The conjugate of the complex number -8 + 2i is -8 -2i. By multiplying the complex number by its conjugate we get the answer 68, which corresponds to option C.
Explanation:To solve this question, we first need to know what a conjugate is. In complex numbers, if a number is represented as a + bi, its conjugate will be a - bi. The provided complex number in the question is -8 + 2i, so its conjugate would be -8 - 2i.
Next, we multiply the complex number by its conjugate. This would give us (-8 + 2i) × (-8 - 2i). Executing this multiplication based on the rule of multiplication of brackets (a+b)(a-b) = a2 - b2, we have (-8)2 - (2i)2, which results in 64 - (-4) = 68.
Therefore, the product of (-8 + 2i) and its conjugate is equal to 68, which is option C.
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What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?
Answer: [tex]3x+4y=16[/tex]
Step-by-step explanation:
Given equation of a line = [tex]3x + 4y = 15[/tex]
i.e. [tex]4y = 15-3x[/tex]
i.e. [tex]y=\dfrac{15}{4}-\dfrac{3}{4}x[/tex]
i.e. [tex]y=-\dfrac{3}{4}x+\dfrac{15}{4}[/tex] (1)
It is in intercept form [tex]y=mx+c[/tex] (2) , where m is slope.
By comparing (1) and (2) the slope of line : [tex]m=-\dfrac{3}{4}[/tex]
Also the parallel lines have same slope .
The equation of a line passing through a point (a,b) and having a slope of 'm' is given by :-
[tex](y-b)= m(x-a)[/tex]
Then the equation of the line that passes through (8,-2) and having slope of [tex]m=-\dfrac{3}{4}[/tex] is given by :-
[tex](y-(-2))=- \dfrac{3}{4}(x-8)[/tex]
[tex]4(y+2)=-3(x-8)[/tex]
[tex]4y+8=-3x+24[/tex]
[tex]3x+4y=24-8[/tex]
[tex]3x+4y=16[/tex]
Hence , the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is [tex]3x + 4y = 15[/tex] is [tex]3x+4y=16[/tex]
.
Why is it important to simplify rational expressions before multiplying or dividing? How do you determine that a rational expression is in simplest form?
It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.
The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.
What is a rational number?A rational number is a number that can be written in the form of p/q where q is not equal to zero.
We have,
Some examples of rational numbers are:
38/44 or 39/63
We can divide this rational number into a decimal number but it is easier for us if we can simplify it in its simplest form.
There is no common factor between numerator and the denominator in its simplest form.
The simplest form of 38/44.
= 38/44
= 2 x 19 / 2 x 22
= 19/22
The simplest form of 39/62 is
= 39/63
= 3 x 13 / 3 x 21
= 13/21
Thus,
It is important for us to simplify rational expressions before multiplying or dividing because it makes our calculations easier.
The rational expression is in its simplest form when there is no common factor between the numerator and the denominator.
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Express terms in i square root -40
How many centimeters is a piece of paper that measures 12 inches? centimeters?
When you add or subtract a negative number to both sides of an inequality, you should always reverse the sign?
Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
11. Solve for the value of x in the triangle shown below. Show your work! (1 point for equation, 1 point for answer)
3 inside angles need to = 180, since it is a right triangle, the bottom left angle = 80 so the other 2 angles need to equal 90 degrees
so you have:
(8x+2) + (9x+3) = 90
combine like terms to get:
17x+5 = 90
subtract 5 from both sides:
17x = 85
divide both sides by 17
x = 85/17 = 5
x = 5
How to find the square root of an improper fraction?
To find the square root of an improper fraction, simplify the fraction if possible, convert it into perfect squares, or use the properties of exponents. If it is already in simple form like 49/100, directly find the square roots of the numerator and denominator separately. Otherwise, use multiplication to manipulate the fraction into a more manageable form for taking square roots.
To find the square root of an improper fraction, the process involves several steps, similar to finding the square root of any number. First, simplify the fraction if possible. In some cases, this may involve multiplying the numerator and denominator by the same factor to make the radical easier to simplify. For instance, if you have an improper fraction like 49/100, you can easily identify that both the numerator and the denominator are square numbers. So, the square root of 49/100 equals the square root of 49 divided by the square root of 100, which simplifies to 7/10.
When the fraction cannot be simplified easily, a different approach is by converting the numerator and denominator into perfect squares, simplifying the expression within the radical, or using properties of exponents to re-express the square root. For example, if you have a fraction like 1/2, you can multiply both the numerator and denominator by 2 to get 2/4. Then you would rewrite the square root as the square root of 2 over the square root of 4, which simplifies to the square root of 2 over 2.
How to determine if two functions are inverses?
Final answer:
Two functions are inverses if, when composed, they return the original input value (identity function). For example, an exponential function and its inverse, the natural log, undo each other. This can be checked with the equations by rearranging and setting equal to isolate constants or applying the functions one after the other.
Explanation:
How to Determine if Two Functions Are Inverses
To determine if two functions, F and G, are inverses of each other, you can compose the functions and see if the result is the identity function. The composition of two inverse functions will output the original input value, meaning that if you take a value x, apply function F to get F(x), and then apply function G to this result, i.e., G(F(x)), you should get x back if F and G are true inverses. The same must hold true in the reverse order, where G is applied first, followed by F: F(G(x)) = x.
To illustrate this concept, let's consider the exponential function and its inverse function, the natural log.Exponential functions are undone by their inverses, natural logs, according to the relation[tex]eln(x) = ln(ex)[/tex]to see this is with the equations involving a constant A, for instance, these can be rearranged to isolate ln A and set them equal to obtain an identity.
Another familiar context is the square and square root functions. To "undo" a square, you take the square root and vice versa. This "undoing" operation is a key characteristic of inverse functions.
Remember that not all functions have inverses, only those that are one-to-one, meaning for each x there is a unique y and vice versa, have inverses that can be defined over their entire domain.
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(5, −2)
(1, −1)
(−4, 2)
(4, 0)
(−2, 1)
The ordered pairs that satisfy the given inequality is required.
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
The given inequality is [tex]y-4x\geq -5[/tex]
Let us substitute each point in the inequality
[tex](5,-2)[/tex]
[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]
[tex](1,-1)[/tex]
[tex]-1-4\times 1\\ =-5\geq -5[/tex]
[tex](-4,2)[/tex]
[tex]2-4\times -4\\ =18\geq -5[/tex]
[tex](4,0)[/tex]
[tex]0-4\times 4=-16\ngeq -5[/tex]
[tex](-2,1)[/tex]
[tex]1-4\times -2=7\geq -5[/tex]
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
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Which of the following phrases could represent the expression k - 4?
A.a number subtracted from four
B.four less a number
C.a number decreased by four
D.a number less than four
A deli offers a choice of 3 breads, 4 meats, and 7 toppings. Using these ingredients, how many possible sandwich combinations are there?
Answer:
3*4*7
Step-by-step explanation:
There is total of 84 combinations
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
6 less than the product of 3 and a number.
The algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.
What is an algebraic expression?An algebraic expression is a combination of terms separated by mathematical operations (+, -, *, /).
A term is a combination of numerals and variables where variables are raised to integral powers.
How to solve the question?In the question, we are asked to write the algebraic expression that represents the words "6 less than the product of 3 and a number".
Assuming the number to be x.
We first try to make the terms.
The term that will be formed using the words the product of 3 and a number is 3 * x = 3x.
The term using the word 6 is 6.
Now, to complete the expression, we combine the terms.
The words less than implies the difference. Thus the expression can be written as 3x - 6.
Thus, the algebraic expression representing the words "6 less than the product of 3 and a number" is shown as 3x - 6.
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Mrs garcia is is 1 year less than 3 times as old as her daughter. seven years from now, she will be 4 years more than twice as old as her daughter will be then
Which is cheaper for a $56 item that cost $9.25 to ship, a $15 off coupon off the cost or free shipping
Which improper fraction is equal to the mixed number 4 7/9 btw its a mixed number fraction
A. 37/9
B. 47/9
C. 43/9
D. 20/9
plz help asap
Select "Growth" or "Decay" to classify each function.
Function Growth Decay
y=200(0.5)^2t
y=1/2(2.5)^t/6
y=(0.65)^t/4
Which equation can be used to find the solution of (1/3)^d−5 = 81 ?
A. −d−5=4
B. d + 5 = 4
C. d−5=4
D. −d+5=4
1. The growth rate equation has a general form of:
y = A (r)^t
The function is growth when r≥1, and it is a decay when r<1. Therefore:
y=200(0.5)^2t --> Decay
y=1/2(2.5)^t/6 --> Growth
y=(0.65)^t/4 --> Decay
2. We rewrite the given equation (1/3)^d−5 = 81
Take the log of both sides:
(d – 5) log(1/3) = log 81
d – 5 = log 81 / log(1/3)
d – 5 = - 4
Multiply both sides by negative 1:
- d + 5 = 4
So the answer is D
Cole has 67 coins and 23 of them are nickels. 25% of the remaining coins are dimes. How many dimes does Cole have?
Which statement is true about the value of |-5|
A. It is the distance that –5 is from 0 on the number line.
B. It is the distance that –5 is from 5 on the number line.
C. It is less than 5.
D. It is greater than 5.
What is the measure of MOP?
Answer:
(C) [tex]{\angle}MOP=61^{\circ}[/tex]
Step-by-step explanation:
Given: It is given that angle MON is a straight angle and OP is bisects angle MOQ.
To find: The measure of the angle MOP.
Solution: It is given that angle MON is a straight angle and OP is bisects angle MOQ.
Thus, using the straight line property, we get
[tex]{\angle}MOP+{\angle}POQ+{\angle}QON=180^{\circ}[/tex]
[tex]2{\angle}MOP+{\angle}QON=180^{\circ}[/tex]
Substituting the given values, we get
[tex]2{\angle}MOP+58^{\circ}=180^{\circ}[/tex]
[tex]2{\angle}MOP=122^{\circ}[/tex]
[tex]{\angle}MOP=61^{\circ}[/tex]
Hence, option (C) is correct.
Answer: C - 61°
Step-by-step explanation: edge
Directions: Use a proportion to solve the problem.
Emily weighs six times as much on Earth as she does on the Moon. If her weight is ninety pounds on earth, what would her weight be on the moon?
What is a 401(k) plan? an investment plan offered by an insurance company a retirement plan offered by employers a personal retirement plan
Trisha needs 4 yards of fabric to do a project. If she already has of a yard of fabric, what is the minimum amount of fabric she must buy to be able to complete her project? A. 3 5/6 B.4 1/12 C.4 1/6
Answer:
The answer is A. OR 3 5/6
A pool is being drained at a rate of 120 gallons per minute.What is this rate in quarts per hour?
A mixture can be classified as a solution, suspension, or colloid based on _____. its total number of particles
the color of its particles
the scattering of its particles
the size of its particles
How to find the values of the six trigonometric functions for 180?
Will a negative number become positive when exponent is positive fraction
Bailey writes the expression g2 + 14g + 40 to represent the area of a planned school garden in square feet. If g = 5, what are the dimensions of the school garden?
HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks. How many snacks are in one pack of granola bars and one pack of fruit rolls?
Answer: The number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Step-by-step explanation:
Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .
Then according to the question we have the following system of equations :
[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]
Multiply equation (1) by 2 we get
[tex]20x+12y=304......................(3)[/tex]
Subtract equation (2) from equation (3), we get
[tex]13x=104\\\\\Rigtarrow x=8[/tex]
Substitute x=8 in (1), we get
[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]
Hence, the number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?
Final answer:
Tom would need to rent the basketball court 15 times for the gym membership to be more cost-effective than paying the non-member rental fee.
Explanation:
To determine how many times Tom would need to rent the basketball court to make the membership cheaper than being a non-member, we can set up a cost equation and find the breakeven point. Let's assume that Tom rents the court x times. For a non-member, the cost is $11 each time, which results in 11x dollars. For a member, the cost includes the one-time membership fee of $135 plus $2 each time the court is rented, summing to 135 + 2x dollars.
To find the breakeven point, we equate the two costs and solve for x:
11x = 135 + 2x
9x = 135
x = 135 / 9
x = 15
Thus, Tom would need to rent the court 15 times for the membership cost to be cheaper than paying as a non-member.