \rightarrow \: - b + 9[/tex]
[ if b is a negative number, it will come out of modulus with a negative sign, to make the overall term out of modulus positive ]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
a soda company had sales of $35,109 million in 2010 and $45,984 million in 2014. use the midpoint formula to estimate the sales in 2012. assume that the sales followed a linear pattern.
The sales in 2012 is estimated to be $40546.5 million if we use the midpoint formula assuming that the sales followed a linear pattern.
Midpoint is a term used in geometry and can be described as the center or middle point of a line segment. It enables you to take two endpoints, and then by using these endpoints you can find the point that is midway between them in the line segment.
Considering,
[tex]P_{1} = (x_{1},y_{1})[/tex]
[tex]P_{2} = (x_{2},y_{2})[/tex]
Here;
[tex]x_{1}[/tex] = 2010
[tex]x_{2}[/tex] = 2014
[tex]y_{1}[/tex] = $35,109 million
[tex]y_{2}[/tex] = $45,984 million
The formula for the midpoint is given as;
[tex]P_{m}[/tex] = {( [tex]x_{1} + x_{2}/2[/tex] ), ( [tex]y_{1} + y_{2} / 2[/tex] )}
[tex]P_{m}[/tex] = {(2010 + 2014 / 2), (35109 million + 45984 million / 2)}
[tex]P_{m}[/tex] = {(4024 / 2), (81,093 million / 2)}
[tex]P_{m}[/tex] = {2012 , 40546.5 million}
Therefore, the sales in 2012 are calculated to be $40546.5 million by using the midpoint formula.
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[tex]2(40 - 5y)=10y+5(1 - y)[/tex]
Answer:
y = 5
Step-by-step explanation:
2(40 - 5y) : 80 - 10y
10y + 5(1 + y) : 5y + 5
80 - 10y = 5y +5
-10y = 5y -75
-10y - 5y = 5y - 75 - 5y
-15y/-15 = -75/-15
-15y/-15 : y
-75/-15 : 5
Hence, The answer should be 5
Use the point-slope form of the straight line to find the equation of the straight line which passes through the point (2, 1) and is parallel to the line 5x + y = 1.
Answer:
y=-5x+6
Step-by-step explanation:
the two lines are parallel so they have the same slope and if you put the like in y=mx+b it would be y=-5x+1 so the slope is -5
Then you need to put it into point slope for to figure it out y-y1=m(x-x1)
y-1=-5(x-1) (simplify)
y-1=-5x+5 (add 1 to both sides)
y=-5x+6
An arcade in Boulder, Colorado uses 3 different colored tokens for their game machines. For $20 you can purchase any of the following mixtures of tokens: 14 gold, 20 silver, and 24 bronze; OR, 20 gold, 15 silver, and 19 bronze; OR, 30 gold, 5 silver, and 13 bronze. What is the monetary value of each token?
The monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.
What is defined as the elimination method?The elimination method involves removing a single variables by combining the two equations. This method eliminates one variable, enabling you to solve for the other. Since there are two variables in a two-equation system, eliminating one simplifies the purpose is to solve for the other.The given conditions in the question are-
Let the monetary value of gold be 'a'.
Let the monetary value of silver be 'b'.
Let the monetary value of bronze be 'c'.
The total monetary value is $20.
The equation will be;
14 gold, 20 silver, and 24 bronze
14a + 20b + 24c = 20 .......eq1
20 gold, 15 silver, and 19 bronze
20a + 15b + 19c = 20 .......eq 2
30 gold, 5 silver, and 13 bronze.
30a + 5b + 13c = 20 .....eq 3.
Solving equation 1,2 and 3 by elimination method.
a = 1/2
b = 7/20 and
c = 1/4
Thus, the monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.
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Theo is going on holiday across Europe and needs to change pounds into other currencies.
Ai) 5575 Swedish kronor 500*11.15
Aii) 312.50 swiss frans 250*1.25
B) £345 407.10/1.18
Hope this helps, have a great day!!
I don't understand this question
can u please help!
i will give u 11 points <3
Answer:
year 7 have 135 students
year 9 have 45 students
Step-by-step explanation:
200=total students
360=value of the whole chart
1/2×360
=180
year 8 have 180students
360-180=180
the students remain are 180
1/4×180
=45
year 9 have 45 students
180-45
=135
year7 have 135 students
I need help please on this it is very hard for me
Answer:
Below in bold.
Step-by-step explanation:
3/20
We divide 3 by 20:-
3 / 20 = 0 so we divide 30 by 20 and proceed as below:
20)3.00 ( 0.15
20
100
100
......
The answer is 0.15 which is terminating.
5/11
If we divide as above we get 0.45454545....
The 45 keeps repeating
2/15
Dividing gives 0.133.........
Repeating
7/8 = 0.875
terminating.
9/16
= 0.5625
terminating.
Answer:
3/20 = 0.15 (Terminating)
5/11 = 0.45454 (Repeating)
2/15 = 0.13333 (Repeating)
7/8 = 0.875 (Terminating)
9/16 = 0.5625 (Terminating)
Explanation:
The definition of Terminate means to bring to an end. This would also apply to the decimals. To find whether a fraction is terminating or not, is to simply divide and you will get a decimal, unless it is mixed fraction. Terminating will bring an end, Ex: 1/2 ( 1 ÷ 2 ) which would equal = 0.5 This is an example of a terminating decimal. A repeating decimal is a decimal that never ends of its repetition, Ex: 0.13333333 (Continuous).
I hope this helps my grammar might bit a bad sorry.
Hope you get an A ^^
Have a great day
Kaj is 1.55 meters tall at 11 am she measures the length of a trees shadow to be 26.15 meters and she stands 22 meters away from the tree so the tip of her shadow meets the tip of the trees shadow find the hight of the tree round to the nearest hundredth
Answer: 9.77 m
Step-by-step explanation:
xyz
12x=12x+3 solve for x step by step!!
answer:
I hope the solution is helpful.
the population of a village increased from 234 to 275 during one year.Find the percentage increase
Answer:
275-234 = 41
41/275 times 100
4100/275
=14.90909
=15%
Step-by-step explanation:
1. Jackie's balance at the beginning of October was $432.23. During that month she made
deposits totaling $752.34, wrote checks totaling $532.13, paid a maintenance fee of $11, and
earned $3.42 in interest on the account. What was the balance at the end of the month?
Based on the beginning balance to Jackie's account and the deposits as well as the checks written, the balance at the end of the month was $644.86
How to find the balance at the end of the month?At the end of the month, the simple formula to determine Jackie's balance is:
= Beginning balance + Cash inflows - Cash outflows
This means that to calculate the balance on Jackie's account at the end of October gives:
= Beginning balance + Deposits + Interest earned - Checks written - maintenance fee
= 432.23 + 752.34 + 3.42 - 532.13 - 11
= $644.86
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I will Mark Brainlist Please Help!!! its a algebra 2 Question image is attached below thanks so much !!
Using the law of indices, [tex]1024^{\frac{2}{5} } = 16[/tex]
How to solve exponent using law of indices?The expression can be solved using the law of indices as follows:
[tex]1024^{\frac{2}{5} }[/tex]
using law of indices, involving bracket.
Brackets with indices are where we have a term inside a bracket with an index (or power) outside of the bracket.
To do this we can raise everything inside the bracket to the power.
[tex](a^{b} )^{x} = a^{bx}[/tex]
Therefore,
1024 = 2¹⁰
Hence,
[tex]2^{\frac{2}{5} (10)} = 2^{\frac{20}{5} } = 2^{4} = 16[/tex]
Therefore,
[tex]1024^{\frac{2}{5} } = 16[/tex]
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Evaluate the expression
x-y
if
x = -2
y = −3
z=5
Show your work.
Given: x = -2; y = -3; z = 5
It is clear that a numerical term can only be evaluated from an expression filled with numbers (no variables). In the expression provided, we have two variables, where y is being subtracted from x.
The expression can't be simplified because there is no like terms in the expression. However, since there are specific numerical values for each variable, we can substitute the numerical values for the variables in the expression and simplify the expression.
Step-2: SolvingAs planned, let's substitute the variables into the expression
⇒ x - yHere, we know that x = -2 and y = -3.
⇒ -2 - (-3)If -2 is being subtracted by a negative integer, the negative integer will become positive, and the "minus sign" will be converted to a "plus sign".
⇒ -2 + 3 = 1Step-3: ConcludeWe can conclude that 1 is the solution to the expression.
A water desalination plant can produce 2.6 x 10^6 gallons of water in one day. How many gallons can it produce in 6 days? Write your answer in scientific notation.
Amount of water produced in 6 days is 15.6×10⁶.
We will simply perform multiplication to find the amount of water produced in 6 days.
Amount of water produced in 6 days = amount of water produced in one day × 6
Amount of water produced in 6 days = 2.6×10⁶×6
Performing multiplication to find the amount of water produced in 6 days
Amount of water produced in 6 days = 15.6×10⁶
The answer is in scientific notation as 15.6 is coefficient, 10 is base and 6 is exponent. Therefore, amount of water produced by plant in 6 days is 15.6×10⁶.
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Two angles form a linear pair. One angle is 5
more than four times the size of the other angle.
Find the measure of the largest angle.
Answer:
The measure of the largest angle is 145°
Step-by-step explanation:
Since the angles form a linear pair taking two angles that add to 180 and solving for x will give you the answer. the sentence "One angle is 5 more than four times the size of the other angle." your equation should look like this:
5 + 4x. the other angle uses the variable x. So the equation 5 + 4x + x = 180 should result in x = 35. That saying, the smaller angle is 35 and to find the larger angle either plug in x or subtract 180-35. both shoukd result in 145° which is the larger angle.
Starting from scratch, Tori finished 1/6 of a reading assignment Monday afternoon and another 1/3 of it on Tuesday afternoon. What fraction of the reading assignment was done by Tuesday night?
Write your answer as a fraction or as a whole or mixed number.
The fraction of the reading assignment done by Tuesday night is 1/2.
What are fractions?Fractions are the numbers that make up a portion of the whole. An object or a collection of objects can be a whole. If a quantity or item is divided into equal pieces, each piece will represent a portion of the entire.A fraction is represented by the ratio a/b, where a represents the numerator and b is the denominator.Given:
Let the total reading assignment be x.
Fraction of the reading assignment finished by Tori on Monday afternoon = (1/6)x
Fraction of the reading assignment finished by Tori on Tuesday afternoon = (1/3)x
The fraction of the reading assignment done by Tuesday night is,
Total - Fraction of the reading assignment completed by Tori
= [tex]x -(\frac{x}{6} + \frac{x}{3} )[/tex]
= [tex]x -(\frac{x+ 2x}{6} )[/tex]
= [tex]x - \frac{3x}{6}[/tex]
= [tex]x -\frac{x}{2}[/tex]
= [tex]\frac{2x-x}{2}[/tex]
= [tex]\frac{x}{2}[/tex]
So, 1/2 of the reading assignment(x) was done by Tuesday night.
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