Answer:
[tex]s = \frac{5i}{-2-6i} = -\frac{30}{40}-\frac{10}{40}i[/tex]
Step-by-step explanation:
We have the following complex number [tex]s = \frac{5i}{-2-6i}[/tex], we proceed to simplify the expression as follows:
1) [tex]\frac{5i}{-2-6i}[/tex] Given.
2) [tex](5i)\cdot (-2-6i)^{-1}[/tex] Definition of division.
3) [tex][(5i)\cdot (-2-6i)^{-1}]\cdot [(-2+6i)\cdot (-2+6i)^{-1}][/tex] Modulative and associative properties/Existence of the additive inverser
4) [tex][(5i)\cdot (-2+6i)]\cdot [(-2-6i)^{-1}\cdot (-2+6i)^{-1}][/tex] Commutative and associative properties.
5) [tex][(5i)\cdot (-2+6i)]\cdot [(-2-6i)\cdot (-2+6i)]^{-1}[/tex] [tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]
6) [tex][(5i)\cdot (-2+6i)]\cdot [4+36]^{-1}[/tex] [tex](a+b)\cdot (a-b) = a^{2}-b^{2}[/tex]/Definition of complex number/ [tex]a\cdot (-b) = -a\cdot b[/tex]
7) [tex][(5i)\cdot (-2)+(5i)\cdot (6i)]\cdot 40^{-1}[/tex] Definition of sum.
8) [tex](-10\cdot i+30\cdot i^{2})\cdot 40^{-1}[/tex] [tex]a\cdot (-b) = -a\cdot b[/tex]/Associative and commutative properties.
9) [tex](-30-10i)\cdot 40^{-1}[/tex] Commutative properties/Definition of complex number/ [tex]a\cdot (-b) = -a\cdot b[/tex]
10) [tex]-30\cdot 40^{-1}-(10i)\cdot 40^{-1}[/tex] Distributive property.
11) [tex]-\frac{30}{40}-\frac{10}{40}i[/tex] Definition of division/Result.
[tex]s = \frac{5i}{-2-6i} = -\frac{30}{40}-\frac{10}{40}i[/tex]
jamie reads 15 pages in 25 minutes and wants to know how many pages she can read in 65 minutes
Answer:
39
Step-by-step explanation:
15/25 = 0.6 - She can read 0.6 pages in 1 minute.
0.6 X 65 = 39
There are 39 pages she can read in 65 minutes.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Jamie reads 15 pages in 25 minutes
And, wants to know how many pages she can read in 65 minutes
Now, Let number of pages read in 65 minutes = x
Hence, We can formulate;
x / 65 = 15 / 25
x = 15 x 65 / 25
x = 39
Thus, There are 39 pages she can read in 65 minutes.
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Jylene and her brother had a total of $35.19 to buy school supplies. Jylene’s school supplies cost $12.78
Answer:
whats the question
Step-by-step explanation:
Answer:
What is the question???
Step-by-step explanation:
5th grade math. Correct answer will be marked brainliest. What goes in the blank box?
Answer:
The answer is 1.97 meters per second
Step-by-step explanation:
Plz give brainliest thanks :) Let me explain you how you do this Housefly is 1.967
The 7 is the tenth and the 6 is the hunderth
1.967 round to 1.96 from the hunderths because the last number is greater than 5 so you round up!
Answer:
1.97
Step-by-step explanation:
REMEMBER: 5 or higher, round up, 4 or lower, round down
Since 7 is above 5, we round it up, turning 1.967 to 1.97
Cows and horses cost $250 each and sheep and goats each cost $200 at the county fair. Chickens sell for $50. How much could McDonald make by selling all his animals except the dogs and cats?
Answer:
the total amount of animals in McDonald's farm is missing, so I looked for a similar question and found the attached image:
McDonald can earn:
15 cows x $250 = $3,750
2 horses x $250 = $500
20 sheep x $200 = $4,000
25 goats x $200 = $5,000
17 chickens x $50 = $850
total = $14,100
What is the Least Common Multiple (LCM) of 3 and 6?
Answer:
6
Step-by-step explanation:
Both numbers can evenly go into 6: 3 can go into 6 two times, and 6 can go into 6 one time.I hope this helps!
The LCM of 3 and 6 is 6, which is the smallest positive integer that is a multiple of both numbers.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
We can use the prime factorization method to find the LCM. We can write each number as a product of its prime factors:
3 = 3
6 = 2 x 3
The LCM is the product of the highest powers of all the prime factors.
Here, the highest power of 2 is 2, and the highest power of 3 is 3. So, the LCM is:
LCM(3, 6) = 2 x 3 = 6
Thus, the LCM of 3 and 6 is 6, which is the smallest positive integer that is a multiple of both numbers.
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If f(x) = 2x - 2 and g(x) = x + 1, then f(x) = g(x) when
Answer:
When x = 3
Step-by-step explanation:
I'm sorry not to give explanation but I can't put my thoughts into words its weird but yeah
pls help i need help quickly
Answer: 5/6?
Step-by-step explanation:
The amount of seed a landscaper uses and the area
of lawn covered have a proportional relationship
Complete the table.
Answer/Step-by-step explanation:
Since there is a proportional relationship between amount of seed a landscaper uses and the area of lawn covered, therefore: constant of proportionality = area covered / seed.
The constant of proportionality would be same for all pairs of values given in the table.
Thus:
[tex] \frac{75}{3} = \frac{25}{1} = 25 [/tex]
[tex] \frac{100}{4} = \frac{25}{1} = 25 [/tex]
Answer:
25/1, 25
Step-by-step explanation:
please help! all answers are appreciated
I think it would be 1,200ml or 800 try 1,200ml first
Answer:
Its A. 600 ml.
Step-by-step explanation:
1st. Find the ml of milk for one pancake. So 400 divided by 10, it equals 40ml. So to find how many ml for 15 pancakes...you multiply 15 and 40 ml, and that will give you 600ml needed.
5 · 6 – 33 ÷ 3 + (5 · 2) what is the awnser
Answer:
29
Step-by-step explanation:
Answer quick please!!
Answer:
8
Step-by-step explanation:
need help with these 3
Answer:
1.) x = 110
[tex]\frac{3}{22} =\frac{15}{x}[/tex]
So for 3 to become 15 it would have to be multiplied by 5 because 3 x 5 = 15. And if I multiply the numerator by anything I always have to do the same to the denominator. So I multiply 22 x 5 = x. x = 110
[tex]\frac{3 * 5}{22*5} =\frac{15}{110}[/tex]
2.) x = 72
[tex]\frac{x}{16} =\frac{9}{2}[/tex]
For 16 to become 2 it has to be divided by 8 because 16 ÷ 8 = 2. And I have to do the same to the numerator of course, so i have to find x ÷ 8 = 9. I know the answer by memory, but for some it's easier to rewrite this as 9 × 8 = x. x=72
[tex]\frac{72}{16} =\frac{9}{2}[/tex]
3.) c = 24
[tex]\frac{3}{5} =\frac{c}{40}[/tex]
For 5 to become 40 it must be multiplied by 8 because 5 × 8 = 40. I have to multiply 8 by the numerator as well and 3 × 8 = 24. c = 24
[tex]\frac{3*8}{5*8} =\frac{24}{40}[/tex]
Answer:
_
1. x=7.3
2. x= 72
3. c= 24
Step-by-step explanation:
Hope This Helps!!!
URGENT.
The ice cream shop sells sundaes for $2 each and banana splits for $3 each. One day, the shop sold 8 more sundaes than banana splits and also made a total of $156. Which system of equations represents the situation?
Answer:
156=2s+3b s-8=b
Step-by-step explanation:
s=sundaes
b=banana splits
What is the main idea of the White House
Answer:
The White House is the solemn residence and the workplace of the President in the United States Of America. The president can also have his family there.
Step-by-step explanation:
The main motto or goal of the white house is to give and protect the fundamental rights of United States citizens
*PLEASE ANSWER* // *ASAP PLS*
Answer: I do not know
Step-by-step explanation:
Consider these functions: f(x)= -2x - 1 g(x)= -1/2x + 1/2 Which statements, if any, are true about these functions? I. The function f(g(x)) = x for all real x. II. The function g(f(x)) = x for all real x. III. Functions f and g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.
Answer:
A. I only
Step-by-step explanation:
Given the functions
h(x)= -2x - 1 g(x)= -1/2x + 1/2
h(g(x) =h( -1/2x + 1/2)
=f((-x+1)/2)
We are to replace x in h(x) with -x+1/2
h((-x+1)/2) = -2(-x+1)/2 + 1
h((-x+1)/2) = -(-x+1)+1
h((-x+1)/2)= x-1+1
h((-x+1)/2) = x
h(g(x) = x
Also for g(h(x))
g(h(x)) = g(-2x-1)
Since g(x) = -x+1/2
g(-2x-1) = -(-2x-1)+1/2
g(-2x-1) =2x+1+1/2
g(-2x-1) = 2x+2/2
g(-2x-1) = 2(x+1)/2
g(-2x-1) = x+1
Sine g(h(x)) ≠ h(g(x)), hence both functions are not inverses of each other
Hence I. The function h(g(x)) = x is the only correct option. Option A is correct
The correct option is: A. I only
We have functions:
[tex]h(x)= -2x - 1 \\g(x)= -\frac{1}{2} x +\frac{1}{2} \\h(g(x)) =h(-\frac{1}{2} x +\frac{1}{2}) \\h(g(x))=f(\frac{-x+1}{2} )[/tex]
Now, replace x in h(x) by [tex]\frac{-x+1}{2}[/tex]
So,
[tex]h(\frac{-x+1}{2} ) = -2(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} ) = -(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} )= x-1+1\\h(\frac{-x+1}{2} )=x\\h(g(x)) = x[/tex]
Now, g(h(x))
g(h(x)) = g(-2x-1)
Since [tex]g(x) = \frac{-x+1}{2}[/tex]
[tex]g(-2x-1) = \frac{-(-2x-1)+1}{2} \\g(-2x-1) =\frac{2x+1+1}{2}\\g(-2x-1) =\frac{2x+2}{2}\\g(-2x-1) = x+1[/tex]
As g(h(x)) ≠ h(g(x)),
Therefore, both functions are not inverses of each other.
Hence A. I only
The function h(g(x)) = x is the only correct option.
So, option A is correct.
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Name the property. 7xy = 7yx
Solving each system elimination.
(Help I’ll mark you brainly)
Answer:
1) x=6, y=-6 which is (6,-6) as an ordered pair
3) x=10, y=-1 which is (10,-1) as an ordered pair
Step-by-step explanation:
Question 1:
Solve them like an addition problem:
-4x-2y=-12
4x+8y=-24
________
(-4x+4x)+(-2y+8y)=(-12+-24)
0x+6y=-36
6y=-36
y=-6
Plug value of y into one of the original equations:
4x+8(-6)=-24
4x-48=-24
4x=24
x=6
Question 3:
Solve them like an addition problem:
x-y=11
2x+y=19
_______
(x+2x)+(-y+y)=11+19
3x+0y=30
3x=30
x=10
Plug value of x into one of the original equations:
10-y=11
-y=1
y=-1
WILL GIVE BRAINLEST! Is this relationship proportional why or why not?
Yes it is because it passes the line and made at exact point on 12. :)) ^^ give them brainly though
What is the slope of the line that goes through points (−3,−4) and (−7,16)? please help
Answer:
5
Step-by-step explanation:
slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
The second y point is 16 and the first is -4, so:
(16) - (-4)
Which can be written as 16 + 4 because a double negative makes a positive. Do the same for the x points, -7 and -3:
(-7) - (-3)
(-7) + (3)
Now solve both of them:
16 + 4 = 20
(-7) + 3 = -4
Remember, the slope formula is y over x, so we still need to put it into the fraction form:
[tex]\frac{20}{-4}[/tex]
You can reduce this to [tex]-\frac{5}{1}[/tex], or 5.
The slope of the line will be "-5".
Given points are:
[tex](x_1,y_1) = (-3,-4)[/tex][tex](x_2,y_2) = (-7,16)[/tex]As we know the formula,
→ Slope, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we get
[tex]= \frac{16-(-4)}{-7-(-3)}[/tex]
[tex]= \frac{16+4}{-7+3}[/tex]
[tex]= -\frac{20}{4}[/tex]
[tex]= -5[/tex]
Thus the above answer is correct.
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whats 10 plus 10 ..........................
Answer:
20!!!!!!!!!
Step-by-step explanation:
When converting rational exponents to radical notation, which of the following are correct? Choose all that apply:
1. Numerator of the rational exponent becomes index of the radical notation
2. Negative exponent of the rational exponent makes the radical notation a negative value
3. Denominator of the radical exponent becomes the power of the radicand in the radical notation
4. Denominator of the rational exponent becomes the index of the radical notation
5. Numerator of the rational exponent becomes power of the radicand in the radical notation
Given:
Converting rational exponents to radical notation.
To find:
The correct statements.
Solution:
According to the property of exponents, conversion of rational exponents to radical notation is
[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]
In [tex]x^\frac{a}{b},[/tex] x is base, a is numerator of the rational exponent and b is denominator of the rational exponent.
In [tex]\sqrt[b]{x^a}[/tex], x is radicand, a is power of radicand and b is index of radical notation.
Denominator of the rational exponent becomes the index of the radical notation.
Numerator of the rational exponent becomes power of the radicand in the radical notation.
Therefore, the correct options are 4 and 5.
Using the conversion of rational exponents to radical notation, it is found that the correct options are:
4. Denominator of the rational exponent becomes the index of the radical notation
5. Numerator of the rational exponent becomes power of the radicand in the radical notation
The conversion of rational exponents to radical notation is modeled by:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
That is:
The numerator becomes the power of the radicand, hence item 5 is correct.The denominator becomes the index of the radical notation, hence item 4 is correct.A negative exponent just is represented by a fraction, as [tex]a^{-\frac{n}{m}} = \frac{1}{a^{\frac{n}{m}}}[/tex], hence the radical is not negative, and item 2 is incorrect.
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The graph shows the first quadrant portion of four exponential functions. Which equation could generate the BLUE curve? Assume a > 0 for all functions.
A) y = a-x
B) y = a-x + 1
C) y = a-x + 2
D) y = a-x + 3
Answer:a
Step-by-step explanation:
The solution is:
The initial value of the function is 2
The base of the function is 3
The function shows exponential growth
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
f(x) = 2(3^x)
Exponential functions are those with the following equation:
y = a*b^x
where a ≠ 0, b > 0 and b ≠ 1 and x is a real number.
a is the y-intercept and b is the base.
The initial value of the function is the same as the y-intercept
If a is positive, the function growth. If a is negative, the function decay
Hence, The initial value of the function is 2
The base of the function is 3
The function shows exponential growth
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complete question:
Consider the exponential function f(x) = 2(3x) and its graph.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. The equation of the function is y = f (x). The function crosses the y-axis at (0, 2).
The initial value of the function is.
The base of the function is.
The function shows exponential
A side of the triangle below has been extended to form an exterior angle of 132°. Find the value of X
Answer:
x = 114°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, thus
x + 18° = 132° ( subtract 18° from both sides )
x = 114°
The value of angle x in the triangle will be equal to 114°.
What is an exterior angle?When one side of a triangle is extended, an external angle of the triangle is created. The external angle of the triangle is the non-straight angle (the one that is not simply the extension of the side) that is outside the triangle but close to an interior angle.
Given that a side of the triangle below has been extended to form an exterior angle of 132°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, thus
x + 18° = 132° ( subtract 18° from both sides )
x = 114°
Therefore, the value of angle x in the triangle will be equal to 114°.
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When you add 2 positive intergers, the answer is always positive. When you subtract 2 positive intergers, is their difference always a positive interger? Explain.
Answer:
No. If the second positive integer is larger than the first positive integer in a subtraction problem, the difference will be negative.
Step-by-step explanation:
The numbers in this number set are _______ their absolute values. Answer choices: Smaller than, the same, and larger than. Numbers larger than 1: Zero: Negative Numbers: Positive Proper fractions Non- negative numbers:
Answer:
Smaller than
Positive numbers
Step-by-step explanation:
The absolute value of a number is the distance from the zero. This can be positive or negative forming the absolute number. The distance is negative when the number is positive. The absolute numbers are used in the equations for the solutions. The numbers greater than zero are positive numbers.
For question 2, find the x- and y-intercept of the line.
5x + 4y = 80
O A. x-intercept is 4; y-intercept is 5.
O B. x-intercept is 20; y-intercept
16.
O C. x-intercept is 5; y-intercept is 4.
O D. x-intercept is 16; y-intercept is 20.
: Suppose that you plan to take a trip to your dream destination. You
would like to know the shortest distance between your starting point and your
destination. When calculating distances on a plane, you need only consider two
dimensions because you are on a flat surface. However, when finding distances
between two points on Earth, you must take into the account the curvature of a
sphere. In this portfolio, you will extend your knowledge of two-dimensional vectors
to three-dimensional vectors in order to find the shortest distance between two
points on the surface of Earth.
Answer:
idk
Step-by-step explanation:
i still don't know........
yes.
*tbh idk why i just put yes, and i also dont know what this is asking so...hehe
Find the rate of change from the given table.
Answer the answer is 2:)
Step-by-step explanation:
Answer:
D. 8
Step-by-step explanation:
To find rate of change
m=y2-y1
------
x2-x1
I'm gonna use coordinates (7,56) and (9,72)
m= 72-56
---------
9-7
m= 16
---
2
m=8
x/4 + 5 = 8
PLEASE HELP ME
Answer:
hiii...hopefully this is correct x=12