We can not write the given complex number in to (a + ib) form.
What is complex number?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers with a particular element denoted I also known as the imaginary unit, and satisfying the equation i^2=-1.
The complex number is (x - 2)^2.
We have to write this complex number into a + ib form.
Let,
(x - 2i)^2 = (x - 2i)(x - 2i)
= x^2 - 2xi - 2xi + 4(i^2)
= x^2 - 2xi - 4
(x - 2i)^2 = x^2 - 2xi - 4
Here we can not write the given complex number in to (a + ib) form.
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At a football stadium, 4% of the fans in attendance were teenagers. If there were 170 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
4,250
Step-by-step explanation:
If 4% of all fans were teenagers, and 100 divided by 4 is 25, simply math of 170 times 25 gives you 4,250
Therefore, the answer is 4,250
Answer:
Total number of people = 4,250
Step-by-step explanation:
4% of 4,250 = 170
Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.
Which equation can Amy use to find how many games of Balloon Bouncer, g, she played?
How many games of Balloon Bouncer did Amy play?
games
Amy play 11 games of Balloon bouncer. If Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.
Define algebraic equation.An algebraic equation is a formula that expresses the equivalence of two expressions by applying the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and root extraction to a collection of variables. An algebraic equation, sometimes known as a polynomial equation, in mathematics is a formula of the form P=0, where P is a polynomial with coefficients in some field, typically the field of the rational numbers. A mathematical statement with variables, constants, coefficients, and algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expressions do not use equal signs, in contrast to algebraic equations.
Given
Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.
Algebraic Equation:
2 + 3g = 35
3g = 35 - 2
3g = 33
g = 11
Amy play 11 games of Balloon bouncer.
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Please help me with this question!
Answer:
Step-by-step explanation:
the answer is 11/12
Geometric Transformations
The four letter code from the transformations is given as follows:
FB H.
How to obtain the four letter code?The four letter code is obtained applying the transformations to the given points.
The coordinates of point 1 are given as follows:
(-4,2).
The transformation is a reflection over the x-axis, which has the rule given as follows:
(x,y) ->(x,-y).
Hence the coordinates of the image of point 1 are given as follows:
1'(-4,-2).
Meaning that the first letter is of F.
The coordinates of point 2 are given as follows:
(-2,3).
The transformation is a reflection over the y-axis, which has the rule given as follows:
(x,y) ->(-x,y).
Hence the coordinates of the image of point 2 are given as follows:
2'(2,3)
Meaning that the second letter is of B.
The coordinates of point 4 are given as follows:
(-1,2)
The transformation is a reflection over the line y = x, which has the rule given as follows:
(x,y) ->(y,x).
Hence the coordinates of the image of point 4 are given as follows:
4'(2,-1)
Meaning that the fourth letter is of H.
Missing InformationThe third transformation is missing.
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The equation 4(2x 1) = 6x − 12 models the change in water level in a lake in one month. solve for x, which is change in height in inches. x equals negative thirteen halves x = −8 x = 8 x equals eleven halves
From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
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Joe bought a box of laundry that contains 195 scoops. Each load of laundry uses 2 1/2 scoops. If the box of detergent costs $19.99, how much is he paying per load of laundry?
Answer:
a) Number of laundry he can do with this box = 78 laundries.b) Price he paying for each load = 0.256
Simplify each expression.
8x+13 - 3x + 9/1/2
Answer:5x+22
there you gooo
Answer:
5x+ 45/2
Step-by-step explanation:
Consider this right triangle. 20 m 37° Enter the length of side AB, to the nearest tenth.
Answer:
15.1
Step-by-step explanation:
tan(angle) = opposite/adjacent
tan 37 = AB/20
AB = 20 x tan 37 = 20 x 0.754 = 15.08 or 15.1
to reduce the chance of messing up range specifications and minimize the likelihood that errors will creep in when columns and rows are added later:_____.
To reduce the chance of messing up range specifications and minimize the likelihood that errors will creep in when columns and rows are added later: apply names in the spreadsheet
The correct answer is an option(D)
In this question, we have been given a statement.
We need to select the correct option to complete given statement.
We know that the most common uses for spreadsheet software are to create budgets, produce graphs and charts, and for storing and sorting data.
Data filtering is used to access subsets of information Excel. AutoFilter function allows to view and subset data easily without making any permanent changes to the original data.
Therefore, to reduce the chance of messing up range specifications and minimize the likelihood that errors will creep in when columns and rows are added later: apply names in the spreadsheet
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The complete question is:
To reduce the chance of messing up range specifications, and minimize the likelihood
that errors will creep in when columns and rows are added later:
A) manually inspect all formulas on the spreadsheet
B) do not hide columns in the spreadsheet
C) always use absolute cell references in all formulas
D) apply names in the spreadsheet
Ray bd bisects angle abc. To prove angle abd and angle cbd are congruent using a proof by contradiction, what is the assumption statement that starts the proof? angle abd and angle cbd are adjacent angles. Angle abd and angle cbd are supplementary angles. Angle abd and angle cbd are not complementary. Angle abd and angle cbd are not congruent.
To prove angle abd and angle cbd are congruent using a proof by contradiction, the assumption statement that starts the proof is Angle abd and angle cbd are not congruent.
What is proof by contradiction?Proof by contradiction is a technique used in logic and mathematics to verify the truth or validity of a claim by demonstrating how presuming the proposition to be incorrect results in a contradiction.
A proof by contradiction first starts with the negation, or opposite of the hypothesis.
In context of the problem, the proof by contradiction will start by the opposite . Since we are to prove that angle abd and angle cbd are congruent, the opposite is Angle abd and angle cbd are not congruent.
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If slope of a line is 7 and y-intercept is 4, then write the equation of that line.
Answer: The answer is y=7x+4
M is the slope and the y-intercept is b
Solve the equation.
[tex]3^{x}+9^{x}+27^{x}=-7[/tex]
Answer:
No solution
Step-by-step explanation:
The range of a parent exponential function is the set of positive real numbers. Thus, the LHS cannot be negative.
Express 80 as the product of its prime factors.
Write the prime factors in ascending order.
Answer: [tex]2^4 \times 5[/tex]
Step-by-step explanation:
[tex]80=2 \times 40\\\\80=2 \times 2 \times 20\\\\80=2 \times 2 \times 2 \times 10\\\\80=2 \times 2 \times 2 \times 2 \times 5\\\\80=2^4 \times 5[/tex]
1.
The band and the orchestra are each having a party to celebrate the
results of their latest competition. The band would like to order cupcakes
from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee. This system {2.90c +22.50 represents the
total cost, T, and the number of cupcakes. Determine how many
cupcakes each club can order if they both have the same amount of
money to spend. Is the solution viable or not viable?
By solving a linear equation, it can be calculated that
Each club can order 21.1 cupcakes if they both have the same amount of
money to spend
What is a linear equation?
Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is called linear equation
Let the number of cupcakes ordered by each club be c
The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
Total amount spent = $(13 + 3.35c)
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee
Total amount spent = $(22.5 + 2.90c)
By the problem,
The linear equation is
13 + 3.35c = 22.5 + 2.90c
3.35c - 2.90c = 22.5 - 13
0.45c = 9.5
c = 21.1
This solution is not viable as the number of cupcakes must be an integer not a decimal.
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g(x)=∣x+1∣
the corresponding functions
The functions are x+1 and x-1.
What is a function?It is an expression, rule, or law that defines a relationship between the independent variable and the dependent variable.
Given that g(x) = |x+1|
Since the modulus function has only real numbers, the function can be x+1 and x-1.
If g(x) = |-(x+1)| then it is also the same as the function x+1.
Hence, the corresponding functions of |x+1| are x+1 and x-1.
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for a particular clothing store a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. suppose six customers are randomly selected and are mailed $10-off coupons. what is the probability that three of the customers redeem the coupon?
The anticipated quantity of coupons as calculated from the data given is 1.6 .
We learn from the question that
The probability of a $10 voucher being redeemed via mail is p = 0.16.
n = 10 is the sample size.
In general, the projected number of coupons redeemed is represented numerically as
E(x) = np [ of PDF ]
= 10 x 0.16
= 1.6
When data follows a normal distribution, the probability density function (PDF) and cumulative distribution function (CDF) assist us in determining probabilities and ranges of probabilities. The CDF is the PDF integration, from left to right. We may construct many forms of probability estimates from our normally distributed data using these two normal distribution functions.
The standard deviation is a technique for us to explain how "spread out" the data is - how far it "deviates" from the mean value. Both and are known as normal distribution parameters.
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Solve for p.
9p3p-5 19
P = ?
The value of p is p = 3.17.
What is a linear equation in one variable?
The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
The given equation is 9p-3p-5=19.
To solve for p, we need to isolate the p term on one side of the equation. Currently, p is part of the term 9p-3p, which can be simplified to 6p.
We can then rewrite the equation as:
6p = 19
To solve for p, we need to divide both sides by 6:
p = 19/6
= 3.17
Therefore, the value of p is p = 3.17.
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round 475 to the nearest tenth
Answer:
480
Step-by-step explanation:
^
Hard A level Maths question, please help ASAP cheers
The value of the shaded area from the rectangle ACDE is approximately 52.124 square centimeters.
How to determine the value of the shaded area
In this problem we must calculate the shaded area of the section within the rectangle ACDE, this can be found by the subtracting the area of the region ABDE, which is the combination of the areas of the right triangle ABE and the arc BDE, whose formulas are shown below:
Triangle ABE
S = (1 / 2) · AB · AE
Arc BDE
S = (1 / 2) · α · ED²
Where α is the central angle, in radians.
Rectangle ACDE
S = ED · AE
If we know that AE = 20 cm, ED = 28 cm, α = π / 4 and AB = 20 cm, then the area of the shaded area is:
S = (28 cm) · (20 cm) - (1 / 2) · (π / 4) · (28 cm)² - (1 / 2) · (20 cm) · (20 cm)
S ≈ 52.124 cm²
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Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings
Help todays the last day for a good grade so ima ask lots of questions bc its a long one
amelia = 5Raj
80 = 5x
x = 16 mins
Help, i dont understand this!
The function is increasing in the interval -1<x<3 (Letter D).
FunctionA function can be represented by a graph or an equation. When you have a linear function the graphic representation is a straight line. If you have a curve, the graph can be represented by a quadratic function, cubic function, and others.
All functions can be classified as:
increasing - when the values of y increase with the increasing of x-values decreasing - when the values of y decrease with the increasing of x-valuesThe question asks for the interval where the function increases. Thus, from the graph is possible to see that the function increases when x is between –1 and 3 because the values of y increase with the increase of x-values.
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Shania bought a $1,500 drum set on an installment plan. The installment agreement included a
15% down payment and 18 monthly payments of $90.00 each.
a. How much is the down payment?
b. What is the total amount of the monthly payments? [
c. How much will Shania pay for the drum set on the installment plan?
d. What is the finance charge?
The answers to each part of the question are -
down payment amount : $225total monthly payments : $1620Shania on the installment plan will pay : $1845 What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Shania bought a $1,500 drum set on an installment plan. The installment agreement included a 15% down payment and 18 monthly payments of $90.
down payment amount :15% of 1500 = (15/100) x 1500 = $225
total monthly payments :90 x 18 = $1620
Shania on the installment plan will pay :$(1620 + 225) = $1845
Therefore, the answers to each part of the question are -
down payment amount : $225total monthly payments : $1620Shania on the installment plan will pay : $1845To solve more questions on functions, expressions and polynomials, visit the link below -
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Help with question 1
Answer: D
Step-by-step explanation:
Given the tally marks its 16ths, and the point is on the 3rd tally so it would be 10-3/16 Hope this helps!
Find the sum of the first 30 terms of the following series, to the nearest integer.
2,8,14
The solution is 2670
The sum of the arithmetic sequence is given by S = 2670 where the first term is 2 and common difference is 6
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the sum of the arithmetic sequence be = S
Let the number of terms be n = 30
Let the series be A = 2 , 8 , 14 , ..
The first term of the arithmetic sequence a = 2
Let the common difference of the series be d = second term - first term
The common difference d = 8 - 2 = 6
Now ,
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Substituting the values in the equation , we get
S₃₀ = ( 30/2 ) [ 2 x 2 + ( 30 - 1 ) 6 ]
S₃₀ = 15 [ 4 + 29 x 6 ]
S₃₀ = 15 [ 4 + 174 ]
S₃₀ = 15 x 178
S₃₀ = 2670
Therefore , the value of S is 2670
Hence , The sum of the arithmetic sequence is given by S = 2670
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PLEASE HELP ME I TOOK A PICTURE
The inequality to describe the possible side length for the third side is 1 < x ≤ 19.
What is the inequality of a triangle?
According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.
The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
We have given,
Two sides of a triangle have lengths 9 and 10.
The third side is represented by x.
So by triangle inequality, we have the following inequality:
x ≤ 9 + 10
x ≤ 19
Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
10 - 9 < x
1 < x
Hence, the inequality to describe the possible side length for the third side is 1 < x ≤ 19.
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Container A has 1000.75 mL of water and is draining 10.8 mL per minute. Container B has 800.75 mL of water and is draining 5.8 mL per minute. After how many minutes will the two containers have the same amount of water?
After 40min. water in both container A & B will be equal.
Let after 't' min. water in both the containers is same.
Water in Container A is 1000.75 ml & is draining at rate of 10.8ml/ min.
after 't' min. water will be = 1000.75 - 10.8t .......(eq 1)
Water in Container B is 800.75 ml & is draining at rate of 5.8ml/ min.
after 't' min. water will be = 800.75 - 5.8t ........(eq 2)
Now, we know that after 't' min. water in both container A & B is equal, so we can equate equation 1 with equation 2 and find out the value of 't' .
1000.75 - 10.8t = 800.75 - 5.8t
1000.75 - 800.75 = 10.8t - 5.8t
200 = 5t
t = 40 min.
Hence, after 40min. water in both container A & B will be equal.
What is a Container?
Something that can hold or move something is known as a container.
Eg- water, oil etc.
What is meaning of Draining Rate?
A channel or drain for water drainage.
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Coach Burgess drew a right triangle on the board. He said the hypotenuse was 13 inches and one of the legs was 5 inches. What is the length of the other leg? Round to the the tenths place
The length of the other leg is 12 inches.
What is the Pythagorean theorem?
The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The hypotenuse of a right triangle is the side opposite the right angle, and the legs of a right triangle are the two sides that are adjacent to the right angle.
If we know the length of the hypotenuse and one leg of a right triangle, we can use the Pythagorean theorem to find the length of the other leg.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
We can use this theorem to write the equation:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
In this problem, the hypotenuse is 13 inches and one of the legs is 5 inches. We can substitute these values into the equation to find the length of the other leg:
c² = a² + b²
(13)² = a² + (5)²
169 = a²+ 25
144 = a^2
a = 12
Hence, the length of the other leg is 12 inches.
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a doctor claims that people are at most 6 pounds overweight. to test the claim, the doctor randomly selects 81 people and calculates the difference between their ideal weight and actual weight. the sample mean and sample standard deviation of that difference were 7 pounds and 2 pounds respectively. can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by rejecting h0. no, conclude the claim is not true by rejecting h0. no, conclude the claim is not true by accepting h0. yes, conclude the claim is true by accepting h0.
we conclude at the 1% level of significance that the claim is true by accepting H₀
What is Hypothesis?
A hypothesis outlines your expectations for the results of your investigation. It is a speculative, untested response to your research question.
Given,
n = 81
x bar = 7
s= 2
Here, a doctor claims that people are atmost 6 pound over weight
H₀ : μ ≤ 6 versus
H₀ : μ > 6 versus
Now,
The Test Stastistic is
t = x bar - μ / s√n
t = 7-6/2√81
t = 4.5
let ∝ = 0.10, then p value = 0.000
p value >∝
yes, conclude the claim is true by accepting H₀
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Select ALL the correct answers.
Consider the graph given below.
Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above.
1)Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
2)Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2
3)Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
4)Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units
5)Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6
6)Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units
The sequences of transformations that could be applied to the parent function are Reflected over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units i.e. Option (4).
What is transformation?
An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.
Given, the parent function, f(x) = x
From the given graph, the equation will be
y = -2x + 6
Then, the transformation will be
Shifted up 6 units
Vertical stretch by a factor of 2
Reflected over the y-axis
Hence, the required answer is Option 4.
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