The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
In the question ,
the equation is given as
(x+yi)+(4+9i)=9-4i
to find the value of x and y , we solve LHS and RHS of the equation separately
So LHS =
(x+yi)+(4+9i)
x+yi+4+9i
Adding the real and imaginary terms , we get
(x+4)+(y+9)i which is equal to RHS that is 9-4i
So , on comparing , we get
x+4 = 9 and y+9 = -4
x= 9-4 and y = -4-9
x = 5 and y = -13
Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
The given question is incomplete , the complete question is
What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i ?
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a manufacturer can produce 2970 cell phones when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 55 x 3 4 y 1 4
The formula in terms of x and y for dy/dx is -3y/x
The value of dy/dx at the point (81,16) is -0.5926
The question is incomplete, the full question is given below:
A manufacturer can produce 2970 cell phones when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is [tex]55x^{\frac{3}{4} } y^{\frac{1}{4} } =2970[/tex]
a. Find a formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
b. Find the value of dy/dx at the point (81,16). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=[tex]\frac{d}{dx} (55x^{\frac{3}{4} } y^{\frac{1}{4} } )=\frac{d}{dx} (2970)[/tex]
=[tex]55(x^{\frac{3}{4} } \frac{d}{dx} (y^{\frac{1}{4} } )+y^{\frac{1}{4} } ((x^{\frac{3}{4} } ))=0[/tex]
=[tex]x^{\frac{3}{4} } y^{\frac{-3}{4} } \frac{dy}{dx} =3y^{\frac{1}{4} } x^{\frac{-1}{4} }[/tex]
= [tex]\frac{dy}{dx} =\frac{-3y^{0.5}x^{-0.5} }{x^{0.75}y^{-0.75} }[/tex]
[tex]=\frac{-3y}{x}[/tex]
=-3y/x
Part b
Value of dy/dx at the point (81,16)
dy/dx at (81,16), x=81, y=16
dy/dx=-3y/x
dy/dx=-3*16/81
dy/dx=-48/81
dy/dx=-16/27
=-0.5926
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Which equation represents a line that passes through the point (6,−3) and is parallel to the graph of y=3x+1? A y=3x−21 B y=3x+15 C y=−13x−1 D y=−13x+5
Answer:
Choice A
Step-by-step explanation:
The line we need to find has the same slope as the slope of the given line which is 3.
Lily solved the equation 3x − 10 = -3x + 8. The explanation of her process is shown. Select the text that shows an error in her process or justification of steps, if one exists. 1. I used the addition property of equality to achieve 6x − 10 = 8. 2. I used the addition property of equality to achieve 6x = 18. 3. I used the subtraction property of equality to achieve the solution of x = 3. There is no error in Lily’s process or justification of steps.
Answer: 3x - 10 = -3x + 8 Add 3x to both sides 6x - 10 = 8 Add 10 to both sides 6x = 18 Divide both sides by 6x = 3
Step-by-step explanation:
Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
y =
The equation that is parallel to y = -3x + 7 and passes through the point (2, -1) is y=-3x+5.
What is slope Intercept form?The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis.
y=mx+b
where m is the slope of the line and b is the y intercept.
The slope of the given equation,
y=-3x+7 is -3.
So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of -3
y-y₁=m(x-x₁)
where (2,-1) are x₁, y₁
y-(-1)=-3(x-2)
y+1=-3(x-2)
Multiply with 3 on RHS side
y+1=-3x+6
We have to write in slope intercept form, so shift 1 to RHS.
y=-3x+6-1
y=-3x+5
As you can see, the slope of this line is -3
, which means that the two equations are parallel to each other.
Hence y=-3x+5 is the equation that is parallel to y = -3x + 7 and passes through the point (2, -1).
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Pleaseeee help me with this
The solution of scalar multiplication 2A is Option(D).
[tex]2A = \left[\begin{array}{ccc}10&2&6\\12&8&4\\\end{array}\right][/tex]
What is scalar multiplication in matrices?A matrix is a rectangular array of numbers divided into rows and columns. A matrix element or entry is each number in the matrix. If A = [tex][aij]_{m*n}[/tex] is a matrix and k is a scalar, then kA is a matrix formed by multiplying each element of A by the scalar k. Real numbers are considered as scalars while working with matrices. The product of a real number with a matrix is referred to as scalar multiplication. Each entry in the matrix is multiplied by the given scalar in scalar multiplication. It is a straightforward multiplication.The given matrix is:
[tex]A = \left[\begin{array}{ccc}5&1&3\\6&4&2\\\end{array}\right][/tex]
To do the scalar multiplication to determine 2A, just multiply a 2 on every entry in the matrix:
[tex]2A = \left[\begin{array}{ccc}2*5&2*1&2*3\\2*6&2*4&2*2\\\end{array}\right][/tex]
[tex]2A = \left[\begin{array}{ccc}10&2&6\\12&8&4\\\end{array}\right][/tex]
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a process capability index has been calculated for a stable, non-automated process, then the operator is told to check samples at random and make centering adjustments to the process based on the sample readings. based on this information one would expect to find:
The process capability index gauges how much variance a process encounters in comparison to its specification parameters.
We might compare various procedures in terms of the ideal circumstance or whether they live up to our expectations. In the event that the process is not centered, the capability ratio formula is employed.
Process capability uses capability indices to compare an in-control process output to the specification's upper and lower bounds.
Calculated for steady, non-automated processes is the process capability index. The operator is then instructed to check samples at random and center the process.
The processing capability declined.
One would expect to find that the process capability has gotten worse.
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please help tomorrow is my exam please help
Answer:
30.2 meters
Step-by-step explanation:
The key is to realize that a 30 60 90 triangle can be constructed and the height of the house can be found from there. It may be helpful to draw a diagram.
I will use the diagram attached for reference to this solution.
Remember that the answer is asking for y, or the length of DE.
The angle CAB is 30 degrees, and the angle ACB is 90 degrees
The length of CB is 25 * sqrt3
Since ACB is a 30 60 90 triangle, and we know the length of one of the sides, the length of the other sides can be calculated.
CB is the shortest length, and so the middle length, AC, is sqrt(3) times longer than the length of the shortest length, CB
CB's length * sqrt 3 = AC's length = 25 * sqrt3 * sqrt3
AC = 75
length of A to F (I can't combine the letters a and f because then brainly thinks i'm swearing ) = 75 + x = 107
x = 32
Since length of BE = length of CF,
32 = BD + DE = 1.8 + y
y = 30.2 meters
if you have more questions please comment
The theatre can seat 10,950 people.There are 90 rows of seats in the theater. If each row has the same number of seats, how many seats are in each row?
122
Step-by-step explanation:
u just say 10 950 dividied by 90 which is 121 recurring and then u say 121 plus 1 because it has a remainder
Which of the following are possible
side lengths for a triangle?
A. 18, 12, 6
B. 9, 15,4
C. 5, 18, 14
Answer:
C
Step-by-step explanation:
when u take the 2 shortest sides and add them up, they must be greater than the longest length.
Write the equation of the ellipse that has its center at the origin with focus at (0,4) and vertex (0,7).
1) Notice that, in this case, the center is at (0,0) the focus at (0,4) and the Vertex is at (0,7)
2) Since the focus is at the y-axis, and the center is at the origin we can start from the following formula:
[tex]undefined[/tex]The cost of the entrance tickets to the zoo for 2 adults and 3 children is $78.80. the cost of the entrance tickets for 1 adult and 1 child is $33.10 . what is the cost of the entrance ticket for a child
The cost of the entrance ticket for a child is $12.80.
Using algebraic expression and equation, we can express each statement and determine the cost of the entrance ticket for a child
Let x = cost of the entrance ticket for a child
y = cost of the entrance ticket for an adult
If the cost of the entrance tickets to the zoo for 2 adults and 3 children is $78.80, then we can express this as:
3x + 2y = $78.80 (equation 1)
If the cost of the entrance tickets for 1 adult and 1 child is $33.10, then we can express this as:
x + y = $33.10 ⇒ x = $33.10 - y (equation 2)
Substitute equation 2 to equation 1 and solve for y.
3x + 2y = $78.80 (equation 1)
3($33.10 - y) + 2y = $78.80
$99.30 - 3y + 2y = $78.80
3y - 2y = $99.10 - $78.80
y = $20.30
Substitute the value of y to equation 2 and solve for x.
x = $33.10 - y (equation 2)
x = $33.10 - $20.30
x = $12.80
cost of the entrance ticket for a child = $12.80
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identify the mapping diagram that represents the relation and determine whether the relation is a function {(-3,-6),(-1,-6),(5,-6),(8,-6)}
Answer:
hola amigos como estan me saludan
And why there two possible solutions to the equation, X over 2 = 100?
There are two possible solutions because a power is involved. This can be shown in the graph. When we graph to the power of 2, we get a parabola. This gives us two x-intercepts, giving us two answers.
And why is this? When you square a negative number, you get a positive number since a negative times a negative is a positive.
Example: 2 * 2 equals 4, and -2 * -2 also equals 4. This means both 2² and (-2)² are equal to 4.
This means that we will get a positive and negative number value that both equal the same thing when being squared, which is why you get two possible solutions to this equation.
Jake got a part-time job to make some extra money. His goal was to make $150 per week. He was within $25 of his goal. If x represents Jake’s earnings, write an equation that represents the minimum and maximum that he could have earned.
Answer:
minimum: 125
Maximum: 175
Step-by-step explanation:
To do this, you know that Jake had a goal of getting $150 in the week. He was within $25 of reaching his goals. This means that he could have $25 less than or more than $150.
You can subtract 25 from 150 to get his minimum:
$150 - $25 = $125
And you can add 25 to get his maximum:
$150 + $25 = $175
You decide to go to a basketball game. The tickets cost $37 each and you paid for you and your cousin to get in.
How much did 2 basketball tickets cost?
Answer:
$74.00
Step-by-step explanation:
Two tickets at $37 apiece, we cal calculate a total by adding 37 + 37,
OR by multiplying
2×37
Either way, the total works out to be $74
highest common factor of 350 and 150
Answer: 50
Step-by-step explanation: Common factor of 150 and 350 = 1, 2, 5, 5. Highest common factor of 150 and 350 = 2 × 5 × 5 = 50.
find the value of the variable
Answer:
Step-by-step explanation:
Set 3y+53 equal to 7y-55
3y+53=7y-55 //subtract 3y
53=4y-55 //add 55
108=4y //divide by 4
y=27
|-7| and |7|
what does the | mean?
Solve: 2(7-4k) > 12 or 5 < 0.2(15k + 10)
The solution the inequality expression given as 2(7-4k) > 12 or 5 < 0.2(15k + 10) is 0.25 > k > -0.4
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
2(7-4k) > 12 or 5 < 0.2(15k + 10)
Open the brackets
So, we have
14 - 8k > 12 or 5 < 7.5k + 2
Collect the like terms
So, we have
- 8k > 12 - 14 or 5 - 2 < 7.5k
Evaluate the like terms
So, we have
- 8k > -2 or -3 < 7.5k
Divide both sides by the coefficient of k
So, we have
k < 0.25 or -0.4 < k
Rewrite as
0.25 > k or k > -0.4
Combine
0.25 > k > -0.4
Hence, the solution is 0.25 > k > -0.4
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y = x2 + 5x + 8 y = -x +3 Select the correct choice and fill in any answer boxes in your O A. The solution(s) is/are (Type an ordered pair. Use a comma to separate answe B. There is no solution.
To determine whether or not this system has a solution, we proceed as follows:
[tex]-x+3=x^2+5x+8\Rightarrow x^2+6x+5=0[/tex]Now, we use the quadratic function to solve, that is:
[tex]x=\frac{-(6)\pm\sqrt[]{6^2-4(1)(5)}}{2(1)}\Rightarrow\begin{cases}x=-1 \\ x=-5\end{cases}[/tex]From this, we have that the system has two solutions, we determine which replacing x in one of the functions, that is:
[tex]y_1=-(-1)+3\Rightarrow y_1=4[/tex]One solution is the point (-1, 4).
[tex]y_2=-(-5)+3\Rightarrow y_2=8[/tex]And, another solution is the point (-5, 8).
We can see each solution in the following graph:
Dilate a square with vertices $\left(0,\ 0\right)$(0, 0) , $\left(0,\ 4\right)$(0, 4) , $\left(4,\ 4\right)$(4, 4) , and $\left(4,\ 0\right)$(4, 0) using the scale factor $k=0.5$k=0.5 . What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio (new to original) of the perimeters is equal to 1/2 or 0.5. Also, the ratio (new to original) of the areas is equal to 1/4 or 0.25.
How to determine the value of the ratio (new to original)?In Mathematics, the ratio of the perimeters of two (2) geometric figures would be equal to the scale factor when the two (2) geometric figures are similar;
Let z represent the scale factor.Let y represent the perimeter of the original square.Let x represent the perimeter of the new square.Mathematically, the scale factor of a geometric figure can be calculated by using this formula:
Scale factor, z = Dimension of image/Dimension of original figure = y/x
Scale factor, z = 1/2 or 0.5.
In Geometry, the ratio of the areas of two (2) geometric figures would be equal to the square of scale factor when the two (2) geometric figures are similar.
Scale factor, z = (y/x)²
Scale factor, z = (1/2)²
Scale factor, z = 1/4 or 0.25.
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Complete Question:
Dilate a square with vertices (0, 0). (0, 4). (4, 4), and (4, 0) using the scale factor k = 0.5. What is the value of the ratio (new to original) of the perimeters? the areas?
The ratio of the perimeters is
The ratio of the areas is
Now, let’s say the children sold 50 cups of lemonade on the first day and 90 cups on the second day. Which proportion can be used to calculate the percent increase in the number of lemonade cups sold?
If the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%
The number of cups of lemonade sold on first day = 50 cups
The number of cups of lemonade sold on second day = 90 cups
The percentage increase = (New value - Old value)/Old value × 100
Substitute the values in the equation
The percentage increase in the number of lemonade cups sold
= [tex]\frac{90-50}{50}[/tex]×100
= 0.8×100
= 80%
Hence, if the children sold 50 cups of lemonade one the first day and 90 cups on the second day. then the percentage increase in the number of lemonade cups sold 80%
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Answer:
90-50/50 = P/100
Step-by-step explanation:
This is the correct answer on T4L!
does anyone know what to put on these boxes
Answer:
You should ask your teacher what the heck that means!
Step-by-step explanation:
But still, -7+10=3
The time it takes to read 20 pages of a book can be represented with the equation y = 12.4 over 20 x near the line. Where y represents the total time in minutes and x represents the number of pages read. Determine how long it will take to read a book that has 424 pages.
Answer choses
262.88 min
683.87 min
424.38 min
2,012.4 min
Please help me
Using the equation y = 12.4/20, the amount of time it would take to read a book that has 424 pages is: A. 262.88 min.
What is a Proportional Relationship Equation?The equation, y = kx, represents a proportional relationship where the value of k is the unit rate of the relationship between the two variables, x and y.
In the scenario given:
x = number of pagesy = total time in minutesThe equation given that models how long (y) in minutes it would take to read x amount of pages is, y = 12.4/20x.To find how long it will take to read a book with 424 pages, substitute x = 424 into the equation y = 12.4/20x:
y = 12.4/20(424)
y = 262.88 minutes.
To read 424 pages, it will take: A. 262.88 min.
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Evaluate the expression if g=2, r=3, and t=11
The result of the expression 3g × [tex](g+r)^2[/tex] - 1, when g = 2 , r = 3 , and t = 11 is 149
The given expression is
3g × [tex](g+r)^2[/tex] - 1
The expression is the mathematical a sentence with a minimum of two variables and at least one math operation, the math operation might be addition, subtraction, division, multiplication etc..
The value of g = 2
The value of r = 3
The value of t = 11
Substitute the values in the expression
= 3×2× [tex](2+3)^2[/tex] - 1
Do the arithmetic operation in bracket first
= 6×[tex]5^2[/tex] - 1
= 150 - 1
= 149
Hence, the result of the expression 3g × [tex](g+r)^2[/tex] - 1, when g = 2 , r = 3 , and t = 11 is 149
The complete question is :
Evaluate the expression 3g × [tex](g+r)^2[/tex] - 1, if g=2, r=3, and t=11
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Decide whether each table could represent a proportional relationship what dose k =
Table A doesn't represent the constant of proportionality.
Table B doesn't represent the proportional relationship.
How to explain the constant?Treat the values in table as (x,y) values. The result is a linear function
For A, 85/5 = 17 while 79 / 10 = 7.9. This doesn't illustrate a constant.
For B, 1.49/16 and 1.59/20 have different values. In this case, 1.49/16 = 0.093 and 1.59/20 = 0.0795.
Therefore. they don't have a constant of proportionality. This was because the values that were gotten for both A and B aren't equal.
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Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?
1. How loud a sound is depending on how far away you are
5 85
10 79
20 73
40 67
b. The fountain drinks at hot dog hut.
16 1.49$
20 1.59$
30 1.89$
Using the slope formula, find the slope of the line through the given points.
(1,1) and (8,8)
Work Shown:
[tex](x_1,y_1) = (1,1) \text{ and } (x_2,y_2) = (8,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - 1}{8 - 1}\\\\m = \frac{7}{7}\\\\m = 1\\\\[/tex]
Question 7 Mai and Tyler are selling items to earn money for their elementary school. The school earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. This situation is represented by this system of equations: { 14 w + 3 p = 70 . 50 10 w + 7 p = 62 . 50 Which statements are true in explaining why it makes sense that the solution of this system is also a solution to 4 w + ( − 4 p ) = 8 . 00 ? Select all that apply. (Lesson 2-15) Multiple select question. A) Because 10 w + 7 p is equal to 62.50, subtracting 10 w + 7 p from the left side of 14 w + 3 p = 70 . 50 and subtracting 62.50 from its right side keep the two sides equal. B) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of adding the two equations in the system and then dividing the result by 6. C) The equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation. D) The equation 4 w + ( − 4 p ) = 8 . 00 represents the difference between Mai's sales and Tyler's sales, or the result of subtracting Tyler's sales from Mai's. E) The left side of the equation 4 w + ( − 4 p ) = 8 . 00 shows the difference in terms of the items sold. The right side shows the difference in dollars. The cost per wreath, w, and the cost per potted plant, p, haven't changed.
Option (C) is correct which is the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation.
Mai and Tyler are selling items to earn money for their elementary school.
Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Mathematically we can write,
14 w + 3 p = 70.50 equation 1
Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50. Mathematically we can write,
10 w + 7 p = 62.50 equation2
equation 1 - equation 2 , we get
4 w + ( - 4 p ) = 8.00
which is the required equation.
We can conclude that the equation 4 w + ( − 4 p ) = 8 . 00 is the result of subtracting the second equation in the system from the first equation
So, option (C) is correct.
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PLEASE help ( What's the slope of a line that passes through points C (1,3) and B (4,7)
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = C (1, 3 ) and (x₂, y₂ ) = B (4, 7 )
m = [tex]\frac{7-3}{4-1}[/tex] = [tex]\frac{4}{3}[/tex]
which numbers are prime numbers
Answer:
1,3,5,7,17,23
Step-by-step explanation: