Solve the quadratic equation by completing the square
x^2-6x-4=0
Answers
The quadratic equation x² - 6 · x - 4 = 0 has two roots: 3 + √13, 3 - √13
How to solve a quadratic equation by completing the square
In this problem we find a quadratic equation, that is, polynomial of second order of the following form:
a · x² + b · x + c = 0
Where a, b, c are the coefficients of the quadratic equation.
The roots of the quadratic equation can be found analytically by means of completing the square, that is, modifying a part of the polynomial by using the case of perfect square trinomial.
First, write the polynomial:
x² - 6 · x - 4 = 0
Second, use algebra properties until a perfect square trinomial is found:
x² - 6 · x + 9 = 13
(x - 3)² = 13
Third, use square root properties and algebra properties until roots are found:
x - 3 = ± √13
x = 3 ± √13
The roots of the quadratic equation are 3 + √13 and 3 - √13.
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Related Questions
the length of a living room carpet what metric unit would you use
Answers
Answer:
meters
Step-by-step explanation:
There are 3.28 feet in a meter
Craig has a job waiting tables where he earns $3.35 per hour plus tips. Craig earned $73.96 in tips during his shift yesterday.
Q.If x represents the number of hours Craig worked yesterday, which of the following equations can be used to find the amount of money Craig earned yesterday?
A.y = 3.35x - 73.96
B.y = 73.96x + 3.35
C.y = 73.96x - 3.35
D.y = 3.35x + 73.96
Answers
Answer:
The correct answer is D. y = 3.35x + 73.96.
Step-by-step explanation:
D. y = 3.35x + 73.96
What is the value of the algebraic expression if x = 1/2, y = -1, and z = 2?Here is the algebraic expression: 6x(y to second power z)
Answers
The value of the algebraic expression if x = 1/2, y = -1, and z = 2 is 6.
The given expression is \(6xy^{2}z\) and we need to evaluate its value when x = 1/2, y = -1, and z = 2
Simply assign the values of each variable to the variables in the algebraic expression and evaluate the result to get the value of the expression. What we do is:
\(6xy^{2}z\\\\=6 * \frac{1}{2}*(-1)^{2} *2 \\\\=6 * \frac{1}{2}*1 *2\\\\=6\)
The algebraic expression's value would be 6, then. In an algebraic expression, the variables are denoted by letters, in this case x, y, and z; the coefficients are denoted by numbers, such as 6, and the exponents are, in this case, 2, as in the expression above. Expressions frequently include several terms made up of those components.
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percentage less formula; price reduction calculator; time reduction calculator; if a number decreases from 1500 to 300 what is the rate of decrease; percentage increase and decrease questions and answers; how to less percentage; percent increase and decrease problems; x is what percent more than y
Answers
The percentage decrease when a number decreases from 1500 to 300 is 80%
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Initial number = 1500
Number after decrease = 300
Percentage decrease = Initial number - Number after decrease/Initial number*100
Substituting the values in the formula we get the following:
= 1500 - 300/1500*100
= 80%
So, the percentage decrease is 80%
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Solve the following equation just for x: 3x - 3 = 2x + 7 FOR CREDIT! ✓ Submit
Answers
Given the equation:
3x - 3 = 2x + 7
Let's solve the equation for x.
• Step 1:
Add 3 to both sides of the equation.
3x - 3 + 3 = 2x + 7 + 3
3x = 2x + 10
• Step 2:
Subtract 2x from both sides of the equation
3x - 2x = 2x - 2x + 10
x = 10
ANSWER:
x = 10
16. Using a standard 52 card deck, what is the probability of pulling the king of hearts if you are
given two attempts (you will pull out one card and then another card)?
Answers
Answer:
Step-by-step explanation:
The way to do this (I think) is to figure out the probability of not getting said king on either throw.
First Throw: P(no King Hearts) = 51/52
Second Throw: P(no King Hearts) = 50/51
Total probability = 51/52*50/51 = 50/52
Therefore the probability of getting it right is
P(KH) = 1 - 50/52 = 2/52 = 1/26
I have a feeling that this is not correct. If you get a different answer that looks reasonable, take it.
- 0.2 times - 5/6 please help :(
Answers
Step-by-step explanation:
0.16666666666
Learn at brainlyWrite out the correct word form of each number.
10) 8,924,600.32
11) 707.91
12) 641,971.44
Answers
Seven hundred seven and ninety-one hundredths
6 hundred forty-one thousand nine hundred seventy-1 and 44 hundredths
what are the x intercepts of y=4x^2-12x+4
Answers
The x-intercepts of the given equation 4x^2-12x+4 is -3/2
What is Quadratic equation ?
Quadratic equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0
where c is a constant.
Given equation ,
y = 4x^2+12x+4
so we have to find the x-intercept , make y = 0
and we have to solve for the given quadratic equation
so,
we get
4x^2+12x+4 = 0
(2x)^2 + 9 + 12x = 0
(2x+3)^2 = 0
x = -3/2
There is double root unique intercept or tangent at x = -3/2
Therefore, The x-intercepts of the given equation 4x^2-12x+4 is -3/2
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4 x 6 + 29 divided by 5 - 4
Answers
Answer:
25.8
Step-by-step explanation:
pls mark this as brainliest! thx hope this helped. :)
Answer:
The answer would be 25.8 or you can do 258
Step-by-step explanation:
Determine wether the relation is a function (4,0),(2,0),(1,2),(2,4),(4,4),(5,2)
Answers
Answer:
This is not a function
Step-by-step explanation:
Hope this helps
The volume V, of a cylinder is V=pie times radius to the power of 2 h, where r is the radius of the cylinder and h is the height. Using rounding to the nearest whole number, which of the following is an estimate of the volume of a cylinder with a radius of 3.75 inches and height of 6.21 inches
Answers
Answer:
\(274\,\text{in}^3\)
Step-by-step explanation:
\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 18, 24, and 30 and a second triangle labeled D prime with side lengths of 6, 8, and 10
Determine the scale factor used.
Scale factor of one third
Scale factor of 3
Scale factor of 4
Scale factor of one fourth
Answers
The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.
To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.
In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.
To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.
Scale factor = Length of corresponding side in D' / Length of corresponding side in D
For the corresponding sides, we have:
Scale factor = 6/18 = 1/3
Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.
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How do I graph the solution
Answers
What is the constant in 12r + r/2-19
Answers
Answer:
constant is - 19
Step-by-step explanation:
the constant is the term in an expression with no variable attached to it.
12r + \(\frac{r}{2}\) - 19
the only term without the variable r attached to it is - 19
then the constant term is - 19
Find the volume of a coffee can with r= 7.5 cm, h= 16.8 cm, to the nearest cubic centimeter.
Answers
Answer:
2969 cm³
Step-by-step explanation:
Volume of cylinder is
V=πr²h
=π*7.5²*16.8
=2968.8
=2969 cm³
5 liters of petrol is needed for a motorbike to cover 200km. 1)what is the mileage of the bike. 2)how much petrol is needed to cover 320km.
Answers
Answer:
1. mileage of the bike = 40Km
2. petrol needed to cover 320Km = 8L
Kara mixes different colors of paint to create new colors. The table shows the amount of paint Kara mixes per batch.
Select all the batches that will create the same colors as the first batch.
A. Batch 2
B. Batch 3
C. Batch 4
D. Batch 5
E. Batch 6
Answers
Answer:
I've done this question: Its batch 5
Step-by-step explanation:
It has to be all equal proportions
Step-by-step explanation:
D batch 5
c. batch 4
so d and c
100 POINTS!
STATS
EXPLANATION NEEDED
Answers
Answer:
Step-by-step explanation:
Answer:
500 dollars
Step-by-step explanation:
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answers
Answer:
(c) I paid 200% of what I could have online and on sale.
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
In this question:
You paid twice, which means that the multiplier is 2. So
a is the increase, as a percent.
\(1 + \frac{a}{100} = 2\)
\(\frac{a}{100} = 1\)
\(a = 100\)
You had an increase of 100% on the price. Since the original amount was 100% you paid 100 + 100 = 200%(100% more, 2 times) of what you could have paid.
So the correct answer is:
(c) I paid 200% of what I could have online and on sale.
A total of 100 people went to the
movies. A ticket cost $4 for adults and
$2 for children. The total sales
amounted to $276. How many children
and adults attended the movies?
Answers
Using a system of equations, the number of children and adults who attended the movies is as follows:
Children = 62Adults = 38.What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also known as simultaneous equations.
The total number of people who went to the movies = 100
The unit cost of adult tickets = $4
The unit cost of children tickets = $2
The total sales = $276
Let the number of children who attended the movies = x
Let the number of adults who attended the movies = y
Equations:x + y = 100 ... Equation 1
2x + 4y = 276 ... Equation 2
Multiply Equation 1 by 2:
2x + 2y = 200 ... Equation 3
Subtraction Equation 3 from Equation 2:
2x + 4y = 276
-
2x + 2y = 200
2y = 76
y = 38
Substitute y = 19 in equation 1:
x + y = 100
x + 38 = 100
x = 62
Check in Equation 2:
2x + 4y = 276
2(62) + 4(38) = 276
124 + 152 = 276
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if you invest $550.00 and your annual interest is 4%, what will be the interest
Answers
The annual interest is $22.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
Amount invested= $550
Annual interest= 4%
SI= 550*4*1/100
=5.5*4
=22
Therefore, the simple interest will be $22.
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or
Colleen made a scale drawing of a house. She used the scale 3 millimeters = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Answers
The scale factor that the drawing use is 3/1000.
How to calculate the scale?From the information, Colleen made a scale drawing of a house and she used the scale 3 millimeters = 1 meter.
It should be noted that 1000 millimeters = 1 meter
Therefore, the scale factor that the drawing use is:
= 3 millimeters / 1 meter
= 3/1000
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Please help I’m doing online classes and i’m stuck
Answers
Answer:
C
Step-by-step explanation:
3y+2y+11y=16y
-4+7+(-9)=-6
Answer:
6y^2+24y-37 (a)
Step-by-step explanation:
math.
Help. I have no idea what to do
Answers
Answer: The answer is to ask your parents because something is definitely wrong with your teacher to give such a hard sun to solve like that.
Step-by-step explanation: sorry man that hard.
What is the sign of -456 +456
Answers
Answer:
0
Step-by-step explanation:
-456 +456
( - , + ) = -
so answer is 0
Answer:
0
Step-by-step explanation:
bc i know
Mitchell received a stipend at the beginning of the semester to buy textbooks. During the semester, he spent $430.84 on textbooks. He had $136.04 of the stipend left at the end of the semester.
x - $430.84 = $136.04
How much was Mitchell's stipend?
A.
$566.88
B.
$702.92
C.
$362.82
D.
$294.80
Answers
Answer:
$566.88
Step-by-step explanation:
$430.84 + $136.04 = $566.88
Answer:
294.80
Step-by-step explanation:
D
the small intestine is about 23 feet long while the large intestine is only 5 feet long what is the ratio of the large intestine to small intestine write in 3 ways
Answers
Answer:
it's answer is 4:1
Because length of small intestine is 6 m and length of large intestine is 1•5m
So 6/1•5 =4:1
Rewrite 2+(1/b-2) = (3b/b+2) as a proportion. Which of these proportions is equivalent to the original equation?
A. (3/b-2) = (3b/b+2)
B. (2b+3/b-2) = (3b/b+2)
C. (2b-3/b-2) = (3b/b+2)
and asking 2nd part question and answer. thx
Answers
Answer:
C for the first one
1,6 for the second
Neither for the third
Step-by-step explanation: EDGE 2021
Answer:
The first Question is C
Question 2 is 1,6
Question 3 is Neither
Step-by-step explanation:
trust me I took the quiz
need help fast please help me
Answers
Don’t ask how ik it’s just the logical answer
Good luck hope this helps
:))