∫f(x)dx=43x3−3x2+7x+Cf(x)=4x2−6x+7∫f(x)dx=∫(4x2−6x+7)dx=4⋅∫x2dx−6⋅∫xdx+7⋅∫1dx=4x33−6x22+7x11+C=43x3−3x2+7x+C
Solve |3x - 4| = 6
{-2/3, 10/3}
{-10/3, 10/3}
{-2/3, 2/3}
Answer:
{-2/3, 10/3}
Step-by-step explanation:
Let's solve your equation step-by-step.
|3x−4|=6
Solve Absolute Value.
|3x−4|=6
We know either3x−4=6or3x−4=−6
3x−4=6(Possibility 1)
3x−4+4=6+4(Add 4 to both sides)
3x=10
3x/3 = 10/3
(Divide both sides by 3)
x=10/3
3x−4=−6(Possibility 2)
3x−4+4=−6+4(Add 4 to both sides)
3x=−2
3x/3 = −2/3
(Divide both sides by 3)
x= −2/3
edie earned a gross pay of $927.88 last week. determine the amount that edie contributed to both social security and medicare
Based on the gross pay to Edie of $927.88, the amount contributed by Edie Social Security was $57.53 and the amount to Medicare was $13.45
How to find contribution to social security?The current Social Security tax rate is 6.2% which means that to find the Social Security tax that Edie will contribute will be:
= Social security tax rate x Gross pay of Edie
= 927.88 x 6.2%
= $57.52856
= $57.53
The Medicare tax rate is 1.45%. The Medicare tax can therefore be found by multiplying the gross pay by the Medicare tax rate:
= 927.88 x 1.45%
= $13.45
Find out more on Medicare and Social Security at https://brainly.com/question/19815763
#SPJ1
Solve for n.
n+m= 16
Answer:n=16-m
Step-by-step explanation:
n+m=16
Subtract m from both sides.
n=16−m
How many times larger is 5.025 x 1010 than 1.5 x 108?
335
299
29.9
3.35
[tex]\frac{5.025 \times 10^{10}}{1.5 \times 10^{8}} \\ \\ =\frac{5.025}{1.5}(100) \\ \\ =\boxed{335}[/tex]
Option A is correct, 5.025 x 10¹⁰ is 335 times larger than 1.5 x 10⁸.
To determine how many times larger one number is than another, we divide the larger number by the smaller number.
In this case, we want to find how many times larger 5.025 x 10¹⁰ is than 1.5 x 10⁸.
Dividing the larger number by the smaller number:
(5.025 x 10¹⁰) / (1.5 x 10⁸)
To simplify, we can divide the coefficients (5.025 / 1.5) and subtract the exponents (10¹⁰ - 10⁸):
(5.025 / 1.5) x 10¹⁰⁻⁸
Evaluating the division of the coefficients:
(3.35) x 10²
Therefore, 5.025 x 10¹⁰ is 3.35 x 10² times larger than 1.5 x 10⁸.
In decimal form, this can be expressed as:
3.35 × 10² = 335
Therefore, 5.025 x 10¹⁰ is 335 times larger than 1.5 x 10⁸.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
find three consecutive integers such that the sum of the first and twice the second is 98 minus three times the third
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let the numbers be : x, x + 1 and x + 2 ~
now, according to given condition :
[tex]\qquad \sf \dashrightarrow \: x + 2(x + 1) = 98 - 3(x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: x + 2x + 2 = 98 - 3x - 6[/tex]
[tex]\qquad \sf \dashrightarrow \: x + 2x + 3x = 98 - 6 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x = 90[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 90 \div 6[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 15[/tex]
So, tge required numbers are : 15, 16 and 17
These questions are about calculus, I would greatly appreciate your help on both questions!
asap, please!
For the function f(x) =(4 sin x)/(1+cosx) , then f'(x) = 4/(1+cosx) using quotient rule of differentiation and f'(2) = 2.00
What is quotient rule for differentiation?Quotient rule for differentiation states that the differentiation the division of two functions u, v is given as
(u/v)' = (u' v - u v')/v² , where ' represents first derivative with respect to independent variable
Given f(x) = (4sinx)/(1+cosx)
let u =4 sin x , v = 1+cos x , u'=4cos x , v' = -sin x
Then f(x) =u / v
Using quotient rule of differentiation:
f'(x) = ( u' v -u v' )/v² = (4cosx(1+cosx) +4sin²x )/(1+cos x)²
f'(x) = = 4(cos x +cos² x +sin² x)/(1+ cos x)² = 4(cos x +1)/(1+ cos x)²
f'(x) = 4/(1+ cos x)
To find value of f'(x) at x= 2
f'(5) = 4/(1+cos2) = 2.000609= 2.00(rounding off )
Therefore if f(x) = (4x² tan x)/sec x then f'(x) = 4/(1+cos x) and f'(2) =2.00
Also. Learn more about differentiation rules from the link below:
https://brainly.com/question/14406735
#SPJ1
Write equation in slope-intercept form (9,-5) slope -4/3
The equation of the line in slope intercept form is y = (-4/3)x + 7.
According to the slope intercept form, the equation of a line is given as-
y = mx + c
where m is the slope and c is the y intercept.
Here we are given that an equation passes through the point (9,-5) and has a slope of -4/3.
According to the point slope form, the equation of a line passing through (x1, y1) and slope m is given as-
(y - y1) = m(x - x1)
Here,
x1 = 9, y1 = -5 and m = -4/3
Thus,
(y + 5) = -4/3(x - 9)
3(y + 5) = -4(x - 9)
3y + 15 = -4x + 36
3y = -4x + 21
y = (-4/3)x + 21/3
y = (-4/3)x + 7
This is our equation in slope intercept format as m = -4/3 and c = 7
Thus, the equation of the line in slope intercept form is y = (-4/3)x + 7.
Learn more about equation of a line here-
https://brainly.com/question/13763238
#SPJ9
ILL GIVE BRANNIEST TO THE CORRECT ANSWER Find the coordinates of the point
7/10 of the way from A to B.
Answer: X = 8.4 Y= 3.5
Step-by-step explanation:
Translate the sentence into an equation or formula.
The surface area SA of a rectangular prism is 2 times the sum of the width (w) times height (h), and length (
l
) times width, and length times height.
A translation of the equation for the surface area of this rectangular prism is given by: SA = 2(WH + LW + LH).
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
How to translate the sentence into an equation or formula?Mathematically, the surface area of a rectangular prism can be calculated by using this equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.In this context, we can reasonably and logically deduce that a translation of the equation for the surface area of this rectangular prism is given by:
SA = 2(WH + LW + LH).
Read more on surface area of a rectangular prism here: https://brainly.com/question/28185251
#SPJ1
Express the given function
Answer:
f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]
Step-by-step explanation:
If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]
Find the distance between the points A (13, 2) and B (7, 10).
Answer:
[tex]\sqrt{89}[/tex]units
Step-by-step explanation:
[tex]\sqrt{(7-13)^2+(10-2)^2}[/tex]
(-5)^2+(8)^2=25+64
25+64=89
[tex]\sqrt{89}[/tex]
the answer would be [tex]\sqrt{89}[/tex]
Solve 19×50 numerically
The solution of expression 19×50 is found as 950.
What is defined as the distributive property?This property states that multiplying the product of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.
The distributive property holds true for division the same way that it holds true for multiplication. However, with division, the concept of "breaking apart" or "distributing" can only be applied by dividing the numerator into lesser numbers that are exactly divisible even by divisor.In other words, the distributive property requires a phrase of the form:
A (B + C) can be simplified as A (B + C) = AB + AC.
This same applies foe the subtraction;
Thus, for the given numerical;
= 19×50
Using distributive property.
= (20 - 1)×50
Open the braces;
= 20×50 - 1×50
= 1000 - 50
= 950
Therefore, the solution of the numerical 19×50 is 950.
To know more about the distributive property, here
https://brainly.com/question/2807928
#SPJ9
Question 2 (1 point)
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
O a
O b
O c
Od
Change 1,000 to Scientific notation and then add to (2.3 x 10^2)
Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
The correct answer choice as required in the task content is; Choice B; Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6).
To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
Scientific notationThis is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.
which number is one thousand times larger than 2.3 x 10²
Change 1,000 to Scientific notation and then multiply by (2.3 x 10²)1000 to scientific notation
= 10³
2.3 x 10² × 1000
= 2.3 x 10² × 10³
= 2.3 × 10^5
Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.
Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
Learn more about scientific notation:
https://brainly.com/question/27862246
#SPJ1
3. Jerry purchased two cans of paint. He used 6/4 of it. How much did Jerry have
used in decimal?
A. 6.40
B. 4.60
C. 1.50
D. 0.67
The amount used in decimal is 1.50
How to determine the amount used?The given parameters are
Cans = 2
Amount used = 6/4
The amount used in decimal is calculated as:
Amount used = 6/4
Divide 6 by 4
So, we have
Amount used = 1.50
Hence, the amount used in decimal is 1.50
Read more about decimals at:
https://brainly.com/question/1827193
#SPJ1
Part A
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more. Choose the explicit formula to represent the situation.
A. an = 14 + 9(n + 1)
B. an = 5 + 9n
C. an = 14 + 9n
D. an = 5 + 9(n + 1)
Part B
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more. Choose the recursive formula to represent the situation.
A. an = an – 1 + 5; a1 = 14
B. an = an – 1 + 23; a1 = 9
C. an = an – 1 + 14; a1 = 9
D. an = an – 1 + 9; a1 = 14
Answer:
C. an = 14 + 9n
Step-by-step explanation:
The cost of having one pizza delivered is $14. Each additional pizza costs $9 more.
Let n= additional pizza
an = 14 + (9 × n)
an = 14 + 9n
Melanie receives a 9% commission on every house she sells. If she received a commission of $20,340, what was the value of the house she sold?
i need help for a good grade thank youuu
Answer:
Here us the answer in the attachment
Answer:
the person above is correct
Step- by-step explanation:
The total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2013, what was the initial total attendance?
The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.
How to calculate the value?It should be noted that from the information, the total attendance at a science museum is modeled by the function
In this case, the total attendance when x=0 will be:
f(x) = 17,371(1.041)x.
f(x) = 17,371(1.041^0)
= 17371 × 1
= 17371
Therefore, the total attendance when x = 0 will be 17371.
Learn more about functions on:
brainly.com/question/25638609
#SPJ1
K
Convert the angle to a decimal in degrees.
16°43'27"
The value of the angle 16°43'27"is approximately 16.724167 degrees.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.
The radian is the SI unit for measuring angles.1 degree = [tex]\frac{\pi}{180}[/tex] radiansA complete rotation around a circle is 180°.A degree is a narrow enough angle for many practical tasks where full degrees are enough for precision. In those instances when this is not the case, such as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be expressed in decimal degrees.To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.
1 degree=60 minutes.
1 minute = 60 seconds.
The given angle is 16°43'27"
27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree
43 minutes= 43 ÷ 60 degree = 0.71666666..
Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...
Therefore required angle ≈ 16.7241667 degrees.
To learn more about degree visit:
https://brainly.com/question/4244059
#SPJ9
y = x – 2
y = –3x – 2
Answer:
y=3x-2
Step-by-step explanation:
if for y=-3x-2 is being solved for x your answer would be:
y=3x-2
3x-2=y
3x=y+2
3x/3=y+2/3
so your final answer for this question is: x=y+2/3
and for the first one y=x-2 there is no answer for it
If Xi = 1,3,5,8,12,15,9. Find the mean and median of the data set
The mean of the given data is 7.57 and the median of the given data is 8
Given that a data set i.e. Xi= 1,3,5,8,12,15,9. asked to find the mean and median of the given data.
Mean:
The mean is the average of the supplied numbers and is computed by dividing the total number of numbers by the sum of the given numbers.
Mean= [tex]\frac{sum of observation}{number of observation}[/tex]
Mean=[tex]\frac{1+3+5+8+12+15+9}{7}[/tex]
Mean=[tex]\frac{53}{7}[/tex]
Mean=7.57
The mean of the given data is 7.57
Median:
The median is a statistical metric that identifies the midway value of an ascending-ordered dataset (i.e., from smallest to largest value). The metric separates the dataset's lower and upper halves.
Arranging in ascending-order⇒1,3,5,8,9,12,15.
Then median=8
Therefore,The mean of the given data is 7.57 and the median of the given data is 8
Learn more about mean here:
https://brainly.com/question/13451489
#SPJ9
A brokerage company evaluated the three services its call centers provide for reliability. The results showed the following:
Service Reliability Percentage
Checking customer account status .85
Confirming orders .72
Stock quotes .96
Compute the over-all reliability of the call center (round to 2 decimals) _____________
Show computation:
If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
Over-all reliability of the call centerUsing this formula to calculate the over-all reliability of the call center
Over-all reliability of the call center=Checking customer account status × Confirming orders× Stock quotes
Where:
Checking customer account status =.85
Confirming orders= .72
Stock quotes= .96
Let plug in the formula
Over-all reliability of the call center=.85×.72×.96
Over-all reliability of the call center=0.58752
Therefore If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
Learn more about Over-all reliability of the call center here:
https://brainly.com/question/17511330
#SPJ1
4. Given 6 (1-x) what is the value of the
expression when x = -8?
Answer:
let x be -8
6(1-8)
6(7)
6x7=42
answer=42
How much is 2 tablets 3 x per day for 14 days
Answer:
84 tablets with 6 per day
logs (20x + 5y) using the properties of logarithms to expand
The logarithmic expansion of logs(20x + 5y) by using the properties of logarithmic is log(5)+log(4x+y).
The basic logarithmic function is of the form f(x) = logₐx(r)n = logₐx, where a > 0. It is the inverse of the exponential function aⁿ = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic functions is very useful in various mathematical computations.
Given that, log(20x+5y) and we have to expand it by using the properties of logarithms. So, let's proceed to solve the question.
log(20x+5y)
we can write 20 in terms of powers like 20 = (2²)x5
log((2².5)x+5y)
log(5(2².5x/5+5y/5))
log(5(2²x+y))
log(5(4x+y))
∵ log(ab) = log(a)+log(b)
⇒log(5(4x+y)) = log(5)+log(4x+y)
Hence, on expanding log(20x+5y) by using the properties of logarithms we get log(5)+log(4x+y) as our required answer.
Learn more in depth about the logarithms at https://brainly.com/question/13473114
#SPJ9
I need help with this question
Answer:
Step One: Evaluate the Function for A and B
f(1) = -6
f(2) = -1.5
Step Two: Use the Average Rate of Change Formula
f(b) - f(a) / b - a
-1.5 - -6 / 2 - 1
4.5 / 1
4.5
The average rate of change is equal to 4.5
In short, use
[tex] \frac{f(2) -f(1) }{2 - 1} [/tex]
Step-by-step explanation:
To explain, substitute 1 and 2 for f(x) then divide the difference of the two answers by the difference of the two x coordinates above to find the average rate of change
Which of the following equations has no solutions?
4x - 4 = -4(-x + 1)
-9x + 2 = -3(3x + 2)
-6x + 1 = -3(2x + 1) + x
-5 + 14x = 7(2x) - 5
Answer:
-9x + 2 = -3(3x + 2).
Step-by-step explanation:
-9x + 2 = -3(3x + 2)
-9x + 2 = -9x - 6
0 = -8, which is absurd, so :-
No solutions.
Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure.
Answer:
Slope of one of the dotted lines:
[tex]y=x[/tex] or [tex]y=x+5[/tex]
Slope of the line of reflection:
[tex]y=-x[/tex]
Step-by-step explanation:
When seeing the dotted lines, both of them have a rise & run of 1, indicating that y = x. However, one of the lines has a y-intercept of 5, making it y = x + 5. So, the slopes for the dotted lines are [tex]y=x[/tex] or [tex]y=x+5[/tex].
The line of reflection has a rise & run of -1, and goes through the origin, indicating that the equation is y = -x.
Split the fraction using partial fraction decomposition;
Please see the attached image for your answer. Hope this helps! If you can't read something please let me know.
HELP Trapezoid A'B'C'D' is the image of trapezoid ABCD under a rigid transformation.
The Image of the trapezoid under rigid transformation is given by A'B'C'D' attached below.
The unique process of changing an existing graph or graphed equation to create a completely different version of the given graph is known as graph transformation.
Without changing the figure, a transformation shifts it up, down, to the right, to the left, or diagonally.Rotation is the term used to describe the transformation of a figure around a specific point. A fixed point is used to rotate the figure either clockwise or counterclockwise.In the given figure we can see that the Trapezoid ABCD is rotated around a fixed point to get the image of the trapezoid A'B'C'D'.
So the figure gets a rotational transformation.
From the figure we can assume that the figure is rotated about 135° clockwise about a fixed point.
To learn more about transformation visit:
https://brainly.com/question/11709244
#SPJ9