Answer:
6x^2+10x-6=0
Step-by-step explanation:
First, you need to add all like terms:
6x^2+8x-6=-2x
Now move the -2x to the other side:
6x^2+10x-6=0
Answer:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
6*x^2+8*x-6-(2-2*x-2)=0
Step by step solution :
STEP 1 :
The Equation at the end of step 1
(((2•3x2) + 8x) - 6) - -2x = 0
STEP 2 :
STEP 3 :
Pulling out like terms
3.1 Pull out like factors :
6x2 + 10x - 6 = 2 • (3x2 + 5x - 3)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 + 5x - 3
The first term is, 3x2 its coefficient is 3.
The middle term is, +5x its coefficient is 5.
The last term, "the constant", is -3
Step-1: Multiply the coefficient of the first term by the constant 3 • -3 = -9
Step-2: Find two factors of -9 whose sum equals the coefficient of the middle term, which is 5.
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
Observation: No two such factors can be found !!
Conclusion: Trinomial can not be factored
The Equation at the end of step 3 :
2 • (3x2 + 5x - 3) = 0
STEP 4 :
Equations which are never true:
4.1 Solve : 2 = 0
This equation has no solution.
A non-zero constant never equals zero.
Parabola, Finding the Vertex:
4.2 Find the Vertex of y = 3x2+5x-3
Parabolas have the highest or lowest point called the Vertex. Our parabola opens up and accordingly has the lowest point (AKA absolute minimum). We know this even before plotting "y" because the coefficient of the first term, 3, is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x-intercepts (roots or solutions) of the parabola. That is if the parabola has indeed two real solutions.
Parabolas can model many real-life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that an object, thrown upwards, can reach. For this reason, we want to be able to find the coordinates of the vertex.
For any parabola, Ax2+Bx+C, the x -coordinate of the vertex is given by -B/(2A). In our case, the x coordinate is -0.8333
Plugging into the parabola formula -0.8333 for x we can calculate the y -coordinate :
y = 3.0 * -0.83 * -0.83 + 5.0 * -0.83 - 3.0
or y = -5.083
Parabola, Graphing Vertex, and X-Intercepts :
Root plot for : y = 3x2+5x-3
Axis of Symmetry (dashed) {x}={-0.83}
Vertex at {x,y} = {-0.83,-5.08}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.14, 0.00}
Root 2 at {x,y} = { 0.47, 0.00}
Solve Quadratic Equation by Completing The Square
4.3 Solving 3x2+5x-3 = 0 by Completing The Square.
Divide both sides of the equation by 3 to have 1 as the coefficient of the first term :
x2+(5/3)x-1 = 0
Add 1 to both side of the equation :
x2+(5/3)x = 1
Now the clever bit: Take the coefficient of x, which is 5/3, divide by two, giving 5/6, and finally square it giving 25/36
Add 25/36 to both sides of the equation :
On the right-hand side we have :
1 + 25/36 or, (1/1)+(25/36)
The common denominator of the two fractions is 36 Adding (36/36)+(25/36) gives 61/36
So adding to both sides we finally get :
x2+(5/3)x+(25/36) = 61/36
Adding 25/36 has completed the left-hand side into a perfect square :
x2+(5/3)x+(25/36) =
(x+(5/6)) • (x+(5/6)) =
(x+(5/6))2
Things which are equal to the same thing are also equal to one another. Since
x2+(5/3)x+(25/36) = 61/36 and
x2+(5/3)x+(25/36) = (x+(5/6))2
then, according to the law of transitivity,
(x+(5/6))2 = 61/36
We'll refer to this Equation as Eq. #4.3.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/6))2 is
(x+(5/6))2/2 =
(x+(5/6))1 =
x+(5/6)
Now, applying the Square Root Principle to Eq. #4.3.1 we get:
x+(5/6) = √ 61/36
Subtract 5/6 from both sides to obtain:
x = -5/6 + √ 61/36
Since a square root has two values, one positive and the other negative
x2 + (5/3)x - 1 = 0
has two solutions:
x = -5/6 + √ 61/36
or
x = -5/6 - √ 61/36
Note that √ 61/36 can be written as
√ 61 / √ 36 which is √ 61 / 6
Solve Quadratic Equation using the Quadratic Formula
4.4 Solving 3x2+5x-3 = 0 by the Quadratic Formula.
According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 3
B = 5
C = -3
Accordingly, B2 - 4AC =
25 - (-36) =
61
Applying the quadratic formula :
-5 ± √ 61
x = —————
6
√ 61, rounded to 4 decimal digits, is 7.8102
So now we are looking at:
x = ( -5 ± 7.810 ) / 6
Two real solutions:
x =(-5+√61)/6= 0.468
or:
x =(-5-√61)/6=-2.135
HOPE THIS HELPS!
PLEASE MARK BRAINLIEST IF THIS HELPED YOU LEARN! :)
Write an equation for the following data plz :)
Answer:
y = 4x + 1
Y values increase by 4, X values increase by 1.
M or slope, = 4/1 or 4
Y-intercept is when x = 0
When x = 0 in this case, y = 1.
So,
y = 4x +1
Answer:
y = 4x + 1
Step-by-step explanation:
This is the y = mx + b format, hopefully its useful for you! It's a linear equation because all the values grow at a constant rate.
The y-intercept is 1 and it's rise over run which means that you start at 1 on your y-intercept when graphing and then rise 4 and run 1 to the right because it's a positive slope.
Use the chart to help u ;-;"
Hey, can someone help me with my math homework?
aqueell ears hanan pus
Solve the system by elimination
Answer:
x= -2 y= -5
Step-by-step explanation:
Eliminate y by subtract = 3x-6x-2y+2y=6 ; x=-2
plug-in x = -2
-6-2y = 4 y = -5
Answer:
(- 2, - 5)
Step-by-step explanation:
[tex]\left \{ {{3x-2y=4} \atop {6x-2y=-2}} \right.[/tex]
(2) - (1)
(6x - 3x) + [- 2y - (- 2y)]= - 2 - 4
3x = - 6 ⇒ x = - 2
3( - 2) - 2y = 4 ⇔ - 6 - 2y = 4 ⇒ y = - 5
(- 2, - 5)
Write the number 76,689 in expanded form
happy veterans day everybody!!!
Answer:
happy vets day
Step-by-step explanation:
Solve the function below for y when x=12.
y=−3x+20
Answer:
y = -16
Step-by-step explanation:
y = -3(12) + 20
y = -36 + 20
y = -16
Hope this helps and pls do mark me brainliest if you can:)
X varies directly as the cube root of y .x=6when y=8.Find the value of x when y=64.
Answer:
The value of x is 12.
Step-by-step explanation:
Given that x is directly proportional to y so the expression will be x = k (³√y) where k is the constant. First, you have to find the value of k :
[tex]x = k \: (\sqrt[3]{y} )[/tex]
[tex]let \: x = 6,y = 8[/tex]
[tex]6 = k \: (\sqrt[3]{8} )[/tex]
[tex]6 = k(2)[/tex]
[tex]k = 3[/tex]
Next, you have to find the value of x, by substituting y = 64 into the expression :
[tex]x = 3 \: ( \sqrt[3]{y} )[/tex]
[tex]x = 3( \sqrt[3]{64} )[/tex]
[tex]x = 3(4)[/tex]
[tex]x = 12[/tex]
The median of the set (n, n+5, n+6, n+9, n+15) is 9. What is the mean?
HELP ME
Answer: 10
Step-by-step explanation:
tbh its too long to explain i gtg now but plz just trust me
Daikwon and Chris are about to record a new CD. They have a choice between two back up bands. One band charges $50 plus $20 for each take. The second band charges S20 plus $25 for each take.
Answer:
The second band
Step-by-step explanation:
50+20=70
20+25=45
the 15% tip on craig's lunch bill came to $2.40 what was the amount of bill before the tip? show workouts
At a football stadium, 4% of the fans in attendance were teenagers. If there were 120 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
3000 people
Step-by-step explanation:
4% teenagers --> 120 teenagers were there
120/4 means 1% so 30 is 1%
1% times 100 is 100% so 30 times 100 equals 100% so 3000 is 100% of the people at the stadium
Determinar que Recipiente tiene mayor densidad; el recipiente A pesa 1.2 toneladas y tiene un volumen de 120 m³ mientras que el recipiente B pesa 2.4 toneladas y tiene un volumen de 240 m³. ¿Cuál recipiente tiene mayor densidad?
Answer:
Ambos recipientes tienen la misma densidad, es decir, 10 kilogramos por metros cúbicos.
Step-by-step explanation:
Recordamos que la densidad de un material uniforme ([tex]\rho[/tex]), medido en kilogramos por metro cúbico, está definido por:
[tex]\rho = \frac{m}{V}[/tex] (1)
Donde:
[tex]m[/tex] - Masa, medido en kilogramos.
[tex]V[/tex] - Volumen, medido en metros cúbicos.
Ahora calculamos la densidad de cada recipiente:
Recipiente A ([tex]m =1200\,kg[/tex], [tex]V = 120\,m^{3}[/tex])
[tex]\rho = \frac{1200\,kg}{120\,m^{3}}[/tex]
[tex]\rho = 10\,\frac{kg}{m^{3}}[/tex]
El recipiente A tiene una densidad de 10 kilogramos por metro cúbico.
Recipiente B ([tex]m = 2400\,kg[/tex], [tex]V = 240\,m^{3}[/tex])
[tex]\rho = \frac{2400\,kg}{240\,m^{3}}[/tex]
[tex]\rho = 10\,\frac{kg}{m^{3}}[/tex]
El recipiente B tiene una densidad de 10 kilogramos por metro cúbico.
Ambos recipientes tienen la misma densidad, es decir, 10 kilogramos por metros cúbicos.
To convert 36 mL to L, you would move the decimal point ____ places to the ____.
Answer:
3
left
Step-by-step explanation:
1000/36=0.036
hope this helps
Is 23 x 10^8 written in scientific notation
Answer:
yes,it is written in scientific notation.
Yes, the given number is written in scientific notation.
What is scientific notation?
A method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy.
Yes, 23 x 10^8 is showing a specified degree of accuracy.
Therefore, it is written in scientific notation.
For more references on scientific notation, click;
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Sally was walking to Ocean Front Housing Complex, In miles, how far is her distance?
mi,
Sally plans to stop half way and pick up something to eat at the deli. What coordinate is the deli?
Answer:
Sally is 10 miles
The coordinate ofthe deli is (1, -1)
Step-by-step explanation:
✍️Coordinate of Sally = (-3, 2)
Coordinate of Ocean Front = (5, -4)
The distance of Sally to Ocean Front Housing Complex = the distance between point (-3, 2) and (5, -4).
Use the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to calculate the distance between (-3, 2) and (5, -4):
[tex] d = \sqrt{(5 -(-3))^2 + (-4 - 2)^2} [/tex]
[tex] d = \sqrt{(8)^2 + (-6)^2} [/tex]
[tex] d = \sqrt{64 + 36} [/tex]
[tex] d = \sqrt{100} = 10 [/tex]
✅The distance of Sally is 10 miles
✍️the coordinate of Deli would be half the distance between Sally and Ocean Front.
Therefore, use the midpoint formula to calculate the coordinate of the midpoint between Sally (-3, 2) and Ocean Front (5, -4).
Midpoint of (-3, 2) and (5, -4).
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Plug in the values
[tex] M(\frac{-3 + 5}{2}, \frac{2 +(-4)}{2}) [/tex]
[tex] M(\frac{2}{2}, \frac{-2}{2}) [/tex]
[tex] M(1, -1) [/tex]
✅The coordinate ofthe deli is (1, -1)
I’ll give brainliest
Answer:
1 1/9
Step-by-step explanation:
The answer is 1 1/9. Hope it is correct! You can give a brainliest if it is correct.
An isosceles triangle has base angles that each measure 42 degrees.Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees
Answer:
z+42+42=180
Step-by-step explanation:
Since it is an isosceles triangle, the two base angles are the same and remember all the angles add to 180. So use this equation:
z+42+42=180
If you need to find z, it is 96.
Check: 96+42+42=180
Considere la siguiente ecuación: 16a – ( 3a – (6 – 9a) ) = 30a + ( – (3a + 2) – (a + 3) ) III) Al romper paréntesis, agrupar términos semejantes y simplificar. La ecuación queda:
Answer:
La ecuación simplificada es [tex]a = \frac{11}{19}[/tex].
Step-by-step explanation:
Tenemos la siguiente ecuación simultánea: [tex]16\cdot a - [3\cdot a - (6-9\cdot a)] = 30\cdot a +[-(3\cdot a+2)-(a+3)][/tex]. El procedimiento consiste en destruir los paréntesis desde dentro hacia fuera, agrupar los términos semejantes y simplificar. Presentamos el proceso paso por paso:
1) [tex]16\cdot a - [3\cdot a - (6-9\cdot a)] = 30\cdot a +[-(3\cdot a+2)-(a+3)][/tex] Dado
2) [tex]16\cdot a -\{3\cdot a + (-1)\cdot [6+(-1)\cdot 9\cdot a]\} = 30\cdot a +\{(-1)\cdot (3\cdot a +2)+(-1)\cdot (a+3)\}[/tex] [tex]-b = (-1)\cdot b[/tex]
3) [tex]16\cdot a -\{[(-1)\cdot (6)+(-1)\cdot (-1)\cdot 9\cdot a]\}= 30\cdot a +\{\left[(-1)\cdot (3\cdot a) + (-1)\cdot (2)\right] +[(-1)\cdot a +(-1)\cdot (3)] \}[/tex] Propiedad distributiva
4) [tex]16\cdot a -(-6+9\cdot a) = 30\cdot a +(-3\cdot a -2-a-3)[/tex] [tex]-b = (-1)\cdot b[/tex]/ [tex](-b)\cdot (-c) = b\cdot c[/tex]
5) [tex]16\cdot a +(-1)\cdot (-6+9\cdot a) = 30\cdot a -4\cdot a-5[/tex] Propiedad distributiva/Definiciones de adición y sustracción/[tex]-b = (-1)\cdot b[/tex]
6) [tex]16\cdot a +[(-1)\cdot (-6)+(-1)\cdot (9\cdot a)] = 26\cdot a -5[/tex] Propiedad distributiva/Definiciones de adición y sustracción/Propiedad modulativa.
7) [tex]16\cdot a +6-9\cdot a = 26\cdot a - 5[/tex] [tex]-b = (-1)\cdot b[/tex]/ [tex](-b)\cdot (-c) = b\cdot c[/tex]
8) [tex]7\cdot a +6 = 26\cdot a - 5[/tex] Propiedad distributiva/Definiciones de adición y sustracción.
9) [tex]6+5 = 26\cdot a -7\cdot a[/tex] Compatibilidad con la adición/Definición de sustracción.
10) [tex]11 = 19\cdot a[/tex] Propiedad distributiva/Definiciones de adición y sustracción.
11) [tex]19\cdot a = 11[/tex] Simetría de la igualdad.
12) [tex]a = \frac{11}{19}[/tex] Compatibilidad con la multiplicación/Existencia del inverso multiplicativo/Propiedad modulativa/Definición de división/Resultado.
La ecuación simplificada es [tex]a = \frac{11}{19}[/tex].
PLZ HELP WITH THIS, I'LL MARK BRAINLIEST
Answer:
With something like this you have to start out with 3 givens. what I do for these specific kinds of questions is just put something random in the first half, then put something random twice in the second slot, click clear, then it'l give you a button that says "clear" then a little after it'll say "hint" or "demo" the click those buttons and just put the second half in something random until it pops off, this works every time and will allow you to go to the next task.
Step-by-step explanation:
May I have brainliest please? :)
Answer:
Statement: ∠1 ≅∠2
Reason: When two parallel lines are cut by a transversal, alternate exterior angles are congruent
Step-by-step explanation:
Solve the equation 186+10x=25.5x to find how many diving lessons x Jacy can take for the cost to be the same with and without a membership.
__ lesson(s)
Answer:12 lessons
Steps in image below:
The number of lessons that take for the cost to be the same with and without a membership will be 12.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equation is given below.
186 + 10x = 25.5x
Simplify the equation, then we have
25.5x - 10x = 186
15.5x = 186
x = 186 / 15.5
x = 12
The number of lessons that take for the cost to be the same with and without a membership will be 12.
More about the solution of the equation link is given below.
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What is the distance between the
two points
(7.8)
{3,2)
To find the exact difference, we have to subtract the two decimal points.
1. First, we'll subtract the whole number. Then, we'll subtract the decimal number. This will make mental math easier.
a. 7 - 3 = 4
b. 8 - 2 = 6
2. Add the answers together to get your final answer.
a. = 4.6
The exact distance between the two points is 4.6. If you can't figure this strategy out, do algorithm. The simplist way to solve this is to use a calculator, which I checked my answer on. Have a nice day! :)
Jaime purchased both a trumpet and a violin for the same amount of money for his music store where he sells used instruments. He marked the trumpet up 40% and sold it for $84. He marked the violin up 45% and sold it to a customer who had a coupon for 15% off any instrument. How much did the customer pay for the violin?
Answer:
12
i think this correct answer
pls help with this one -4 divided by - 2/3
Answer:
6
Step-by-step explanation:
what you do is because you are dividing -4 by -2/3 you have to flip -2/3 to make it -3/2..
so ...
-4/ -2/3 = -4 x -3/2 ( so here you take -2/3 and flip it and multiply by -4)
now all you do is multiply
12/2 you get 6 ! HOPE this helped out alittle
Help me solve this problem please
Answer:
y= 2/3x+6
Step-by-step explanation:
if we multiply we can get the answer
A car uses 8.4 liters of petrol for a 112 mile journey. When the tank is full, the car holds 54 liters of petrol. How far should the car be able to travel on a full tank of petrol.
Answer:
720 miles
Step-by-step explanation:
A car uses 8.4 liters of petrol for a 112 mile journey.
In 1 litres = [tex]\dfrac{112}{8.4}\ \text{miles}[/tex] of journey
We need to find far should the car be able to travel on a full tank of petrol i.e. 54 litres of petrol.
[tex]54\ l=\dfrac{112}{8.4}\times 54\\\\=720\ \text{miles}[/tex]
So, the car can travel 720 miles when it holds 54 lirres of petrol.
Yesterday, the temperature at noon was 10.4°F. By midnight, the temperature has decreased by 16.7 degrees. What was the temperature at midnight?
I'm in 7th grade by the way
Answer:
-6.3 degrees
Step-by-step explanation:
First I formed the equation 10.4-16.7=x, which the answer came to be -6.3 degrees.
What is the equation of the línea perpendicular to y= -3x + 3/5 that Goes through point (-2, 3 )
Answer:
y=1/3x+11/3
Step-by-step explanation:
y=mx+b
y=1/3x+b
3=1/3(-2)+b
3 = -2/3+b
+2/3 +2/3
11/3=b
So the equation of the line that perpendicular to y= -3x + 3/5 that Goes through point (-2, 3 ) is y=1/3x+11/3.
Devin paid $30 to be a member of the Fox Lake Gym. When he takes the boxing
class, it costs him $2. How many classes can he take if spent $42?
Answer:
30 + 2x = 5x i hope this helps
What is the value of a?
Step-by-step explanation:
The value of a is 3 million points
Answer:
What is the question, so we can help you.
Step-by-step explanation: