Answer:
[tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Step-by-step explanation:
The factorization is in the form (x-a)(x-b) where a,b are zeros of the equation [tex]x^{2} +50=0[/tex].
[tex]x^{2} =-50[/tex]
[tex]x =\sqrt{-50}[/tex]
[tex]x =\sqrt{50}i = 5\sqrt{2}i[/tex] and [tex]x =-\sqrt{50}i = -5\sqrt{2}i[/tex]
So, the factorization is [tex](x+5\sqrt{2}i)(x-5\sqrt{2}i)[/tex]
Complex numbers are numbers with real and imaginary part.
The factorized expression is [tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
The expression is given as:
[tex]\mathbf{x^2 + 50}[/tex]
Set to 0
[tex]\mathbf{x^2 + 50 = 0}[/tex]
Subtract 50 from both sides
[tex]\mathbf{x^2 = -50}[/tex]
Take square roots
[tex]\mathbf{x = \sqrt{-50}}[/tex]
Expand
[tex]\mathbf{x = \sqrt{25 \times -2}}[/tex]
Take square roots of 25
[tex]\mathbf{x =\pm 5\sqrt{-2}}[/tex]
Expand
[tex]\mathbf{x = \pm5\sqrt{2 \times -1}}[/tex]
Split
[tex]\mathbf{x =\pm 5\sqrt{2} \times \sqrt{-1}}[/tex]
In complex numbers,
[tex]\mathbf{\sqrt{-1} = i}[/tex]
So, we have:
[tex]\mathbf{x = \pm5i\sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{x^2 + 50 = (x^2 +5i\sqrt 2)(x^2 -5i\sqrt 2) }[/tex]
Read more about complex numbers at:
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Mike can stitch 7 shirts in 42 hours. He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt.
Answer:
He can Stitch 1 shirt in 6 Hours And in Hour He Can Stitch 6/10 Of a Shirt
Step-by-step explanation:
This Answer Is Correct Because He Can Stitch 7 Shirts In 42 Hours Which Is Wrong.
Say that you are about to make a major purchase and would like to save money on sales tax. Which of these is a viable way to reduce the amount you will pay on sales tax?
a.
Sales tax is a tax like any other, so you can claim additional dependents and get a deduction on it.
b.
Businesses are allowed to charge a 1% fee for automatically calculating sales tax for you, so you should calculate the sales tax out yourself.
c.
Sales tax varies by state, so you can travel to a state with a lower tax rate and make your purchase there.
d.
If you buy an item on credit, the credit bureau must pay the sales tax instead of you, so you should make your purchase using a credit card.
The answer is c. sales tax varies by state.
Multiply. 3 ⋅ 3/5 whats the answer
Determine whether the formula describes y as a function of x. Explain your reasoning. y=-3x^2-7x-6
A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship?
A .Yes, y = 2x. B. Yes, y = 20x. C. No, y = x + 10. D. No, y = x + 20.
The answer is A. yes, Y= 2x
How Do I do proofs for proving triangles?
in what quadrant is an angle of 1.75 found
What is 4.898979486 rounded to the nearest 10?
What is the quotient? 2m+4/8÷m+2/6
Answer:
3/2 (D on Edge)
What is the expanded form of the expression 3 sigma i^3 i=0
Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivative test does not?
The critical numbers of [tex]\( f(x) = x^6 (x-1)^5 \)[/tex] are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex]. The first derivative test determines maxima/minima by sign change, while the second derivative test confirms concavity but not explicit categorization.
1. Calculate the first derivative [tex]\( f'(x) \)[/tex]:
Use the product rule and simplify:
[tex]\[ f(x) = x^6 (x-1)^5 \] \[ f'(x) = 6x^5 (x-1)^5 + x^6 \cdot 5(x-1)^4 \] \[ f'(x) = 6x^5 (x-1)^4 [x + 5(x-1)] \] \[ f'(x) = 6x^5 (x-1)^4 (6x - 5) \][/tex]
2. Find critical points:
Critical points occur where [tex]\( f'(x) = 0 \)[/tex] or is undefined.
Set [tex]\( f'(x) = 0 \)[/tex]:
[tex]\[ 6x^5 (x-1)^4 (6x - 5) = 0 \][/tex]
This equation is zero when:
[tex]\( 6x^5 = 0 \) -- \( x = 0 \)\\ \( (x-1)^4 = 0 \) -- \( x = 1 \)\\ \( 6x - 5 = 0 \) -- \( x = \frac{5}{6} \)[/tex]
So, the critical numbers are [tex]\( x = 0, 1, \frac{5}{6} \)[/tex].
3. First Derivative Test vs. Second Derivative Test:
- First Derivative Test: This test uses the sign of the derivative ( f'(x) ) to determine the nature of critical points:
- If [tex]\( f'(x) > 0 \) to \( f'(x) < 0 \)[/tex] at x, then ( f(x) ) has a local maximum at x.
- If [tex]\( f'(x) < 0 \) to \( f'(x) > 0 \)[/tex] at x, then ( f(x) ) has a local minimum at x.
- Second Derivative Test: This test uses the sign of the second derivative [tex]\( f''(x) \)[/tex]:
- If [tex]\( f''(x) > 0 \), \( f(x) \)[/tex] has a local minimum at x.
- If [tex]\( f''(x) < 0 \), \( f(x) \)[/tex] has a local maximum at x.
4. Difference between the tests:
- The first derivative test provides information about the nature (whether maximum or minimum) of critical points based on the sign change of the derivative.
- The second derivative test provides more precise information by confirming the concavity of the function around the critical point, but it does not give explicit information about whether the critical point is a maximum or minimum (it only confirms the direction of concavity).
PLEASE HELP!!
To the nearest square unit, what is the area of the regular heptagon shown below?
A. 2772 square units
B. 1572 square units
C. 792 square units
D. 5545 square units
Answer:
1572 Square Units
Step-by-step explanation:
First, find the perimeter by multiplying 20.8 * 7 which is 145.6. Then multiply the perimeter with the apothem. After that, you divide by 2.
So, 145.6*21.6/2= 1572.
Woodland Bicycles makes two models of off-road bicycles: the Explorer, which sells for $250, and the Grande Expedition, which sells for $350. Both models use the same frame, but the painting and assembly time required for the Explorer is 2 hours, while the time is 3 hours for the Grande Expedition. There are 375 frames and 450 hours of labor available for production. How many of each model should be produced to maximize revenue?
To maximize revenue, we need to determine the number of each model of off-road bicycles that should be produced based on the given constraints. The revenue generated from selling each model is multiplied by the number of units sold. We set up a system of equations to represent the constraints and objective function, and then use graphical methods or linear programming algorithms to find the optimal solution.
Explanation:To maximize revenue, we need to determine the number of each model of off-road bicycles that should be produced. Let's assume x represents the number of Explorer bicycles and y represents the number of Grande Expedition bicycles.
The revenue generated from selling the Explorer bicycles is 250x, while the revenue from selling the Grande Expedition bicycles is 350y.
We are given that the painting and assembly time required for the Explorer is 2 hours, so the total time used for producing the Explorer bicycles is 2x hours. Similarly, the total time used for producing the Grande Expedition bicycles is 3y hours.
We also know that there are 375 frames and 450 hours of labor available. Each bicycle requires one frame and a certain number of labor hours, so the total number of frames used is x + y, and the total labor hours used is 2x + 3y.
We can set up the following system of equations to represent the constraints:
x + y ≤ 375 (due to the limited number of frames)
2x + 3y ≤ 450 (due to the limited number of labor hours)
To maximize revenue, we need to maximize the objective function R = 250x + 350y. Since we are dealing with a linear programming problem, we can use graphical methods or linear programming algorithms to find the optimal solution.
HELP Use the properties of sigma notation and the summation formulas to evaluate. See attached
The lines described by y = (a + 12)x + 3 and y = 4ax are parallel. what is the value of a
The lines are parallel if and only if the values of their slopes are equal. In a standard form of the equation of the line, the slope is the numerical coefficient of x. Given this condition, we determine the value of a by equation a + 12 and 4a.
Slope = a + 12 = 4a
The value of a from the equation is 4.
Answer: 4
distribute 4(y5-2 i neeed help
[tex]\text{Distributive property:}\ a(b+c)=ab+ac\\\\4(y^5-2)=(4)(y^5)+(4)(-2)=\boxed{4y^5-8}[/tex]
If your brother is 12 years old and you are 10 years old. How old will you have to be to be half your brother's age?
Answer:
6
Step-by-step explanation:
What is the value of the expression?
(52)2+334
Enter your answer in the box.
Answer:
438
Step-by-step explanation:
(52*2)+334
104+334=
438
The value of the numerical expression (52)² + 334 will be 3,038.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ (52)² + 334
Simplify the numerical expression, then we have
⇒ (52)² + 334
⇒ 2,704 + 334
⇒ 3,038
The value of the numerical expression (52)² + 334 will be 3,038.
More about the Algebra link is given below.
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Simplify 5x + 8y + 4x
A.17x
B.9x + 8y
C.5x + 12y
D.17xy
Which of the above charts does NOT accurately reflect public goods and services?
A.
chart A
B.
chart B
C.
chart C
D.
chart D
Answer:
The answer is A! I hoped this helped! :3
Step-by-step explanation:
2,) What is the solution of the system?
Use the substitution method.
y+6=4x
8x−2y=14
A) The only solution is (14, 12)
B)The only solution is (12, 14)
C)There are an infinite number of solutions.
D)There is no solution.
Use the dustributive property to express 16+48?
If f(x) = 2x2 + 4, find f(3). (1 point) 22 16 −0.5 40
If ABC and DEF are supplementary, then ABC and DEF form a linear pair
The statement is true. If two angles are supplementary meaning their sum is 180 degrees, they form a linear pair because in a linear pair too, the sum of the two angles is 180 degrees.
Explanation:The question is related to the concept of angles in geometry. When angles are supplementary, it means that the sum of the two angles is 180 degrees. In a linear pair, two adjacent angles form a straight line, which also sums up to 180 degrees.
So, if angles ABC and DEF are supplementary, meaning ABC + DEF = 180 degrees, they indeed form a linear pair. Because in a linear pair too, the sum of the two angles is 180 degrees. Therefore, the statement 'If ABC and DEF are supplementary, then ABC and DEF form a linear pair' is true.
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The correct question is given below:
If ABC and DEF are supplementary, then ABC and DEF form a linear pair. True or False?
For which to pairs of function is (f•g) (x) =x
Answer:
[tex]f(x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]
Step-by-step explanation:
To prove that we have to demonstrate [tex](f*g)(x)=x[/tex]
This proof is about a composition of functions, where we have to enter one function inside another, in this case, [tex]g(x)[/tex] goes inside [tex]f(x)[/tex]. So if results in [tex]x[/tex], then will be proved.
[tex](f*g)(x) = \frac{2}{\frac{2}{x} }[/tex]
As you can see, the composition is to replace [tex]g(x)[/tex] for the variable of [tex]f(x)[/tex].
Solving the expression:
[tex](f*g)(x) = \frac{2}{\frac{2}{x} }=\frac{2x}{2}=x[/tex]
After replacing and applying the composition, we have [tex]x[/tex] as a result. Therefore, we can say that the pair of functions of option B is the answer, because they satisfy the expression given.
Does the density of an iron bar depend on the length of the bar
Experts/acee plz helppp
standard form is y = mx+b
the correct answer is the 4th one y =4x+15
Write a function rule to represent the situation. the total cost C for pp pound of beef if each pound costs $4.01
Joana is 4 years older than her brother. Which of the following expressions shows the sum if their ages if b represents joanas brothers age?
What is the area of the polygon below