Answer:
[tex]z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]
Step-by-step explanation:
The given complex numbers are;
[tex]z_1=-8+3i[/tex]
and
[tex]z_2=7-4i[/tex].
The midpoint of any two complex numbers,
[tex]z_1=a_1+a_1i[/tex] and [tex]z_2=a_2+a_2i[/tex] is
is given by,
[tex]z_m=\frac{a_1+a_2}{2}+\frac{a_1+a_2}{2}i[/tex].
The midpoint of the complex numbers can be found by adding the corresponding real parts and imaginary parts and then dividing each by 2.
This is the same as;
[tex]z_m=\frac{z_1+z_2}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-8+3i+7-4i}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-8+7+3i-4i}{2}[/tex]
[tex]\Rightarrow z_m=\frac{-1-i}{2}[/tex]
[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{i}{2}[/tex]
or
[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]
the body building club has an annual fee of $350. You plan to visit 10 times each month. how much is your cost per visit?
Answer:
≈ $2.92 per visit
Step-by-step explanation:
10 times each month
so 12 months = 12 x 10 = 120
an annual fee of $350
$350 / 120 ≈ $2.92
A 5 pound bag of potatoes cost $3.40 what is the cost per pound
It would be $0.68.
To find it, divide the cost by the weight. So, the equation would be 3.40/5 or 3.40 divided by 5.
The cost per pound of potato would be $0.68.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We are given that 5 pound bag of potatoes cost $3.40
Then the cost per pound of potato .
We have to divide the cost by the weight.
So, the equation would be;
3.40 divided by 5.
3.40/5 = 0.68
The cost per pound of potato would be $0.68.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Using synthetic division, what is the quotient (3x^3 + 4x − 32) ÷ (x − 2)?
Answer:
q1 = 3x^2 + 6x + 16
Step-by-step explanation:
2 || 3 0 4 - 32
6 12 32
========================
3 6 16 0
q(x) + r(x)/(x - 2)
r(x) = 0
q(x) = 3x^2 + 6x + 16
This does not factor down any further unless you have take complex number. The only real root isw
x = 2
Just in case you have done complex numbers
x2 = -1 + 2.0817i
x3 = -1 - 2.0817i
It takes 24 feet of fence to surround a square piece of land in Sam's backyard. Sam wants to plant flowers everywhere but on the diagonal sidewalk (shaded in the diagram attached). Note that there is 1 foot of sidewalk along two sides of the square as indicated in the diagram attached. What is the area of the sidewalk?
Answer:
Option B. 5.5 ft²
Step-by-step explanation:
Perimeter of the square piece of land = length of fence required
4(length of a side of the square) = 24 ft
Length of a side = 6 ft
Area of the square land = (Side)²
= 6²
= 36 square ft
Area of the side walk = Area of the square - [Area of two triangles separated by the sidewalk]
= 36 - [[tex]\frac{1}{2}(\text{Area of the square})+\frac{1}{2}(\text{Base})\tmes (\text{height})[/tex]]
= 36 - [[tex]\frac{36}{2}+\frac{1}{2}(6-1)(6-1)[/tex]]
= 36 - (18 + 12.5)
= 36 - 30.5
= 5.5 ft²
Therefore, Option B. is the correct answer.
what other information must be given in order to be able to prove the two triangles congruent by AAS
find tge slope and the y-Intercept 7x-9y=1
Define perpendicular lines.
A.
Lines that cut across two or more lines.
B.
Two coplanar lines that intersect at a 90 degree angle.
C.
Two coplanar lines that do not intersect.
D.
Two non–coplanar lines that do not intersect
Perpendicular lines are two coplanar lines that intersect at a 90-degree angle, option B in the question.
Perpendicular lines are defined as two coplanar lines that intersect at a 90 degree angle. This means that the correct answer to the given question is B. It's important to understand that when lines are perpendicular, they create four right angles at the point where they intersect. Various geometrical theorems relate to the properties of perpendicular lines, for example:
Theorem 15 states that if two planes are perpendicular, a line drawn in one perpendicular to their intersection is perpendicular to the other plane.
Theorem 14 explains that if a line is perpendicular to two intersecting lines at their intersection, it is perpendicular to all lines on their plane that pass through this point.
Theorem 11 describes that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities will make equal angles with them.
In advanced contexts, such as the geometry of spacetime, perpendicularity can be defined differently, often using the concept of the dot product being zero to identify perpendicular vectors.
Kate and did a hike at an elevation of 400 m above sea level she had started at an elevation 02 150 m below sea level which integer represents Kates change in elevation
Answer:
2550 m
Step-by-step explanation:
Change in elevation = 400 – (-2150)
Change in elevation = 400 + 2150
Change in elevation = 2550 m
The stem and lead plot below displays the ages of 30 attorneys at a small firm
Stems | Attorneys
2 | 99
3 | 00112589
4| 1234458
5| 1233458
6 | 0137
7 | 12
What is the age of the oldest attorney? What is the age of the youngest attorney?
pleaseeee helppp i keep getting the wrong so can somebody give me the correct answer
Answer: 39.25 miles per gallon.
Step-by-step explanation: To find miles per gallon, divide 314 miles by 8 gallons =
39.25 miles per gallon.
The answer is 39.25
note: if your teacher wants a fraction instead of a decimal, then it would be 157/4
=============================
Explanation:
Divide 314 over 8 to get 314/8 = 157/4 = 39.25
----
You can think of it as the ratio
314 miles: 8 gallons
(314/8) miles: (8/8) gallons <--- divide both parts by 8
(157/4) miles: 1 gallon
39.25 miles: 1 gallon
Meaning you can drive 39.25 miles on one gallon of gas
Which of the following theorems states, “If a line divides two sides of a triangle proportionally, it is parallel to the third side.”? Triangle Proportionality Theorem Converse of the Triangle Proportionality Theorem Pythagorean Theorem Converse of the Pythagorean Theorem.
Answer:
Converse of triangle proportionality theorem
Step-by-step explanation:
We are given that in a triangle ABC, D and E are some points in AB and AC respectively.
D and E divide AB and AC such that
AD/DB =AE/DC
To prove that DE is parallel to third side BC>
This can be proved using converse of triangle proportionality theorem
REcollect the triangle proportionality theorem that
If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion
So converse is is a line intersects the other sides make proportional intercepts then the line is parallel to the third side.
Answer:
The answer is Converse of the Pythagorean theorem
Step-by-step explanation:
An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found—one at position (1,4) and the other at (5,2) how far apart were the two artifacts? Round to the nearest tenth of a unit if necessary
Answer:
aproximatley 6 units
Step-by-step explanation:
Is 3x+12-2x equivalent to x +12? Use two properties of operations to justify your answer.
Answer:
Yes, x + 12
Step-by-step explanation:
Simplify the following:
3 x - 2 x + 12
Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:
(3 x - 2 x) + 12
3 x - 2 x = x:
Answer: x + 12
Answer:
Yes, it is.
Step-by-step explanation:
3x + 12 - 2x =
Use the commutative property of addition to change the order of the addition.
= 12 + 3x - 2x
Use the distributive property of addition over multiplication in reverse (which is factoring).
= 12 + x(3 - 2)
Do the operation: 3 - 2 = 1
= 12 + x * 1
Simplify x * 1 to just x.
= 12 + x
Use the commutative property of addition.
= x + 12
There you have x + 12 from 3x + 12 - 2x by using properties and operations.
if the discount is 30% and the sale price is $206.50 what is the original price
To determine the original price before a 30% discount resulted in a sale price of $206.50, we calculate the sale price as 70% of the original price, leading to the original price being $295.00.
Explanation:If the discount is 30% and the sale price is $206.50, we need to determine the original price before the discount. To do this, we first understand that the sale price represents 70% of the original price, because a 30% discount has been applied. Thus, to find the original price, we can set up the following equation where original price × 70% = $206.50.
Converting 70% to decimal form, we get 0.70. The equation then becomes original price × 0.70 = $206.50. To find the original price, we divide both sides of the equation by 0.70:
Original price = $206.50 / 0.70
Original price = $295.00
Therefore, the original price of the item before the 30% discount was applied is $295.00.
HELP PLEASE!!!!!!!!!!!!
Karen is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:
She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption?
A. 6:7 ≠ 2:7
B. 6:8 ≠ 7:10
C. 6:2 ≠ 7:10
D. 6:2 ≠ 3:2
Answer:
Option B
Step-by-step explanation:
In order to prove that segment DE is not parallel to segment BC, Karen takes an indirect way, that is she assumes that DE is parallel to BC, then by using the basic proportionality theorem,
[tex]\frac{AD}{AB}=\frac{AE}{AC}[/tex]
Now, AD=6, AB=AD+DB=8, AE=7 and AC=10
therefore, [tex]\frac{6}{8}=\frac{7}{10}[/tex] according to basic proportionality theorem, but in actual, [tex]\frac{6}{8}{\neq}\frac{7}{10}[/tex].
Thus, DE is not parallel to BC, therefore Option B is correct.
Answer:
B, 6:8 ≠ 7:10.
Step-by-step explanation:
An angle whose measure is 405 is in standard position. In what quadrant does the terminal side of the angle fall?
Answer:
The angle is in quadrant one because one rotation is 360° and it’s just 45° more than 360°.
Q1
What’s standard form of y=6x-4
To convert the slope-intercept form of a line, y = 6x - 4, to standard form, subtract 6x from both sides of the equation. The resulting standard form is -6x + y = -4.
Explanation:You asked about writing the equation y = 6x - 4 in standard form. The standard form for the equation of a line in mathematics is usually given as Ax + By = C, where A, B, and C are constants, and A should ideally be a positive integer. To convert the given equation into standard form, we want to rearrange it so that both x and y are on the same side of the equation and the constant is on the other side.
Here are the steps to convert y = 6x - 4 to standard form:
Subtract 6x from both sides of the equation to obtain -6x + y = -4.If necessary, multiply the entire equation by -1 to ensure the coefficient of x is positive. However, since standard form can also accommodate a negative A (it's just not preferred), we can leave the equation as is.Therefore, the standard form of the equation is -6x + y = -4.
3(x−0.50)=5.97
what does x equal?
Answer:
x=2.49
Step-by-step explanation:
3(x−0.50)=5.97
Distribute the 3
3x - 3*.5 = 5.97
3x -1.5 = 5.97
Add 1.5 to each side
3x -1.5+1.5 = 5.97+1.5
3x = 7.47
Divide each side by 3
3x/3 = 7.47/3
x=2.49
If one crate of apples weighs 85 pounds, how much less do 13 crates of apples weigh than 15 crates of apples?
The calculation shows that 13 crates weigh 170 pounds less than 15 crates.
To find out how much less 13 crates of apples weigh than 15 crates of apples, we need to first determine the weight of the two different amounts of crates.
We know that one crate weighs 85 pounds.
So, for 15 crates, we multiply 15 by 85 to get the total weight:
= 15 crates x 85 pounds per crate = 1275 pounds
Next, we calculate the weight for 13 crates:
= 13 crates x 85 pounds per crate = 1105 pounds
Now, we subtract the weight of 13 crates from the weight of 15 crates:
= 1275 pounds - 1105 pounds = 170 pounds
Therefore, 13 crates of apples weigh 170 pounds less than 15 crates of apples.
HELPP PLEASE I WILL CROWN YOU!!!!!
(Solve for X)
Please make sure it correct
Thank you
Answer:
x=9
Step-by-step explanation:
These two angles are equal because they are corresponding angles and the two lines are parallel.
13x-7 = 11x+11
Subtract 11x from each side
13x-11x -7 = 11x-11x+11
2x-7 = 11
Add 7 to each side
2x-7+7 = 11+7
2x = 18
Divide each side by 2
2x/2 = 18/2
x =9
Solve: -6x-1+5x^2=8x^2
Answer:
[tex]x_{1} = -1 - \sqrt{\frac{2}{3}} ; x_{2} = -1 +\sqrt{\frac{2}{3}}[/tex]
Step-by-step explanation:
-6x -1 + 5x² = 8x² Move all terms to the right-hand side
0 = 8x² - 5x² + 6x +1 Combine like terms
3x² + 6x + 1 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 3; b = 6; y = 1
[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}[/tex]
[tex]x = \frac{-6\pm\sqrt{36-12}}{6}[/tex]
[tex]x = \frac{-6\pm\sqrt{24}}{6}[/tex]
[tex]x = \frac{-6\pm \sqrt{4\times6}}{6}[/tex]
[tex]x = \frac{-6\pm 2\sqrt{2}}{6}[/tex]
[tex]x = -1 \pm \sqrt{\frac{2}{3}}[/tex]
[tex]x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}[/tex]
The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.
An ice sculpture is melting because of heat. Assuming its height changes bynegative 5 over 32m every hour, what will be the change in height after 4 hours? negative 20 over 8 meters 5 over 8 meter negative 5 over 32 meter negative 5 over 8 meter
Answer:
[tex]-\frac{-5}{32} *4=- \frac{5}{8}[/tex]
Step-by-step explanation:
Answer:
- 5/8
Step-by-step explanation:
To solve you would do - 5/32 times 4/1 to get 20/32, then you would simplify to get 10/16, then you would simplify that to get - 5/8.
The cheese club members bought 6 tickets to a tournament for $15 how much would they have paid if all 9 members wanted to go
First you have to find out the cost of the ticket. To do so you have to Divide 15 and 6. Which equals $2.50. So each ticket is $2.50 dollars. Now you have to multiple 2.50 times 9. which equals 22.5. So your total answer is $22.50 dollars
How many solutions does the system of equations have ? Y= 6x +2 and 3y-18x=12
Answer:
0 solutions
Step-by-step explanation:
same slope, different y intercepts so they never intersect
Answer:
As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution. (Please see the picture below)
Step-by-step explanation:
1. First write the system of equations:
[tex]y=6x+2[/tex]
[tex]3y-18x=12[/tex]
2. Solve y for the second equation:
[tex]3y-18x=12[/tex]
[tex]3y=18x+12[/tex]
[tex]y=\frac{18x+12}{3}[/tex]
[tex]y=6x+4[/tex]
3. Re write both equations in the form y=mx+b, where m is the slope and b is the value of y when x=0 :
[tex]y=6x+2[/tex]
[tex]y=6x+4[/tex]
As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution.
prove that sin3a-cos3a/sina+cosa=2sin2a-1
Answer:
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
Step-by-step explanation:
we are given
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
we can simplify left side and make it equal to right side
we can use trig identity
[tex]sin(3a)=3sin(a)-4sin^3(a)[/tex]
[tex]cos(3a)=4cos^3(a)-3cos(a)[/tex]
now, we can plug values
[tex]\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)} [/tex]
now, we can simplify
[tex]\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)} [/tex]
now, we can factor it
[tex]\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]
we can use trig identity
[tex]sin^2(a)+cos^2(a)=1[/tex]
[tex]\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]
we can cancel terms
[tex]=3-4(1-sin(a)cos(a))[/tex]
now, we can simplify it further
[tex]=3-4+4sin(a)cos(a))[/tex]
[tex]=-1+4sin(a)cos(a))[/tex]
[tex]=4sin(a)cos(a)-1[/tex]
[tex]=2\times 2sin(a)cos(a)-1[/tex]
now, we can use trig identity
[tex]2sin(a)cos(a)=sin(2a)[/tex]
we can replace it
[tex]=2sin(2a)-1[/tex]
so,
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
Answer:
To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1
Step-by-step explanation:
\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S
Since, sin(2a)= 2sin(a)cos(a)
2sin(2a)= 4sin(a)cos(a)
Plz Help I do not understand this
Cain is about to start a new job and his opponent employer has offered him two different options to get paid. Option A gives Cain $20 to start plus an additional $10 an hour option b gives Kane $40 to start plus an additional $5 an hour. Define your variables then create a system of equations.
Define Variables:
x =______
y =______
Equations
Option A: ______
Option B: ______
Hello,
So Y variable is what you would start with.
20 <= he'll start off with for a
40 <= what he'll start off with for b
And X variables would be the # of hours you're working.
10 <= meaning every hour worked is worth 10 dollars
5 <= meaning every hour worked will be paid 5 dollars
So let's just say for option a he works two hours
(Option A)
10 (2) + 20
20 + 20
= 40
(Option B)
5 (2) + 40
10 + 40
50
As for your equations
Y = 10x + 40
Y= 5x + 40
i am completely lost... Is this a direct variation or an inverse variation? Explain.
You get 5x=y. The larger the x, the larger the y. So, this is a direct variation.
Help me with this please
Answer:
(4,2)
Step-by-step explanation:
how many tenths are in 3.6
Answer:
Step-by-step explanation:
3.6/10=3.3/5
получется 3 целых 6 десятых сокращаем и получается 3 целых 3 пятых
T(p) is a function that models the average yearly temperature based on the degree latitude(p) of the location on earth. The lines of latitude run from East to West, but they are measured in terms of North and South, extending from −90° to +90°. Which domain is appropriate for this function?
Answer:
All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].
Step-by-step explanation:
T(p) models the average yearly temperature based on degree latitude of the location.
Since the lines of latitude runs from East to West and extending from [tex]-90^\circ[/tex] to [tex]+90^\circ[/tex], they can be included in the domain.
Also, the degrees of latitude can be fractional units, positive units, or negative units. Therefore, the domain appropriate for this function is All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].
Answer:
D = all real numbers between ± 90, inclusive
Step-by-step explanation:
Degrees of latitude can be fractional units, positive units, or negative units.
**If you are on USA Test prep, the correct answer choice should be D