The other midpoint is 3+9i in the given complex plane.
Given that,
We know that the middle point is: (-1+i)
And the end point is: (-5-7i)
We know that the formula to find the middle point is:
(x1+ x2 /2, z1+z2/2)
We wish to find the point x1,z1
So we can write the following equation
x1 + (-5)/2 = -1 --------> 1
and
z1 + (-7i)/2 = i ----------->2
Now we clear x1 from equation (i) and clear z1 from equation (ii)
For equation (i) we have:
-2 = x1 -5
x1 =3
For equation (ii) we have:
2i = z1 - 7i
z1 = 9i
Then the initial point is: 3+9i
So, The other endpoint is 3+9i
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is a monotone sequence? if such an exists give the least value of . if it does not exist then enter na.
Yes, monotone is a sequence.
We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n.
Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.
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equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six
The equivalent Algebraic Expression is represented by [ (1.5)³/(1.3)⁴ ]⁻⁶ .
An Algebraic Expression is defined as an expression that is made up of constants and variable and joined by mathematical operators .
In the question ,
a expression is expressed in words , we have to write an equivalent expression for it .
the statement 1.5 cubed is (1.5)³
1.5 cubed over 1.3 is = (1.5)³/1.3
1.5 cubed over 1.3 raised to the fourth power = (1.5)³/(1.3)⁴
and all raised to the power of negative six = [ (1.5)³/(1.3)⁴ ]⁻⁶
Therefore , The equivalent Algebraic Expression is represented by [ (1.5)³/(1.3)⁴ ]⁻⁶ .
The given question is incomplete , the complete question is
Write an equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six ?
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There were 320 students enrolled at forest high school last year this year there are 352 students enrolled what is the percent change in enrollment from last year to this year
percent change in enrollment from last year students is
How do you determine a population decline in percentage terms?Work out the difference (reduction) between the two numbers you are comparing before calculating the percentage drop. Then, increase the result by 100 after dividing the decrease by the initial number. The outcome expresses the change as a percentage, or the change in percentage.
Last year students =320
This year students =352
We need to find the percent increase in enrollment.
The increase in no of students = 320 -352
= 32
Percentage = (increase/initial no of students) × 100
% =32/352*100
9%
Hence, the percent increase is 9%.
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can you guys please answer this? its timed so dont take too long!
The expression equivalent to (5z² + 3z + 2)² is 25x⁴ + 30z³ + 29z² + 12z + 4.
The correct answer option is option D
What is the equivalent expression?(5z² + 3z + 2)²
Expand the expression(5z² + 3z + 2) (5z² + 3z + 2)
= 25z⁴ + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4
collect like terms= 25x⁴ + 15z³ + 15z³ + 10z² + 9z² + 10z² + 6z + 6z + 4
= 25x⁴ + 30z³ + 29z² + 12z + 4
In conclusion, the equivalent expression is 25x⁴ + 30z³ + 29z² + 12z + 4.
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Which represents the explicit formula for the arithmetic sequence an = 15 + 5(n - 1) in function form?
The explicit formula for the arithmetic sequence an = 15 + 5(n - 1) in function form is; aₙ = 5n + 10
How to find the explicit formula for an arithmetic sequence?The explicit formula for an arithmetic sequence is usually expressed as;
an = a + (n - 1)d
It could also be that any term of the sequence can be computed, without even knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic sequence.
We are given that the arithmetic sequence is represented by;
aₙ = 15 + 5(n - 1)
To write in function form, we apply distributive property to the terms within the bracket (parentheses) to get:
aₙ = 15 + 5n - 5
Rearranging gives us;
aₙ = 15 - 5 + 5n
aₙ = 5n + 10
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Complete question is;
Which represents the explicit formula for the arithmetic sequence an=15+5(n−1) in function form?
A
f(n)=5n+15
B
f(n)=n+20
C
f(n)=5n+10
D
f(n)=n+10
need help with another math problem
Answer: y = -x-1
Step-by-step explanation:
A boat's speed in still water is 4 km/h. The boat cruises from A to B along a river flowing at an average speed of x km/h in the direction A to B. If the distance AB is 5 km and the boat takes 2 hours more on its return journey, determine x. Hence, find the total time taken for the whole journey.
x is 6.215 km and the total time taken for the whole journey is 3.61 hours.
Boat's speed in still water = u = 4 km/h
Speed of stream = v
Distance between A and B = 5 km
Upstream speed = u - v
= 4 - v
Time taken = [tex]T_{1}[/tex] = [tex]\frac{5}{4-v}[/tex]
Downstream speed = x = u + v
= 4 + v
Time taken = [tex]T_{2}[/tex] = [tex]\frac{5}{4+v}[/tex]
According to question,
[tex]T_{1}= T_{2}+2[/tex]
[tex]\frac{5}{4-v}=\frac{5}{4+v}+2[/tex]
[tex]\frac{5}{4-v}=\frac{5+2(4+v)}{4+v}[/tex]
[tex]\frac{5}{4-v}=\frac{5+8+2v}{4+v}[/tex]
5(4+v) = (13+2v)(4-v)
20+2v = -2[tex]v^{2}[/tex]-5v+52
[tex]2v^{2}+10v-32 = 0[/tex]
[tex]v^{2}+5v-16 = 0[/tex]
v = 2.215 or -7.215
Speed can't be negative.
Therefore, v = 2.215
Upstream speed = 4 - 2.215
= 1.785 km/h
Downstream speed = 4 + 2.215
= 6.215 km/h
[tex]T_{2}[/tex] = 5/6.215
= 0.805 h
[tex]T_{1}[/tex] = 2 + 0.805
= 2.805 h
Total time = 2.805 + 0.805
= 3.61 h
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Hailey is shopping at a department store during a 20% off everything sale. She also has a coupon for $5.00 off the sale amount. Hailey wants to keep her total under $65.00 before tax, so she creates this inequality:
0.80x − $5.00 ≤ $65.00.
Which inequality represents all possible solutions for x?
A.
x ≤ $75.00
B.
x ≤ $76.25
C.
x ≤ $86.25
D.
x ≤ $87.50
Answer:
Step-by-step explanation:
c
Answer:
D
Step-by-step explanation:
hope it helped:)
Suki has placed $800 in an account that pays 4 percent interest compounded quarterly. At the end of two years (eight quarters), the balance in the account will be $. That means suki will have earned $ in interest during that time. (round your answers to the nearest cent. ) what will be the balance in the account at the end of two years (eight quarters)? how much interest will suki have earned during that time? (round your answers to the nearest cent. ).
The account balance at the end of two years (eight quarters) is $866.24.
Suki earned $66.24 interest during that time.
What do you mean by interest rate?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
According to data in the given question,
We have:
Placed amount= A= $800
Interest rate (quarterly)= r= 4%
Time= t = 2 years
Now, we will using the formula below:
[tex]A=P(1+\frac{r}{n} )^{nt}\\=800(1+\frac{0.04}{4} )^{4*2}\\=800(1+0.01 )^{8}\\=800(1.0828)\\=866.24[/tex]
So, the account balance at the end of two years (eight quarters) is $866.24.
Then, we have to determine the earned interest during that time,
Earned interest= A-P
= 866.24 - 800
= 66.24
Therefore, she earned $66.24 interest during that time.
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Given that
x
= 8.1 m and
θ
= 28°, work out BC rounded to 3 SF.
The length of BC rounded to 3 decimal places is 4.307 meters.
What is Pythagoras theorem ?
It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the base and perpendicular. Mathematically -
h² = p² + b²
We have the following length and angle as shown in the figure -
[x] = AB = 8.1
θ = ∠BAC = 28°
Using the tangent rule we can write -
tanθ = BC/AB
BC = AB tanθ
BC = 8.1 x tan(28°)
BC = 4.307
Therefore, the length of BC rounded to 3 decimal places is 4.307 meters.
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Find the sum of the interior angle measures of the polygon.
The sum of the angles is
Answer:
2160°
Step-by-step explanation:
We have,
Number of Sides, n = 14
So,
Sum of all interior angle = pi ( n - 2 )
or, Sum of all interior angle = pi ( 14 - 2 )
or, Sum of all interior angle = 12 pi radians.
We know,
1 radian = ( 180 / pi ) (degree)
or, 12 radians = 2160 (degree)
2. Which of the following is true for f?
f(x)=
3x + 1, if -9 < x < -2
-5, if-2 < x≤ 1
(x-6, if 1
A The domain is -9 < x < -2, -2
B The range is (-26, 1).
The function is decreasing over the interval (-2, 1).
D The rate of change over the interval (-9, 1] is 3.
The statement (B) "the range is (-26, 1)" is TRUE.
What is a domain in functions?The range of values that we are permitted to enter into our function is known as the domain of a function.The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, this set of values is what the function outputs.So, we have:
f(x) = 3x + 1, if -9 < x < -2-5, if-2 < x≤ 1x-6, if 1The statement is:
A) The domain of this function is 9 < x ≤ 1.B) The range is (-26, 1).C) The function is decreasing over the interval [-9,-2] and increasing over the interval [-2,1].D) The rate of change for the function over the interval is -2.Therefore, the statement (B) "the range is (-26, 1)" is TRUE.
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6% of a length is 390m what is the original length?
The original Length is, 6500 m.
What is Length?The industry norm for graphics is width by height (width x height). Hence, you should always write your measurements from your perspective, starting with the width.The value-length command defines the longest value, in bytes, that the parse action will allow in a document.Considering that 390 m equals 6% of a lengthLet the starting length be aThe original length is 6500 m because 6% of a = 390 a*6/100 = 390 a = 390*100/6 a = 6500.The earliest known units used by ancient peoples to measure length are the Egyptian cubit, the Indus Valley units of length mentioned above, and the Mesopotamian cubit, all of which were in use in the third millennium BC.To learn more about Length refer to:
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The amount of money earned, in dollars, varies directly as the number of hours worked. After 9 hours, 270 dollars were earned.
How long, in hours, does it take to earn 390 dollars? Do not include units in your answer.
Answer: 13 Hours
Step-by-step explanation:
1. 270/9 = 30 dollars per hour
2. 390/30 = 13 hours
5.7 gal/h = c/min? What is the answer
Answer:
5.7 gal / hour
5.7 gal / 60 min
5.7(16) c / 60 min
help ima have a panic attack again.
Answer:
39mm=6m52/39= 1 1/31 1/3 times 6 meters4/3 times 6/1 = 24/324/3=8The actual length of the living room is 8 meters
Compute the sample standard deviation for strength of the concrete (in psi).
3940, 4140, 3200, 3200, 2990, 3810, 4140, 4040
The range is 1150 psi.
S=__psi
(Round to one decimal place as needed.)
Answer: The standard deviation is 443.6 (rounded up to one decimal place)
Step-by-step explanation:
σ2 = (Σ(xi - μ)^2)/N
= ((3940 - 3682.5)^2 + ... + (4040 - 3682.5)^2)/8
= 1574150/8
= 196768.75
σ = [tex]\sqrt{196768.75}[/tex]
= 443.58623738795
Frequency Table
Value Frequency
2990 1 (12.5%)
3200 2 (25%)
3810 1 (12.5%)
3940 1 (12.5%)
4040 1 (12.5%)
4140 2 (25%)
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For a circle with a radius = 4.3, find the following
The circumference is 27.004 and the Area is 58.0586 calculated for the circle with radius of 4.3 and π = 3.14
Circumference and Area of a circleThe circumference of a is the arc length of the circle with the formula 2πr. While the area of a circle is calculated with formula πr²
Given radius r = 4.3 and π = 3.14
circumference = 2 × 3.14 × 4.3
circumference = 27.004
Area of the circle = 3.14 × 4.3²
Area of the circle = 3.14 × 4.3 × 4.3
Area of the circle = 58.0586
Therefore, the circumference and area of the circle with radius of 4.3 is 27.004 and 58.0586 respectively.
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Match the expression on the left with its simplified form on the right. Answer options on the right may be used more
than once.
-(-1)
-|-1|
-|1|
|1|
|-1|
1
-1
The solutions of the expressions -(-1), -|-1|, -|1|, |1|, and |-1| are 1, -1, -1, 1, and 1.
We are given five expressions. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. The first expression is -(-1). The simplified solution of the first expression is 1. The second expression is -|-1|. The simplified solution of the first expression is -1. The third expression is -|1|. The simplified solution of the first expression is -1. The fourth expression is |1|. The simplified solution of the first expression is 1. The fifth expression is |-1|. The simplified solution of the first expression is 1.
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HELP PLEASE HELP I NEED THIS IN A FEW MINUTES ITS URGENT PLEASEEEE T.T
using the expression x+3 write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions.
a. The equation that has one solution will be;
⇒ x + 3 = 4x
b. The equation that has no solution will be;
⇒ x + 3 = x
c. The equation that has infinitely many solution will be;
⇒ x + 3 = 3 (x/3 + 1)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x + 3
Now,
Use the expression x + 3, we can find as;
Let us defined an expression as;
⇒ x + 3 = 4x
Solve for x as;
⇒ x + 3 = 4x
⇒ x + 3 - 4x = 0
⇒ - 3x = - 3
⇒ x = 1
Hence, The equation has one solution.
Let us defined an expression as;
⇒ x + 3 = x
Solve as;
⇒ x + 3 = x
Subtract x both side, we get;
⇒ x + 3 - x = x - x
⇒ 3 ≠ 0
Thus, The equation has no solution.
Let us defined an expression as;
⇒ x + 3 = 3 (x/3 + 1)
Solve as;
⇒ x + 3 = 3 (x/3 + 1)
⇒ x + 3 = 3x/3 + 3
⇒ x + 3 = x + 3
Subtract x we get;
⇒ 3 = 3
Thus, The equation has infinitely many solution.
Therefore,
a. The equation that has one solution will be;
⇒ x + 3 = 4x
b. The equation that has no solution will be;
⇒ x + 3 = x
c. The equation that has infinitely many solution will be;
⇒ x + 3 = 3 (x/3 + 1)
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Answer:
1/ x+3 = 4x
2/ x=x
3/ x+3 = 3
Step-by-step explanation:
Hope you find it helpful!
If you can please give me a Brainliest, thank you!
Find the perimeter of a rectangle with length 8 inches and width 9 inches.
Answer:
P=34in
Step-by-step explanation:
just want to help <33333
Answer:34
Step-by-step explanation:34
whats an equation where the slope is 2/3 and y-intercept is -8
Answer: y=2/3x-8
Step-by-step explanation:
Insert the given information into the y=Mx+b equation
Solve two-thirds + five-eighths = ___.
Answer:
1 7/24
Step-by-step explanation:
2/3+ 5/8= (2 × 8)(3 × 8)+ (5 × 3)(8 × 3) = 16/24+ 15/24= 16 + 15/24= 31/24 = 1 7/24
Answer:1 7/24
Step-by-step explanation:
Please help me!!!!!!!
Answer:
Step-by-step explanation:
The range is [-4, ∞)
Using a graphing calculator (desmos) we can obtain a graph of the following function.
Explanation:
In the graph, we can see that there is a point a -4 and nothing lower, making it our minimum y-value. However, we cannot see an ending for the function; therefore, it is indeterminable and thus, infinity. As for notation. we use the solid bracket because we know the definite point, though because infinity is not definite we just use a parentheses to enclose it.
i need help on this thanks
The value of x that makes m || n is x = 20
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
The alternate interior angles of two intersecting lines, such as line "m" and line "n" in the exercise, must both be congruent in order for m || n to exist. Realizing that congruent means the same thing.Two alternate internal angles in the exercise are (2x+20)° and 3x°Solving this for ''x'' :.
3x=2x+20x=20The value of x that makes the opposite inner angles congruents (making 3x° congruent to 2x+20°) is x = 20.
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a spinner is broken into sections labeled 1 to 37. what is the probability that, on your next spin, that you will spin a number greater than 9?
The probability of getting a number < 9 is 28/37.
What is probability?
The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.
Probability(Event) = Favorable Outcomes / Total Outcomes
Main Body:
Total numbers on the spinner greater than 9 = 37 - 10 + 1 = 28
(we are subtracting 10 because we need number that is greater than 10.)
and adding 1 because both the ends of interval is counted.
total numbers on spinner =37
P( x>9) = 28/37.
Hence the probability of getting a number greater than 9 on spinning is 28/37.
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Amir drove from Jerusalem to the lowest place on Earth, the Dead Sea.
His altitude relative to sea level (in meters) as a function of time (in minutes) is graphed.
The first and fourth quadrants of a coordinate plane. The horizontal axis is from zero to seventy-two with a scale of eight and is titled Time in minutes. The vertical axis is from negative four hundred to four hundred eighty with a scale of eighty and is titled Altitude in meters. The graph of the line is y equals negative eleven x plus four hundred forty.
The first and fourth quadrants of a coordinate plane. The horizontal axis is from zero to seventy-two with a scale of eight and is titled Time in minutes. The vertical axis is from negative four hundred to four hundred eighty with a scale of eighty and is titled Altitude in meters. The graph of the line is y equals negative eleven x plus four hundred forty.
How fast did Amir descend?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
404040 meters per minute
(Choice B)
B
101010 meters per minute
(Choice C)
C
202020 meters per minute
(Choice D)
D
111111 meters per minute
The function (equation) that returns Amir's altitude, y, with respect to time, x, y = -11·x + 440, when differentiated, to find the rate of change of the altitude, indicates that rate at which Amir descended is D. 11 meters per minute
What is differentiation in mathematics?Differentiation is the process or method by which the derivative of a function is found. The derivative indicates the instantaneous rate at which the value of the function changes with respect to the change in the argument of the function.
The equation of the function that gives his altitude relative to the sea level as a function of time is; y = -11·x + 440
The differentiation of the function for the height, y, in terms of the time, x, gives the speed which is the same as the at which Amir descended as follows;
[tex]Speed = \dfrac{dy}{dx} = \dfrac{d}{dx} \left(-11\cdot x+400\right) = -11[/tex]
The speed with which Amir descends is 11 meters per minute
The correct option is D. 11 meters per minute
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I have 4 Friends. But I gain a new friend. But then 4 of my friends did me dirty by stealing my house keys. So how many friends do I have?
Answer:
1
Step-by-step explanation:
4+1=5
5-4=1
Answer:
you have 1 friend
Step-by-step explanation:
you have 4 then you add another
that's 5
then you lose 4
5-4 is 1
I need help with 9-11. I really don’t understand this, please help me!!!
Step-by-step explanation:
9.
we get the extreme values of y (a function) by finding the zeroes of the first derivative (that gives us the x-positions) and then using these x values in the original function.
a quadratic function has only one extreme value (1 less than the degree of the polynomial). but 2 zeroes (exactly the degree of the polynomial) - don't mix these two things up.
as the leading coefficient is positive (1), we know that the parabola is opening upwards, and the extreme value will be the vertex and therefore the minimum.
y = (x + 4)² + 6
y = x² + 8x + 16 + 6 = x² + 8x + 22
y' = 2x + 8
2x + 8 = 0
2x = -8
x = -4
(-4 + 4)² + 6 = 0² + 6 = 6
the smallest possible value of y = 6 (at x = -4).
10.
the intercept form of a parabola equation is
y = a(x - p)(x - q)
p and q are the x-intercept values.
in our case we see p = -3, q = 3.
also, we see the vertex being (0, 9), which we need to get "a".
y = a(x - -3)(x - 3) = a(x + 3)(x - 3)
using the vertex coordinates to get a :
9 = a(0 + 3)(0 - 3) = -9a
a = 9/-9 = -1
so, the quadratic equation is
y = -(x + 3)(x - 3) = -(x² - 9) = -x² + 9
11.
I assume the thinking here is : the flight curve of every falling object is a parabola.
the vertex of this parabola is (0, 36), as x represents the time in seconds, and y represents the height in ft.
the vertex form of a parabola is
y = a(x - h)² + k
with (h, k) being the vertex.
y = a(x - 0)² + 36 = ax² + 36
a must be negative, as the fall parabola opens downwards.
for typical fall situations on Earth a = -g/2 ≈ -16 (g being the gravity constant of 32.17405... ft/s²).
so, we have
y = -16x² + 36
for what x is y = 0 ?
0 = -16x² + 36
16x² = 36
x² = 36/16 = 9/4
x = 3/2 = 1.5
the coin hits the water after 1.5 seconds.
Planes x and y are perpendicular. Points a, e, f, and g are points only in plane x. Points r and s are points in both planes x and y. Lines ea and fg are parallel. Based on this information, which pair of lines, together, could be perpendicular to rs? select two options.
The pair of lines perpendicular to RS are EA and FG.
A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.
What is plane?
A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.
Main Body:
Given
E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.
Explanation:
The lines which together could be perpendicular to RS are EA and FG.
We have to first draw both the planes according to the given information in question.
X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.
Hence we can observe that lines EA and FD are perpendicular on line RS.
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