The given expression is proved above to its equivalent value.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is an exponential expression.
[tex]$e^{(2\pm3\pi i)} = -e^{2}[/tex]
We can write the given expression in two possible ways -
[tex]$e^{2} e^{3\pi i}[/tex] and [tex]$\frac{e^{2} }{e^{3\pi i} }[/tex]
Now, we know using the De - Moivre's theorem, we can write -
[tex]$e^{i\theta} =[/tex] cos(θ) + i sin(θ)
Now -
[tex]$e^{3\pi i} =[/tex] cos(3π) + i sin(3π) = - 1
So, we can write -
[tex]$e^{2} e^{3\pi i}[/tex] = - e²
and
[tex]$\frac{e^{2} }{e^{3\pi i} }=\frac{e^{2} }{-1}[/tex]
[tex]$\frac{e^{2} }{e^{3\pi i} }=-e^{2}[/tex]
Therefore, the given expression is proved above to its equivalent value.
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BEST ANWER GETS BRAINLIEST PLEASE HELP!! :( THIS IS A FINAL!1
2. Apple is also analyzing their profit of the iPhones they sell.
Apple: Profit from iPhones Sold
iPhones sold (in millions) i Profit (in millions of dollars) P(i)
-1 0
2 -9
5 0
6 7
7 16
A. Based on the table, create an equation in factored form (hint: look for the x-intercepts of the function). Then translate the factored form into completed the square form and standard form.
Factored form P(i) =
Standard form P(i) =
The x-intercept of the function is where y=0 and x = -1 or x=5
What is x-intercept?You should be aware that the x-coordinate of a point where a line, curve, or surface intersects the x-axis. Also, The x-intercept for any curve is the value of x coordinate of the point where the graph cuts x-axis
Considering the table
i P(i)
-1 0
2 -9
5 0
6 7
7 16
The factored form would be
P(i) = (i+1)(i-5)
The standard form would also be
P(i) = i²-5i+i-5
= i²-7i-5
Therefore the factored and standard forms are (i+1)(i-5) and i²-7i-5 respectively
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the area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 miles. What is the width,in miles of the park
If the area of the rectangular city park is 25/54 square miles and the length is 5/9 miles, the width of the park, in miles, is 5/6 miles.
What is the formula for the area?The area is the product of the length and width of a rectangle.
To determine one side given the area and another side, we divide the area by the given side's length.
Area = 25/54 square miles
Length = 5/9 miles
Area = Length x Width
Width = 25/54 ÷ 5/9
= 25/54 x 9/5
= 5/6
Thus, the width is 5/6 miles.
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The ratio of number of number of stamps collected by Susan and Latha is 5:7. If Latha has collected 105 stamps, what is the number of stamps with Susan?
Please answer
Answer:
Step-by-step explanation:
105 divided by 7 =15 so if 15 times 7=105 then 15 times 5 is 75. so susan has 75 stamps. please mark me brainliest.
The short leg of a right triangle is 10 meters and the acute angles measure 25° and 65°. find the measures of the longer leg of the right
triangle.
When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.
what is right angle ?Right angles are created when two straight lines cross at a 90° angle or are perpendicular to one another at the intersection. The sign stands for a right angle. Different right angle formations can be seen in the above image. The proper angles can be found in shapes. Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees.
given
x / sin 65° = 10 / sin 25°
x = 10 sin 65°/ sin 25°
x = 21 .45 meters
as law of sine
a / sinA = b / sinB = c / sinC
When the short leg of a right triangle is 10 meters long and the sharp angles are present, the right triangle's longer leg has a measurement of 21.45 meters.
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Answer the question below. View the rubric linked above for help if needed.
Simplify the expression (6²a⁻³ / b⁻¹c)⁻². Show all work and explain each step.
Answer:
[tex] \frac{ {a}^{ 6 } {c}^{2} }{1296 {b}^{2} } [/tex]
Step-by-step explanation:
By Using
[tex] {(\frac{a}{b} )}^{ - n} = {(\frac{b}{a})}^{n} [/tex]
Express the phrase as a positive power
We apply power in fractions for a
Six to two power can be multiplied, then multiplying the number behind A, 36
Now because on top of a fraction there is a negative power, it transferred to below the deduction, but we make the power positively
Now it's a "A" turn
After sorting the phrase "A" to the back of "c" of the phrases to power two
[tex] \frac{ {a}^{6} {c}^{2} }{1296 {b}^{2} } [/tex]
3. Writing to Explain At a cat and dog hospital, 9 of the patients
were cats, 17 were dogs. Use this fact to write two ratios.
Explain what each ratio means.
Answer:
[tex]\frac{9}{17}[/tex] or 9:17 This is the ratio of cats to dogs.
[tex]\frac{17}{9}[/tex] or 17:9 This is the ratio of dogs to cats.
Step-by-step explanation:
Ana has 111 ounces of water in a pitcher. After she fills 8 glasses with the same amount of water, there are 15 ounces of water left in the pitcher.
How much water is in each glass?
A jug of milk holds 4 quarts. How many liters of milk does the jug hold? Round your answer to the nearest hundredth of a liter. 1 L ≈ 1.06 qt
A. 0.27 L
B. 3.77 L
C. 4.24 L
D. 5.06 L
Please help !!
Answer: B: 3.77 L.
Step-by-step explanation:
To solve this problem, you need to know that 1 quart is equal to approximately 0.94 liters. This means that 4 quarts is equal to approximately 3.76 liters. Rounding this number to the nearest hundredth of a liter gives you an answer of approximately 3.76 liters, or 3.76 L. Therefore, the correct answer is choice B: 3.77 L.
A subtraction square is a 3 by 3 grid of integers where, in each row from left to right, and in each column from top to bottom, the first integer minus the second integer equals the third integer. The integer k is in the top left unit square of the subtraction square, as shown. When the subtraction square is filled in completely, what is the sum of all nine integers? Express your answer in simplest form in terms of k.
The sum of all nine integers in the subtraction square is equal to 9 times the number in the top left unit square, which is k.
1. Fill in the subtraction square with three rows and three columns.
2. In each row from left to right, and in each column from top to bottom, the first integer minus the second integer equals the third integer.
3. The sum of all nine integers is equal to the sum of the numbers in each row plus the sum of the numbers in each column.
4. The sum of the numbers in each row is equal to k + (k - k) + (k - (k - k)) = 3k
5. The sum of the numbers in each column is equal to k + (k - (k - k)) + (k - (k - (k - k))) = 3k
6. So the sum of all nine integers is 9k.
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Just plug in numbers.
This grid works
k k 0k k 00 0 0
so the answer is 4k.
given the following table with selected values of f(x) and g(x) evaluate f(g(1))
The value of f(g(1) from the table of functions is given as 1.
What is Functions ?Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.
when x = 1
g(x) = 3
or f(g(1) = f(3) = 1
The value of f(g(1) from the table of functions is given as 1.
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please really need help, no spamming will make brainliest 20 points!!!!!!!!!!!!!!!!!!!!!!!!
Triangles ΔICR and ΔISU are congruent by SAS rule of congruency, therefore; ∠CIR ≅ ∠SIU by CPCTC
What are congruent triangles?Two triangles, ΔABC and ΔXYZ are said to be congruent by the Side-Angle-Side, SAS congruency rule, if the two sides and an included angle of triangle ΔABC, are congruent to two sides and an included angle of triangle ΔXYZ.
The specified measurements are;
∠1 ≅ ∠4
CU = RS
IC = IS
IC ≅ IS (Definition of congruency)
The congruency of the sides IC and IS indicates that the triangle ΔICS is an isosceles triangle
Therefore, ∠2 ≅ ∠3 by the properties of the base angles of an isosceles triangle
CU - RU = RS - RU (subtraction property)
RU ≅ RU, (reflexive property of congruency)
CU - RU = CR
RS - RU = SU
CR = SU (Substitution property)
CR ≅ SU (Definition of congruency)
ΔICR is congruent to ΔISU by Side-Angle-Side, SAS, rule of congruency.
∠CIR ≅ ∠SIU by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
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(1) Complete the number sequences.
(a) 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0,
The next three numbers of sequence is,
⇒ 2.8, 8.4, 8.2
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The sequence is,
⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,
Now,
Since, The sequence is,
⇒ 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0, .., .., ...,
Clearly, The pattern of the sequence is,
⇒ 0.4 - 0.2 = 0.2
⇒ 0.2 × 3 = 0.6
⇒ 0.6 - 0.2 - 0.4
⇒ 0.4 × 3 = 1.2
⇒ 1.2 - 0.2 = 1.0
⇒ 1.0 × 3 = 3.0
⇒ 3.0 - 0.2 = 2.8
⇒ 2.8 × 3 = 8.4
⇒ 8.4 - 0.2 = 8.2
Thus, Next three terms of the sequence is,
⇒ 2.8, 8.4, 8.2
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Evaluate the expression √ − 6 /√ − 6 √ − 7 and write the result in the form a + b i
Answer:
√ − 6 /√ − 6 √ − 7 = -1 + 0i
Step-by-step explanation:
Graph the arithmetic sequence.
$4,\ 12,\ 20,\ 28,\ ...$
Keyboard Instructions
Initial graph state
The horizontal axis goes from -0.8 to 6 with ticks spaced every 1 unit(s).
The vertical axis goes from -2 to 30 with ticks spaced every 4 unit(s).
The graph of the arithmetic sequence is added as an attachment
How to graph the arithmetic sequence?From the question, we have the following parameters that can be used in our computation:
Sequence: 4, 12, 20, 28....
The above sequence is an arithmetic sequence with the following parameters
First term, a = 4
Common difference, d = 8
So, the x-th term is
f(x) = a + (x - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(x) = 4 + (x - 1) * 8
This gives
f(x) = 8x - 4
So, the equation to plot is f(x) = 8x - 4
See attachment for the graph
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what is the answer for this question
The
number
of
pupils
that prefer
English
as their favorite subject from the table is 26
How to determine the total number
From the table provided, we have to fill the empty spaces before finding the sum of the numbers.
To calculate the
number
of girls that chose
English
= Total number of girls - sum of Mathematics and Sciences
= 38 - (20 + 12)
= 38 - 32 = 6
To calculate the exact number of boys that chose English, we have;
= Total for Mathematics- Girls that chose Mathematics
= 25 - 20 = 5
Also,
To find the
total
pupils for all the courses - total for girls in general
= 70 -38 = 32
Then,
= 32 - ( 5 + 7)
= 32 - 12 = 20
The total pupils that chose English
= 20 + 6
= 26 pupils
Thus, the
number
is 26
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july 15, 2017 + 7months
Answer:
February 15, 2018
Step-by-step explanation:
Not sure but I think
Deandre rented a movie. He started the movie at 11:48 PM, and it was 2 hours 37 minutes long. When did the movie end?
Answer:
2:25 am is the right answer.
Answer:
02:25 or 2:25 AM
Step-by-step explanation:
Add 2 hours yo 1148 to get 0148 now add 37 more minutes to get 02:25
This figure is made up of two rectangular prisms what is the volume
The required volume of the given figure is 1134 cubic in.
What is volume?
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Given that,
A figure made up of two rectangular prisms has shown, we have to determine the volume of the prism.
Here,
The required volume of the figure is given as,
Volume = Volume of the bottom prism + Volume of the top prism
Volume = [7 ×2 × 21 ] + [12 × 10 × 7]
Volume = 294 + 840
Volume = 1134 cubic in.
Thus, the required volume of the given figure is 1134 cubic in.
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Find the solution of the differential equation
y' = 2 square root y . x
The required solution of the differential equation is given as; y = x⁴/4 + c₁x²/2 + c₁².
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.
We are Given the differential equation,
y' = 2 √y . x
y' = dy/dx so,
Therefore, we have
dy/dx = 2√y.x
dy/√y = 2x dx
y = [1/2(x² + c₁)]²
y = x⁴/4 + c₁x²/2 + c₁²
Thus, the solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁² .
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Sams total bill was $39.57. If she left $50.50 how much did she tip the waiter?
Answer:
$10.93
Step-by-step explanation:
Solve the equation : 3x^2=2x-10
Answer: 1/3 ± √29/3i
Step-by-step explanation:
To solve these equations, move everything to one side:
3x^2-2x+10 = 0
This cannot be factored, so use the quadratic formula:
x = -(-2) ± √( (-2)^2 - 4(3)(10)) / 2
x = (2 ± √4 - 120) / 6
x = 2 ± (√116 • i) / 6
x = 2 ± (2√29•i) / 6
x = 1/3 ± (√29/3)i
In the figure below, N is between M and O, and O is between N and P. If MP=9, MO=6, and NP=7, find NO.
Length of NO = 4 unit.
What is length?Length is the distance of any object or any figure form one end to another end. In the above question, length of different part of a same straight line is measured one by one.
What is the length of NO given in question?
MP is a straight line. N, M, O, P are all lying on this line. N is between M and O and O is between N and P.
length of MP = 9 unit
length of MO = 6 unit
length of NP = 7 unit
As per the statement, MP - NP = MN
MN = 9 - 7
length of MN = 2 unit
as N is between M and O
so, NO = MO - MN
NO = 6 - 2
length of NO = 4 unit
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Put these numbers in order from least to greatest 7.9 7.5 7.541 8.401 7.19
Answer: 7.19, 7.5, 7.541, 7.9, 8.401
Step-by-step explanation: I would recommend creating a number line and plotting to points, this may help you visual it from least-> great :)
3. Students from 4 classes at Franklin Elementary School are going on a field trip to the theater. Each
class has 30 students. There will also be 6 teachers and 14 parents on the trip. There are 20 seats in
each row at the theater. How many rows should be reserved for the field trip?
A 2
B 7
C 74
D 140
Answer:
B) 7
Step-by-step explanation:
Given information:
Number of classes = 4Number of students in each case = 30Number of teachers = 6Number of parents = 14Number of seats per row = 20If there are 30 students in each class, and there are 4 classes, the total number of students is:
[tex]\begin{aligned}\implies \textsf{Total students}&=\textsf{Students per class} \times \textsf{Number of classes}\\&=\sf 30 \times 4\\&=\sf 120\end{aligned}[/tex]
Therefore, the total number of people going on the trip is:
[tex]\begin{aligned}\implies \textsf{Total number of people}&=\sf Students+Teachers+Parents\\&=\sf 120+6+14\\&=\sf 140\end{aligned}[/tex]
As there are 20 seats in each row at the theater, to calculate how many rows should be reserved for the trip, divide the total number of people by the number of seats per row:
[tex]\begin{aligned}\implies \textsf{Rows to reserve}&=\sf \dfrac{\sf Total\;people}{\sf Seats\;per\;row}\\\\&=\sf\dfrac{140}{20}\\\\&=\sf 7\end{aligned}[/tex]
Therefore, 7 rows should be reserved for the field trip.
15 + 12 + 9.6 + ...; n = 40
The sum of the first 40 terms of the geometric sequence 15 + 12 + 9.6 is given as follows:
75.
How to obtain the sum?The sum for this problem is defined as follows:
15 + 12 + 9.6 + ..., n = 40.
The ratio between the consecutive terms of the sequence is given as follows:
12/15 = 9.6/12 = 0.8.
This means that the sequence is a geometric sequence, for which:
The first term is of [tex]a_1 = 15[/tex]The common ratio is of q = 0.8.The sum of the first n terms of a geometric sequence is given by the equation presented as follows:
[tex]S_n = \frac{a_1(q^n - 1)}{q - 1}[/tex]
Considering the numeric values of the parameters [tex]a_1[/tex] and q, the numeric value of the sum is given as follows:
S = 15 x (0.8^40 - 1)/(0.8 - 1)
S = 75.
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is it consistent dependent or indepdent?
Answer:
consistent
Step-by-step explanation:
the other ones are spelled wrong also dependent
supply the missing numerator or denominator
Answer:
You need to find a pattern in order to solve (check explanation)
Step-by-step explanation:
The easiest way to find a pattern is by knowing the difference between two numbers; in this case, it's 3 and 6 (a-numerators), 3 - 6 = 3 we know you could get this by multiplying 3 x 2
Now that you know this-- the other a-numerators are products of 3
A) 3, 6 , 9 , 12 , 15, 18
20
____
I'm not so sure as for the b problem, I genuinely don't want to give a bad answer, but possibly using the same tactic could work, it does seem like the denominator is more important for b.
PLEASE HELP ASAP. Name the marked angle in 2 different ways.
Find c for the inequality 5/7c +2greater than or equal to 4/7
The solution for the given inequality (5/7)*c + 2 ≤ 4/7 is the one on the third option:
c ≤ -2
How to solve inequality?Here we want to solve the following inequality:
(5/7)*c + 2 ≤ 4/7
We want to solve this for the variable c, to do so, we need to isolate that variable.
We can start by subtracting 2 in both sides, so we will get:
(5/7)*c + 2 ≤ 4/7
(5/7)*c +2 - 2 ≤ 4/7 - 2
(5/7)*c ≤ 4/7 - 14/7
(5/7)*c ≤ -10/7
Now we can multiply both sides by 7/5 to get:
(7/5)*(5/7)*c ≤ (-10/7)*(7/5)
c ≤ -10/5
c ≤ -2
Then the correct option is the third one.
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Melissa receives a daily wage of $50 for each shift at the mall as well as a commission of 3% on her sales. Her sales range from $0 per day to $2000 per day
a. Graph her earnings and write an equation for the relation
B. State the y-intercept and its meaning
C. Create a data table with 4 possible data points on the graph
a. The linear function that models her earnings is given as follows:
y = 50 + 0.03x.
The function is graphed on the image given at the end of the answer.
b. The y-intercept of 50 represents her fixed pay of $50 per shift.
c. Four points from the graph are given as follows:
(0, 50), (100, 53), (1000, 80), (2000, 110).
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
m is the slope, representing the rate of change of the linear function.b is the y-intercept, representing the value assumed by the linear function when x assumes a value of zero.Melissa receives a daily wage of $50, hence the intercept b is given as follows:
b = 50.
She also earns a commission of 3% on her sales, hence the slope m is given as follows:
m = 0.03.
Meaning that the function is defined as follows:
y = 50 + 0.03x.
The domain of the function is given as follows:
0 ≤ x ≤ 2000.
As it is the amount of sales that she can earn per day.
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