Answers
(3x-21)-(3x+21)
Flip the signs in the second binomial
(3x-21)-3x-21
Combine like terms
3x-3x-21-21
-21-21
-42
The final answer is -42. X is irrelevant because whatever you plug in will always equal -42.
Related Questions
write the number 32.56 corrrect to one decimal place
Answers
What is the surface area of the square pyramid?
(Figure is not drawn to scale.)
Answers
area of 1 traingle = 1/2 * 8 * 5.4 = 21.6
there are 4 triangular sides so their area = 4 * 21.6 = 86.4
Total surface area = 64 + 86.4 = 150.4 cm2
D
Identify the number that does not belong with the other three. Explain your reasoning.
Answers
It is the only number in the set that cannot be expressed as a fraction (or ratio) meaning it is an irrational number
Use newton's method to find the absolute minimum value of the function f(x)=x2+sinx correct to six decimal places.
Answers
The solution would be like this for this specific problem:
f(x) = x^2 + sin(x)
f '(x) = 2x + cos(x)
The minimum value is at f '(x) = 0,
So, let g(x) = 2x + cos(x)
Thus, g '(x) = 2 - sin(x)
x(new) = x - g(x) / g '(x)
or
x(new) = x - [2x + cos(x)] / [2 - sin(x)]
Calculation
x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)]
= -0.4506266931
x2 = -0.4501836476
x3 = -0.4501836113
x4 = -0.4501836113
This value for x, f(x) = -0.2324655752.
After converting to 6 decimal places: the minimum point is (-0.450184,
-0.232466).
Final answer:
To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.
Explanation:
To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).
Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.
The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).
what is the domain and range for the following function and its inverse f(x) = x2 – 2
Answers
The domain is from -∞ to +∞, while the range is from -2 to +∞.
Answer:
x2-2 domain an range are 0, -2
Step-by-step explanation:
The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to
Answers
The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.
Explanation:The expression sin 50 cos 40 + cos 50 sin 40 can be simplified using the trigonometric identity:
sin(a + b) = sin a cos b + cos a sin b
By applying this identity, we can rewrite the expression as:
sin(50 + 40) = sin 90 = 1Therefore, the expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.
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Donna the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 7 clients who did Plan A and 9 who did Plan B. On Saturday there were 5 clients who did Plan A and 3 who did Plan B. Donna trained her Friday clients for a total of 12 hours and her Saturday clients for a total of 6 hours.
How long does each of the workout plans last?
Answers
7x + 9y = 720
5x + 3y = 360.....multiply by -3
---------------
7x + 9y = 720
-15x - 9y = -1080 (result of multiplying by -3)
---------------add
-8x = - 360
x = -360/-8
x = 45 minutes <== plan A
5x + 3y = 360
5(45) + 3y = 360
225 + 3y = 360
3y = 360 - 225
3y = 135
y = 135/3
y = 45 minutes <== plan B
so both plans last 45 minutes <==
If the mean of a symmetric distribution is 82, which of these values is most likely to be the median of the distribution? A.92 B. 85 C.78 D.82
Answers
So its 82
Susie divided a9-pound bag of apples into 5 equal piled. How many pounds of apples are in each piles?
Answers
divide the total weight by the number of piles
9/5 = 1.8 pounds per pile
The function h(x) = x2 + 6x + 7 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)
Part C: Determine the axis of symmetry for h(x). (2 points)
Answers
Part A.
The given equation is:
y = x^2 + 6x + 7
By completing the square:
y = (x^2 + 6x + 9) + 7 – 9
y = (x + 3)^2 – 2
y + 2 = (x + 3)^2
Part B.
The vertex form of a parabola is in the form:
y – k = 4p (x – h)^2
Where (h, k) is the vertex (x, y) of the parabola.
Therefore the vertex: (-3, -2)
Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.
Part C.
The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3
PLEASE HELP.
Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
The company also discovered that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.
Find the total cost of producing 6 widgets.
Answers
y = ax^2 + bx + d
c (x) = ax^2 + bx + d
c (3) = a (3^2) + b (3) + d
c (3) = 9a + 3b + d = 15.50
c (7) = a (7^2 + b (7) + d
c (7) = 49a + 7b + d = 23.50
c (12) = a (12^2) + b (12) + d
c (12) = 144a + 12b + d = 56
solve using simultaneous equations... to get a b and d
use that to solve for x = 5
hope this helps?
Answer:
The total cost of producing 6 widgets is $231.
Step-by-step explanation:
Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
To find : The total cost of producing 6 widgets.
Solution :
Cost is given by [tex]c (x) = ax^2 + bx + d[/tex]
Cost $23 to produce 2 widgets,[tex]c(2) = a(2)^2 + b(2) + d[/tex]
[tex]23= 4a+2b+d[/tex] .........[1]
Cost $103 to produce 4 widgets,[tex]c(4) = a(4)^2 + b(4) + d[/tex]
[tex]103= 16a+4b+d[/tex] ............[2]
Cost $631 to produce 10 widgets.,[tex]c(10) = a(10)^2 + b(10) + d[/tex]
[tex]631= 100a+10b+d[/tex] ...........[3]
Now, we solve equation [1], [2] and [3]
Subtract equation [2]-[1] and [3]-[2]
[2]-[1] → [tex]12a+2b=80[/tex] ........[4]
[3]-[2] → [tex]84a+6b=528[/tex] .......[5]
Solving equation [4] and [5] by elimination method,
Multiply equation [4] by 3 and subtract from [5]
[tex]84a+6b-3(12a+2b)=528-3(80)[/tex]
[tex]84a+6b-36a-6b=528-240[/tex]
[tex]48a=288[/tex]
[tex]a=6[/tex]
Put in equation [4]
[tex]12(6)+2b=80[/tex]
[tex]72+2b=80[/tex]
[tex]2b=8[/tex]
[tex]b=4[/tex]
Substitute the value of a and b in [1] to get d
[tex]23= 4a+2b+d[/tex]
[tex]23= 4(6)+2(4)+d[/tex]
[tex]23= 24+8+d[/tex]
[tex]23= 32+d[/tex]
[tex]d=-9[/tex]
Substitute a=6,b=4,d=-9 in the cost equation,
The required equation form is [tex]c(x) = 6x^2 + 4x-9[/tex]
The total cost of producing 6 widgets.
Put x=6
[tex]c(6) = 6(6)^2 + 4(6)-9[/tex]
[tex]c(6) = 216+15[/tex]
[tex]c(6) =231[/tex]
Therefore, The total cost of producing 6 widgets is $231.
write the expression in factored form: m²-n²
Answers
[tex]m^2 - n^2 = (m + n)(m - n)[/tex]
m^2 - n^2 = (m - n)(m + n)
Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plus 1 − 3 + 3 = x + 3 Square root of negative 2x plus 1 = x + 3 Square root of negative 2x plus 1 − 1 = x + 3 − 1 Square root of negative 2 x = x + 2 (Square root of negative 2 x)2 = (x − 4)2 −2x = x2 − 8x + 16 −2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 16 0 = (x + 2)(x + 8) x + 2 = 0 x + 8 = 0 x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8 x = −2 x = −8 Both solutions are extraneous because they don't satisfy the original equation. What error did Eloise make?
Answers
Please see attached image for the choices and proper formatting of the problem.
What she did:
[tex] \sqrt{-2x + 1 } - 1 = x + 3 - 1 \sqrt{-2x} = x + 2[/tex]
What she should have done:
[tex]( \sqrt{-2x + 1} ^{2} = (x + 3)^2 -2x + 1 = (x + 3)^2 -2x + 1 - 1 = (x + 3)^2 - 1 -2x = (x +3)^2 - 1[/tex]
The error that Eloise made in solving the radical equation was that she subtracted 1 before squaring both sides.
To add, the equation where at least one variable expression is fixed inside a radical, usually a square root is called a radical equation.
Answer:
We need to subtract 1 after squaring both sides
Step-by-step explanation:
Step1: [tex]\sqrt{-2x+1} -3 = x \\[/tex]
adding 3 both sides
[tex]\sqrt{-2x+1} =3 + x \\[/tex]
we need to square here first and then we need to subtract
and this is the error which Eloise make in solving it .
How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long? 0?
Answers
the volume of the hole would be 3*3*3 = 27 cubic feet.
however since it is a hole, there is nothing in it.
HELP ROUND 1.75170179212 TO 6 DECIMAL PLACES
Answers
There are 11 decimal places here. We only need 7 to complete.
1.751701(7)xxxx
^
We need to round the 7th place to round to 6 decimals
If the 7th decimal place < 5, round to 1.
If the 7th decimal place > or = 5, round to 2.
Because 7 > 5, It rounds to 1.751702.
Answer:
The answer is 1.751702
Step-by-step explanation:
In this number there are 11 decimal places which can be found after the decimal point.
1.75170179212
As we want 6 decimal places, we need to look at the digit to the right of sixth decimal place. Therefore:
1.75170179212
So, in this case, the digit in the seventh place is a '7'.
If we want to round a number, there are two ways:
If the digit is less than 5, you leave the sixth decimal as it is.If the digit is equal or greater than 5, you add 1 up to the sixth decimal.As the seventh decimal is a '7' which is greater than '5'.
We add a 1 to the Sixth decimal place.
As the sixth decimal place was a '1'. When we round it, it will be a 2
1.751702
Tamara earns $8 an hour at her job working 25 hours per week. If 25% of her paycheck goes to taxes, what is Tamaras monthly cash flow? (Asssume this is her only source of income and that there are 4 pays per month)
Answers
so, she gets $150 a week.
According to a recent survey, the salaries of assistant professors have a mean of $41,750 and a standard deviation of $7000 . assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn more than $48,000 . round your answer to at least four decimal places.
Answers
z=(x-mean)/s.d
x=48000
mean=41,750
s.d=7000
thus;
z=(48000-41750)/7000
=0.8929
the probability associated with z-score is:
P(48000)=0.8133
thus the probabilty of those who are earning more than $48,000 will be:
1-0.8133
=0.1867
Using the z score formula and the z table, we find that approximately 18.67% of assistant professors earn more than $48,000 given a mean salary of $41,750 and a standard deviation of $7000.
Explanation:The question is asking for the proportion of assistant professors who earn more than $48,000 based on a normal distribution of salaries with a mean of $41,750 and a standard deviation of $7,000. To find this, we first need to calculate the z score, which is the number of standard deviations a data point is from the mean. The z score can be calculated using the formula z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get z = (48,000 - 41,750) / 7,000 = 0.8929. Looking up this z value in the z table, we find that the proportion for z = 0.89 is 0.8133. This is the proportion of salaries that are below $48,000. Thus, to find the proportion of salaries above $48,000, we subtract this value from 1, giving us 1 - 0.8133 = 0.1867 or 18.67% when expressed as a percentage. So, approximately 18.67% of assistant professors earn more than $48,000.
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A simple random sample of 1350 registered voters shows that 58% favor Candidate A over Candidate B. Which is the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B.
Answers
Final answer:
The 99% confidence interval for the percentage of registered voters who prefer Candidate A is between 54.6% and 61.4%.
Explanation:
To calculate the 99% confidence interval for the percentage of the population of registered voters who prefer Candidate A over Candidate B, you can use the formula for the confidence interval of a proportion:
The sample proportion (p') is given as 58%, which is 0.58 in decimal form. The size of the sample (n) is 1350.
To calculate the confidence interval, we also need the z-value for the 99% confidence level. The z-value for a 99% confidence level is approximately 2.576 (you can find this value in a standard z-table).
The formula for the margin of error (EBP) is:
EBP = z * sqrt((p'*(1-p'))/n)
Plugging the values into the formula:
EBP = 2.576 * sqrt((0.58*(1-0.58))/1350)
EBP ≈ 0.034
The confidence interval for the true binomial population proportion is given by:
(p' - EBP, p' + EBP)
Therefore, the 99% confidence interval is:
(0.58 - 0.034, 0.58 + 0.034)
(0.546, 0.614)
Interpreting this, we can say with 99% confidence that the true percentage of all registered voters who prefer Candidate A over Candidate B is between 54.6% and 61.4%.
Final answer:
To calculate the 99% confidence interval for the percent of registered voters who prefer Candidate A, we can use the formula CI = p ± Z * √(p*(1-p)/n). Plugging in the values, we find the 99% confidence interval is between 54.6% and 61.4%.
Explanation:
To calculate the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B, we can use the formula:
CI = p ± Z * √(p*(1-p)/n)
Where:
p = sample proportion
Z = Z-value for the desired confidence level
n = sample size
In this case, the sample proportion is 0.58, the sample size is 1350, and the Z-value for a 99% confidence level is approximately 2.58.
Plugging in these values, we get:
CI = 0.58 ± 2.58 * √(0.58*(1-0.58)/1350)
Simplifying the equation gives us the 99% confidence interval for the percent of registered voters who prefer Candidate A: between 0.546 and 0.614, or 54.6% and 61.4%.
How high is a 40-foot ramp if it is propped at a 30 degree angle?
Answers
sin theta=[opposite]/[hypotenuse]
theta=30
opposite=x
hypotenuse=40 ft
hence;
sin 30=x/40
thus;
x=40sin30
x=20 ft
the ramp is 20 ft high
Which of the following statements are true? I. -(-6) = 6 and -(-4) > -4 III. 5 + 6 = 11 or 9 - 2 = 11 II. -(-4) < 4 or -10 > 10 - 10 IV. 17 > 2 or 6 < 9
Answers
The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
I. -(-6) = 6 and -(-4) > -4
Here -(-4) > -4 is incorrect
-(-4) = 4 is correct
These statements are not true
III. 5 + 6 = 11 or 9 - 2 = 11
Here 9 - 2 = 11 is incorrect
So 9 - 2 = 7 is correct
These statements are not true
II. -(-4) < 4 or -10 > 10 - 10
Here -(-4) < 4 is incorrect
So -(-4) = 4 is correct
These statements are not true
IV. 17 > 2 or 6 < 9
Here 17 is greater than 2 and 6 is less than 9 is always true.
Hence, the correct answer would be an option (D)
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A district manager rewards sales teams based on overall sales generated in a month. The data for earnings are shown in the table, where Low represents the lowest sales and High represents the highest sales generated by a single sales team member.Team Low High Range Mean Median IQR σTeam X 1970 2970 1200 2571.9 2684 426.3 313.8Team Y 250 375 125 315.8 311 59 37.8Team Z 950 1900 950 1529.9 1473 276 180.7Part A: If the manager wants to award the sales team that has the most consistent earnings among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)Part B: If the manager wants to award the sales team with the highest average earnings, which team should it choose and why? Justify your answer mathematically. (5 points)
Answers
The most consistent team is the team who has the lowest range, IQR and standard deviation (σ). From the table, the team who has the lowest range, IQR and the standard deviation is team Y.
Lower range indicates a small range of data interval, meaning that there is no extremely low or high value on a set. It also means that most of the data values are repeated and therefore is more consistent.
PART B:
Average of a data can be shown by the value of the mean or median. From the table, we can see that team A has the highest mean and median. These values indicate the earning by sales each team member would have made.
The product of a positive number and 14 more than seven times the number is 105. Find the two numbers. first number =______ and second number =_________
Answers
The expression is
[tex]x(14+7x)=105[/tex]⇒ expanding the bracket gives,
[tex]14x+7 x^{2} =105[/tex] ⇒ rearranging to equate one side to zero
[tex] 7x^{2} +14x-105=0[/tex] ⇒ Dividing each term by 7 to simplify
[tex] x^{2} +2x-15[/tex] ⇒ Factorising gives
[tex](x+5)(x-3)=0[/tex]
[tex]x=-5[/tex] and [tex]x=3[/tex]
Hence, the first number is -5 and the second number is 3
Answer:
can you explain it in more depth please
Step-by-step explanation:
The area of a square is 2500 cm .what is the side legth of the painting?
Answers
Area = 2500 sq. cm
s² = 2500
s = √(2500)
s = √(5² × 10²)
s = 5 × 10
s = 50 cm
A ______ is an expression that can be written in the form of p/q where p and q are polynomials and q
Answers
The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.
Answers
y = -10x² + 160x - 430
In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50
Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0
Answer:
This quadratic equation can be solved by factorization.
Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0 => x = 4, and
x - 12 = 0 => x = 12
a. The required equation is x² - 16x + 48 = 0
b. I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
a.
The required equation is x² - 16x + 48 = 0
The required equation
Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.
So, y = -10x² + 160x - 430
-10x² + 160x - 430 = 50
-10x² + 160x - 430 - 50 = 0
-10x² + 160x - 480 = 0
Dividing through by -10, we have
x² - 16x + 48 = 0
So, the required equation is x² - 16x + 48 = 0
b.
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
The methodTo determine the method you would use to solve the equation, you would need to determine the value of the discriminant.
DiscriminantFor a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac
Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48
= 256 - 192
= 48
= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,
So, x² - 16x + 48 = 0
x² - 4x - 12x + 48 = 0
x(x - 4) - 12(x - 4) = 0
(x - 4)(x - 12) = 0
x - 4 = 0 or x - 12 = 0
x = 4 or x = 12
I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.
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The population of greenville is currently 50,000 and declines at a rate of 1.2% every year. This models:
Exponential growth.
Exponential logarithm
Exponential decay
Answers
So. the answer is
Exponential decay
Formula: 50000/1.12^years, which could be rewritten as 50,000/e^(number*years), and so it is exponential.
So its decay
Choice C
HELP
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp.
Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points)
Answers
alligators:
x = total number of alligators
n = number of years
x=20x1.25^n
crocodiles:
y = total number of crocodiles
n = number of years
y=25+10n
Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1
Answers
T2= 5(-4)= -20 don the same thing for all of them :
-100 t3
-500. T4
-2500 t5
-12500 is t6
what is 17pi/4 in decimal form nearest the thousandth
Answers
17 x PI = 53.40707511
divided by 4 = 13.35176878
rounded to nearest thousandth = 13.352
using the graph of f(x)=log2x below approximate the value of y in the equation 2^2y=4
Answers
For find the results in the graph, we need to calculate the value of argument, wich we will search in graph.y=los_{2}x For use this graph we need to change our equation, to bring the equation to the form with such base. For that, we will use the properties of logarithms.log_{4}4=Log_{(2^2)}4=Log_{2}4^(1/2)=log_{2}2.Now for recieve the value of Y, we must to find "2" in axis OX, to build the line at right angle (from axis) into the graph. After that, we turn to axis OY at right angle, and we make the line to axis OY. In result we have the value on the axis OY, it's will be the desired value. And it must be 1.