The roots of the quadratic equation 6x²-2x=8 are x=4/3 and x=-1.
Given that,
The equation is 6x²-2x=8
To find : The roots of the quadratic equation 6x²-2x=8
Any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known values, where a 0, is referred to as a quadratic equation in algebra (from Latin quadratus, "square"). The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.
We know that,
The solutions are x1 and x2 = -b±√b²-4ac/2a
Here b = -2 ,a = 6 and c= -8
No substitute those values in the formula,
= -b±√b²-4ac/2a
= -(-2) ± √(-2²)-4(6)(-8) / 2(6)
x = 4/3 and x =-1
So, The roots of the quadratic equation 6x²-2x=8 are 4/3 and -1
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One meter equals 3.281 feet, so 4 meters=
Do not round your asnwer.
feet
Answer:
13.124 ft
Step-by-step explanation:
1 m = 3.281 ft
4 m = 4 × 3.281 ft = 13.124 ft
what is the value of 1/2 divided by 1/3
Answer:
1 1/2
Step-by-step explanation:
write an explicit formula for a subscript n, the nth term of the sequence 8, 11, 14,...
please please help
The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values.
here,
The Sequences 8, 11, 14,...
first term a = 8
common difference = 11 - 8 = 3
Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3
Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.
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the cost in the dollar of operating machine per day is given the formula by C = 3T2 -96t + 1,014 , where is T is the time of the machine operating in hours
What is the maintenance cost of running the machine?
Answer:
T is the cost
Step-by-step explanation:
by looking at the question you can see the answer.
What is a 2 term polynomial?.
Two term polynomial called as a binomial .
An algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variables known as polynomial.
But when we reduce more than two terms into only two terms we get binomial.
A formula in algebra that expresses the difference or sum of two terms is known as binomial.
For example:
[tex]x^{4} + x y^{2} +x^{2} + x[/tex] is polynomial because it has more than two separate terms which are [tex]x^{4}[/tex] , [tex]x y^{2}[/tex] , [tex]x^{2}[/tex] and [tex]x[/tex]
[tex]x^{2} + y^{2}[/tex] is binomial because it has only two separate terms which are [tex]x^{2}[/tex] and [tex]y^{2}[/tex].
[tex]4x+6y[/tex] is also binomial because it has also only two separate terms which are [tex]4x[/tex] and [tex]6y[/tex]
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Why earthquakes with the greatest magnitude do not always cause the highest number of deaths?.
The earthquakes with the greatest magnitude do not always cause the highest number of death because other factors like area ( ground, water , sand etc.), soil structure, buliding constutor material etc. also affect the earthquake intensity.
The biggest earthquakes are not necessarily the most devastating ones. But other factors are also involved here. In areas of water-saturated sand, shaking loosens the sand particles from each other, causing them to "float" on the water and turn into quicksand. Sand at rest is still and hard, but when shaken it forms liquid mud. Buildings and other structures built on such sand simply sink and collapse. Other types of soil structures and terrain can amplify and resonate seismic waves, potentially causing more damage. Of course, if an earthquake occurs at sea, it can create a devastating tsunami. Also, certain structures and buildings are less susceptible to vibration than others due to how they are constructed and the materials used. For example, a large magnitude 9.0 earthquake might cause minor damage due to its remote location. But if 6.0 occurs in an underdeveloped and densely populated area, it could kill thousands.
The more people there are, the more people die. For example, the 2001 earthquake in India occurred in a densely populated area.
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How do you identify the horizontal asymptote of a graph?.
The horizontal asymptote of the graph is the horizontal line y = b and the graph approaches a straight line as the input approaches ∞ or −∞.
Horizontal Asymptote: As x moves towards infinity or -infinity, the curve approaches a constant value b, called a horizontal asymptote with equal numerator and denominator. The following are used to determine the horizontal asymptotes:
If the degree of numerator and denominator polynomials are equal, then the horizontal asymptotes is obtained by dividing the highest degree cofficientes.If the numerator degree is less than the denominator degree, the horizontal asymptote is y = 0.If the numerator degree is greater than the denominator degree, there is no horizontal asymptote.For example, function f(x) = 2x / (x - 3) and we have to determine the horizontal asymptotes. As we see the degree of polynomials both in numerator and denominator is equal. So, horizontal asymptotes is equal to number which is obtained by dividing the hightest degree coefficients i.e., 2/1 = 2. Thus, the function has only one horizontal asymptote which is y = 2. Here is the graphical verification.
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SOMEONE PLS HELP
1 1/2 - 3 2/3
Answer:
= -13/6 OR -2.1667
Step-by-step explanation:
1 1/2 - 3 2/3
=3/2 - 11/3
LCM of 2 and 3 is 6
3/2 - 11/3
= 9 - 22
6
= - 13/6 OR -2.5
Answer: is it
-2 1/6
Step-by-step explanation:
Rewriting our equation with parts separated
=1+12−3−23
Solving the whole number parts
1−3=−2
Solving the fraction parts
12−23=?
Find the LCD of 1/2 and 2/3 and rewrite to solve with the equivalent fractions.
LCD = 6
36−46=−16
Combining the whole and fraction parts
−2−16=−216
Simple bro
Two torage hed are to have the ame area. One i quare and one i rectangular. The rectangular hed i 3 meter wide and 12 meter long
By using the area of the square formula, it can be concluded that the side of the square shed is 6 meters.
The area of a square or a rectangle can be defined as the number of square units needed to fill it.
Area of a Square = side × side = side²
Area of a rectangle = width x length
Area of the square = area of the rectangle
Rectangle width = 3 meter
Rectangle length = 12 meter
To find the side of the square shed, we can do the following:
Area of the square = Area of the rectangle
side² = width x length
= 3 x 12
= 36
side = √36
= 6
Thus the side of the square shed is 6 meters.
Two storage sheds are to have the same area. One is square and one is rectangular. The rectangular shed is 3 meters wide and 12 meters long. How large is one side of the square shed in meters?
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Solve the multi-step equation. Type in your solution (ie, x=3, 4=7, 5=5).
6x+7= 2(3x+5)+9
The equation 6x + 7 = 2(3x + 5) + 9 has no solution.
How to solve an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's solve the equation for variable x.
A variable is a number represented with letter in an equation. Therefore,
6x + 7 = 2(3x + 5) + 9
6x + 7 = 6x + 10 + 9
6x + 7 = 6x + 19
6x - 6x = 19 - 7
0x = 12
Therefore, the equation cannot be solved.
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Point MM is located at (-4,4)(−4,4) on the coordinate plane. Point MM is reflected over the yy-axis to create point M'M
′
. Point M'M
′
is then reflected over the xx-axis to create point M''M
′′
. What ordered pair describes the location of M''?M
′′
?
The ordered pair which describes the location of M''M" is (4, -4).
What is a reflection?In Geometry, a reflection over the y-axis is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of the image coordinates include the following:
(x, y) → (-x, y)
Coordinate M = (-4, 4) → Coordinate M' = (-(-4), 4) = (4, 4).
Next, we would apply a reflection over the x-axis to the above coordinates as follows:
(x, y) → (x, -y)
Coordinate M' = (4, 4) → Coordinate M" = (4, -(4)) = (4, -4).
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To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.
Identify the linear equation?Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12
We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.
Take the provided linear equation system into consideration.
3x - 2y = 4 ................(1)
9x - 6y = 12 ..................(2)
Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12
The slopes of the provided equations are also same.
Difference with regard to x for equation (1) yields,
additional to equation (2),
With regard to x, we can differentiate to get,
The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.
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Answer this functions question
Answer:
ff(x)=9x-48
Step-by-step explanation:
f(x)=3x-12
ff(x)=f(3x-12)
=3(3x-12)-12
= 9x-36-12
= 9x-48
Estimation Rita goes to the mall. If b is the number of items she bought, the expression 13.06b+ 29 gives the amount she
spent in dollars at one store. Then she spent 22 dollars at another store. Find the expression which represents the amount
Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.
What expression represents the amount in dollars that Rita spent at the mall? Help please! This is due tomorrow!
The total amount Rita spend on the mall for 2 items is $77.12.
How to solve the expression to find total amount?When we combine numbers and variables in a valid way, using operations like addition, subtraction, multiplication, division, exponentiation, and other yet unlearned operations and functions, the resulting combination of mathematical symbols is known as a mathematical expression.Given that,
The expression of amount spend on the first store = 13.06b + 29
The amount spend on the second store = 22
Total amount Rita spends= 13.06b + 29 + 22
= 13.06b + 51
Then to estimate the amount Rita spent if she had bought 2 items.
Now, we have the value of b = 2.
So by substituting,
= 13.06 x 2 + 51
= 77.12
Therefore the total amount Rita spend on the mall is $77.12.
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help with this question
Answer:
Answers in the attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, do note this question is testing on the knowledge of Pythagoras' Theorem.
What is the degree of the polynomial function f x 2x3 7x5 − 4x − 12?.
The highest power of this function is 5 , so the degree of this polynomial is 5 .
The degree of polynomial is highest power of variable in a polynomial expression. The polynomial’s degree is the greatest power of a variable in a polynomial equation. The degree of polynomial indicates the highest exponential power in polynomial (the coefficients are ignored).
the polynomial function is ⇒ f(x) = 2x³ + 7x⁵ + 4x + 12 ;
we see that the second term "7x⁵" has the greatest power ,
So , we can conclude that the degree of the polynomial function is 5 .
The given question is incomplete , the complete question is
What is the degree of the polynomial function f(x) = 2x³ + 7x⁵ + 4x + 12 ?
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Help need fast - What is the area of the shape?
Answer:
Area = 28
Area of cutout = 1/2 * 2 * 4 = 4
Area of entire rectangle without cutout = 32
(Also 4 * 4 + 2 * 4 + 1 * 4 = 28)
Can a negative number be an exponential function?.
Yes, it is possible for a negative number to be an exponential function.
The number of times a number is multiplied by itself is indicated by the positive exponent, as we are aware. In contrast, the negative exponent indicates how many times the base number must be divided. The negative exponent, in other words, indicates how many times the reciprocal of the base must be multiplied. 3-2 is a prime example of a negative exponent.Two negative exponents can be multiplied together in the same way as two numbers. Since we are aware that negative exponents can be reduced to fractions, simplifying negative exponents is simple. Converting the negative exponents to their fractional form is the first step in multiplying negative exponents, after which the procedure is the same as multiplying two fractional numbers.
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JK is a tangent to the circle KLM at K and JML is a straight line. The value of x is
A. 30° B. 45° C. 60° D. 75°
The value of angle x is 45°. Thus, option B is correct.
How to find the value of x?A corner is an angle if it forms a projecting part or a partially enclosed space. An angle is a figure made up of two lines that extend from the same point. a measurement of an angle or the amount of turning required to align or make parallel two lines or planes.
step1:
o is center
JK is a tangent
so <OKJ =90°
<OKM=90°-30°=60°
OM=OK=><OMK=60°
step2:
because LO=LO, LM=LK, ON=OK
So Triangle OLM ≅ Triangle OLK => <LOM=<LOK
so <LOM=150° => <LMO =15°
so 60° +15° =30°+x°=>x= 45
so the answer is B. 45°
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Example 1: Fill in the missing values in the table of solutions for the linear equation, y=-x+4, plot the points, and then draw the line through the points
Answer:
so plot a 4 and the go up one over right one that way you have the linear equation graphed
how does understanding unit rates help us with unit pricing
How to multiply 2 digit numbers by 2 digit numbers without regrouping?.
Multiply the number in the one's place. Multiply the number in the ten's place. And then add them up.
Multiply 2-Digit Numbers Without Regrouping:
Follow along with example 43 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Draw a line beneath the bottom number.
4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6) and one's place of the second number by the ten's place of the first number (2 × 4 = 8). Place the 6 below the line in the ones' place column and 8 below the line in the tens' place column.
4 3
×3 2
_________
8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9 and Multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12. Now add the numbers and place the answer below the line.
4 3
×3 2
__________
8 6
12 9×
__________
13 76
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!!! 50 points !!!
Rug to place in the middle of his bedroom. He draws a diagram to show where he will place is rug. Part A: Sam needs to find the perimeter of his bedroom. Use the picture to write three expressions that represent the perimeter, in feet, of Sam’s room.
Part B: now, Sam wants to find the area of his bedroom. He says that he can find the area using the expression 40x + 12 square feet. Is he correct? If he is incorrect, how many square feet is he off by?
Part C: Sam’s friend Carla has a square a bedroom with side length 4x + 6. Compare the perimeter of Carla’s room to the perimeter of Sam’s room.
**I need all answers and explanations, as I am required to show my work!**
A:Expression 3: 4(4x + 6) = 16x + 24 feet, B: No, he is incorrect
C: The perimeter of Carla’s room is 16x + 24, which is the same as Sam’s room.
What is an expression?An expression is a combination of numbers, symbols, and variables that represents a certain value otherwise set of values.
For example, 2x + 5 is an expression that represents any value that can be obtained by substituting any number for the variable x.
In this question
Part A:
The perimeter of Sam's bedroom can be expressed using the following equations:
1. P = 2(x+2) + 2(y+2)
2. P = 2x + 4 + 2y + 4
3. P = 2x + 2y + 8
Part B:
No, Sam is incorrect. The correct expression for the area of his bedroom is A = (x+2)(y+2). He is off by 8 square feet.
Part C:
The perimeter of Carla's room is 4x + 12, which is 4 more than the perimeter of Sam's room.
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Branly. Com math mr klammer ha a garden. One half of her garden i planted in vegetable and the other half i planted in flower he planted cucumber in 1/3 of the vegetable part of the harden how much of the whole garden i planted in cucumber. Brainly
1/6 of the whole garden is planted in cucumber.
What is cucumber ?
Cucumber is a type of vegetable that belongs to the cucurbit family, which also includes melons, squash and gourds. They are typically long, cylindrical in shape, and have a green skin that is typically eaten raw.
The proportion of the garden planted in cucumber is 1/3 of the vegetable part of the garden. To find out what proportion of the entire garden is planted in cucumber, we can use this proportion and multiply it by the proportion of the garden that is planted in vegetables.
Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.
1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,
(1/2) x (1/3) = 1/6
So, 1/6 of the whole garden is planted in cucumber.
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Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.
1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,
(1/2) x (1/3) = 1/6
1/6 of the whole garden is planted in cucumber
The ratio of boys to girls in the 9th grade is 7 to 9. There are 218 girls. Set up a proportion to model this information.
Answer:
7/9=b/218
Step-by-step explanation:
AXYZ has side lengths of XY = 2, YZ = 2,
XZ = 1.5. After it has been dilated with a scale factor of
2, what are the side lengths of AX'Y'Z*?
a = 14, b = 3.5
what are the side lengths of AX'Y'Z*?XZ = XY , then
2a + 3b = 11b ( subtract 3b from both sides )
2a = 8b ( divide both sides by 2 )
a = 4b
The perimeter is 91 , so
11b +2a + 3b + a = 91
14b + 3a = 91 ← substitute a = 4b
14b + 3(4b) = 91
14b + 12b = 91
26b = 91 ( divide both sides by 26 )
b = 3.5
and a = 4b = 4 × 3.5 = 14
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After it has been dilated with a scale factor of 2 the side lengths of AX'Y'Z is: a = 14, b = 3.5
what are the side lengths of AX'Y'Z*?XZ = XY , then
2a + 3b = 11b ( subtract 3b from both sides )
2a = 8b ( divide both sides by 2 )
a = 4b
The perimeter is 91 , so
11b +2a + 3b + a = 91
14b + 3a = 91 ← substitute a = 4b
14b + 3(4b) = 91
14b + 12b = 91
26b = 91 ( divide both sides by 26 )
b = 3.5
and a = 4b = 4 × 3.5 = 14
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The graphs of f (x) and g (x) are shown below.
Answer:
B) (-∞, 2)
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=-0.5x[/tex]
To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:
[tex]\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}[/tex]
Therefore, the interval for which the composite function (f - g)(x) is negative is:
(-∞, 2)What is the slope of a line whose equation is 3x 2y 8?.
The slope of the given equation is -3/2.
The equation of a line in the form 3x + 2y = 8 is not in the standard form of a linear equation, also known as slope-intercept form. In order to find the slope of the line, we need to express the equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To do this, we can start by isolating y on one side of the equation. We can subtract 8 from both sides, resulting in 3x + 2y -8 = 0.
Next, we can divide both sides by 2, which gives us (3/2)x + y - 4 = 0. This is the equation in the slope-intercept form.
The slope of the line is represented by the coefficient of x, which in this case is (-3/2). It tells us that for every 1 unit increase in x, the value of y will decrease by 3/2 units.
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How do you write greater than 4?.
To show that one value is greater than another, use the "greater than" symbol (>). It can be used to express a comparison between two values in mathematical operations, programming, and other forms of notation.
For instance, the "greater than" symbol can be used to compare integers in mathematical operations. For instance, you would write "x > y" to indicate that x is greater than y. This can alternatively be understood as "x exceeds y."
Other comparison symbols, such as "less than," "greater than," and "less than or equal to," can be used in addition to the "greater than" symbol. These symbols can be used to describe many forms of value comparisons in programming and mathematical processes.
The word "greater than" is represented by the symbol ">," therefore to write "greater than 4" you would write ">4".
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PLEASE HURRY
What is the highest fraction that is reduced to 1/2
I WILL MARK U BRAINLIST
Answer:
The fractions which are equivalent to 1/2 are 2/4, 3/6, 4/8, 6/12 etc.
But there are more fractions that are equivalent to 1/2 such as 7/14, 8/16, 9/18, 10/20, 11/22, 12/24, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 20/40, 21/42, 22/44, 23/46, 24/48, 25/50, 26/52, 27/54, 28/56, 29/58, 30/60 and so on.
I might not get it but I tried :)
