Answer:
[tex]\displaystyle x_1 = 2-\sqrt{3} \text{ and } y_1 = \frac{\sqrt{3}-1}{2}[/tex]
Or:
[tex]\displaystyle x _ 2 = 2 + \sqrt{3} \text{ and } y _ 2 = -\frac{1+\sqrt{3}}{2}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]\displaystyle (x^2 + 2xy) + i(y-1) = (x^2 -2x + 2y) - i(x +y)[/tex]
And we want to find the values of x and y such that the equation is true.
First, distribute:
[tex]\displaystyle (x^2 + 2xy) + i(y-1) = (x^2 -2x + 2y) +i(-x -y)[/tex]
If two complex numbers are equivalent, their real and imaginary parts are equivalent. Hence:
[tex]\displaystyle x^2 + 2xy = x^2 - 2x +2y \text{ and } y - 1 = -x -y[/tex]
Simplify:
[tex]\displaystyle 2xy = -2x +2y \text{ and }x = 1 - 2y[/tex]
Substitute:
[tex]\displaystyle 2(1-2y)y = -2(1-2y) + 2y[/tex]
Solve for y:
[tex]\displaystyle \begin{aligned} 2(y - 2y^2) &= (-2 + 4y) + 2y \\ 2y - 4y^2 &= 6y -2\\ 4y^2 + 4y - 2& = 0 \\ 2y^2 + 2y - 1 &= 0 \\ \end{aligned}[/tex]
From the quadratic formula:
[tex]\displaystyle \begin{aligned} y &= \frac{-(2)\pm\sqrt{(2)^2 - 4(2)(-1)}}{2(2)} \\ \\ &= \frac{-2\pm\sqrt{12}}{4} \\ \\ &= \frac{-2\pm2\sqrt{3}}{4}\\ \\ &= \frac{-1\pm\sqrt{3}}{2} \end{aligned}[/tex]
Hence:
[tex]\displaystyle y_1 = \frac{-1+\sqrt{3}}{2} \text{ or } y_2 = \frac{-1-\sqrt{3}}{2}[/tex]
Then:
[tex]\displaystyle x _ 1 = 1 - 2\left(\frac{-1+\sqrt{3}}{2}\right) = 1 + (1 - \sqrt{3}) = 2 - \sqrt{3}[/tex]
And:
[tex]\displaystyle x _ 2 = 1 - 2\left(\frac{-1-\sqrt{3}}{2}\right) = 1 + (1 + \sqrt{3}) = 2 + \sqrt{3}[/tex]
In conclusion, the values of x and y are:
[tex]\displaystyle x_1 = 2-\sqrt{3} \text{ and } y_1 = \frac{\sqrt{3}-1}{2}[/tex]
Or:
[tex]\displaystyle x _ 2 = 2 + \sqrt{3} \text{ and } y _ 2 = -\frac{1+\sqrt{3}}{2}[/tex]
Help! given 2(x-9)=-10 prove x=4 with statements and reasons
Step-by-step explanation:
Proof:
2 ( x - 9) = - 10 when x = 4
2 ( 4 - 9) = -10
8 - 18 = -10
-10 = -10 ..........hence proven
Reasons
- When you replace X with 4, you can clearly see that the equation is equal to -10.
sorry I couldn't answer accurately, but I hope this helps
3. Multiply: (x + 8)(x - 12)
Please show work
Answer:
x^2-4x-96
Step-by-step explanation:
x^2-12x+8x-96
=x^2-4x-96
Answer:
[tex] {x}^{2} + 20x + 96[/tex]
Step-by-step explanation:
[tex](x + 8) \times (x - 12)[/tex]
➡️ [tex]x \times (x + 12) + 8(x - 12)[/tex]
➡️ [tex] {x}^{2} + 12x + 8x + 96[/tex]
➡️ [tex] {x}^{2} + 20x + 96[/tex]
Find the distance between the points (3, –8) and (0, –9).
A. 3.16
B. 17.26
C. 2.98
D. 1.06
Answer:
a. 3.16
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[-9 - (-8)]² + (0 - 3)²
√(-1)² + (-3)²
√(1) + (9)
√(10)
= 3.16
Find the median of the following set of data: 52,84,94,102,94,89,73
Answer:
Step-by-step explanation:
the median is 89, the mode is 94, and the mean is 84
Can anyone help with this please
Answer:
None
Step-by-step explanation:
Simply, the absence of s^-1 shows the answer as none
Does this picture indicate that < JAC =
Answer:
No
Step-by-step explanation:
<JAC = 93
< DBE = 90
The two angles are not equal
Find the value of x,
Answer: x = -7
Concept:
From the given graph, we can see that it is an isosceles triangle since the two base angles are congruent.
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.
Solve:
Given information
First Side = 7
Second Side = x + 14
Given expression deducted from the definition of an isosceles triangle
Second Side = First Side
Substitute values into the expression
x + 14 = 7
Subtract 14 on both sides
x + 14 - 14 = 7 - 14
[tex]\boxed{x=-7}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
11. The news reports that today's high temperature is 16°F colder than
yesterday's high temperature. Yesterday's high temperature was -2°F.
a. Write an expression to represent today's high temperature.
b. Reasoning is today's high temperature positive or negative? Why?
The expression to represent today's temperature is given by
- 2°F - 16°F = - 18°F and todays high temperature is negative as the
temperature is colder.
Temperature is a numerical expression of how hot a substance or radiation is.
There are three different types of temperature scales: those that are defined by the average translational kinetic energy per freely moving microscopic particle, like an atom, molecule, or electron, in a body, like the SI scale. Those that rely only on macroscopic properties and thermodynamic principles, like Kelvin's original definition of temperature. Those that are not defined by theoretical principles but rather by useful empirical properties of particulate matter.The temperature yesterday was -2°F . The temperature is colder today and by 16°F more cold.
Since colder temperature is denoted by negative sign and hotter temperature by the positive sign then when the temperature is colder today then we have to subtract the values to the given values.
Hence - 2°F - 16°F = - 18°F .
So todays high temperature will be a negative value.
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The meter is defined as the _______________ traveled by _______________ in absolute vacuum in 1⁄299,792,458 of a second
Answer:
1.) Distance
2.) Speed of light
Step-by-step explanation:
What is 3x+5=2x-2x+29?
Answer:
3+5=2−2+29
3x+5=2x-2x+293x+5=2x−2x+29
Solve
1
Combine like terms
}+293x+5=2x−2x+29
3+5=29
3x+5=293x+5=29
2
Subtract
5
55
from both sides of the equation
3
Simplify
2 more steps
Solution
=8
The answer you are looking for is
Solution/Explanation:
First, writing out the equation,
3x+5=2x-2x+29.
Next, making the equation more simple by subtracting 2x-2x, which is 0,
3x+5=0+29.
3x+5=29.
Now, subtracting 5 from both sides of the equation,
3x+5-5=29-5.
3x=24.
Finally, dividing both sides of the equation by 3,
3x/3=24/3.
x=8.
So, therefore, the final answer is x=8.
I hope this has helped answer your question. Enjoy your day, and take care!
In the proof of the Law of Cosines, the equation [tex]c^2=h^2+(b-x)^2[/tex] was created using the Pythagorean theorem. Which equation is a result of expanding [tex](b-x)^2[/tex]?
A [tex]c^2=h^2+b^2-x^2[/tex]
B [tex]c^2=h^2+b^2-2bx+x^2[/tex]
C [tex]c^2=h^2+b^2+x^2[/tex]
D [tex]c^2=h^2+b^2-2bx-x^2[/tex]
9514 1404 393
Answer:
B c² = h² + b² -2bx +x²
Step-by-step explanation:
The square of the binomial can be expanded using the distributive property:
c² = h² +(b -x)²
c² = h² +(b -x)(b -x)
c² = h² +b(b -x) -x(b -x)
c² = h² +b² -xb -bx +x²
c² = h² +b² -2bx +x² . . . . . matches choice B
Anton joined a golf club. He pays an annual membership fee of $895 and greens fee of $30 each time he plays golf. Last year he paid $2,065 as a total golfing fee. How many games did he play? Write and solve the equation.
Answer: f(g) = 895 + 30g
-----------------------------------------------------------------
He paid $2065. Number of games he played:
-----------------------------------------------------------------
2065 = 895 + 30g
30g = 2065 - 895
30g = 1170
g = 39
-----------------------------------------------------------------
Answer: He played 39 games.
Step-by-step explanation:
Number of games anton played is 39; the equation is 2065 = 895 + 30G
How to find the system of equations needed to solve an equation?An equation usually consists of equality of two mathematical expressions. Let it be
A = B
. If we take them to be equal to third variable, then:
A = B = C
type of equation is obtained.
We can then take it as system of two equations as:
A = C\\ B=C
Solution to this system will give us the solution to the considered equation.
Solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.
The equation will be f(g) = 895 + 30G
Amount anton paid = $2065.
Number of games he played;
2065 = 895 + 30G
30g = 2065 - 895
30g = 1170
G = 39.
Therefore, the solution of the equation os 39
Learn more about equation here:
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Solvin
Is 5.787787778... a rational or irrational number?
Explain.
Answer:
For a number to be rational, it must:
-terminate (0.5) or repeat (0.3333...)
-be able to be written as a fraction
If a number does not meet this criteria, then it is irrational. Thus, 5.787787778... is irrational.
Step-by-step explanation:
BRAINLIEST, PLEASE!
What is the slope of the line represented by the equation y = 4/5x-3?
Answer:
The slope is 4/5
Step-by-step explanation:
The slope in a y=mx+b equation is always in front of the x. Remember that! :)
Step-by-step explanation:
4/5.
this equation is slope in intercept form following the template of y=mx+b .m is your slope and by looking at the corresponding part tell you 4/5 is the slope
Use the slope formula to find the slope of the line through the points (−3,−6) and (0,3).
Suzannes school are painting a rectangular mural outside the buillding that will be 15 feet by 45 feet the students are also going to paint a smaller mural inside the building the scale is 1 unit = 3 feet
Answer:
THE LENGTH OF THE STUDENTS PAINTING=15/3=5
THE BREADTH OF THE STUDENTS PAINTING=45/3=15
AREA OF THEIR PAINTING=15×5=75
How would I write a number subtracted from 2 times a number is 19 as an equation?
Answer:
[tex]let \: the \: number \: be \:2 x \\ 2x - x = 19 \\ x = 19 [/tex]
This is the answer
if wrong please correct me ! :)
m3+ 3 m3 + 4 m²
simplify
Answer:
[tex] {m}^{3} + {27}^{m} + 4 {m}^{2} [/tex]
Step-by-step explanation:
[tex] {m}^{3} + {3}^{m 3} + 4 {m}^{2} [/tex]
[tex] {m}^{3} + {3}^{m \times 3} + 4 {m}^{2} [/tex]
[tex] {m}^{3} + {3}^{3m} + 4 {m}^{2} [/tex]
[tex] {3}^{3m} = ({3}^{3} {)}^{m} = {27}^{m} [/tex]
➡️ [tex] {m}^{3} + {27}^{m} + 4 {m}^{2} [/tex]
help with this plzzzzzzz
Answer:
x = 6
Step-by-step explanation:
According to the rules of segment addition, AB+BC=AC.
Since the length of AB is x+5, length of BC is 2x+10, and total length of AC is 33, we can create the equation: (x+5) + (2x+10) = 33.
To solve, we combine like terms: 3x + 15 = 33.
Subtract 15 from both sides: 3x = 18.
Divide both sides by 3: x = 6.
Help please due today
Answer:
3.2=6
4.2=8
5.2=10
the scale factor is 2
A fine jewelry store leased a space at the mall with a base rent of $1,800 a month, plus 4% of all sales over $200,000. If the gross sales were $325,000, what was the total amount of rent paid by Heinz Fine Jewelry at the end of the year?
Answer:
So, first, we have to establish how much the base rent ends up costing. So to find that, we do 1,800x12=21,600. So the base rent is $21,600. Then, we add the 4% of sales which is 125,000x0.04=5,000. So, we add $21,600 with $5,000 and we get a final answer of $26,600 owed at the end of the year :)
Step-by-step explanation:
How do i reflect triangle ABC if A (2,3), B (1,1), C(4,-3) over the x axis. Also rotating the triangle 90 degrees clockwise about the origin.
9514 1404 393
Answer:
see attached. red = reflected; blue = rotated
Step-by-step explanation:
The relevant coordinate transformations are ...
(x, y) ⇒ (x, -y) . . . . . reflection over the x-axis
(x, y) ⇒ (y, -x) . . . . . rotation 90° CW
In the attached figure, the red triangle A'B'C' is reflected. The blue triangle A"B"C" is rotated.
__
Additional comment
Learning to visualize these transformations can take a little practice. It can help to draw the figure on a graph, trace it on another piece of paper or transparency, then move the copy to the new position relative to the old axes.
For reflection across the x-axis, the x-axis of the copy is aligned with the original, but the copy is flipped over so the old +y axis is aligned with the -y axis, and vice versa.
For rotation 90° CW, what was the +y axis becomes aligned with the +x axis, and what was the +x axis becomes aligned with the -y axis. That is, the figure is rotated 90° CW about the origin so anything in the first quadrant is moved to the 4th quadrant.
Identify a pair of supplementary angles in the diagram below.
Answer:
a & b
Step-by-step explanation:
Supplementary angles add up to 180°
Angles a and b are both on a straight line which the sum is 180°
I hope this helps.
Can anyone help?
Plis
Answer:
B. 50%
Step-by-step explanation:
7/20 = 35%
35% + 15% = 50%
100% - 50% = 50%
white → 15%
red → 7/20 · 100% = 35/100 · 100% = 35%
blue → 100% - 35% - 15% = 50%
Answer: B)
Find the area of each shaded region. Show your reasoning.
maybe we could answer if there waas a pic=]
How are angles 1,2,3,4 related in the trapezoid
Answer:
The degree measure of the four add up to 360 degrees. This is actually true of any quadrilateral. Let lower case letter a,b,c and d represent the angle of trapezoid ABCD. Then a+b+c+d= 360 degreees.
How can I multiply this without a claculator 4103 x 25?
You just mutiple 4103×25and it =102575
Suppose that an individual has a body fat percentage of 14.5% and weighs 184 pounds. How many pounds of his weight is made up of fat? Round your
answer to the nearest tenth.
9514 1404 393
Answer:
26.7 lb
Step-by-step explanation:
The weight of fat is ...
14.5% × 184 lb = 0.145 × 184 lb ≈ 26.7 lb
About 26.7 pounds of his weight is made up of fat.
Evaluate the expression: p(6 – n) – m ÷ 5 Use m = 5, n = 2, and p = 4
Answer:
15
Step-by-step explanation:
m = 5, n = 2, and p = 4
Substituting the values in the equation p(6 – n) – m ÷ 5 ,
4(6-2) - 5/5
4(4) - 1
16 - 1
=> 15
Find the midpoint of the line segment joining the points (-3,-2) and (-7,5)
Answer:
The midpoint is (-5,1.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -3+-7)/2 = -10/2 = -5
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
( -2+5)/2 = 3/2 = 1.5
The midpoint is (-5,1.5)