The solution to the quadratic equation is x = 2 ± √3
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 4x + 1 = 0 be equation (1)
And , roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
On simplifying , we get
x = [ -4 ± √ ( 4 )² - ( 4 ) ( 1 ) ( 1 ) ] / 2
x = [ -4 ± √ ( 16 - 4 ) ] / 2
x = [ -4 ± √12 ] /2
On further simplification , we get
x = [ -4 ± 2√3 ] /2
x = 2 ± √3
Therefore , the value of x is 2 + √3 or 2 - √3
Hence , the roots of the quadratic equations is x = 2 ± √3
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ASAP During a 4-month-long drought, the water level in a lake changed by
−3
1
2
feet. The water level changed at the same rate each month.
What is amount the water level changed in 1 month?
Enter your answer in the box.
3 1/2 = 7/2
7/2 / 4 = 7/8
it changed by -7/8 feet = 10 1/2 inches each month
The amount of changes of water level in a lake for 1 month will be
⇒ - 7/8 feet
What is mean by Fraction?
The fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
In 4 month long drought,
The changes of water level in a lake = - 3 1/2 feet.
Now,
Find the changes in water level for 1 month as;
Since,
The changes of water level in a lake for 4 month = - 3 1/2
After change the mixed fraction in a improper fraction as;
- 3 1/2 = - 7/2
Thus, The changes of water level in a lake for 4 month = - 7 / 2
So, The changes of water level in a lake for 1 month = - 7 / 2 ÷ 4
After divide we get;
The changes of water level in a lake for 1 month = - 7 / (2 x 4)
= - 7 / 8
Therefore,
The amount of changes of water level in a lake for 1 month will be
⇒ - 7/8 feet
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can someone help me with these 3
the high school marching band rehearses with either 6 or 10 members in every line.What is the smallest number of people who can be in the marching band?
Answer:
The smallest number of people who can be in the marching band are 30.
Step-by-step explanation:
The high school marching band rehearses with either 6 or 10 members in every line.
To get the smallest number of people who can be in the marching band, we will find the LCM of 6 and 10.
6 = 2 x 3
10 = 2 x 5
The LCM is 2 x 3 x 5 = 30.
Hence, the smallest number of people who can be in the marching band are 30.
If the students are 6 in each line, then there will be 5 lines in total.
If the students are 10 in each line, there will be 3 lines in total.
Taylor buys 6 bus tickets. He pays for the tickets with a $20 bill. Let c represent the cost of each ticket. Which expression shows how much change Taylor will receive?
Answer:
(20 - 6c)
Step-by-step explanation:
Taylor buys bus tickets = 6
Let the cost of the one ticket = c
Cost of 6 tickets = $6c
If Taylor has paid $20 for these 6 tickets then the change he will receive = $20 - $6c
Therefore, the expression to calculate the change Taylor will receive will be
(20 - 6c)
3/8__1/4
greater than
less than
equal too
EXPLAIN
3/8 = 0.375
1/4 = 0.25
0.375 is greater than 0.25
so 3/8 is greater than 1/4
I need help I don't understand this!!
Write a real world situation that could be modeles by the equation 8+2x=6x.Then solve the problem
A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money. To solve the problem, isolate the variable x by subtracting 2x from both sides and dividing both sides by 4.
Explanation:A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. Let's say you have $8 and you are earning $2 per hour. On the other side, you have $6 and you are earning $6 per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money.
To solve the problem, you need to isolate the variable x. Start by subtracting 2x from both sides to get 8 = 4x. Then, divide both sides by 4 to get x = 2. Therefore, it will take 2 hours for your earned money to equal $6.
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. Which customer will be the first to receive both gift cards?
Julie's yard is rectangular one side of the yard is 100 feet wide. The total area of the yard is 3000 square feet. What is the length of the other side of the yard ?
snow fell 20% of the days in November. How many days in November did it snow. (Hint There are 30 days in November. )
Female elk can weigh up to six hundred pounds. In standard form, how many non-zero digits does this weight contain
There were 58 adults who completed the 16-mile charity bike ride. There were 65 (1 pt) children who completed the 10-mile charity bike ride. What is the total number of miles ridden by all the adults and children in the bike
Using isosceles triangle theorems solve for x and y
To solve for x and y in a right triangle, use the Pythagorean Theorem (x² + y² = h²) and trigonometric relationships (x = hcosΘ and y = hsinΘ). The Isosceles Triangle Theorem, which states the base angles of an isosceles triangle are equal, isn't directly used to solve for x and y.
Explanation:In solving for x and y using isosceles triangle theorems, we often utilize the Pythagorean Theorem and trigonometric relationships. Since this involves a right triangle, where x is the adjacent side, y is the opposite side, and h is the hypotenuse, we can use the formula for the Pythagorean Theorem, x² + y² = h².
To find x, we rearrange the trigonometric definition of cosine (cosΘ= x/h) to get x = hcosΘ. Similarly, we can find y using the definition of sine (sinΘ = y/h) and get y = hsinΘ. These solutions use trigonometry.
Keep in mind, the Isosceles Triangle Theorem states that the base angles of an isosceles triangle (a triangle with at least two equal sides) are equal. However, this theorem isn't directly involved in solving for x and y. Instead, the trigonometric relationships and Pythagorean Theorem solves for these values within a right triangle.
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Identify the multiplier for 2/9 = 6/27
The multiplier for the number 2 / 9 will be 3 / 3.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.
The given number is 2 / 9. The multiplier for the number will be calculated as below:-
2/9 = 6/27
( 2 / 9) x ( 3 / 3 ) = ( 6 / 27)
( 6 / 27 )= ( 6 / 27 )
Therefore, the multiplier for the number 2 / 9 will be 3 / 3.
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The total land area on earth is about 6×10 to the seventh power square miles. The layered of Australia is about 3×10 to the six power square miles. About how many times larger is the land on earth than land of Australia
Math help please!! ^o^
Answer: I say c too. I trust you with that answer.
Step-by-step explanation:
how to show the tens fact you used. write the difference.
14-6=____
10-___=____
The tens facts approach simplifies subtraction by reducing numbers to multiples of ten. In the given problem the difference of 14-6 is 8 and this can be represented with tens facts as 10-2=8.
Explanation:The question pertains to the calculation of the difference between numbers using tens facts. Tens facts are a strategy applied in subtraction operations to simplify problems by making them multiples of ten. Here, the problem involves 14-6. In order to represent this using tens facts, the target is to reduce the first number (14) to a multiple of ten, which is 10 in this case. You can achieve this by subtracting the 4 from 14 to get 10. It's the same total of 4 that we also subtract from the 6 to arrive at our answer of 2. So, it can be shown as;
14 - 6 = 810 - 2 = 8Learn more about Tens Facts here:https://brainly.com/question/29636684
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The graph shows the number of laps that Jan runs as her coach times her.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is_ .
This means that Jan runs _ laps every_minutes .
Answer:
Jan run 2 laps every minute
Step-by-step explanation:
angles x and y are supplementary.angle x is 3 times the measure of angle y what is the measure of angle x
Three bags of wheat, two bags of corn, and one bag of oats weigh the same as one bag of wheat, one bag of corn and five bags of oats. If two bags of corn and one bag of oats weighs 26 pounds, and one bag of corn weighs 10 pounds, how much does one bag of wheat weigh?
Maggie bought 3/4 of a pound of bananas and 4 boxes of cereal for $10.11. If each box of cereal cost $2.40, what was the price of a pound of bananas?
Answer:
$0.51
Step-by-step explanation:
estimate 392÷9 show how you estimated
217+37(3x−5)=−4 Drag and drop the statement that shows the solution to the equation into the box.
does this help? :D
Answer on picture
the cost of 3 candles is 19.50 what is the unit price with work shown
Answer:
$6.50/candle
Step-by-step explanation:
The unit price here is the total price divided by the number of candles, or
$19.50
---------------- = $6.50/candle
3 candles
Find the difference between 7/10 and 14/15
Answer:
The answer is - 7/30
Step-by-step explanation:
LCM between 10 and 15 is 30 so that would be your denominator.
The subtract: 7-14 = -7 so that would be your numerator.
HOPE THIS HELPS!!! :D
The difference between the numbers of fraction 7 / 10 and 14 / 15 would be 7 / 30.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
The number of the fraction are;
⇒ 7 / 10 and 14 / 15
Now,
Find the difference between the fraction 7 / 10 and 14 / 15 as;
The mathematical expression is,
⇒ 14 / 15 - 7 / 10
Make denominator same to solve the fraction as;
LCM { 10 , 15 } = 30
Therefore, We get the expression ;
⇒ 14 / 15 - 7 / 10
⇒14 × 2 / 15 × 2 - 7 × 3/ 10 × 3
⇒ 28 / 30 - 21 / 30
⇒ (28 - 21) / 30
⇒ 7 / 30
Thus, 14 / 15 - 7 / 10 = 7 / 30
Therefore, The difference between the fraction of numbers 7 / 10 and 14 / 15 would be 7 / 30.
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Grade 9 mathematics please help asap. Thank you so much!!!
How does identifying the part and the whole help you to write the percent proportions
Which doubles fact can help you solve 4+5=?
The question seeks an applicable double fact to help solve 4+5, however, no exact double fact would provide the precise result because they pertain only to pairs of the same number. The closest double fact is 4+4, and though this is not an exact match, it helps to get a ballpark figure.
Explanation:The question asks: Which doubles fact can help you solve 4+5=? In this case, you might think of using the double fact of 4+4. Although it's not exactly the same as 4+5, it's close and can give you a good guess. However, no exact double fact would help you to get the exact answer to 4+5 because these are two different numbers. The sum of 4+5 equals to 9. The purpose of double facts is to aid in mental mathematics by recalling the results of certain simple additions, but only pairs of the same number are used;
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a triangle has sides of lengths 6 and 9. What value could the length of the third side?
there are 17 men and 26 women in a choir the choir is going to sing at a concert one of the men and women are going to be chosen to make a pair to sing the first song. work out the number of different pairs that can be chosen
The total number of different pairs that can be formed for the song, with one man and one woman in each pair, is 442 pairs.
Explanation:This is a classic mathematical problem known as combinations. In this case, we want to know how many different pairs can be formed from a group of 17 men and 26 women where one man and one woman form a pair.
To calculate the number of different combinations, we multiply the number of choices for the first element (a man) by the number of choices for the second element (a woman). Thus, we have 17 different choices for the man and 26 different choices for the woman. So the total number of different pairs that can be formed is: 17 men * 26 women = 442 pairs.
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