The value of a and b in the given complex expression is 1/10 and -1/10 respectively.
This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.
(2i/2+i) - 3i/(3+i) = a + bi
{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi
6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi
(-2 + 3) / (6 + 5i - 1) = s+bi
1 / (5 + 5i) = a+bi
Now we multiply top and bottom by 5 - 5i :
5 - 5i / (5 + 5i)(5 - 5i) = a+bi
5 - 5i / 25 -25i² = a+bi
5 - 5i / 50 = a+bi
1/10 - 1/10i = a+bi
On comparing the real and imaginary part on the both sides:
a= 1/10 , b= -1/10.
To know more about the complex numbers, refer:
https://brainly.com/question/20566728?referrer=searchResults
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 8.5 centimeters and is 6 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(8.5)2(6)
V = (3.14)(6)2(8.5)
V = (3.14)(4.25)2(6)
V = (3.14)(6)2(4.25)
Answer:
V = (3.14)(4.25)²(6)
Step-by-step explanation:
Pablo used a total of 5 3/4 gallons of gas while driving his car. Each hour he was driving, he used 5/6 gallons of gas. What was the total number of hours he was driving? Write your ans
A 25-foot tree casts a 10-foot shadow. At the same time, a nearby cell tower casts a 30 -foot shadow. How tall (in feet) is the cell tower?
Plot axis of symmetry H(x) = -(x+2)2 + 8
The x-coordinate of the vertex is given by h = -2 and the equation of the axis of symmetry is x = -2.
Given function is H(x) = -(x + 2)² + 8.
The axis of symmetry of a quadratic function y = ax² + bx + c is defined by x = -b/2a.
So, let's solve the problem as follows:
To find the axis of symmetry, we need to convert the given function into standard form y = a(x - h)² + k.
We can do this by completing the square.
For that, we have
H(x) = -(x + 2)² + 8H(x)
= -1(x² + 4x + 4) + 8H(x)
= -1(x + 2)² + 8
The standard form is y = a(x - h)² + k, so the given function is y = -1(x + 2)² + 8.
The vertex form of a quadratic equation is y = a(x - h)² + k
Where(h, k) is the vertex.
The vertex form of the given function H(x) = -(x + 2)² + 8 can be calculated as follows:
y = a(x - h)² + k
The vertex form is y = a(x - h)² + k.
Where the vertex form of the given function is:
y = -1(x + 2)² + 8.
Since the vertex form is y = a(x - h)² + k the vertex form of the given function is y = a(x + 2)² + 8 and (h, k) = (-2, 8).
Vertex is given by h = -2.
Axis of symmetry is x = -2.
For more related questions on symmetry:
https://brainly.com/question/1597409
#SPJ8
Select the correct answer from each drop-down menu.
Given: Line segment WU is the perpendicular bisector of line TV.
Prove: Line TU ≠ Line VU
WU is the perpendicular bisector of TV and W is the midpoint of TV.
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.
Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.
Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.
All right angles are congruent.
Reflexive property of congruence: Any segment or angle is congruent to itself.
Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.
Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.
Therefore, the correct statements and reasons are:
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector.
Definition of midpoint.
Given.
All right angles are congruent.
Reflexive property of congruence.
CPCTC.
CPCTC.
Learn more about triangle here:
https://brainly.com/question/17335144
#SPJ8
what is the result of converting 2.3 miles into yards ? remenber that 1 mile=1760 yards.
4048 yards is the answer
Step-by-step explanation:
2.3 × 1760
Suppose a random sample of size 44 is selected from a population with =8 . Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
the size is n=500
the size is 5,000
the size is 50,000
Case 1: SE = s / √500
Case 2: SE = s / √5,000
Case 3: SE = s / √50,000
To find the standard error of the mean in each of the given cases, we can use the formula:
Standard Error (SE) = population standard deviation / square root of sample size
However, since the population standard deviation is not provided, we'll need to use an estimated value. We'll assume the population standard deviation is unknown and use the sample standard deviation as an estimate.
Given that the sample size is 44 and the population mean (μ) is 8, we'll calculate the standard deviation for each case:
Case 1: Sample size (n) = 500
The sample size (500) is larger than 5% of the population (44), so we can assume it's a large enough sample. In this case, we'll use the standard formula for the standard error of the mean without the finite population correction factor:
SE = sample standard deviation / square root of sample size
= s / √n
Case 2: Sample size (n) = 5,000
Similar to Case 1, the sample size (5,000) is larger than 5% of the population (44), so we'll use the standard formula without the finite population correction factor:
SE = s / √n
Case 3: Sample size (n) = 50,000
In this case, the sample size (50,000) is much larger than the population size (44), which means we have a large enough sample. Therefore, we'll also use the standard formula without the finite population correction factor:
SE = s / √n
for such more question on standard error
https://brainly.com/question/30404883
#SPJ8
What is the volume of the triangular prism?
3 in.
15 in.
13 in.
a. Find the open intervals on which the function is increasing and those on which it is decreasing.
b. Identify the function's local extreme values, if any, saying where they occur.
a. The open interval on which the function is increasing is [-2/3, 0].
The open intervals on which the function is decreasing are [-∞, -2/3] and [0, -∞].
b. The function's has a local maximum at (0, 0) and a local minimum at (-2/3, -4/27).
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the following open intervals:
increasing = [-2/3, 0].
decreasing = [-∞, -2/3] and [0, -∞].
Part b.
The local minimum of a graph is the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (-2/3, -4/27);
h(x) = -x³ - x²
h'(x) = -3x² - 2x
0 = -3x² - 2x
3x² = -2x
3x = -2
x = -2/3
h(-2/3) = -(-2/3)³ - (-2/3)²
h(-2/3) = -4/27.
For the local maximum, we have:
(0, 0)
Read more on function here: brainly.com/question/9795474
#SPJ1
Mathematical Literacy/Term 2 Assignment 6 NSC Grade 12 RTB/MAY 2023 QUESTION 4 Ms Lerato bakes rusks and sells them in 500 g packs, at R55,00 per pack. Table 3 shows the main ingredients of the rusks. TABLE 3: MAIN INGREDIENTS TO BAKE 800 g OF RUSKS 2 500 g Self-raising flour 10 cups Bran flour 200 g Raisins 1 000 g Butter Use the information above to answer the questions that follow. 4.1 Convert the mass of the self-raising flour to kg. 4.2 Determine the number of cups of bran flour needed to bake 400 g of rusks. 4.3 Write, in simplified form, the ratio of raisins to butter. 4.4 The rusks were placed in the oven to bake at 14:40. Write down, in words, the time the rusks were placed in the oven. (2) (2) (2) (2) [8]
[tex]{\huge{\blue{\tt{Step\:by\:step\:solution}}}}[/tex]
4.1 To convert the mass of the self-raising flour to kg, we can divide the mass by 1000, since there are 1000 grams in a kilogram:
2 500 g ÷ 1000 = 2.5 kg
So the mass of the self-raising flour is 2.5 kg.
4.2 To determine the number of cups of bran flour needed to bake 400 g of rusks, we can use a proportion:
800 g of rusks requires 10 cups of bran flour
400 g of rusks requires x cups of bran flour
We can set up the proportion as:
800 g ÷ 10 cups = 400 g ÷ x cups
Cross-multiplying, we get:
800 g x cups = 10 cups x 400 g
Simplifying, we get:
x = 5 cups
So 5 cups of bran flour are needed to bake 400 g of rusks.
4.3 To write the ratio of raisins to butter in simplified form, we can divide both quantities by their greatest common factor. The greatest common factor of 200 g and 1 000 g is 200 g, so we can divide both by 200 g:
200 g ÷ 200 g = 1
1 000 g ÷ 200 g = 5
So the simplified ratio of raisins to butter is 1:5.
4.4 The rusks were placed in the oven to bake at 14:40. In words, this time is "twenty to three in the afternoon" (assuming that the time is given in a 12-hour clock format).
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Mr. Marshal spent his salary of $8 400 in the following manner: Rental .....1/5 Food.......1/10 Bank ......1/4 Miscellaneous ......... the remainder. what fraction of the money was spent on miscellaneous. how much did he spend on rental. if marshal spent 4/9 of miscellaneous on a trip what fraction of his entire salary was spent on the trip ?
Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.
To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.
Rental: 1/5
Food: 1/10
Bank: 1/4
To find the fraction spent on miscellaneous:
Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)
Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40
Fraction spent on miscellaneous = 1 - 17/40 = 23/40
So, Mr. Marshal spent 23/40 of his salary on miscellaneous.
To find the amount spent on rental, we multiply the fraction spent on rental by his salary:
Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680
Therefore, Mr. Marshal spent $1,680 on rental.
If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.
Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90
For similar question on fraction.
https://brainly.com/question/30154928
#SPJ8
Which graph shows a dilation? On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).
Find the linear function
The linear function for this case is:
f(x) = 5,000*x + 7,000
How to find the linear function?The general linear function is written as:
f(x) = a*x + b
Where a is the slope and b is the y-intercept.
Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:
f(x)= a*x + 7,000
Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:
f(x) = 5,000*x + 7,000
Learn more about linear functions at:
https://brainly.com/question/15602982
#SPJ1
PLSSSS HELPPP I WILL FIVE BRAINLY!!!!
Answer:
The first box : -4 the second one : 6
Step-by-step explanation:
subtract 7 from 3 for the first box, then add 10 to -4 for the second one.
A ____ is just another way of saying what we want to count by on our graph.
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
answer a) and b) please
a : 10<x<=20
b: 20<x<=30
I only need help with the f(0)= the equation is above all the rest is filled in thank you
f(0) = -3
I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.
However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.
Hope this helps.
write y+4=-2(x-1) in slope intercept form
Answer:
y=2x-6
Step-by-step explanation:
y+4=-2(x-1)
Since the slope intercept form is in the form of:
y=mx+c
Making above equation in this form.
y+4=-2(x-1)
opening bracket
y+4=2x-2
subtracting both side by 4.
y+4-4=2x-2-4
y=2x-6
This equation is the slope intercept form.
In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?
-b± √b²-4ac
2a
Quadratic formula: x =
O x= -2±√19
3
Ox=-
2+2√19
3
0 x= 2+√15
3
0 x = 2+2√/19
3
Answer:
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula:x = (-b ± √(b² - 4ac)) / (2a)In this case, a = -3, b = -4, and c = 5. Plugging these values into the formula, we get:x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))Simplifying further:x = (4 ± √(16 + 60)) / (-6) x = (4 ± √76) / (-6) x = (4 ± 2√19) / (-6)We can simplify the expression further:x = -2/3 ± (√19 / 3)Therefore, the solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are:x = (-2 ± √19) / 3The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))
= (4 ± √(16 + 60)) / (-6)
= (4 ± √76) / (-6)
= (4 ± 2√19) / (-6)
= -2/3 ± (1/3)√19
Therefore, the solutions to the quadratic equation are:
x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19
In simplest radical form, the solutions are:
x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
These expressions cannot be further simplified since the square root of 19 is not a perfect square.
Know more about quadratic equation here:
https://brainly.com/question/30164833
#SPJ8
Research has shown that approximately 1 woman in 500 Carrie’s a mutation of particular gene. About 48% of women with this mutation develop colon cancer find the probability that a randomly selected woman will carry the mutation of this gene and will develop colon cancer
If Jackson deposits $110 at the end of each month in a savings account earning interest at a rate of 3%/year compounded monthly, how much will he have on deposit in his savings account at the end of 3 years, assuming he makes no withdrawals during that period? (Round your answer to the nearest cent.)
Answer:
The formula for calculating the future value (VF) of a periodic sum of money is:
VF = P * [(1 + r) n - 1] / r
where:
VF is the future value (the total amount in the savings account)
P is the periodic amount (monthly deposit)
r is the periodic interest rate (annual interest rate divided by the number of periods in the year)
n is the total number of periods (months)
In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).
Using these values in the formula, we can calculate the future value (VF):
VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025
Now let’s calculate this:
VF = 110 * [(1.0025) 36 - 1] / 0.0025
110 * (1.0965726572 - 1) / 0.0025
110 * 0.0965726572 / 0.0025
So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.
Step-by-step explanation:
The Hernandez family orders 3 large pizzas. They cut the pizzas so that each pizza has the same number of slices, giving them a total of 24 slices.
The Wilson family also orders several large pizzas from the same pizza restaurant. They also cut the pizzas so that all their pizzas have the same number of slices. For the Wilson family, the equation y = 10x represents the relationship, where x represents the number of pizzas and y represents the number of total slices.
Which statements best describe the pizzas bought by the Hernandez and Wilson families? Select two options.
please help!! need it fast, will give brainliest!! and pls show work !!
Find the measure of angle AEB
Answer:
An acute angle
Step-by-step explanation:
An acute angle is smaller than an obtuse ad right angle.
hope this helps and hope it was right 'cause I really don't know what you meant. :)
Find the area of
the parallelogram.
8
11
7
Use the
formula:
a = bh
area = base x height.
b = 11
h = 7
a = [?]
Answer:
77 units^2
Step-by-step explanation:
Since the formula for the area of a parallelogram is Area = Base x Height, you can multiply the Base (11) by the Height (7)
So, A = (7) x (11) = 77 units^2
The 8 in this case is not necessary. You only need the base and height. Hope this helps!
Choose the expression that is equivalent to fraction with 3 raised to the negative tenth power in the numerator and 3 raised to the fourth power times 3 raised to the zero power in the denominator.
Answer:
[tex]3^{-14}[/tex] or [tex]\displaystyle \frac{1}{3^{14}}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3^{-10}}{3^4*3^0}=\frac{3^{-10}}{3^4}=3^{-10-4}=3^{-14}[/tex]
Which set of numbers are integers but not whole numbers or natural numbers?
Step-by-step explanation:
C
A study was completed in Georgia. In northern Georgia, the study involved 3,000 patients; 84% of them experienced flulike symptoms during the month of December. The study had a margin of error of 1.7% What does that mean for the study?
Factorise the formula y = 4x² + 16x +15 in the form y = (2x +...)(2x + ...). help
Answer:
y = (2x + 5)(2x + 3)
Step-by-step explanation:
y = 4x² + 16x + 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 15 = 60 and sum = + 16
the factors are + 10 and + 6
use these factors to split the x- term
y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )
y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term
y = (2x + 5)(2x + 3)
since multiplication is commutative , then could be
y = (2x + 3)(2x + 5)
14Y - 7y = 35. solve for y
Answer:
y = 5
Step-by-step explanation:
[tex]14y-7y=35\\7y=35\\y=5[/tex]
14 minus 7 is 7
7Y is equal to 35
divide both sides by 7 is equal to 5
