The complex conjugate of 4 − 3i is;
4 - (-3i) = 4 + 3i .
Now, According to the question:
The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.
Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.
The complex conjugate of a + bi is a - bi
So, the complex conjugate of 4 − 3i is;
4 - (-3i) = 4 + 3i .
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Each gift bag include a bouncy ball,ticker,and cookie. There are red,yellow,or green bouncy ball;iri,lily,or daiy ticker;and chocolate chip or oatmeal cookie. How many different gift bag could be made?
There are a probability of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie.
There are a total of 6 different possible combinations of the gift bag with a bouncy ball, ticker, and cookie. These combinations include a red bouncy ball, an iri, lily, or daiy ticker, and either a chocolate chip or oatmeal cookie. The red bouncy ball offers a vibrant and exciting option, while the iri, lily, and daiy ticker add a fun element of surprise. The two cookie options offer something delicious and comforting to enjoy. With all of the different combinations, there is something for everyone to enjoy! Each combination offers a unique and special gift bag that will be sure to bring a smile to anyone's face.
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PLEASE HELPPP I REALLY NEED HELP
Answer: y = -2/3x+4
Step-by-step explanation:
negative slope
y intercept (0,4)
4th answer choice.
Answer:
D.
Step-by-step explanation:
It's really blurry but here's what I did
Pick two random points:
(0, 4) and (6,0) is what I picked personally.
Calculate slope: rise/run = [tex]\frac{0 - 4}{6 - 0} = \frac{-4}{6} = \frac{-2}{3}[/tex]
b is the y-int at 4 therefore your equation is [tex]y = \frac{-2}{3}x + 4[/tex]
Please help for 10 points… I need this asap!!!
Answer: Is there an answer for 1/2? I'm not sure.
Step-by-step explanation: If you look at the line it's going up by one and over by 2.
To solve for slope (Rate of Change) you need to find the change and y over the change in x. (y2-y1) divided by (x2-x1) take two points on the graph that is touching a line.
Two points on your graph is (2,2), and (6,4). You would take the second y which is 4 and subtract it from the first y which is 2. (4-2 = 2). Then you take the second x (6) and subtract it from the second y (2). (6-2 = 4). Now that you have the change and x over the change in y. you divide the top number by the bottom number. If it's a fraction just simplify it. (2/4 = 1/2). I'm not that good at explaining but I hope this helps a lot!
For the following equation, a. Write the value or values of the variable that make a denominator zero. These are the
restrictions on the variable. b. Keeping the restrictions in mind, solve the equation.
For the given equation, the value of x = -21.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
For the given equation,
x ≠ ±3
On taking LHS,
⇒ [tex]\frac{5}{x+3} - \frac{2}{x-3}[/tex]
Taking LCM,
⇒ [tex]\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}[/tex]
⇒ [tex]\frac{5x - 15 - 2x - 6}{x^2 - 9}[/tex]
⇒ [tex]\frac{3x - 21}{x^2 - 9}[/tex]
On Comparing both sides,
⇒ [tex]\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}[/tex]
⇒ 3x - 21 = 4x
⇒ x = -21
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find the product of 7/2 and 22
Answer:
98765
Step-by-step explanation:
How many times as intense as a standard earthquake is an earthquake measuring 3. 1 on the Richter scale?.
On the Richter scale is 1258.93 times as intense as a standard earthquake.
The Richter scale is a base-10 logarithmic scale, which means that each order of magnitude is 10 times more intensive than the last one. We have,
the an earthquake measuring 3. 1 on the Richter scale.
On Richter Scale, A = log(I/Iₛ)
here, A ---> amplitude
I --> intensity of earthquake
Iₛ ---> standard intensity of earthquake
As, A = 3.1
=> 3.1 = log(I/Iₔ)
Taking anti-logarithm both sides
=> 10³·¹ = I/Iₛ
=> 1258.93 = I/Iₛ
=> I = 1258.93 Iₛ
Therefore, the earthquake with measuring 3.1 on Richter scale is 1258.93 times as intense as a standard earthquake.
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Find the bearing of b from a in each diagram
Answer:
well where is your diagram
write an inequality whos solution is an empty set
Inequality 5 > 6 is an example of an inequality whose solution is an empty set.
What is inequality?
An inequality is a statement that compares two expressions using one of the following mathematical symbols: <, >, ≤, ≥, ≠. It shows the relationship between the values of the expressions, but unlike an equation, it does not show that the expressions are equal.
For example, the inequality 3x + 4 > 7 compares the value of the expression 3x + 4 to the value of 7. It shows that 3x + 4 is greater than 7 for all values of x.
An inequality that has an empty set as its solution is one that has no solutions. For example, inequality 5 > 6 is an example of an inequality whose solution is an empty set because it is impossible for any value of x to satisfy the inequality. Any value of x will be less than 6 so it is impossible for x to be greater than 6.
Hence, Inequality 5 > 6 is an example of an inequality whose solution is an empty set.
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Geometry
You randomly select 3 cards from a standard deck of 52 playing cards. What is the probability that all 3 cards are hearts when...
a. You replace each card before selecting the next card.
b. You do not replace each card before selecting the next card?
a. You replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is also 13/52 or 1/4. And the probability of drawing a heart on the third draw is also 13/52 or 1/4.
Since the events are independent, we can multiply the probability of each event to find the probability that all three cards are hearts: (1/4) * (1/4) * (1/4) = 1/64.
b. You do not replace each card before selecting the next card.
The probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing a heart on the second draw is 12/51 since we already drew a heart before, the total number of cards left in the deck is 51. The probability of drawing a heart on the third draw is 11/50 since we already drew 2 hearts before, the total number of cards left in the deck is 50.
The probability that all three cards are hearts is (1/4) * (12/51) * (11/50) = 0.0217 or approximately 2.17%.
It's important to note that in the first case the probability of drawing a heart on the second and third draw is still 1/4 because we are replacing the cards back before drawing the next one, so all 52 cards are available again. While on the second case, we don't replace the cards back and that's why the probability of drawing a heart on the second and third draw is different.Answer:
Step-by-step explanation:
a penguin walks 12 feet in 8 seconds at this rate:
how far can the penguin walk in 32 minutes?
how far can the penguin walk in 1 hour?
If f(x)= 2x2 + x - 7 and g(x)= x + 5, then evaluate g(f(3)).
Answer:
g(f(3)) = 19
Step-by-step explanation:
This would be your functions: [tex]\displaystyle{f(x)=2x^2+x-7}[/tex] and [tex]\displaystyle{g(x)=x+5}[/tex]. In order to evaluate g(f(3)), we must find the value of f(3) first which we can find by substituting x = 3 in the f(x).
[tex]\displaystyle{f(3)=2(3)^2+3-7}\\\\\displaystyle{f(3)=2\cdot 9 - 4}\\\\\displaystyle{f(3)=18-4}\\\\\displaystyle{f(3)=14}[/tex]
Therefore, g(f(3)) is basically equal to g(14), we substitute x = 14 in the g(x).
[tex]\displaystyle{g(f(3))=g(14)=14+5 = 19}[/tex]
Hence, g(f(3)) is 19.
9. Oscar's rectangular room has an area of 6x6y8 square units. If the width of Oscar's room can be represented by 2x³y2, which of the following represents the length of the room?
According to the given statement, 3x^3y^4 represents the length of the room.
What does word rectangle mean?Its length w is calculated using the formula h = A/w if you have an area A and a width w. Its length can be determined using the formula h = P/2w if you know its perimeter (P) and width (W). The length is given by h = (d2w2) if the diagonal d and width w are present.
Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.
The area of a square box is length x width, so that we can set up the calculation:
length x (2x³y²) = 6x6y8
To find the length of the court, we can divide both sides by 2x³y²:
length = (6x6y8) / (2x³y²)
so the length of a room is represented by 3x^3y^4
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The complete question is -
Oscar's rectangular room has an area of 6x^6y^8 square units. If the width of Oscar's room can be represented by 2x^3y^2, which of the following represents the length of the room?
(a)3x^2y^4
(b)3x^3y^4
(c)12x^9y^10
(d)12x^18y^16
Kelly made fruit punch to erve at a party for her che team he mixed 1 2/5 liter of cranberry juice and 1 3/5 liter of pineapple juice together how much fruit punch did he make all together
Kelly pours 1/3 litre of fruit punch into each glass at a party for her chess team.
What does the division do?
divides left-hand operands into right-hand operands while performing a division operation in mathematics.
For instance, 4/2 = 2.
She combined the prescribed amounts of 1 2/5 litres of cranberry juice and 1 3/5 litres of pineapple juice.
The appropriate response to the aforementioned situation would be
⇒ 1 2/5 + 1 3/5
fractionalizing mixed numbers
⇒ 7/5 + 8/5
Consider the LCM in the previous equation.
⇒ (7 + 8)/5
⇒ 15/5
⇒ 3
She then divided the fruit punch equally among the nine cups.
3 litres of fruit punch must now be divided among 9 glasses.
3/9, therefore, equals 1/3 litres of fruit punch.
She, therefore, fills each glass with a third of a litre of fruit punch.
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How do you solve complex fractions and unit rates?.
A unit rate is a ratio that has a denominator of 1, such as miles per hour or dollars per item. To solve a complex fraction that involves a unit rate, you can follow the same steps as solving a regular complex fraction, but with an additional step to convert the final expression to a unit rate.
Factor the numerator and denominator of the complex fraction if possible.
Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator.
Simplify the resulting expression by combining like terms, if possible.
Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.
Divide the numerator by the denominator to get the unit rate.
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What are the values of the three basic trigonometric ratios?.
The values of the three basic trigonometric ratios are Sine, Cosine, tangent.
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions can be used to obtain the other significant trig ratios, cosec, sec, and cot.
Sine: The ratio of the perpendicular to the hypotenuse is known as the sine ratio for every given angle. Sine of angle in the given triangle can be expressed as sin = AB/AC.Cosine: The proportion of an angle's base to its hypotenuse is known as the cosine ratio. The cosine of angle in the given triangle can be expressed as cos = BC/AC.Tangent: The ratio of the perpendicular to the base is known as the tangent ratio for every given angle. The tangent of angle in the given triangle can be expressed as tan = AB/BC.Learn more about trigonometric ratios;
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What are the 7 types of symmetry?.
The seven types of symmetry are Euclidean, Reflectional, Point reflection, Rotational, Translational, Glide reflection, Helical and Double rotation symmetry.
In math the term symmetry is defined as one shape is exactly like the other shape when it is moved, rotated, or flipped.
Here we need to identify the seven types of symmetry.
As per the definition of symmetry here we have identified the types of symmetry as are possible for a geometric object depend on the set of geometric transforms available and on what object properties should remain unchanged after a transformation.
They are listed as follows, Euclidean symmetries, Reflectional symmetry, Point reflection and other involutivity isometries, Rotational symmetry, Translational symmetry, Glide reflection symmetry, Helical symmetry and Double rotation symmetry.
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(-4 + 9) x (8 - 3) Pls help asap
Answer:
25
Step-by-step explanation:
(-4 + 9) x (8 - 3)
= (5) x ( 5)
= 25
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(-4 + 9) \times (8 - 3)}\\\\\mathsf{-4 + 9 = \boxed{\frak 5}}\\\mathsf{8 - 3 = \boxed{\frak 5}}\\\\\mathsf{= (-4 + 9) \times (8 - 3)}\\\mathsf{= 5\times5}\\\mathsf{= 25}[/tex]
[tex]\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{25}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Which model shows 2 + 0.4?
(use photo)
Answer:
B
Step-by-step explanation:
2 ÷ 0.4 = 5
----------------
introduction paragraph about Peter G. L. Dirichlet
Answer:
Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʀiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician who made contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis
[tex] \frac{?}{?} [/tex]
5 to the power 0
To the power of 5, 0 is 1 . Any power with a value of 0 yields a response of 1. [tex]5^0[/tex] = 1 can be used to represent 5 to the power of 0.
Why any number to the power of 0 is 1?Because 1*x = x for any other number x, the number 1 is the multiplicative identity. Due to the fact that every integer raised to the power of zero is just the sum of zeroes, or the multiplicative identity, 1, any number raised to this power is one.
The value 0 to the power 0 cannot have any values since they would conflict. In this way, 0 to the power 0 is undefinable. Reverse values are indicated by negative exponents. A negative power of a number is one more than the positive opposite power of the same number. Negative zero is a mathematical nonsense. the sign bit of a binary integer is set to 1, and all other bits are set to zero.
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Pleaseeee help
Consider the function f(x)=x^3-1. Which of the following functions is f^-1(x)?
The inverse function of f(x) = x^3 - 1 is f^-1(x) = (x + 1)^(1/3).
What is the inverse of a function?
An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function that gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.
The inverse of a function f(x) is denoted as f^-1(x), and it is defined as the function that "undoes" f(x).
To find the inverse of a function, we need to swap the roles of x and y, and then solve for y in terms of x.
Given f(x) = x^3 - 1, the inverse function f^-1(x) is the function such that:
f(f^-1(x)) = x
f^-1(f(x)) = x
So we need to solve for x in terms of y.
x^3 - 1 = y
x = (y + 1)^(1/3)
Therefore, the inverse function of f(x) = x^3 - 1 is f^-1(x) = (x + 1)^(1/3).
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A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
!!! 50 points !!!
Rug to place in the middle of his bedroom. He draws a diagram to show where he will place is rug. Part A: Sam needs to find the perimeter of his bedroom. Use the picture to write three expressions that represent the perimeter, in feet, of Sam’s room.
Part B: now, Sam wants to find the area of his bedroom. He says that he can find the area using the expression 40x + 12 square feet. Is he correct? If he is incorrect, how many square feet is he off by?
Part C: Sam’s friend Carla has a square a bedroom with side length 4x + 6. Compare the perimeter of Carla’s room to the perimeter of Sam’s room.
Aadan and Chinyelu viit the market in Gao to buy an Azawakh, a breed of dog that i popular for guarding ancient Mali village. When Aadan' dog wa a puppy, it weighed `8` kg, which i `30\%` of it current adult weight. What i the current weight of Aadan’ dog?
Write an equation in which `x` repreent the current weight of Aadan' dog
The current weight of Aadan's dog is approximately 26.67 kg.
What is weight ?
Weight is a measure of the force of gravity on an object. The weight of an object is equal to the force exerted on the object by gravity. The weight of an object is typically measured in units of force such as newtons (N) or pounds (lb). On Earth, the weight of an object is equal to its mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s².
Let's call the current weight of Aadan's dog as "W".
As per the information given,
Aadan's dog was a puppy and it weighed 8 kg which is 30% of it's current adult weight.
So, 8kg = 30/100*W
We can find the current weight of Aadan's dog by solving the equation above:
8 = 30/100W
8 = 3/10W
8 = 0.3W
W = 8/0.3
W = 8/(3/10)
W = 8(10/3)
W = 8*3.333
W = 26.666 kg ( approx 26.67 kg)
So the current weight of Aadan's dog is approximately 26.67 kg.
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8kg = 30/100*W
8 = 30/100W
8 = 3/10W
8 = 0.3W
W = 8/0.3
W = 8/(3/10)
W = 8(10/3)
W = 8*3.333
W = 26.666 kg ( approx 26.67 kg)
A well, whose diameter is 3 m, has been dug 21 m deep and the earth dug out is used to form an embankment 4 m wide around it. Find the height of the embankment.
Answer:
31.875 m
Step-by-step explanation:
We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.
The volume of the well is given by the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).
V = π(1.5)^2(21) = 42.5π m^3
The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:
V = 1/3 πr^2h
where r is the radius of the base of the cone (4 m) and h is the height of the embankment.
V = 1/3π(4)^2h = 4/3πh m^3
Now we know that the volume of the embankment is equal to the volume of the well:
V = 42.5π m^3 = 4/3πh m^3
Then we can solve for h by dividing both sides by 4/3π:
h = 42.5π m^3 * 3/4π = 31.875 m
So the height of the embankment is 31.875 m.
A river guide conducts kayak and canoe tours along a scenic river. He charges a booking fee plus a variable rate depending on the number of passengers. The total cost for different numbers of passengers, including the initial fee, is shown on the graph.
Find and interpret the rate of change.
For the specified Data, the rate of change will be 8.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given this, Kayak and canoe experiences are led by a river guide along a beautiful river. In addition to a booking fee and a variable tariff based on the number of passengers, he charges. The graph displays the total cost for various passenger counts, including the booking fee.
From general formula of rate of change = (y₂ - y₁)/ (x₂ - x₁)
in our case
y₂ = 72
y₁ = 56
x₂ = 4
x₁ = 2
thus rate of change = 16/2 = 8
Since A rate of change is the proportion of one quantity's change to another's change. There is a constant rate of change in linear relationships.
Therefore, The rate of change for the given equation will be 8.
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What is the range of the function f x equals 3x to the power of 2+ 6x 8?.
Answer:[-11, ∞]
The range of the function f(x) = 3x2 + 6x - 8 is [-11, ∞].
Step-by-step explanation:
What are the solutions of the equation x4 5x2 36 0?.
The solutions of the equation x⁴ - 5x² - 36 = 0 are: x = -3, x = 3, x = 2i and x = -2i
Consider given equation x⁴ - 5x² - 36 = 0
Let us assume that x² = p
so, we get an equation,
p² - 5p - 36 = 0
Now we solve above quadratic equation.
p² - 5p - 36 = 0
using the Quadratic Formula where
a = 1, b = -5, and c = -36
[tex]\Rightarrow p=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow p = \frac{5\pm \sqrt{25+144} }{2}\\\\\\\Rightarrow p = \frac{5\pm \sqrt{169} }{2}\\\\\\ \Rightarrow p=\frac{5\pm 13 }{2}[/tex]
So, p = 9 and p = -4
But p = x²
So, x² = 9 OR x² = -4
For x² = 9, by taking square-root we get x = 3, x = -3
an equation x² = -4 has complex roots, x = 2i and -2i
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Been stuck on this for a while Please Help!
Answer:
x = 23°
Step-by-step explanation:
Sum of interior angle
(n - 2)180. note: the sides are 3
(3 - 2)180
(1)180
180°.
the value of x
31° + 3x° + 34° + 2x° = 180°
31° + 34° + 3x + 2x = 180°.
65° + 5x = 180°
5x = 180° - 65°
5x = 115°
5x/5 = 115/5
x = 23°
10-2 skills practice simplifying radical expressions
1. On simplifying the radical expression √28 the result is 2√7.
2. On simplifying the radical expression √40 the result is 2√10.
3. On simplifying the radical expression √72 the result is 6√3.
4. On simplifying the radical expression √99 the result is 3√11.
What is a radical expression?
Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.
The first radical expression is -
√28
Take the LCM of 28.
The LCM is obtained as - 2 × 2 × 7.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 2√7.
Therefore, the expression is 2√7.
The second radical expression is -
√40
Take the LCM of 40.
The LCM is obtained as - 2 × 2 × 2 × 5.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 2√10.
Therefore, the expression is 2√10.
The third radical expression is -
√72
Take the LCM of 72.
The LCM is obtained as - 2 × 2 × 2 × 3× 3.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 6√3.
Therefore, the expression is 6√3.
The fourth radical expression is -
√99
Take the LCM of 99.
The LCM is obtained as - 3 × 3 × 11.
The number that is repeated twice will be outside the square root symbol. The number that is obtained only once should be inside the square root symbol.
So, the simple form is 3√11.
Therefore, the expression is 3√11.
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