Answer:
The sum of the two solutions to the given equation is 1/3.
Step-by-step explanation:
Nature of Roots of a Second-Degree Equation
Given a quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The roots of the equation are:
[tex]\displaystyle x_1=\frac{-b+ \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\displaystyle x_2=\frac{-b- \sqrt{b^2-4ac}}{2a}[/tex]
The sum of the roots is:
[tex]\displaystyle x_1+x_2=-\frac{b}{a}[/tex]
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.
We are given the equation:
[tex]3x^2 - x = 4[/tex]
Rearranging:
[tex]3x^2 - x - 4=0[/tex]
The coefficient b is b=-1, and the leading coefficient is a=3, thus the sum of the roots is:
[tex]\displaystyle x_1+x_2=-\frac{-1}{3}[/tex]
[tex]\displaystyle x_1+x_2=\frac{1}{3}[/tex]
The sum of the two solutions to the given equation is 1/3.
la expresión que se muestra abajo re presenta la utilidad en la producción de una nueva libreta profesional ,¿para que el valor positivo "X" la utilidad resulta igual a cero?
a)10
b)10/9
c)770/9
d)670/9
ayúdenme porfavor
Answer: a) 10
Step-by-step explanation:
Buscando en google, encuentro que la expresión es:
C(x) = 9*x^2 - 80*x - 100
Queremos encontrar el valor de x (positivo), tal que esa expresión sea igual a cero, entonces tenemos que resolver:
9*x^2 - 80*x - 100 = 0.
Para ello podemos recordar la ecuación de Bhaskara, que para una ecuación de la forma:
a*x^2 + b*x + c = 0
Las soluciones son:
[tex]x = \frac{-b +-\sqrt{b^2 - 4*a*c} }{2a}[/tex]
en este caso, tenemos:
a = 9
b = -80
c = -100
Entoces, las soluciones van a ser:
[tex]x = \frac{-(-80) +- \sqrt{(-80)^2 - 4*9*(-100)} }{2*9} = \frac{80 +- 100}{18}[/tex]
Entonces las dos soluciones son:
x = (80 - 100)/18 = -20/18 = -10/9
Esta solución la descartamos, pues es negativa. La otra solución es:
x = (80 + 100)/18 = 180/18 = 10
La opción correcta es a: 10
Mrs. King takes out a personal loan for $10,000 at a yearly simple interest rate of 9.1%. How much total interest will she owe at the end of 6 years?
Answer:
$5,460
Step-by-step explanation:
Given that :
Loan taken = principal (p) = $10,000
Simple Interest rate (r) = 9.1% = 0.091
Interest owed at the end of 6 years = t
Simple interest = (principal * rate * time)
Interest owed = 10,000 * 0.091 * 6
Interest owed = 910 * 6
Interest owed = $5,460
Please help with this assignment
Answer:
3
Step-by-step explanation:
Answer:
24 yards long
What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the standard deviation was 275? step by step how to get +1.09
get marked the brainliest
mu = 1100 = population mean
sigma = 275 = population standard deviation
x = 1400 = raw score
z = z score
z = (x-mu)/sigma
z = (1400-1100)/(275)
z = 300/275
z = 1.0909090909091 approximately
z = 1.09
Convention is to round to two decimal places so that you can use a Z table to look up the area under the curve (which helps determine probability).
The positive z score is due to Paula's raw score being above the mean.
Two neighbors in a rural area want to know the distance between their homes in miles. What should the neighbors use as a conversion factor to convert this distance to miles ?
Answer:
1 foot = 0.000189394 miles
Step-by-step explanation:
The two neighbors in the rural community could measure the distance between their homes first in feet. So that the value in feet can now be converted to miles by multiplying it by 0.000189394.
Since,
1 foot = 0.000189394 miles
Let us assume that the distance between the two houses is 500 feet, then;
1 foot = 0.000189394 miles
500 feet = x miles
x = 500 x 0.000189394
= 0.094697
So that for the considered example, the distance is approximately 0.095 miles.
Thus, the required conversion factor is;
1 foot = 0.000189394 miles
Please help me im new to the site. A soda company had sales of $35,119 million in 2010 and $45,962 million in 2014. Use the Midpoint Formula to estimate the sales in 2012. Assume that the sales followed a linear pattern.
Answer:40533.5
Step-by-step explanation:
Midpoint formula
(35113, 2010) > (X1, Y1)
(45954, 2014) > (X2, Y2)
Plug it into the midpoint formula
The factory makes boxes that each hold one candle. The boxes measure 1 inch × 1 inch × 9 inches. The factory owner makes a stack of 40 candle boxes. What is the volume of the stack?
Answer:
360 inch^3
Step-by-step explanation:
Volume of 1 box = 1 x 1 x 9 = 9 inch^3
Volume of 40 boxes = 40 x 9 = 360 inch^3
This is a topic on mensuration. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!
Answer:
360 in
Step-by-step explanation:
L × W × H
1 × 1 ×9 = 9in
9 × 40 = 360 in
The cards in Kaylens' hand had a value of 2.75, but then he added five (-1.5)
cards to his hand. What is the new value of the cards in his hand?
Answer:
1.25
Step-by-step explanation:
adding a positive to a negative it would go down to 1.25
Find the slope and y-intercept for the table.
slope:
y-intercept:
Answer: 5 y=5
x=3
Step-by-step explanation:
What are the domain and range of the relation given in the table?
Answer:
C
Step-by-step explanation:
all x values is domain, all y values are range
Answer:
Its c
Step-by-step explanation:
Domain = x value
Range = y value
I need help ASAP
3k+30=95+k+2k-5
Answer:
Step-by-step explanation:
3k+30=95+k+2k-5
3k+30=100+3k
-30 -30
3k=70+3k
-3k -3k
k=70
PLEASE HURRY ILL GIVE BRAINLEST AND 50 POINTS FOR THE CORRECT ANSWER ASAP
Answer:
m∠W is 28°
m∠X is 24°
Step-by-step explanation:
In any triangle, the measure of an exterior angle at one vertex of a triangle equals the sum of the measures of the two interior angles opposite to this vertex
In the given figure
∵ ∠WYZ is an exterior angle of Δ XYW at vertex Y
∵ ∠W and ∠X are the interior angles of Δ XYW opposite to the vertex Y
→ Use the fact above
∴ m∠WYZ = m∠X + m∠W
∵ m∠WYZ = 52°
∵ m∠X = 3y°
∵ m∠W = (4y - 4)°
→ Substitute them in the equation above
∵ 52 = 3y + 4y - 4
→ Add the like terms
∴ 52 = 7y - 4
→ Add 4 to both sides
∵ 52 + 4 = 7y - 4 + 4
∴ 56 = 7y
→ Divide both sides by 7
∵ [tex]\frac{56}{7}[/tex] = [tex]\frac{7y}{y}[/tex]
∴ 8 = y
→ Substitute y in the measures of ∠X and ∠W
∵ m∠X = 3(8)
∴ m∠X = 24°
∵ m∠W = 4(8) - 4 = 32 - 4
∴ m∠W = 28°
97700000000000000000000 in scientific notation
Answer:
That number is 9.77 x 10²² .
Step-by-step explanation:
Answer:
9.777 x 10^22
Step-by-step explanation:
in order to put a number in scientific notation, you have to move the invisible decimal over to the right since the number is a large number. in this case, the invisible decimal would start between 9 and 7. if you put this decimal to the right until you reach the last zero of the right, you would have move the decimal 22 spaces to the right
A neon sign blinks every 6 minutes, and another sign blinks every 8 minutes. How often do they blink at the same time?A.Every 14 minutesb.Every 24 minutesc.Every 48 minutesd.Every 2 minutes
Answer:
b. Every 24 minutes
Step-by-step explanation:
A neon sign blinks every 6 minutes, and another sign blinks every 8 minutes.
The first step is to:
Find and list multiples of each time each neon sign blinks.
This means, we find the Multiples of 6 and 8
Multiples of 6:
6, 12, 18, 24, 30, 36
Multiples of 8:
8, 16, 24, 32, 40
The first and common multiple of 6 and 8.
Therefore, the Least common multiple [LCM(6, 8) ] = 24
Hence, they often blink at the same time every 24 minutes.
Therefore, option b.Every 24 minutes is correct.
What is the value of the expression below when y = 8?
2y + 7
Answer:
Submit Answer
Answer:
23
Step-by-step explanation:
we will put 8 instead of "y" in the equation
2 x 8 + 7 = 23
- х= -у
6x - бу = 12
I need to find if it’s a substitution or elimination equation and step by step
Just by looking at this question, I say there is no solution because these two equations do not touch or meet on the xy-plane.
- х= -у.........A
6x - бу = 12.........B
Solve A for x.
-x = - y
Divide both sides by negative 1.
Doing so, we get x = y. Plug this into B.
6x - 6y = 12
6(y) - 6y = 12
The left side becomes zero.
0 = 12 is a false statement.
Answer: There is no solution to this system of
equations in two variables.
Understand?
You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measures of the interior angles of the triangle.
Answer:
Step-by-step explanation:
A linear pair are two given angles whose sum is equal to [tex]180^{o}[/tex].
Let the exterior angle be represented by [tex]x^{o}[/tex], and the three interior angles of the triangle be represented by [tex]a^{o}[/tex], [tex]b^{o}[/tex] and [tex]c^{o}[/tex].
Assume that the vertex angle [tex]c^{o}[/tex] is the linear pair to the exterior angle [tex]x^{o}[/tex].
i.e [tex]x^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)
Thus,
i. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex] (sum of two opposite interior angles is equal to an exterior angle)
⇒ [tex]a^{o}[/tex] = [tex]x^{o}[/tex] - [tex]b^{o}[/tex]
Also,
[tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
But,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
⇒ [tex]c^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]a^{o}[/tex] + [tex]b^{o}[/tex])
and
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]180^{o}[/tex] - [tex]c^{o}[/tex]
ii. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]a^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]b^{o}[/tex] + [tex]c^{o}[/tex])
Also,
[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]x^{o}[/tex]
⇒ [tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]
[tex]c^{o}[/tex] = [tex]180^{o}[/tex] - [tex]x^{o}[/tex]
The value of a stock increases 1423 points twice in one week. The other three days the value decreases by 10 points, 813 points, and 1223 points. By how many points did the value of the stock change that week? A. 2/3 points B. 1/3 points C. −1 1/3 points D. −1 2/3 points
Answer:
Step-by-step explanation:
Remark
Usually the statements are written from your broker's and his accountant's point of view. That being said, he looks at the numbers as a debit for a plus, and a credit as a minus. We'll assume it started out as a new purchase.
Debit Credit Balance
0 0
1423 1423
1423 2846
10 2836
813 2023
1223 800
None of the answers match. I have done it correctly. There is no way you will get a fractional amount from those numbers. You are going to have to take it to your teacher/instructor to find out how it is done.
Factoring Polynomials Completely Step by step
Answer:
x(x-8)(x+8)
Step-by-step explanation:
it ends with a negative 64 and the only one that also end with that would be C because -8×8 = 64
What is the answer???????????????????????????????/
Answer:
Step-by-step explanation:
b
shaun had a collection of 840 matchbox vehicles. of these vehicles, 15% are four wheelers and 30% are convertibles. the rest are fast cars. how many fast cars are shaun matchbox box.
Answer:
462 fast cars please mark brainliest
Step-by-step explanation:
How to do this question plz answer
Answer:
θ= 39.7° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
Evaluate: f(2) if f(x) = 4 - 2x
f(2) = 0
f(2)= 2
f(2)= 4
f(2) = 8
Answer:
f(2) = 0
Step-by-step explanation:
Evaluate: f(2) if f(x) = 4 - 2x; plug in 2 for x
f(2) = 4 - 2(2) = 4 - 4 = 0
Answer:
f(2) = 0
Step-by-step explanation:
Put 2 in the place of x,
f(2) = 4 - 2(2)
f(2) = 4 - 4
f(2) = 0
2 pts
Question 3
Select all parts from the expression above that represents a constant term.
-4.9
-4.9t?
1.8
22
22t
Which ones are constant terms pls help
descending order 20,-30,4,0,-3,10
Answer:
20,10,4,0,-3,-30
Step-by-step explanation:
steph,andra,emily,and becca are planning a road trip from their hometown to san antonio
hometown:8,6
san antonio:-6,-7
a. if the girls take turns driving and each girl drives the same distance,at what point should they stop from emily to begin her turn as the third driver?
b.at what point does emily's turn to drive end?
Answer:
a. Emily should begin her turn as the third driver at point (1, -0.5).
b. Emily's turn to drive end at point (-2.5, -3.75).
Step-by-step explanation:
Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:
Hometown
[tex]H(x,y) = (8,6)[/tex]
San Antonio
[tex]T(x,y) = (-6,-7)[/tex]
Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:
Steph
[tex]S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)][/tex] (1)
[tex]S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]S(x,y) = (8,6) +\frac{1}{4}\cdot (-14,-13)[/tex]
[tex]S(x,y) = (4.5,2.75)[/tex]
Andra
[tex]A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)][/tex] (2)
[tex]A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]A(x,y) = (8,6)+\frac{2}{4}\cdot (-14,-13)[/tex]
[tex]A(x,y) =(1, -0.5)[/tex]
Emily
[tex]E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)][/tex] (3)
[tex]E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]E(x,y) = (8,6)+\frac{3}{4}\cdot (-14,-13)[/tex]
[tex]E(x,y) = (-2.5, -3.75)[/tex]
a. If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver?
Emily's beginning point is the Andra's stop point, that is, [tex]A(x,y) =(1, -0.5)[/tex].
Emily should begin her turn as the third driver at point (1, -0.5).
b. At what point does Emily's turn to drive end?
Emily's turn to drive end at point (-2.5, -3.75).
Solve for x. Round answer to the nearest tenth, if necessary
Answer:
x=15
Step-by-step explanation:
9²+12²=c²
81+144=c²
225=c²
√225=√c
15=c
The measure of the x is 15.
Given
The length of the base is 9 and the perpendicular is 12.
What is the Pythagoras theorem?Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The length of the hypotenuse is x.
Therefore,
[tex]\rm (Hypotenuse )^2= (Base)^2+ (Perpendicular)^2\\\\(x)^2=(9)^2+(12)^2\\\\144+81=x^2\\\\x^2 = 144+81\\\\x^2=225\\\\x=15[/tex]
Hence, the measure of the x is 15.
To know more about Pythagoras theorem click the link given below.
https://brainly.com/question/343682
x^2+1=0
What are the roots of this equation?
Thanks!
this is the answer for this question
the pyramid shown has a rectangular base and faces that are isosceles triangles find the total surface area to the nearest tenth
Answer:
I think is C.
Step-by-step explanation:
I'm so sorry if wrong!
can someone help me please? the last point of the first graph ends on 6
Answer:
a) Yes
b) for reference, draw the line y = x, and reflect it over that, this reflection will be your inverse. Or switch the x and y values of each point of the function.
Here is a photo of the original function in black, it's inverse in red, and the line of reflection y = x in blue:
c) No, because it fails the vertical line test, when you draw a vertical line across the inverse function, it hits it more than once.
d) Domain of the original function: -6 ≤ x ≤ 6 ; x(the domain) is greater than or equal to -6 and less than or equal to 6.
e) Domain of inverse function: 0 ≤ x ≤ 4 ; x(the domain) is greater than or equal to 0 and less than or equal to 4.
f) Range of the original function: 0 ≤ y ≤ 4 ; y(the range) is greater than or equal to 0 and less than or equal to 4.
e2) Range of the inverse function: -6 ≤ y ≤ 6 ; y(the range) is greater than or equal to -6 and less than or equal to 6.
f2) x-intercept of original function: -6
g) y-intercept of the inverse function: -6
h) x-intercept of the inverse function: 4
i) y-intercept of the original function: 4
j) (2,2) or any point where the x, and y are the same within the function, or the point where the function intersects y = x.