The solution of the equation x² - 4x + 6 = 0 using completing the square is x = 2 ± √(-2)
What is an equation?An equation is used to show the relationship between numbers and variables.
Polynomial can be classified based on degree of two as a quadratic equation.
Given the equation:
x² - 4x + 6 = 0
Solving using completing the square method:
subtract 6 from both sides:
x² - 4x = -6
add to both sides the square of half the coefficient of x:
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
Taking square root of both sides:
x - 2 = ±√(-2)
x = 2 ± √(-2)
The solution is x = 2 ± √(-2)
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The graph of a quadratic function with vertex (2, -4) is shown in the figure below.
Find the domain and the range.
101
پہلے
<+
-10
10
Write your answers as inequalities, using x or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
In the graph of a quadratic function with vertex (2, -4) is shown in the figure, the Domain: -∞ < x < ∞ and Range: -4 ≤ x < ∞.
What is quadratic function?When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic function.
A polynomial of degree 2 is referred to as such because the highest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. This function is algebraic.
Domain for this quadratic function is all possible values of x where function is defined.
Thus, Domain: -∞ < x < ∞
Range is the set of value functions that correspond to the value 'x.'
Range: -4 ≤ x < ∞
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What are the exact values of a and b?
CORRECT ANSWER
WITH EXPLANATION
Step-by-step explanation:
TRY WITH SOME Trigonometric FUNCTION.
IF SOMETHING IS Wrong . I AM STILL A STUDENT
YZ ≅ VW, WX ≅ UV, and XY ≅ UZ. Complete the proof that △UVZ ≅ △XWY.
how to work out the area of a parallelogram
the base timed by the height
is a measure of behaviors by producers and consumers in response to changes in price.
Answer: The statement you've provided describes the economic concept of elasticity. Elasticity is a measure of how responsive the quantity demanded or supplied of a good or service is to a change in its price. It measures the responsiveness of the consumers' and producers' behaviors to changes in price, in other words, how sensitive the consumers or producers are to changes in the good or service prices.
There are different types of elasticity, such as price elasticity of demand and price elasticity of supply. Price elasticity of demand measures how much the quantity demanded of a good changes in response to a change in its price. If a good has a high price elasticity of demand, then a small change in its price will result in a large change in the quantity demanded of the good. On the other hand, price elasticity of supply measures how much the quantity supplied of a good changes in response to a change in its price. A good with a high price elasticity of supply will see a large increase in the quantity supplied in response to a small price increase.
Elasticity is a very important concept in economics because it helps to understand how consumers and producers will react to changes in prices and how it would affect the overall economy.
Step-by-step explanation:
A camper lights an oil lantern at 12 noon lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant tare of each hour. At 2 p.m., the amount of oil left in the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 1/2 ounces. Based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at 12 noon?
Show your work.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the oil burns.
1 hour = 2/3 ounce
At 12 noon = 193/3 = 64.33 ounces
At 2 pm = 63 ounces
At 5 pm = 61 ounces
The amount of oil at 12 noon is 64.33 ounces.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.
At 2 p.m., the amount of oil left in the lantern is 63 ounces.
At 5 p.m., the amount of oil left in the lantern is 61 ounces.
This means,
Amount of oil burnt in the lantern from 2 pm to 5 pm.
= 63 ounces - 61 ounces
= 2 ounces
Now,
3 hours = 2 ounces
2 hours = 1.33 ounces
1 hour = 0.67 ounces
Now,
The number of hours from 12 noon to 2 pm.
= 2 hours
So,
The amount of oil at 12 noon.
= 63 + 4/3
= (189 + 4) / 3
= 193/3 ounces
Thus,
The amount of oil at 12 noon is 65 ounces.
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please help me with this thank you.
5x35 65x76 what the the total
The solution to the above math arithmetic is 5115.
Addition and subtraction are what?Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.
What exactly is an algebraic question?This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.
For instance, 5 + 6 = 11 and 11 - 6 = 5.
5x35 + 65x76=5115
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-5 + -3 + 9= please help i'm stuck
Answer:
1
Step-by-step explanation:
Answer:
I believe it is 1
Step-by-step explanation:
This system of equations has been placed in a matrix
y 650x+175
y=25,080-120x
Column 1 Col 2 Col 3
Row 1 : ___ -1 ___
Row 2 : 75 ___ ___
Answer: This system of equations can be represented in matrix form as
| -1 | 650 | 175 |
| 75 | -120 | -25080 |
This matrix is called the augmented matrix of the system of equations. The first and second column of this matrix represent the coefficients of the variables x and y, respectively, in the system of equations. The third column represents the constant terms of the equations.
You can use a method such as Gaussian elimination or Gauss-Jordan elimination to solve the system of equations.
The Gaussian elimination method, you would use elementary row operations to transform the matrix into an echelon form or reduced row echelon form. Then you can back-substitute the variables with their values.
Also, the Gaussian-Jordan elimination is similar to Gaussian elimination, but it keeps continuing the elimination process until the matrix becomes an Identity matrix(A matrix with 1 on diagonal and 0 everywhere else) The values on the diagonal of the matrix will give you the solution of the variables.
Step-by-step explanation:
The value of z varies inversely with the value of w. The constant of variation is 2. Which are possible values for z
3
and w? Check all that apply.
Oz=.
z = 1+₁ w = 2/1/201
O z = 2, w = 3
O z=
z = -1/₁w=2
O z
4,
= 1/5, w = 2/1/201
z = 1/2/3₁, w = 2/1/201
Answer:A,C,D
As a result of the inverse relationship between z and w, their product is constant.
What does "inverse connection" actually mean?There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.
According to the information:z * W is equal to 1.
The statement indicates that the constant's value is 2/3, so:
z * w = 2/3
The result of solving for any of the variables is:
either w = (2/3) / z or z = (2/3) / w
The following values fit that relation:
z w = (2/3) / z
-8/9 (2/3) / (-8/9)
= - (2/3) * (9/8) = -3/4
- 4/9 (2/3) / (-4/9)
= - (2/3) * (9/4) = - 3/2
- 2/9 (2/3) / (-2/9)
= - (2/3) * (9/2) = - 3
2/9 (2/3) / ( 2/9)
= (2/3) * (9/2) = 3
4/9 (2/3) / (4/9)
= (2/3) * (9/4) = 3/2
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Find the slope of the line passing through each of the following pairs of points. (–7, 1) (7, 8)
Answer:
1/2
Step-by-step explanation:
Slope(m)
= (y2 - y1)/(x2 - x1)
= (8 - 1)/(7+7)
= 7/14
= 1/2
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answer: To solve the quadratic equation 8x^2 + 16x + 3 = 0, Patel could use the following steps:
Divide both sides of the equation by 8 to obtain x^2 + 2x + 3/8 = 0.
Rewrite the equation in the form (x + a)^2 = b by completing the square: x^2 + 2x + (1/2)^2 = (1/2)^2 - (3/8).
Rewrite the equation as (x + a)^2 - b = 0. In this case, a = 1/2 and b = -3/8.
Use the quadratic formula to solve for x:
x = (-1/2) +/- sqrt((1/2)^2 - (-3/8))
= (-1/2) +/- sqrt(5/8)
= (-1/2) +/- sqrt(40/64)
= (-1/2) +/- sqrt(10/16)
= (-1/2) +/- (5/8)
= -1 +/- 5/8
= -1 + 5/8 or -1 - 5/8
= -7/8 or 1/8
Therefore, the solutions to the quadratic equation are x = -7/8 or x = 1/8.
Step-by-step explanation:
A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?
Step-by-step explanation:
d = 30m, so r = 15m
h = 20m
We know,
V = πr^2h= (22×15×15×20)/7 [Taking π = 22/7]
= 14142.86m^3
= 14142875.14 litres
‼️PLEASE HELP ASAP!!!!‼️
Select the table that represents a linear function. (Graph them if necessary.)
solve in vertex form?
In algebra, the vertex form of a quadratic equation is a way of expressing the equation in the form:[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola defined by the equation. The value of 'a' determines whether the parabola opens up or down and the value of 'h' and 'k' determine the position of the vertex on the coordinate plane.
For example, the standard form of a quadratic equation is:
[tex]y = ax^2 + bx + c[/tex]
To convert this to vertex form, you would first complete the square to get all the terms of x on one side of the equation and a constant on the other side. Then, you would put the equation in the form shown above.
So, given the equation [tex]y = 3x^2 + 6x - 4[/tex], we can complete the square to get:
[tex]y = 3(x^2 + 2x) - 4[/tex]
then rearrange it to
[tex]y = 3(x^2 + 2x + 1) -7 = 3(x+1)^2-10[/tex] which is in vertex form with vertex (-1,-10)
The vertex form of a quadratic function provides a convenient way to quickly identify the vertex of the parabola without having to complete the square every time.
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The correct question is:
Explain vertex form.
multiply the sum by the difference of 19 and 57
Answer:2009#73
Step-by-step explanation:
3939+373
Ie,ek
URGENT: please help!!!!!!!!!
Answer:
In the form of y=mx+b:
y = -5/6x-5
Step-by-step explanation:
I'm not that good at explaining, but I'll try:
Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.
What is the value of l-14l
Answer:
Step-by-step explanation:
-140
The answer to |-14| is 14
a
=
8.7
rounded to 1 DP
b
=
0.82
rounded to 2 DP
Find the maximum of
a
+
b
The maximum value considering DP of a and b is 9.52.
What is the decimal places of numbers?The decimal places of a number are the number of digits to be considered after the decimal point. E.g Round 4.7583 to 2 dp, we have;
4.76 3 dp
The maximum value of a sum of numbers is the highest value obtained when these numbers are added one to each other. The decimal places of each number is put into consideration in the process.
From the given question;
a = 8.7 and b = 0.82
Thus,
a + b = 8.7 + 0.82
= 9.52
a + b = 9.52
Therefore, the maximum of a + b = 9.52
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A square pryamid have a total surface area of 1,477,500ft² and need to find the slant length. The length is 750ft. Find the slant length.
A.) 610in
B.) 610ft
C.) 3,050ft
D.) 3,050in
If these two shapes are similar, what is the measure of the missing length j?
Answer:
45ft is the missing length j.
Which statement correctly compares the centers of the distributions?
Answer:
B
Step-by-step explanation:
Center of the distributions -> mean/median (preferably mean)
The option with range is eliminated
Median might not be accurate as median is the center person, not the center result.
Based on the graphs, identify the graph with the intervals of greatest frequency.
For North Heights -> between 30 and 32 (right-skewed, some higher values)
For Southview -> between 28 and 30 (most concentrated there)
Hence, mean of Southview is lower than North Heights.
solve for inequality for graph y + 4 > 1/2 {x + 2}
Answer:
y > X/2 - 3
I think that's the answer.
Round 0.09305085 to the nearest hundredth
When fitting a pipe into an existing fitting it allows a diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005" what's the maximum allowable pipe diameter? a. 0.496, b. 0.501, c. 0.499, d. 0.541
Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''
How to find the maximum allowable pipe thicknessThe maximum allowable pipe diameter is calculated by
finding the total thickness of pipe
= interior diameter + 2 * pipe thickness
= 0.49 + 2 * 0.005
= 0.49 + 0.01
= 0.50
The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001
hence
= 0.50 + 0.001
= 0.501
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Evaluate the following expression when c = -3 and d= 2: 6/d -10c - c to the fourth power
The value of the fourth power of the expression is 1679616.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression: 6/d -10c - c, where c = -3 and d= 2
Solving the expression, we get,
6/2-10(-3)-(-3)
= 3+30+3
= 36
We are asked to find the fourth value of 36,
(36)⁴ = 36 × 36 × 36 × 36 = 1679616
Hence, the value of the expression is 1679616.
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Which equation is part of the same fact family as 5 x 4 =20?
jakie pole ma prostokąt o wymiarach 50cm x 16dm?
Solution
16 dm=160 cm
50 cm* 160 cm= 8000 cm²= 0,8 m²
odp C
there are no good answers on brainly can someone pls answer this
Answer:
D
Step-by-step explanation:
explanation on the other response on ur other question