Calculus HW , will someone please teach me how to do this problem. I'm struggling, thanks! 10 Points
Answers
Compute the first two derivative.
[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]
[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]
[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]
Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so
[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]
and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].
Intercepts
Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since
[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]
The first intercept you listed is not a valid intercept. One or both coordinates must be 0.
Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).
[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]
The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).
Relative minima/maxima
Find the critical points. We have [tex]f'(x) = 0[/tex] when
[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]
and [tex]f'(x)[/tex] is undefined when
[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]
Check the sign of the second derivative at the first two critical points.
[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at } f(-2\sqrt2) = -8[/tex]
[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]
For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.
[tex]f(-4) = f(4) = 0[/tex]
So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).
Inflection points
We have [tex]f''(x) = 0[/tex] for
[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]
The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).
Related Questions
What are the excluded values? –4 and –1 -1/2, 1, and 4 1 1 and 4
Answers
The excluded values are x = 4 and x - 1
How to determine the excluded values?The complete question is added as an attachment
The function is given as:
(2x^2 - 7x - 4)/(x^2 - 5x + 4)
Set the denominator to 0
x^2 - 5x + 4 = 0
Expand
x^2 - x - 4x + 4 = 0
Factorize the equation
x(x -1) - 4(x - 1) = 0
This gives
(x - 4)(x - 1) = 0
Solve for x
x = 4 and x - 1
Hence, the excluded values are x = 4 and x - 1
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Answer: Its D 1 and 4
Step-by-step explanation:
I took the assignment
What is the distance between the following points? Khan Academy Distance between two points
Answers
Answer: A
Step-by-step explanation:
The points are (-5, 8) and (4, 6).
The distance is [tex]\sqrt{(-5-4)^2 + (8-6)^2}=\sqrt{85}[/tex]
Line l has a slope of -3. The line through which of the points is perpendicular to l
Answers
Perpendicular lines have opposite reciprocal slopes
So the slope of the line perpendicular to line L is 1/3
If an event has a 55% chance of happening in one trial, how do I determine the chances of it happening more than once in 4 trials?
Answers
The chances of it happening more than once in 4 trials is 13%
How to determine the numberFrom the information given, we have can deduce that;
Probability of 1 trial = 55%
= 55/ 100
Find the ratio
= 0. 55
We are to find the probability of it happening more than once in 4 different trials
If the probability of it happening in one trial is 555 which equals 0. 55
Then the probability of it happening in 1 in 4 trials is given as;
P(1/4 trials) = 1/ 4 × 55%
P(1/4 trials) = 1/ 4 × 0. 55
Put in decimal form
P(1/4 trials) = 0. 25 × 0. 55
P(1/4 trials) = 0. 138
But we have to know the percentage
= 0. 138 × 100
Multiply the values, we have
= 13. 8 %
Thus, the chances of it happening more than once in 4 trials is 13%
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how many significant figures are in this number 6.01x10^3
Answers
Answer:
3
Step-by-step explanation:
6.01 has 3 sig fig
I think that's how I do it
What is the probability that the mean score for 10 randomly selected people who took the LSAT would be above 157? Round your answer to three decimal places. (Example: 0.398)
Answers
Using the normal distribution, there is a 0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching this problem on the internet, the parameters are given as follows:
[tex]\mu = 150, \sigma = 9, n = 10, s = \frac{9}{\sqrt{10}} = 2.85[/tex]
The probability is one subtracted by the p-value of Z when X = 157, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (157 - 150)/2.85
Z = 2.46
Z = 2.46 has a p-value of 0.993.
1 - 0.993 = 0.007.
0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.
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A recipe for lemon bars called for 9" X 13" pan. How many 1" X 1" bars can be cut? How many 2" X 2" bars can be cut? How much is wasted if your serve only 2" X 2" square bars?
Answers
The number of bars which can be cut for the 1" X 1" and 2" X 2" square bars are; 117 and 29 units respectively.
How many bars can be cut from the pan in each case?The total area of the given pan can be evaluated as follows;
Area = length × width
= 9 × 13
= 117 square units.
Hence, the number of 1" X 1" bars can be cut which can be cut from the pan;
= 117/(1×1)
= 117 1" X 1" bars.
For the 2" X 2" square bars, we have;
= 117/(2×2);
29 remainder 1 square unit.
Ultimately, one square unit of the pan is wasted for the 2" X 2" square bars.
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Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415.
Answers
The interest due on financing option is $307.50
What is interest on financing?
Interest on financing is the extra amount paid by the couple when their total payments are compared to the cash price of $6,230.
The total payments would be the 25% down payment plus the sum of the twelve monthly payments of $415 each
Down payment=cash price*25%
Down payment=$6230*25%
Down payment=$1,557.50
Total monthly payments=amount of each monthly payment*number of monthly payments
monthly payment=$415
number of monthly payments=12
Total monthly payments=$415*12
Total monthly payments=$4,980
Total payment under financing=Down payment +Total monthly payments
Total payment under financing=$1,557.50+$4,980
Total payment under financing=$6,537.50
Interest=$6,537.50-$6,230
Interest on financing=$307.50
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Complete question:
Mr. and Mrs. Chan want to buy new furniture that has a cash price of $6230. On the installment plan, they must pay %25 of the cash price as a down payment and make twelve monthly payments of $415. How much interest did they pay due to financing?
Which equation represents a parabola with a vertex at (7,-3)
Answers
Answer:
See Below
Step-by-step explanation:
y = a (x-7)^2 -3 where 'a' is any number except 0
Solve the inequality for x.
OA.
X S
5- 2/2 x ²
x 2
28
OB. x ≤ 7
OC.
28
9
OD. x ≥ 7
Answers
The solution to the inequality x-13<=7+4x is x >= -20/3
How to solve the inequality?The inequality expression is given as:
x-13<=7+4x
Add 13 to both sides of the inequality
x <= 20 + 4x
Subtract 4x from both sides of the inequality
-3x <= 20
Divide both sides of the inequality by -3
x >= -20/3
Hence, the solution to the inequality x-13<=7+4x is x >= -20/3
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Complete question
Solve the inequality for x
x-13<=7+4x
PLEASE HELP!
Let f be the function given by f (x) = (create an original sinusoidal function with an amplitude not equal to 1, a period not equal to 2π, and non-zero phase and vertical shifts).
ex: F of x equals negative one half times sine of quantity 3 times x plus pi over 2 end quantity minus 2
Part A: State the amplitude and vertical shift.
Part B: Determine the period of f (x), showing all necessary calculations.
Part C: Calculate the phase shift of the sinusoidal function with proper mathematical justification.
Part D: Graph the sinusoidal function by hand, using your answers from parts A–C.
Choose an angle θ, in radians, such that 2π < θ < 4π . Let θ = (create an original angle measure).
ex: Theta equals 13 pi over 6
Part E: Determine the exact value of cos θ using the sum formula. Show all necessary mathematical work.
Part F: Determine the exact value of sin θ using the difference formula. Show all necessary mathematical work.
Part G: Calculate the exact value of tan 2θ, using your answers from parts E – F.
Answers
The equation of the function f(x) is f(x) = 2 sin(π/2(x + 6)) - 3
How to create the sine function?A sine function is represented as:
f(x) = A sin(B(x + C)) + D
Where
A = Amplitude
Period = 2π/B
C = Phase shift
D = Vertical shift
The requirements in the question are:
Amplitude not equal to 1Period not equal to 2πNon-zero phase and vertical shiftsSo, we can use the following assumptions
A = 2
Period = 4
C = 6
D = -3
So, we have:
f(x) = 2 sin(B(x + 6)) - 3
The value of B is
4 = 2π/B
This gives
B = π/2
So, we have:
f(x) = 2 sin(π/2(x + 6)) - 3
The amplitude, vertical shift, period of f(x)and the phase shiftUsing the representations in (a), we have:
Amplitude = 2Vertical shift = -3Period = 4Phase shift = 6The graph of the functionSee attachment for the graph of f(x)
The value of cos θLet θ = 3π
So, we have:
cos(3π)
This is calculated as:
cos(3π) = cos(2π + π)
Expand
cos(3π) = cos(2π) *cos(π) - sin(2π) *sin(π)
Evaluate
cos(3π) = -1
The value of sin θLet θ = 3π
So, we have:
sin(3π)
This is calculated as:
sin(3π) = sin(2π + π)
Expand
sin(3π) = sin(2π) *cos(π) + cos(2π) *sin(π)
Evaluate
sin(3π) = 0
The value of tan 2θLet θ = 3π
So, we have:
tan(2 * 3π)
tan(6π)
This is calculated as:
tan(6π) = tan(3π + 3π)
Evaluate
tan(3π) = 0
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f(x) = 2x^2 - x -10
What are the x-intercepts of the graph of f(x)? Show your work
Answers
Answer:
[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=2x^2-x-10[/tex]
The x-intercepts of the graph are the points at which the curve crosses the x-axis, so when f(x) = 0.
To find these points, factor the quadratic equation, set it to zero, then solve for x.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=2 \cdot -10 = -20[/tex]
[tex]\implies b=-1[/tex]
Therefore, the two numbers are -5 and 4.
Rewrite the middle term as the sum of these two numbers:
[tex]\implies 2x^2-5x+4x-10[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x-5)+2(2x-5)[/tex]
Factor out the common term (2x - 5):
[tex]\implies (x+2)(2x-5)[/tex]
Set the factored function to zero:
[tex]\implies (x+2)(2x-5)=0[/tex]
Apply the zero-product property:
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]
Therefore, the x-intercepts of the graph are:
[tex](-2,0) \textsf{ and }\left(\dfrac{5}{2},0\right)[/tex]
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need heeeelp please
Answers
Answer:
(x, y) = (-√3/2, 1/2)
Step-by-step explanation:
The terminal point for that angle can be read from a unit circle chart.
On the attached chart, the point of interest is the first one above the -x axis on the left side. The chart tells you the coordinates are ...
(x, y) = (-√3/2, 1/2)
Can someone please please help me
Answers
Answer:
order: 2, 3, 1
Step-by-step explanation:
Reasonableness checks and your knowledge of integers and fractions will help you solve this. The offered questions are intended to help you think this through.
a.For an output of -31, the machine (x -2)² cannot possibly be last. Its output can only be positive.
machine 2, (x-2)², cannot be last
Also, machine 3 cannot be last. For the output to be -31, the input to machine 3 must be -1/31. Neither of the other machines can produce a fraction with the inputs they might receive.
b.
For an input of x=0, the machine 1/x cannot possibly be first. 1/0 is undefined.
The other two machines will give the following outputs for an input of 0:
machine 1: 4(0) -32 = -32
machine 2: (0 -2)² = 4
It is unlikely that machine 1 will be first, because the other two machines cannot do anything useful with -32 as an input.
machine 3, 1/x, cannot be first
c.The reasoning of part (a) tells you the last machine must be machine 1. The reasoning of part (b) tells you the first machine cannot be 3, so must be 2. The order of the machines must be ...
machine 2: (0 -2)² = 4 . . . . . . . using an input of 0machine 3: 1/4 = 1/4machine 1: 4(1/4) -32 = -31 . . . . desired outputIn 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled,labour cost increased by 30% and transport costs increased by 20%.calculate the cost of manufacturing the article bin 2004
Answers
The cost of manufacturing the article bin 2004 will be 1875.
What is Percentage Increased ?Percentage increase is the ratio of increase to the initial value in percentage.
Given that In 2001 the total cost of manufacturing an article was sh.1250 and this was divided between the cost of materials was doubled, labor cost increased by 30% and transport costs increased by 20%
Given that in 2001, the cost of manufacturing = 1250
If this cost was divided between the Material, labor, and transportation equally, then, cost for each sector will 1250/3 = 416.67
cost of materials was doubled, that is 416.67 x 2 = 833.33labor cost increased by 30% , that is 130/100 x 416.67 = 541.67transport costs increased by 20% that is, 120/100 x 416.67 = 500The cost of manufacturing = 833.33 + 541.67 + 500
The cost of manufacturing = 1875
Therefore, the cost of manufacturing the article bin 2004 will be 1875.
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Two factory plants are making tv panels yesterday plant A produced 3000 panels. Ten percent of the panels from plant A were defective and Three percent from plant B were defective. How many panels did plant be produce if the overall percentage of defective panels from the two plants was 6%. Thanks for the help
Answers
Answer: Plant B produced 4000 panels
Step-by-step explanation: Let the number of panels produced by plant A = a and the number of panels produced by plant B = x. In total, we have 3000 + x. Now for the defective panels. 10% of plant a + 3% of plant b = 6% of both a and b. 300 + 3/100(x) = 6/100(3000 + x). 300 + 0.03x = 180 + 0.06x. Now, we simplify. 300 - 180 = 0.06x = 0.03x. So, 120 = 0.03x and 40 = 1% of x. This means x = 4000. So, therefore, Plant B produced 4000 panels. We can check our work by using the value of x we got. 4000 + 3000 = 7000. 6% of 7000 = 420. 120 = 3% of 4000. 120 + 300 = 420 so the answer we got is correct. Hope this helped
give the answers to the remaining boxes left blank, you can give the answers all in one sentence starting from the first blank box all the way to the last
Answers
The domain of the functions are:
The domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2The domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10The domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5The domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10What are the domains of a function?The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?
How to determine the domain of the functions?Function 1
The function is given as:
f(x) = √4x + 6
Set the radicand greater than 0
4x + 6 > 0
Subtract 6 from both sides
4x > -6
Divide by 4
x > -3/2
Express as interval notation
[-3/2, ∞)
Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2
Function 2
The function is given as:
g(x) = -4√-20x - 6
Set the radicand greater than 0
-20x - 6 > 0
Add 6 to both sides
-20x > 6
Divide by -20
x < -6/20
Simplify
x < -3/10
Express as interval notation
(-∞, -3/10]
Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10
Function 3
The function is given as:
f(x) = 15 + √5x - 16
Set the radicand greater than 0
5x - 16 > 0
Add 16 to both sides
5x > 16
Divide by 5
x > 16/5
Express as interval notation
[16/5, ∞)
Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5
Function 4
The function is given as:
p(x) = √20x + 6
Set the radicand greater than 0
20x + 6 > 0
Subtract 6 from both sides
20x > -6
Divide by 20
x > -6/20
Simplify
x > -3/10
Express as interval notation
(-3/10, ∞]
Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10
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Each outcome or a collections of outcomes in a experiment is called as?
Answers
Answer:
event
What is an event?
An event can be described as an individual or set of outcomes of an experiment.
Events are a subset of the experiment's sample space.
What is sample space?The sample space of an experiment is the complete set of possible outcomes of that experiment.
Paula finished the race at 2:14 p.m Beatrice finished the race 22 minutes earlier what time did Beatrice finish the race a 1:54 p.m b 1:48 p.m. c 1:58 p.m. d 1:52 p.m. e none of these f I don't know yet
Answers
Answer: 1:52 PM
Step-by-step explanation:
PAULA: 2:14PM FINISHED THE RACE
BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA
YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.
SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)
2:00-8 MINS ( REMAINING FROM THE 22 ) THEN 2:00-8 MINS =1:52
ANSWER:1:52PM
|3x-1|=4 help pleaseeeeeeeeee
Answers
Answer: x = -1 or x = 5/3
Step-by-step explanation:
|3x - 1| = 4
=> 3x - 1 = 4 or 3x - 1 = -4
=>x = 5/3 or x = -1
Does the following series converge or diverge?
Σ
n=1
4
8√n +7³√n
O The series diverges.
O The series converges.
Answers
Answer:
converges
Step-by-step explanation:
the individual fraction terms go against 0 with larger and larger n.
and therefore the sum converges.
the numerator of the fractions stays constant (4) but the denominator (bottom) of the fraction increases more and more with investing n (it does not matter that it uses roots, compared to the constant 4 they too grow immensely large with large n).
the limit of a/infinity is defined as 0.
Write your answer as a fraction in simplest form.
-1 3/4 • 2 1/8
Answers
What's the forecasted capital expenditure based on the information below? • Net PP&E beginning of period: 15,000 • Net PP&E end of period: 17,500 Depreciation expenses: 2,400
Answers
The forecasted capital expenditure related to the information below exists at 4,900.
Therefore, the correct answer is option b) 4,900.
What is Capital?Capital exists directed as the lifeblood of any business. It exists the group of assets of the business that contains their financial value to create the production of goods and services.
For calculating the forecasted capital-
Net PP&E beginning of period = 15,000
Net PP&E end of period = 17,500
Depreciation expenses = 2,400
Forecasted capital expenditure = Net PP&E end of period + Depreciation expenses - Net PP&E beginning of the period
= 17500 + 2400 - 15,000
Forecasted capital expenditure = 4,900
Therefore, the correct answer is option b) 4,900.
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The complete question is:
What’s the forecasted capital expenditure based on the information below?
Net PP&E beginning of period: 15,000
Net PP&E end of period: 17,500
Depreciation expenses: 2,400
Review Later
a) 2,500
b) 4,900
c) 100
d) -100
x+2y=5 and 4x+12y=-20 elimination method
Answers
Answer:
x=25 and y=-10
Step-by-step explanation:
x+2y=5 ..........(1)
4x+12y=-20.........(2)
using elimination method.
multiply equ(1) by 4 and equ(2) by 1
so we have
x+2y=5..........*4
4x+12y=-20.........*1
4x+8y=20................(3)
4x+12y=-20.............(4)
subtract eq(4) from (3) we have
-4y=40
y=-10
substitute y=-10 in equation (1)
we have:
x+2(-10)=5
x-20=5
x=25
How many three-digit positive integers have at least one prime digit?
Answers
Answer:
210
Step-by-step explanation:
[tex]512=2^9 \\[/tex] has 9 prime factors
Now, if you want to maximize the number of different prime factor, apply the following method: let [tex]p(n)[/tex] be the nth prime number, in increasing order. Let [tex]v[/tex] define as follow : [tex]v(0)=1,v(n+1)=v(n)p(n+1)[/tex] , and find n such that [tex]v(n) < 1000,v(n+1) > 1000[/tex]. n will be the number of factors and v(n) your integer.
[tex]v(1)=2v(0)=2v(2)=3v(1)=6v(3)=5v(2)=30v(4)=7v(3)=210v(5)=11v(4)=2310[/tex]
There you are, 210 , with only 4 different prime factors.
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What is the range for the possible sizes of x?
(Fill in the boxes)
Answers
Answer:
1.6 and 9.6
Step-by-step explanation:
What is the first step in solving 5 + = 3?
A. add 5 to both sides
B. add 3 to both sides
C. subtract 5 from both sides
D. divide each side by 8
Answers
Answer:
c subtract 5 from both sides
3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4
Answers
The value of 'x' from the expression is 9/ 11
How to simplify the expressionGiven the expression;
3 x +14 (3x-4) +3 x ( 6) +3 (х+2 )=4
First, we expand the bracket
3x + 42x - 56 + 18x + 3x + 6 = 4
collect like terms
3x + 42x + 18x + 3x - 56 + 6 = 4
Add up like terms
66x - 50 = 4
66x = 4 + 50
66x = 54
Make 'x' the subject of formula
x = 54/ 66
x = 9/ 11
Thus, the value of 'x' from the expression is 9/ 11
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What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Square. 5, and -3. C. D. None, because there is no solution. 2x-5--3?
Answers
Hi :)
I'd start by adding 5 to both sides of the equation. That would make the equation easier.
[tex]\boldsymbol{\sqrt{2x}-5=3}}[/tex]
[tex]\boldsymbol{\sqrt{2x}=2}[/tex]
The next step is to get rid of the radical sign.
Which operation will undo the square root? Squaring.
So that's why we square both sides:
[tex]\boldsymbol{2x=4}[/tex]
And Now we just divide both sides by 2
[tex]\boldsymbol{x=2}[/tex]
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You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
-- from image...
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
Answers
Answer:
Step-by-step explanation:
yes
The gross pay, taxable income, withholding taxes, and net pay can be computed as follows:
a) The gross pay per pay period = $500
b) Taxable income per pay period = $425
c) Federal tax withholding per pay period = $46.75
d) FICA withholding per pay period = $26.35
e) Medicare withholding per pay period = $6.16
f) State tax wtihholding per pay period = $10
g) Net pay per pay period = $335.74
How the gross earnings, net pay, taxable income, and withholdings are computed:The number of hours per pay period = 40 hours
The number of pay periods in a month = 2
The total number of hours worked per month = 80 hours (40 x 2)
Earnings per hour = $12.50
a) The gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:
Health care = $25
401k = $50
The gross pay per pay period = $500
Total deductions per pay period = $75
b) Taxable income per pay period = $425 ($500 - $75)
c) Federal tax withholding per pay period = $46.75 ($425 x 11%)
d) FICA withholding per pay period = $26.35 ($425 x 6.2%)
e) Medicare withholding per pay period = $6.16 ($425 x 1.45%)
f) State tax wtihholding per pay period = $10 ($500 x 2%)
Total withholding taxes = $89.26
g) Net pay per pay period = $335.74 ($425 - $89.26)
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