Answer:
(x + 5 y)^2
Step-by-step explanation:
Simplify the following:
4 (x - y)^2 - 12 (x - y) (x + y) + 9 (x + y)^2
(x - y) (x - y) = (x) (x) + (x) (-y) + (-y) (x) + (-y) (-y) = x^2 - x y - x y + y^2 = x^2 - 2 x y + y^2:
4 x^2 - 2 x y + y^2 - 12 (x - y) (x + y) + 9 (x + y)^2
4 (x^2 - 2 x y + y^2) = 4 x^2 - 8 x y + 4 y^2:
4 x^2 - 8 x y + 4 y^2 - 12 (x - y) (x + y) + 9 (x + y)^2
(x + y) (x - y) = (x) (x) + (x) (-y) + (y) (x) + (y) (-y) = x^2 - x y + x y - y^2 = x^2 - y^2:
4 x^2 - 8 x y + 4 y^2 - 12 x^2 - y^2 + 9 (x + y)^2
-12 (x^2 - y^2) = 12 y^2 - 12 x^2:
4 x^2 - 8 x y + 4 y^2 + 12 y^2 - 12 x^2 + 9 (x + y)^2
(x + y) (x + y) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = x^2 + 2 x y + y^2:
4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 x^2 + 2 x y + y^2
Grouping like terms, 4 x^2 - 8 x y + 4 y^2 - 12 x^2 + 12 y^2 + 9 (x^2 + 2 x y + y^2) = 9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2):
9 (x^2 + 2 x y + y^2) + (4 y^2 + 12 y^2) - 8 x y + (4 x^2 - 12 x^2)
4 y^2 + 12 y^2 = 16 y^2:
9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + (4 x^2 - 12 x^2)
4 x^2 - 12 x^2 = -8 x^2:
9 (x^2 + 2 x y + y^2) + 16 y^2 - 8 x y + -8 x^2
9 (x^2 + 2 x y + y^2) = 9 x^2 + 18 x y + 9 y^2:
9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2
Grouping like terms, 9 x^2 + 18 x y + 9 y^2 + 16 y^2 - 8 x y - 8 x^2 = (9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2):
(9 y^2 + 16 y^2) + (18 x y - 8 x y) + (9 x^2 - 8 x^2)
9 y^2 + 16 y^2 = 25 y^2:
25 y^2 + (18 x y - 8 x y) + (9 x^2 - 8 x^2)
x y 18 + x y (-8) = 10 x y:
25 y^2 + 10 x y + (9 x^2 - 8 x^2)
9 x^2 - 8 x^2 = x^2:
25 y^2 + 10 x y + x^2
The factors of 25 that sum to 10 are 5 and 5. So, 25 y^2 + 10 x y + x^2 = (x + 5 y) (x + 5 y):
(x + 5 y) (x + 5 y)
(x + 5 y) (x + 5 y) = (x + 5 y)^2:
Answer: (x + 5 y)^2
[tex]4(x-y)^2-12(x-y)(x+y)+9(x+y)^2 =\\4(x^2-2xy+y^2)-12(x^2-y^2)+9(x^2+2xy+y^2)=\\4x^2-8xy+4y^2-12x^2+12y^2+9x^2+18xy+9y^2=\\x^2+10xy+25y^2[/tex]
which can factorised into [tex](x+5y)^2[/tex]
Which is a correct expansion of (3x + 2)(3x2 + 4)?
The correct expansion of (3x + 2)(3x² + 4) will be 9x³ + 12x + 6x² +8.
How to expand the factor?In order to expand any factor, we need to multiply the first term with all two-term with another bracket.
similarly, multiply the second term with all two-term with another bracket.
Since given that (3x + 2)(3x² + 4)
multiply 3x by (3x² + 4)
⇒ 9x³ + 12x
Now multiply 2 with (3x² + 4)
⇒ 6x² +8
By adding these two we get 9x³ + 12x + 6x² +8 which is the correct expansion of the (3x + 2)(3x² + 4).
Learn more about the expansion of factors.
https://brainly.com/question/10223449
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Final answer:
The correct expansion of the expression (3x + 2)(3x² + 4) is found by multiplying each term of the first binomial by each term of the second polynomial, resulting in the expanded form 9x³ + 12x + 6x² + 8.
Explanation:
The student's question refers to the process of expanding a binomial multiplied by a polynomial using the distributive property (also known as the FOIL method for binomials). To expand it, each term in the first binomial is multiplied by each term in the second polynomial and the results are then added together. Applying this method:
First, multiply 3x by 3x² to get 9x³.Next, multiply 3x by 4 to get 12x.Then, multiply 2 by 3x² to get 6x².Finally, multiply 2 by 4 to get 8.Adding all these products together gives the expanded form: 9x³ + 12x + 6x² + 8. It is important to also combine like terms if there are any; however, in this expansion, there are no like terms to combine.
Which of the following is the solution?
[tex]|x|+5\leq1\\|x|\leq-4\\x\in\emptyset[/tex]
C
The slope-intercept form of the equation of a line that passes through point (–2, –13) is y = 5x – 3. What is the point-slope form of the equation for this line?
Answer:
y+13 = 5(x+2)
Step-by-step explanation:
y = 5x-3
The slope is 5 since it is in the form y= mx +b where m is the slope
The point slope form of the equation of a line is
y-y1 = m(x-x1) where (x1,y1) is the point
y--13 = 5(x--2)
y+13 = 5(x+2)
Answer:
B or y + 13 = 5(x + 2)
Step-by-step explanation:
A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.
Answer:
927 Cubic Inches.
Answer:
Area of the prism = 927 in²
Step-by-step explanation:
Area of the prism is defined by A = Area of the base × height
Since base of the prism is an octagon with side length = 4 inches
and apothem = 4.83 inches
Now area of the octagonal base = [tex]\frac{1}{2}(\text{Perimeter})(\text{Apothem})[/tex]
= [tex]\frac{1}{2}(4)(8)(4.83)[/tex]
= 77.28 inch²
Now area of the prism = 12×77.28 = 927.36 inch²
Therefore, area of the prism having base in the shape of an octagon is 927 inch²
15p!!what is the percent of change from 86 to 77? round to the nearest percent!
Answer:
10%
Step-by-step explanation:
The difference between 86 and 77 is 9.
Divide 9 by 86
[tex]\frac{9}{86} = .1046511[/tex]
Multiply by 100
[tex].1046511 * 100 = 10.46511[/tex]
Round to the nearest percent
[tex]10.46511 \rightarrow 10 \textrm{ percent}[/tex]
Find the slope-intercept form of an equation for the line that passes through (–1, 2) and is parallel to y = 2x – 3.
Question 8 options:
a)
y = –0.5x – 4
b)
y = 0.5x + 4
c)
y = 2x + 4
d)
y = 2x + 3
Answer:
c
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( where m is the slope and c the y- intercept )
Given y = 2x - 3 ← in slope- intercept form
with m = 2
• Parallel lines have equal slopes, hence
y = 2x + c ← is the partial equation of the parallel line
To find c substitute (- 1, 2) into the partial equation
2 = - 2 + c ⇒ c = 2 + 2 = 4
y = 2x + 4 → c
A concession stand sells 50 drinks, of which 49 are lemonade. What is the probability that the next
drink sold will be lemonade? Write your answer as a fraction, decimal, or percent.
49 out of 50 drinks were lemonade.
Divide the number of lemonade drinks by total drinks:
49 / 50 = 0.98 = 98%
98% of the drinks were lemonade, so there would be a 98% chance the next drink was lemonade.
A rectangle is 8m longer than it is wide. Its perimeter is 56m. Find its length and width.
Write values only.
Answer:
The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]
Step-by-step explanation:
Let
x -----> the length of the rectangle
y -----> the width of the rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(x+y)[/tex]
[tex]P=56\ m[/tex]
so
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex] ------> equation A
[tex]x=y+8[/tex] -----> equation B
Substitute equation B in equation A and solve for y
[tex]28=(y+8+y)[/tex]
[tex]28=2y+8[/tex]
[tex]2y=20[/tex]
[tex]y=10\ m[/tex]
Find the value of x
[tex]x=10+8=18\ m[/tex]
therefore
The length is [tex]18\ m[/tex] and the width is [tex]10\ m[/tex]
Find the axis of symmetry of the graph of the function.
f(x) = 2x^2 - 16x + 27
Answer:
the axis of symmetry is x = 4
Step-by-step explanation:
The three coefficients of the polynomial f(x) = 2x^2 - 16x + 27 are a= 2, b = -16 and c = 27. -b
The formula for the axis of symmetry is x = ------------
2a
-(-16)
which here is x = ------------ = 4
2(2)
The equation of the axis of symmetry is x = 4.
What is the distance from (−4, 0) to (2, 5)? Round your answer to the nearest hundredth. (4 points)
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2-(-4)]^2+[5-0]^2}\implies d=\sqrt{(2+4)^2+(5-0)^2} \\\\\\ d=\sqrt{36+25}\implies d=\sqrt{61}\implies d\approx 7.81[/tex]
Which dot plot shows data that is skewed right?
I need this ASAP
Answer:
B
Step-by-step explanation:
A graph skewed right would have LESS dots on the right side
Hope this helped!
Answer:
The correct option is B.
Step-by-step explanation:
Consider the provided graph.
A skewed right: If the distribution has a long right tail then it is know as skewed right. It is also called the positive-skew distributions. Due to a lengthy tail on the number line in the positive direction. The mean is on the right of the peak as well. See figure 1.
Now, consider the provided graph.
Option A is skewed left, so it is not the correct option.
Option B is skewed right, which is the correct option.
Whereas C and D are neither skewed left or right.
Therefore, the correct option is B.
A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.
Final answer:
To find the probability of choosing a random non-honor student who is an athlete, subtract the number of non-honor students who are athletes but not in the 3 honor athletes group from the total non-honor students.
Explanation:
The question: A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.
Step-by-step explanation:
Calculate the total number of students who are not honor students: 40 - 11 = 29.Calculate the number of non-honor students who are athletes but not part of the 3 honor athletes: 10 - 3 = 7.Find the probability that a randomly chosen student who is not an honor student is an athlete: 7 (non-honor athletes) / 29 (total non-honor students) ≈ 0.241.Does the ordered pair (-11/3,2/3) satisfy the following system of equations -x+5y=7 and -x-7y=-1
The answer is:
The ordered pair satisfies the following system of equations since it satisfies both equations.
Why?If we need to know if the ordered pair (-11/3,2/3) satisfies the system of equations we need to evaluate it and check if it satisfies both equations, we must remember that the condition that determines if the system of equations is satisfied is that both equations must be satisfied.
So, evaluating the ordered pair, we have:
First equation:
[tex]-x+5y=7\\\\-(\frac{-11}{3})+5*\frac{2}{3}=7\\\\\frac{11}{3}+\frac{10}{3}=7\\\\\frac{11+10}{3}=7\\\\\frac{21}{3}=7\\\\7=7[/tex]
We have that the equation is satisfied.
Second equation:
[tex]-x-7y=-1\\\\-(\frac{-11}{3})-7*\frac{2}{3}=-1\\\\\frac{11}{3}-\frac{14}{3}=-1\\\\\frac{11-14}{3}=7\\\\\frac{-3}{3}=-1\\\\-1=-1[/tex]
We have that the equation is satisfied.
Hence, we have that the ordered pair satisfies the system of equations since it satisfies both equations
Have a nice day!
Final answer:
The ordered pair (-11/3, 2/3) satisfies both equations in the given system, making it a solution to the system of equations.
Explanation:
To determine if the ordered pair (-11/3, 2/3) satisfies the given system of equations, we substitute x with -11/3 and y with 2/3 into both equations.
For the first equation -x + 5y = 7, we get:
-(-11/3) + 5(2/3) = 7
11/3 + 10/3 = 7
21/3 = 7
7 = 7
This confirms that the ordered pair satisfies the first equation.
For the second equation -x - 7y = -1, we calculate:
-(-11/3) - 7(2/3) = -1
11/3 - 14/3 = -1
-3/3 = -1
-1 = -1
The ordered pair also satisfies the second equation.
Since the ordered pair satisfies both equations, it is a solution to the system.
Use the triangle shown on the right to answer the question. According to the law on sines, which of the following statement(s) are true ? Check all that apply
The statements which are true are:
[tex]a\sin B=b\sin A[/tex][tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex][tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]Step-by-step explanation:In Trigonometry, the Law of Sine relates the length of sides of a triangle to the angle of a triangle.
According to this law if a,b and c are the sides of a triangle and A,B and C respectively are opposite angles to the side.
Hence, we have:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
i.e. we have:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
This could also be given by:
[tex]a\sin B=b\sin A[/tex]
[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Answer:its all of them
Step-by-step explanation:
e2020
Classify the triangle.
obtuse
equiangular
right
acute
Answer:
right
Step-by-step explanation:
there is a right angle in the triangle
Answer:
Right
Step-by-step explanation:
Right... the giveaway was the right angle in the pic
What is the completely factored form of d4 − 81?
(d + 3)(d − 3)(d + 3)(d − 3)
(d2 + 9)(d + 3)(d − 3)
(d2 + 9)(d − 3)(d − 3)
(d2 + 9)(d2 − 9)
For this case we must factor the following expression:
[tex]d ^ 4-81[/tex]
Rewriting the expression:
[tex](d ^ 2) ^ 2-9 ^ 2[/tex]
We factor using the formula of the square difference:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
Where:
[tex]a = d ^ 2\\b = 9[/tex]
So:
[tex](d ^ 2 + 9) (d ^ 2-9)[/tex]
From the second term we have:
[tex]d ^ 2-3 ^ 2 = (d-3) (d + 3)[/tex]
Finally, the factored expression is:
[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]
Answer:
[tex](d ^ 2 + 9) (d-3) (d + 3)[/tex]
The complete factorization of the term:
[tex]d^4-81[/tex] is:
[tex](d-3)(d+3)(d^2+9)[/tex]
Step-by-step explanation:To factor a term means to express is as a product of distinct factors i.e. multiples.
We are asked to factor the algebraic expression which is given by:
[tex]d^4-81[/tex]
We could write this expression as:
[tex](d^2)^2-(3^2)^2=(d^2)^2-(9)^2[/tex]
We know that:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
i.e.
[tex]d^4-81=(d^2-9)(d^2+9)\\\\i.e.\\\\d^4-81=(d^2-3^2)(d^2+9)\\\\i.e.\\\\d^4-81=(d-3)(d+3)(d^2+9)[/tex]
Select the correct answer from each drop-down menu.
Emily is playing a board game that has a spinner divided into equal sections numbered 1 to 18.
The probability of the spinner landing on an even number or a multiple of 3 is . The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is .
Reset Next
Answer:
The probability of the spinner landing on an even number or a multiple of 3 is 0.6667 .
The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is 0.7778 .
Step-by-step explanation:
Be the events
A = even number
B = Multiple of 3
C = Odd Number
D = Number between 4 and 15, both numbers excluded
The sets are as follows:
A = {2,4,6,8,10,12,14,16,18}
B = {3,6,9,12,15,18}
C = {1,3,5,7,9,11,13,15,17}
D = {5,6,7,8,9,10,11,12,13,14}
To calculate the probability that the roulette lands in an even number or in a multiple of 3, we make the union of A and B:
A U B = {2,3,4,6,8,9,10,12,14,15,16,18} = 12 numbers of 18
P (A U B) = 12/18 = 2/3 = 0.6667
To calculate the probability that roulette lands on an odd number or a number between 4 and 15 (both numbers excluded), we make the union of C and D:
C U D = {1,3,5,6,7,8,9,10,11,12,13,14,15,17} = 14 numbers of 18
P (C U D) = 14/18 = 7/9 = 0.7778
The first answer is 0.6667
The second answer is 0.7778
Hope this helps!
Answer:
first one: 2/3
second one: 7/9
Step-by-step explanation:
PLATO
suppose you want to convert kilometers to miles. you use the conversion of 1 mile = 1.6 kilometers. when using this conversion, which unit should be in the denominator?
Answer:
The unit that should be in the denominator is kilometers
Step-by-step explanation:
we know that
[tex]1\ mile=1.6\ kilometers[/tex]
To convert x km to mi
[tex]x\ km*(\frac{1}{1.6})\frac{mi}{km}=\frac{x}{1.6}\ mi[/tex]
therefore
The unit that should be in the denominator is kilometers
PLEASE
I
NEED
HELP
−15x+4≤109 OR −6x+70>−2
Answer:
All values of x are solutions
Step-by-step explanation:
−15x+4 ≤ 109 OR −6x + 70 > −2
-15x ≤ 105 OR -6x > -72
-x ≤ 7 OR -x > - 12
x ≥ -7 OR x < 12
Answer
x ≥ -7 OR x < 12
All values of x are solutions
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation
(x – 8)2 = 144, x represents the side measure of the original lawn.
What were the dimensions of the original lawn?
4 feet by 4 feet
8 + feet by 8 +
8 feet by 8 +
20 feet by 20 feet
Answer:
20 by 20
Step-by-step explanation:
the new dimensions have to be 12 because 12×12 =144 so you would add 8 to 12 and get 20 for each side
Answer:
D) 20 feet by 20 feet
Step-by-step explanation:
Given:
The area of the original grass lawn reduced by 8 feet on each side.
The smaller lawn's area = 144 square feet which is represented by the equation
[tex](x - 8)^2 = 144[/tex], where "x" is the side of the original lawn.
To find the original dimension of the lawn, we need to solve for x from the above equation.
To solve follow the steps.
Step 1:
To get rid of square on the right hand side, we need to take square root on both sides.
Taking the square root on both sides, we get
[tex]\sqrt{(x - 8)^2} = \sqrt{144}[/tex]
[tex](x - 8) = 12[/tex]
Step 2:
Now add 8 on both sides, we get
x - 8 + 8 = 12 + 8
x = 20
Therefore, the original dimensions of the lawn is 20 feet by 20 feet.
Solve: x + 3 = –x + 7
Answer:
x = 2
Step-by-step explanation:
x+3 = -x + 7
x = -x + 4
(2) = -(2) + 4
2 = 2
Answer:
The correct answer is x = 2.
Step-by-step explanation:
To solve this equation, we must get all of the variables (x's) to one side of the equation and get all of the constant terms (numbers only) to the other side.
Starting with this equation, we are going to add x to both sides of the equation. This will cancel out the -x on the right side of the equation, thereby moving all of the variable x's to the left side of the equation.
x + x + 3 = -x + x + 7
If we simplify by combining like terms, or adding the x's together, we get:
2x + 3 = 7
Next, we should subtract 3 from both sides of the equation in order to move all of the constant terms to the right side of the equation.
2x + 3 -3 = 7 - 3
If we simplify, we get:
2x = 4
Finally, we should divide both sides by 2 in order to get the variable x alone on the left side of the equation, solving it.
x = 2
Therefore, your answer is x = 2.
Hope this helps!
What is the measure of A
Answer:
A. 60°
Step-by-step explanation:
From the diagram, in triangle ABC,
AB=BC=CA=15 units.
This means triangle ABC is an equilateral triangle.
All angles in equilateral triangle are congruent. The sum of all interior angles in triangle is always 180°, so one angle of equilateral triangle is equal to 60°. Thus,
∠A=∠B=∠C=60°
what is the slop-intercept of the line that passes through the points (7,-5) and (3,-9)?
y = x + 12
y = x - 4
y = x - 12
y = x + 5
[tex]\bf (\stackrel{x_1}{7}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-(-5)}{3-7}\implies \cfrac{-9+5}{-4}\implies \cfrac{-4}{-4}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=1(x-7) \\\\\\ y+5=x-7\implies y=x-12[/tex]
How to round 56 to the nearest ten
Answer:
The answer would be 60
Step-by-step explanation:
What you do is if the number if 5 or less (ex 55) you would round down to 50. However it is 56 so you would round up to the next highest tenth, 60.
Hope this helps! Have a great day!
[tex]\text{Hey there}[/tex]
[tex]\text{If you come across: 5, 6, 7 , 8 , \& 9 you're going}\uparrow\text{(up)}[/tex]
[tex]\text{If you come across 1 , 2 , 3 , \& 4 you're going}\downarrow\text{(down)}[/tex]
[tex]\text{In this equation we have a SIX (6) at the end of the equation so we're going UP!}[/tex]
[tex]\boxed{\boxed{\bf{Ansewr: 60}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Expressions, Equations & inequalities Question 1
Solve the inequality
12x + 151 - 19
Answer:
I believe the answer is 12 • (x + 11) .
Follow the steps for division.
27/6
Solve each proportion 2/8=x/24
Answer:
x = 6
Step-by-step explanation:
First, write the proportion, using a letter to stand for the missing term. We find the cross products by multiplying 8 times x, and 2 times 24. Then divide to find x. Study this step closely, because this is a technique we will use often in algebra. We are trying to get our unknown number, x, on the left side of the equation, all by itself. Since x is multiplied by 8, we can use the "inverse" of multiplying, which is dividing, to get rid of the 8. We can divide both sides of the equation by the same number, without changing the meaning of the equation. When we divide both sides by 8, we find that the x would equal 6.
Hope this helped!
The answer is B) x = 12.
Here are the steps I did. 1. Simplify 2/8 to 1/4 ( 1/4 = x/48)2. Multiply both sides by 48 ( 1/4 x 48 = x)3. Simplify 1/4 x 48 to 48/4 ( 48/4 = x)4. Simplify 48/4 to 12 ( 12 = x)5. Now reverse it ( x = 12)
which of the following is equivalent to the expression i^88
Answer:
i^88 = 1
Step-by-step explanation:
i^88 = i^ 4*22 = 1 { i^4k = 1 ; i^4k+1 =i ; i^4k+2 = (-1); i^4k+3 = (-i) }
The equivalent expression for i^88 is 1 as the powers of i cycle every 4. Hence (i^4)^22 which is same as 1^22 ends up being 1.
Explanation:In complex numbers, i is the imaginary unit with the property i^2 = -1. The powers of i repeat in a cycle: i^1=i, i^2=-1, i^3=-i, and i^4=1. To find the equivalent expression for i^88, we will the fact that i^4=1 and i^88 would be equivalent to (i^4)^22, because 4*22 = 88.
Therefore, (i^4)^22 = 1^22. The equivalent expression for i^88 is 1.
Learn more about Imaginary Numbers here:https://brainly.com/question/13174285
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Helpppppppppppppp meeee
Answer:
A
Step-by-step explanation:
To evaluate h(6) substitute x = 6 into h(x), that is
h(6) = (3 × 6) - 4 = 18 - 4 = 14 → A
Can anyone answer this ?
For this case we have that by definition, the Pythagorean theorem states that:
[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]
Where:
c: It is the hypotenuse of the triangle
a, b: They are the legs of the triangle
Then, we verify if the theorem for the given triangles is fulfilled:
Triangle 1:
[tex]\sqrt {13} = \sqrt {2 ^ 2 + 3 ^ 2}\\\sqrt {13} = \sqrt {4 + 9}\\\sqrt {13} = \sqrt {13}[/tex]
It is fulfilled!
Triangle 2:
[tex]25 = \sqrt {2 ^ 2 + (3 \sqrt {2}) ^ 2}\\25 = \sqrt {4+ (9 * 2)}\\25 = \sqrt {22}[/tex]
It is not fulfilled!
Triangle 3:
[tex]43 = \sqrt {2 ^ 2 + (3 \sqrt {3}) ^ 2}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {4+ (9 * 3)}\\43 = \sqrt {31}[/tex]
It is not fulfilled!
ANswer:
Triangle A