Question 4
Solve the equation x² - 4x+6=0 by completing the square.
BIUX² X₂ 15px help!!
Answers
After completing the square, the solution of equation are,
⇒ x = (2 + √2i)
And, x = 2 - √2i
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ x² - 4x + 6 = 0
Completing the square as;
⇒ x² - 4x + 6 = 0
⇒ x² - 4x + 4 + 2 = 0
⇒ (x - 2)² + 2 = 0
⇒ (x - 2)² - (√2i)² = 0
⇒ (x - 2 - √2i) (x - 2 + √2i) = 0
This gives two complex solution as;
⇒ x = (2 + √2i)
And, x = 2 - √2i
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Related Questions
Write the expression as a decimal number 2 x 0.1 + 5 x 0.001 =
Answers
The measure of decimal number is 2 tenths + 5 thousandths is 0.205.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given expression
2 x 0.1 + 5 x 0.001
the expanded form is 2 tenths + 5 thousandths
= 2/10 + 5/1000
multiply and divide by 100 in 2/10
we get 200/1000
now 200/1000 + 5/1000 = 205/1000 = 0.205
Hence value of expression is 0.205.
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Mike went on a bicycle trip. Every 4 days he travels 230 miles.
Create a proportional table comparing miles traveled to days spent traveling.
Answers
Calculating the ratio between each pair of values in a table allows you to determine whether a proportional relationship is present. The table depicts a proportional relationship if all of those ratios are the same.
How should an equation for a proportional table be written?y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to depict proportional relationships.
How should a proportional relationship be written?The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
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help ME PLEASE ASAP DUE NOW
Answers
Step-by-step explanation:
{x : x < 100}
means all numbers smaller than 100. but that includes all negative numbers. so, NO.
{y|y > -0.1}
while this includes all positive numbers, it also includes all numbers between -0.1 and 0. e.g. -0.001
so, NO
{x|x in N}
N is the set of all natural numbers. that is the set of all positive integers.
so, YES
{y : 0 < y < 1}
that is all numbers between 0 and 1. that's are only positive numbers between 0 and 1.
so, YES
{x|x in Z}
Z is the set of all integer numbers (including the negative ones). so, NO
{y : 3 <= y < 22}
ask numbers between 3 and 22, including 3. there are only positive numbers, as there cannot be suddenly a negative number between 2 positive numbers.
so, YES.
Work out
2/3 - 2/5
Give your answer in its simplest form.
Answers
Answer:
4/15
Step-by-step explanation:
find common denominators, which is 15
multiply 2/3 by 5 and and 2/5 by 3
2 x 5 = 10 and
3 x 5 = 15
10/15
2 x 3 = 6 and
5 x 3 = 15
6/15
subtract numerators
10 - 6
15
= 4/15
10 gallons 4 quarts = ____ quarts
Please help
Answers
10•4=40
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
8 jars
10 jars
Answers
Answer:
(c) 8 jars
Step-by-step explanation:
You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.
JarsThe number of jars can be found from ...
(2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars
Lorraine can fill 8 jars from the 2.5 gallon pot.
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Sue ate one sweetie one day, and each afterward she ate one sweetie more than she did the day before. How many sweeties did she eat during her first week?
Answers
on solving the provided question we can say that - by unitary method we have 12 days.
What is unitary method ?
The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Sue ate one sweetie one day,
Sue ate 12 sweetie 12 day,
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Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?
Answers
The average like for each minute of the video that he uploads will be 2,000 likes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The total number of likes is calculated as,
Like / View = 1 / 5
Like / 9,000,000 = 1 / 5
Like = 1,800,000
The total number of minutes is calculated as,
Time length = (9,000,000 / 150,000) x 15
Time length = 60 x 15
Time length = 900 minutes
The average like for each minute of the video that he uploads will be given as,
⇒ 1,800,000 / 900
⇒ 2,000
The average like for each minute of the video that he uploads will be 2,000 likes.
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The complete question is given below.
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1: 5. Dagogo wants to reach a total of 9,000,000 views on his channel.
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of the video he uploads?
how many times does 6 go into 137
Answers
Answer: 22 times
Step-by-step explanation: divide 137 by 6
137 divided by 6
Please help me with this question
Answers
Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.
Trigonometry is what?The study of relationships among triangle angles and angles is known as trigonometry. Mathematical modeling is a fundamental idea in all of geometry because it can be used to reduce any straight-sided form to a collection of triangles. Amazingly complex connections exist between trigonometry and other areas of mathematics, particularly mathematics, real or complicated, infinite series, logarithms, and infinite series.
Here,
Given : Cosx = 9/26 (First quadrant)
To find : Cos2x
We use the formula:
=>Cos2x = 2Cos²x -1
=> Cos2x = 2(9/26)² - 1
=> Cos 2x = -0.760355
Therefore , the solution of the given problem of trigonometry comes out to be Cos 2x = -0.760355.
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Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
Answers
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.
The assumption is equivalent to the following two statements:
(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]
(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]
Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].
Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.
Lori works in a restaurant. She earns $7/hr plus tips. If Lori works 4 hours on a Tuesday, has $300 of food sales,
What is her base salary?
What is her Tips (18% of Food-sales) ?
What is her Total earnings?
Answers
Answer: Her total earnings would be $28+$54=$82.
Step-by-step explanation:
Lori's base salary is calculated by multiplying her hourly rate by the number of hours she works. If Lori works 4 hours on a Tuesday and earns $7/hr, her base salary would be 4*$7=$28.
Lori's tips are calculated as 18% of her food sales. If Lori has $300 of food sales on a Tuesday, her tips would be 18%*$300=$54.
Lori's total earnings for the day would be the sum of her base salary and her tips. In this case, her total earnings would be $28+$54=$82.
if (x+A)^2 -3 = x^2 + 4x + B. Find the value of A and B
Answers
The values of A and B are 2 and 4 respectively.
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 the equation as -
(x + A)² - 3 = x² + 4x + B
We can write the given equation as -
(x + A)² - 3 = x² + 4x + B
x² + A² + 2Ax = x² + 4x + B
A² + 2Ax = 4x + B
A² + 2Ax = B + 4x
Equating both sides, we get -
A² = B
and
2A = 4
A = 2
Then B will be equivalent to 4.
B = 4
Therefore, the values of A and B are 2 and 4 respectively.
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if a borrowed car averges 38 miles per gallon how many miles can u travel with 12 gallons of gas
Answers
n% of 28 is 14 `percentage`
Answers
Answer:
The Percentage is 50% because 14 is the half of 28.
Assume that AGHIE ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZL 21
B. IG LM
C. THNM
D. ZN 21
E. GH = LM
F. ZME ZH
Answers
On solving the provided questions, we can say that the congruence of ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F
What is congruence?A figure that can be put exactly on another is said to be "matching." When the bread is piled, it is the same size and shape. The term "match" describes things that are precisely the same shape and size. A pair of geometric figures is said to be congruent or to be in a congruent relationship if one of them can be reliably superimposed over the other.
B D and F.
B because they would go together if the statement were put in that particular sequence. ABC=DEF, where A=D, B=E, and C=F.D because they are equal in length. F due to the same cause as B.
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-POINTS-
(4IZ0 Don’t even try.)
Answers
Answer:
Step-by-step explanation:
axf
A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.
Answers
Answer:
No
Step-by-step explanation:
The ratio used should have been 6 parts yellow paint to 2 parts blue paint
hope this helps
In the construction of bridges, engineers use a formula to help
determine the allowable stress on a bridge rocker, a component of the
bridge that handles the stress and weight placed on the pavement of the
bridge. The engineers use the formula F =11/300d (F − 13), where F is the
strength of the steel in kilopound per square inch and d is the diameter
of the rocker in millimeters.
Solve the formula F =11/300d (F − 13) for d.
Answers
From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))
How to change the subject of the formula?
We are given the engineers formula as;
F = (¹¹/₃₀₀)d(F - 13)
Where;
F is the strength of the steel in kilopound per square inch.
d is the diameter of the rocker in millimeters.
From the given formula, we can start by;
Multiply both sides by 300 to get;
300F = 11d(F - 13)
Divide both sides by 11(F - 13) to get;
d = 300F/(11(F - 13))
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the ratio of the length to the breadth of a room is 5:3 what is the length of the room if the breadth is 6m
Answers
According to the solving If the room's width is 6 meter's, then its length must be 10 meter's.
What is length?Distance is measured by length. The quantity of length has the dimension of distance there in International System of Quantities. Most measurement systems choose a base unit for length from which all subsequent units are derived. The metre serves as the fundamental unit of length in the International System of Units.
How do you determine length?If you have an area A and a width w, you can calculate the length w by using the formula h = A/w. Its length can indeed be calculated using the formula h = P/2w if you know its perimeter (P) and width (W). If you have the width w and the diagonal
According to the give information:
Let length be x By Given Condition
5/3=x/6
x=5/3*6
x=30/3=10
Therefore length of room is 10.
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Nathan and Lucy are selling blueberry and apple pies for a fundraiser. Nathan sold and 13 apple pies for a total of $147. Lucy sold 7 blueberry pies and 11 apple $204. What is the cost of one blueberry pie and one blackberry pie?
Answers
The cost of one blueberry pie and one blackberry pie is $11.30 and $11.373 respectively.
What are mathematical operators?In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:
Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.
Given Nathan sold 13 apples pies for $147,
cost of 13 apple pies = $147
cost of 1 apple pie = 147/13 = $11.30
Lucy sold 7 blueberry pies and 11 apple pie $204.
7 blueberry + 11 apple pie = $204
cost of 11 apple pie = $124.384
cost of 7 blueberry = 204 - 124.384 = $79.615
cost of 1 blue berry = 79.615/7 = $11.373
Hence the cost of 1 apple pie is $11.30 and 1 blueberry is $11.373.
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7X -6Y=-3 what is the slope of the parallel and perpendicular line
Answers
Answer:
parallel: 7/6perpendicular: -6/7Step-by-step explanation:
You want the slopes of the lines parallel and perpendicular to 7x -6y = -3.
SlopeThe slope is the x-coefficient when the equation is in slope-intercept form:
y = mx +b
Solving for y gives ...
-6y = -7x -3
y = 7/6x +1/2 . . . . . divide by -6
The slope of the given line is 7/6.
ParallelA parallel line will have the same slope: 7/6.
PerpendicularA perpendicular line will have opposite reciprocal slope: -6/7.
1) The Cuyahoga River is 306 miles long, but boats can only travel on 134
miles of the total length. Write the ratio of the Cuyahoga's navigable length
to its total length as a fraction in simplest form.
Answers
Answer:
67/153
Step-by-step explanation:
find bce PLEASE AND THANKS
Answers
The unknown angle of the triangle is as follows:
∠BCE = 65 degrees
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, the angle ∠BCE can be found as follows:
∠BAC = 70 degrees
∠ABC = 60 degrees
∠ACB = 180 - 70 - 60
∠ACB = 180 - 130
∠ACB = 50 degrees
Hence, using exterior angle theorem,
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
∠BCD = 60 + 70 = 130 degrees
Hence,
∠BCE = 130 / 2 = 65 degrees
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THIS ONE TOO PLEASE
Answers
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The line going through the origin equation is also y=2x.
A line that crosses the origin is symbolized by the equation y=mx.
Also, y=2x satisfies the point (0,0)
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
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The crew on a fishing boat caught four fish that weighed a total of 1,032 pounds. The tarpon weighed twice as much as the amberjack and the white marlin weighed twice as much as the tarpon. The weight of the tuna was 5 times the weight of the amberjack.
Answers
Using equations, the weights of the four fish are as follows:
Amberjack = 86 poundsTarpon = 172 poundsWhite Marlin = 344 poundsTuna = 430 pounds.What are equations?Equations are mathematical statements showing the equality of two mathematical expressions.
Using the equation sign (=), equations depict that expressions are equal or equivalent.
The total weight of the four fish = 1,032
Let the weight of the Amberjack = x
Weight of the Tarpon = 2x
Weight of the White Marlin = 4x (2 x 2x)
Weight of the Tuna = 5x
x + 2x + 4x + 5x = 1,032
12x = 1,032
x = 86
Weights:Amberjack = 86 pounds (x)
Tarpon = 172 pounds (2x)
White Marlin = 344 pounds (4x)
Tuna = 430 pounds (5x)
Total weight = 1,032 pounds (86 + 172 + 344 + 430)
Thus, we solved the weight of each fish using equations.
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Question Completion:How much did each fish weigh?
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Answers
Step-by-step explanation:
hope this is right hehe.....
The midpoint M of the line segment AB is (1,3). If the coordinate of B is (-5,7), what is the coordinate of the point A
Answers
Answer:
( 7,-1 )
Step-by-step explanation:
Simplify x+2+3x++5+x+3+2x
Answers
Answer: 7x+10
Step-by-step explanation:
combine like terms
x+3x+x+2x+2+5+3
7x+10
Answer:
Step-by-step explanation:
Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
First: find the (x) and collect them, put them in the bracket (to ensure the + or -)
(x + 3x + x + 2x) + 2 + 5 + 3
= 7x + 2 + 5 + 3
Then we add up the numbers
= 7x + 10
This is the end result.
x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
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A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
Answers
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
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