Answer:
[tex]\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i[/tex]
Step-by-step explanation:
[tex]\frac{3-2i}{1+4i}[/tex] <-- Given
[tex]\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i}[/tex] <-- Multiply by the conjugate of the denominator as a factor of 1
[tex]\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}[/tex]
[tex]\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)}[/tex] <-- Use the Distributive Property and FOIL
[tex]\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}[/tex]
[tex]\frac{3-10i-8i^2}{1-16i^2}[/tex]
[tex]\frac{3-10i-8(-1)}{1-16(-1)}[/tex] <-- Rewrite [tex]i^2[/tex] as [tex]-1[/tex]
[tex]\frac{3-10i+8}{1+16}[/tex]
[tex]\frac{11-10i}{17}[/tex]
[tex]\frac{11}{17}-\frac{10}{17}i[/tex] <-- Rewrite in [tex]a\pm bi[/tex] form
Solve the system of equations below using the elimination method.
Show how you determined your solution.
4x+y=23
3x-y=12
Answer:
The solution is (5, 3)
Step-by-step explanation:
To solve this system of linear equations, let's use elimination by addition and subtraction. This approach is particularly easy because one equation already has +y and the other -y, summing up to zero:
4x+y=23
3x-y=12
---------------
7x = 35
Then x must be 5.
Substituting 5 for x in the first equation, we get
4(5) + y = 23. Then 20 + y = 23, or y = 3.
The solution is (5, 3)
I need help with this question. Whoever helps me I will mark branliest! <3
Answer: A, B, C
Step-by-step explanation:
AC is half of AB, so AB = 2AC
1/2 of AB will be AC, and AB
AC = CB
Solve for y.
pls help
Answer:
y= -6
Step-by-step explanation:
Is this triangle similar? Why?
Answer:
IT'S NOT THE SAME BECAUSE THIS TWO TRIANGLE HAS DIFFERENT MEASUREMENT
4(3p+2)-5(6p-1)=2(p-8)-6(7p-4)
100 points my guys
what is the defenition ofmean , medium and mode
Which?
A
B
C
D
Help me for 20 points!!!
Determine the general rule for the sequence 19;11;3;.....
Answer:
Answer 3.0/528 claudiasai 88-2n + 2927,25,23,21,19- 2 difference- 2n + 29-2 x (1 ) + 29 =27-2 x (3) +29 =23
Step-by-step explanation:
Write a recursive formula for each sequence. 3. 1, 6, 11, 16, ... SOLUTION: ... Check for a common ratio by dividing each term by the term that precedes it. = 3 ;. = 3 ; ... 19. 100, 80, 64, 51.2, ... SOLUTION: Subtract each term from the term that follows it. ... Patrick thinks that the sequence can be written as a recursive formula.
Answer:
[tex]a_{n}[/tex] = 27 - 8n
Step-by-step explanation:
There is a common difference between consecutive terms, that is
11 - 19 = 3 - 11 = - 8
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 19 and d = - 8 , then
[tex]a_{n}[/tex] = 19 - 8(n - 1) = 19 - 8n + 8 = 27 - 8n ← general rule
James goes to a meeting that lasts 1 hour and 50 minutes. The clock shows the time the meeting ends. What time did the meeting begin？
The required time, when the meeting begins is given as 11:55 minutes.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
When the meeting end the time was 1:45,
Meeting last for 1 hour and 50 minutes.
Now,
1 hour and 50 minutes. = 01 : 50 minutes
Required time = 12 : 00 + 1:45 - 01:50
= 12 :00 - 00:05
= 11 : 55 minutes
Thus, the time when the meeting begins is given as 11:55 minutes.
Learn more about simplification here:
https://brainly.com/question/12501526
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Find the mean absolute deviation of the following numbers. 10, 8, 5, 12, 20
11.) Evaluate the expression.
Answer:
- 116
Step-by-step explanation:
Given
28 - ( [tex]\sqrt{144}[/tex] )²
= 28 - (12)²
= 28 - 144
= - 116
Simplify using suitable property. Also name the property used:-3/5 x 4/7 + 8/5x 4/7
Answer:
The answer is 4/7 and the property used is the distributive property
Step-by-step explanation:
Recall from the distributive property;
a * (b + c) = ab + ac
Applying same here, we have it that;
4/7 (-3/5 + 8/5)
= 4/7 * ((-3 + 8)/5)
= 4/7 * 5/5
= 4/7 * 1 = 4/7
Nancy made a scatter plot of how much money she had left at the end of each day her vacation which table represents the data in her scatter plot
Answer:
d
Step-by-step explanation:
The blueprint for the pelham's living room has a width of 12 inches using the scale of 2 inches = 7 feet.
The family wants to use a scale of 1 inch = 6 feet. What is the width of the living room on the new blueprint?
Answer:
The new blueprint's width will be 7 inches.
Explaination:
Find the width of the actual roomCreate a proportion: 2in:7ft
Divide 12 by 2 and multiply by 7 to find the real width: 6•7=42
Find new widthDivide actual width by 6 and multiply by 1 to find the new scale: (42/6) •1 = 7
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to construct a 98% confidence interval for the true mean amount of cheese filling is ________. Group of answer choices 2.797 2.492 2.064 3.467 3.745
Answer:
The correct value is t* = 2.492.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.492, which is the answer to this question.
Can someone solve this and show it step by step
−5x + 2[x − (4 + 2x)] ≥ 5 − 2(x − 1)
Step-by-step explanation:
-5x + 2(x -4 -2x) > 5 - 2x -2
-5x + 2x -8 -4x > 3 - 2x
-7x -8 > 3 - 2x
-5x > 11
x < 11:-5
x < -2.2
Answer:
x ≤ 3
Step-by-step explanation:
A rhombus is not a A polygon B. Parallelogram C. Trapezoid
Answer:
Hi, there your answer is polygon
A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. A rhombus has 4 sides.
Hope this helps:) Have a great day!
Step-by-step explanation:
in the given parallelogram ABCD, find the value of x and y
Answer:
see explanation
Step-by-step explanation:
(a)
The consecutive angles are supplementary, sum to 180° , then
3y + 2y - 5 = 180
5y - 5 = 180 ( add 5 to both sides )
5y = 185 ( divide both sides by 5 )
y = 37
Then ∠ A = 3y = 3 × 37 = 111
The opposite angles are congruent , then
3x + 3 = 111 ( subtract 3 from both sides )
3x = 108 ( divide both sides by 3 )
x = 36
---------------------------------------------------------------------
(b)
The diagonals bisect each other , so
x + 8 = 16 - x ( add x to both sides )
2x + 8 = 16 ( subtract 8 from both sides )
2x = 8 ( divide both sides by 2 )
x = 4
and
5y + 4 = 2y + 13 ( subtract 2y from both sides )
3y + 4 = 13 ( subtract 4 from both sides )
3y = 9 ( divide both sides by 3 )
y = 3
whats the value of x? 8(-6 + 6x) = 240
Answer:
x = 6
Step-by-step explanation:
8(-6 + 6x) = 240
Distribute the 8
-48 + 48x = 240
Add 48 to both sides
48x = 288
Divide both sides by 48
x = 6
Which of the following is the definition of the sine ratio in a right triangle
Answer:
Oppositeleg
adjacenleg
Answer:
option 1
Step-by-step explanation:
Just remember this to get the trigonometric ratio in a right triangle :
Old Henry And His Old Aunt
O for opposite
H for hypotenuse
A for Adjacent
Sin = O/ H
Cos = A /H
Tan = O /A
A circle P is circumscribed about a regular hexagon ABCDEF
Arc AB =
Select one:
a. 60
b. 120
c. not enough information
d. 90
Answer:
angle degrees is 60
so the answer would be A
Step-by-step explanation:
because there are 6 sides, 360 is divided by 6.
What is the minimum value of the objective function, C with given constraints? C=5x+3y {⎨x+3y≤9 {5x+2y≤20 {x≥1 {y≥2
Answer:
The answer is below
Step-by-step explanation:
Plotting the following constraints using the online geogebra graphing tool:
x + 3y ≤ 9 (1)
5x + 2y ≤ 20 (2)
x≥1 and y≥2 (3)
From the graph plot, the solution to the constraint is A(1, 2), B(1, 2.67) and C(3, 2).
We need to minimize the objective function C = 5x + 3y. Therefore:
At point A(1, 2): C = 5(1) + 3(2) = 11
At point B(1, 2.67): C = 5(1) + 3(2.67) = 13
At point C(3, 2): C = 5(3) + 3(2) = 21
Therefore the minimum value of the objective function C = 5x + 3y is at point A(1, 2) which gives a minimum value of 11.
NEED HELP! Will give brainiest!! And thanks if you even answer one of them
Answer:
In the questions you are asked to evaluate by substituting the variables to the given number.
PLZ EXCUSE MY HANDWRITING.
PLEASE HELP. !!!!!!!
A person places $81200 in an investment account earning an annual rate of 3.6%, compounded continuously. Using the formula V = Pert, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
Answer:
V=129659.9491≈129659.95
Step-by-step explanation:
CORRECTLY ANSWER PLEASE AND THANK YOU
9514 1404 393
Answer:
(-3, 4)
Step-by-step explanation:
The midpoints of the diagonals of a parallelogram are coincident. This means the sums of coordinates at the ends of the diagonals are the same. For missing point P, we must have ...
P +(0, -3) = (-6, -6) +(3, 7)
P = (-6, -6) +(3, 7) -(0, -3)
P = (-6 +3 -0, -6 +7 -(-3))
P = (-3, 4)
Which of the following is not a disadvantage to cash advances on a credit card?
a.
Cash advances are similar to loans in that they need to be paid back with interest.
b.
Cash advances require a lot of paperwork and are generally difficult to get.
c.
Cash advances are often the last thing to be paid when paying off your credit card.
d.
Cash advances often come with an interest rate much higher than your credit card.
(its not a)
Answer:
B
Step-by-step explanation:
it is b because I got it right on Edu and it was on quiz let
which of the following is the slope of a line perpendicular to the line y = -2/3 x +5
Answer:
-2/3x is the slope
Step-by-step explanation:
y=mx+b is the equation to follow
Help,anyone can help me do quetion.
Answer:
C2- 65° C3- 84°
Step-by-step explanation:
for C2:
the 2 parallel lines and the one cutting fully through form a transversal.
One of the rules for this is that co-interior angles (the 2 on the same side of the intersecting line) add to 180°.
This means that the angle at the top left (still within the triangle) should be 50° (180-121).
The other angle within the triangle (not the x one) is vertically opposite (opposite or "diagonal") with the 65°.
Vertically opposite angles have the same value, meaning the second angle is 65°.
In a triangle, the 3 angles add to 180. In this case, 50+65+x=180, which can be simplified to 115+x=180. Subtracting 115 from both sides gives x=65°.
For C3-
Imagine a parallel line is going through the angle x, splitting it into 2 angles (let's call them a and b).
With a being the top half, you can use the 133° given to help you. Like before, vertically opposite angles are the same, so the value "diagonal" to 133° should also be 133°. Using the co-interior rule, a should be 180-133, which gives 47°.
For b, we can skip this first step entirely. Since 143 and b are co-interior, 180-143=b, therefore b=37°.
To use these, remember a+b=x, which by subbing in the values gives 47+37=x, simplified to x=84°.
** I suggest revising the types of transversal relationships (corresponding, alternate, vertically opposite and co-interior). It's difficult explaining this without diagrams, but if you need more clarification, I'm happy to help!
PLEASE I REALLY NEED HELP
Plans for a new school call for classrooms directly across the hall from each other to be congruent. This computer printout shows a math classroom. If the vertices of a science classroom are located at (-3x¹,y¹). (-3x²,y²), (-3x³, y³), and (-3x⁴, y⁴), will the science classroom be congruent to the math classroom?
The lengths of the horizontal sides of the science class is larger than the
length of the horizontal side of the math class.
The correct option is; No, the the transformation applied was not a rigid motion.
Reasons:
The given vertices of the science classroom are;
(-3·x₁, y₁), (-3·x₂, y₂), (-3·x₃, y₃), and (-3·x₄, y₄)
The coordinates of the vertices math classroom are;
(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄)
Whereby x₁ = x₄, we have;
Length of the vertical side of the rectangular math class = y₁ - y₄
Length of the horizontal side, [tex]L_M[/tex] = x₂ - x₁
Similarly;
The length of the horizontal side of the science class is, [tex]L_S[/tex] = -3·x₂ - (-3·x₁)
Therefore;
[tex]L_S[/tex] = 3·(x₁ - x₂) = [tex]\mathbf{3 \cdot L_M}[/tex]
The length of a side of the science is three times the length of the side of
the math class, which gives that the dimensions of the science class are not
the same as the the dimensions of the math class.
Therefore;
The science class and the math class are not congruent
The the correct option is, no the transformation that gives the science class from the math class is not a rigid transformation.Learn more about non-rigid transformation here:
https://brainly.com/question/2396426
