Solve the equation x squared +6x+1=0
Answers
The solutions to the equation x² + 6x + 1 = 0 are x = -3 + 2√(2) or x = -3 - 2√(2)
What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0 where a, b, and c are constants, and x is the variable. The solutions can be found using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) or by factoring the quadratic expression into two linear factors.
To solve the quadratic equation x² + 6x + 1 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation. Substituting the values from our equation, we get:
x = (-6 ± √(6²- 4(1)(1))) / (2(1))
Simplifying inside the square root, we get:
x = (-6 ± √(32)) / 2
We can simplify the square root further by factoring out a 4:
x = (-6 ± 4√(2)) / 2
Simplifying the fraction, we get:
x = -3 ± 2√(2)
Therefore, the solutions to the equation x² + 6x + 1 = 0 are:
x = -3 + 2√(2) or x = -3 - 2√(2)
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Related Questions
Product of 630 and 7.2X 10 to the 4th power
Answers
Put it into your calculator
Product means multiply \(\times\)
4th power means \(10^4\)
\(630\ \times\ 7.2\times10^4 = 45360000 = 4.536\times10^7\)
Maryam has a coupon for 33% off her entire meal of 232.88 what is the discount.
help!
Answers
Answer:
$156.03
Step-by-step explanation:
33% = 33/100 = 0.33
First, multiply the total cost with 0.33:
232.88 x 0.33 = ~76.85 (round).
Subtract 76.85 from the original cost ($232.88):
232.88 - 76.85 = 156.03
Maryam's meal will cost $156.03 after the discount.
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How do you calculate the range?
Answers
A range is calculating by subtracting the smallest value from the largest value as range from 1 to 5 is 4.
Why do we calculate the range?Utilizing the same units as the data, it measures variability. Greater variability is shown by larger values. The range is the simplest statistical measure of dispersion to compute and explain, but it has significant restrictions.
What is a range of numbers?The difference between a collection of numbers' highest and lowest values is known as the range. Subtract the distribution's lowest number from its greatest number to determine it.
Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; it only considers these two values.
suppose we have a set of values
22,56,43,87,33,12,11
its range will be calculated as;
largest value=87
smallest value=11
range=largest value-smallest value
range=76
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Aaden has 50 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 154 square meters. Solve for the dimensions (length and width) of the field.
Answers
The length of the field is 16m.
The width of the field is 9m
What are the equations that can be formed from this question?Area = length x width
154 = ab
b = 154 / a equation 1
Perimeter = 2(length + width
50 = 2(a + b)
a + b = 50/2
a + b = 25 equation 2
Where:
a = length
b = width
What is the length and width?Substitute for b in equation 2
a + 154/a = 25
a² + 154 - 25a = 0
a² - 9a - 16a + 154 = 0
a(a - 9) -16(a - 9) = 0
a - 16 = 0
a = 16
a - 9 = 0
a = 9
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I need the area can someone help meeee pls?
Answers
Answer:
54ft
Step-by-step explanation:
9ft x 6ft
Celine purchased a ball of red yarn costing $2.33. She gave the cashier $7.19. How much change did the cashier give back to Celine?
Answers
Answer:
$ 4.86
Step-by-step explanation:
Subtract 7.19 and 2.33
7.19-2.33=4.86
The function h(t) = -4.9t^2 + 45t gives the height h of a ball (in meters) thrown upward from theground after t seconds. Suppose the ball was instead thrown from the top of a 22-m building. Relate this new height function b(t) to h(t).Write a formula for b(t) in terms of h(t).b(t) =Write a formula for b(t) in terms of t only.b(t) =
Answers
Solution
For this case we can do the following:
Part a
b(t)= h(t) ++2
Part b
b(t) =-4.9 t^2 +45t +22
To create an entry code, you must first choose 3 letters and then, 3 single-digit numbers. How many different entry codes can you create?
Answers
The number of entry codes will be 720.
What are permutation and combination?The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.
When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.
Given that you must first choose 3 letters and then, 3 single-digit numbers.
The number of arrangements will be calculated as,
Codes = 6!
Codes = ( 6 x 5 x 4 x 3 x 2 x 1 )
Codes = 720
Hence, the combination of the code will be 720.
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Someone is 18 1/2 inches long when they are born and their twin is 20 3/4 inches long. What is the difference between how big they are.
Answers
help me please,
Calculate the external perimeter of the picture frame:
Answers
= 2 (65+42)
= 2*107
= 214 cm
Which sum or difference is modeled by the algebra tiles?
Answers
As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.
what is expression ?It is possible either multiply, distribute, add, or negate in mathematics. The trying to follow is how a expression is put together: Number, expression, and scientific operator The ingredients of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) It is possible to combine expressions and phrases. An expressions, often known as an arithmetic operation, is any mathematical statement that contains variables, numerals, and a numerical operation between them. That instance, the word m there in given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.
given
To address this issue, we just need to determine the total or difference that yields 2x2 + 2x + 2
Option A: ( x2 + 4x -2) + (x2 - 2x - 4) = 2x2 + 2x - 6
Option B: ( x2 + 4x - 2 ) + ( x2 + 2x + 4 ) = 2x2 + 6x + 2
Option C: ( x2 + 4x - 2) - ( -x2 + 2x - 4)= x2 + 4x - 2 + x2 - 2x + 4
= 2x2 + 2x + 2
As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.
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The complete question is:-
Select the correct answer.
Which sum or difference is modeled by the algebra tiles?
A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2
B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2
C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2
D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2
when x > 0 and a is a postive integer, the expression (5x)^a/3 is equivalent to?
Answers
Answer:
Step-by-step explanation:
i don't know man i just need the points!
Answer:
5^ax^a/3
Step-by-step explanation:
Use the tangent to find the length of side A C. Express your answer to the nearest tenth. 27° 7.0 The length of side AC is approximately units.
Answers
From the basic knowledge of trignometry,
tan 27 = x /7.0
cross-multiply
x = 7.0 x tan 27
x = 7.0 x 0.5095
x = 3.5665 = 3.6 units ( nearest tenth)
Which of the following is equivalent to (x + 3)(4x2 + 5)??O A. (x+3)(4x) : (x+3)(5)O B. (x + 3)(4x²) + (x + 3)(5)O C. (x+3)(4x) + (x + 3)(5)O D. (x+3)(4x2) : (x+3)(5)SUBMIT
Answers
Ok, so
We got the expression:
Here, we would distribute:
So, B is the correct answer.
If YG = 12, then EG is?
How is it not 6? Please help, no links
Answers
Answer:
I THINK ANSWER IS 12 because DIAGONALS BISECT EACHOTHER
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The length of a rectangle is twice its width.
The perimeter of the rectangle is 41 cm.
Label the diagram with the correct length and width for the rectangle.
cm
cm
Answers
Answer:
Width=6 5/6cm and Length=13 2/3cm
Step-by-step explanation:
Lets have width=x
Therefore, 4x+2x=41cm
6x=41cm
x=41/6=6 5/6
the width is 6 5/6 cm and length 41/3=13 2/3
I am being timed. Hurry please but take your time.
An unknown fractors is between 0 and 1. Which is true about the equivalent percent and decimal?
A. O The percent and decimal are betwern 0 and 1.
B. O The percent and decimal are greater than 1 and less than 100.
C. O The percent is between 0 and 1, and the decimal is greater than 0 and less than 100.
D. O The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.
Answers
Answer: D. The percent is greater than 0 and less than 100, and the decimal is between 0 and 1.
Graph the equation by creating a table.Equation: 3x+2y=-2
Answers
To create the table we first need to solve the equation for y. Then:
\(\begin{gathered} 3x+2y=-2 \\ 2y=-3x-2 \\ y=-\frac{3}{2}x-1 \end{gathered}\)Now we give values to the variable x and find the corresponding values for y.
So, we have the points (-4,5), (-2,2), (0,-1), (2,4), (4.-7).
Now we graph the points in the plane:
Finally, we join the points with a straight line:
i) Group 1 contains 170 students, all of whom have taken at least one of the three courses listed above. Of these, 61 students have taken Calculus, 78 have taken Sociology, and 72 have taken Spanish. 15 have taken both Cal- culus and Sociology, 20 have taken both Calculus and Spanish, and 13 have taken both Sociology and Spanish. How many students have taken all three classes? (ii) You are given the following data about Group 2. 32 students have taken Calculus, 22 have taken Sociology, and 16 have taken Spanish. 10 have taken both Calculus and Sociology, 8 have taken both Calculus and Span- ish, and 11 have taken both Sociology and Spanish. 5 students have taken all three courses while 15 students have taken none of the courses. How many students are in Group 2?
Answers
The number of students that took all the three classes is 40
The number of students are in Group 2 is 51 students
How to find the number of students that tool all the three classes(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.
Let's call the number of students who have taken all three classes "x".
The number of students who have taken Calculus and Sociology is 15 + x.
The number of students who have taken Calculus and Spanish is 20 + x.
The number of students who have taken Sociology and Spanish is 13 + x.
Adding these three equations, we have:
15 + 78 + 72 = 15 + x + 78 + x + 72 + x
solving for x
165 = 45 + 3x
120 = 3x
isolating x
So, x = 40.
hence, 40 students have taken all three classes.
(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.
Let's call the number of students in Group 2 "y".
The number of students who have taken at least one class is
32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.
Therefore, y = 36 + 15 = 51.
So, there are 51 students in Group 2.
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Kate is taking a short break and wants to pick up lunch from her favorite drive-thru restaurant, Burger Shack. There are two locations of Burger Shack that are equal distance from her office: Mountainview Plaza and Beachside Square. In the past, when Kate has picked up lunch from Burger Shack, she has been to the Mountainview Plaza location 12 times and the Beachside Square location 13 times. In situations when Kate has been to the Mountainview Plaza location, her wait time has been less than 5 minutes 2 times, between 5 minutes and 10 minutes 5 times, and more than 10 minutes 5 times. In situations when Kate has been to the Beachside Square location, her wait time has been less than 5 minutes 8 times, between 5 minutes and 10 minutes 2 times, and more than 10 minutes 3 times. Based on the information above, if Kate's goal is for her wait time at Burger Shack to be 10 minutes or less, which location should she choose? A. There is not enough information to determine the location that Kate should choose. B. Beachside Square C. Moutainview Plaza D. Neither location has an advantage.
Answers
Answer:
B.) Beachside Sqaure
Step-by-step explanation:
The reason why is because, you have to look at her intentions and the time frame she wants to wait for food at these restaurants. Beachside Sqaure has less times they have made her wait for her food more than 10 minutes, so that would be their advantage.
Stem and leaf due soon pls help easy
Answers
Answer:
Problem 21: 3 numbers have a 5 in the ones place
Problem 20: 3 numbers have 3 in the ones place
Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). Mark this and return
Answers
The variable y is directly proportional to x, which is the definition of direct variation.
What is coordinate geometry?The intersection of two perpendicular lines, the x-axis and the y-axis, results in a 2D plane known as a coordinate plane. In geometry, a coordinate system is a method for calculating the positions of the points using one or more integers or coordinates.
The graph that represents a function with direct variation is a coordinate plane with a line passing through (0, 0) and some other point that is not the origin.
Out of the given options, the graph that represents a function with direct variation is the coordinate plane with a line passing through (negative 4, 0) and (0, negative 2).
This is because the equation of this line can be written in the form y = mx, where m is the slope of the line. In this case, the slope is:
m = (0 - (-2)) / (-4 - 0) = 1/2
So the equation of the line is y = (1/2)x - 2, which is in the form of y = kx, where k = 1/2. This means that y is directly proportional to x, which is the definition of direct variation.
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In the diagram below,
ZCAB≈ ZCDE. Solve for x. Round
your answer to the nearest tenth if
necessary.
14
A
D
X
с
18.7
E
9.3
B
Answers
Answer:14 a
Step-by-step explanation:
The explanation is that it is E
Which net represents this solid figure?
________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
_________________________________
Answers
Answer:
D.
Hope this helps!
Step-by-step explanation:
A and C are both squares and B is a rectangle but is different because the values are in different spots than the on the solid figure shown.
A triangle has sides with lengths 8, 15, and 17.
a. Verify this is a Pythagorean triple.
Type your response in the space below.
b. Approximate the acute angles in this triangle. Round each angle to the nearest degree.
Type the answers in the boxes below.
Answers
The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.
What is Pythagoras TripleA Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.
In this problem, we can we can check if the values are for a right angle triangle.
Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.
c = hypothenuse = 17a = leg = 15b = 8c² = a² + b²
17² = 15² + 8²
289 = 225 + 64
289 = 289
From the calculation above, the values of is a Pythagorean triple.
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What is the answer to: 4 2/3÷(-1 1/4)
A. 2.57
B. 7 20/21
C. 1/36
Answers
= 14/3 divided by -3/4
= 14/3 * 4/-3
= 56/-9
Carl brown stein is a golf course groundskeeper whose annual gross pay is $45,500 . He has exemptions of &3,000. The state tax on the first 2,500?is 1.5% and 3% on amounts over 2,500
Answers
Answer:
no it's not
Step-by-step explanation:
3% of 45,500 is 1455 which is less then 2,500 which also means 1.5% is not more then 2,500
Use the order of operations to evaluate the expression
4x(3/4-1/2)+3x6
Answers
Answer:
4×(3-2)/4+18
=4×1/4+18
=4/4+18
=1+18
=19
An amount of $8,000 is invested at a simple interest rate
of 2%. What is the interest earned after 3 years?
Answers
Total amount after three years
= $8.360
Explanation:
Given -
Principal amount
p = $.8,000
Rate of interest
r = 1.5%
Duration
n = 3 years
Total amount after three years = Principal amount + Interest amount
Total amount after three years
= p + (pnr) = 8000 + (8000×1.5100×3) = 8000 + 360 = $8.360
Total amount after three years
= $8.360
Answer:
$8.360
Step-by-step explanation:
HELP ASAP
What is the perimeter of rectangle MNOP, rounded to the nearest tenth of a meter?
M
60°
N
O
O
28 m
79.2 m
67.6 m
88.1 m
76.5 m
30°
Answers
Answer: 76.5 meters
Step-by-step explanation:
To find the side lengths you use trig ratios for 30,60,90 triangles. The ratio is n (attached to the opposite side of the 30-degree angle, or the smallest leg), n\(\sqrt{3}\) (attached to the opposite side of the 60-degree angle, or the longest leg), 2n (attached to the hypotenuse). Using the inner triangle you can use 2n=28 to find the side opposite the 30-degree angle, 14. Then you plug 14 into every n and add the sides. the full answer is 76.4974226 but this problem said to round making your final answer 76.5 meters. always remember to give proper units.