Answers
The solutions are:
[tex] \frac{3 + i}{2} [/tex] and [tex] \frac{3 - i}{2} [/tex]
Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
2x² - 6x + 5 = 0
By comparison:
a = 2
b = -6
c = 5
Now, to get the solutions of the equation, we will have to use the quadratic formula shown in the attached image.
By substituting in the formula, we would find that:
either x = [tex] \frac{6 + \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 + i}{2} [/tex]
or x = [tex] \frac{6 - \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 - i}{2} [/tex]
Hope this helps :)
Related Questions
Which pair of expressions is equivalent?
Answers
Hope this helps!
hey can you please help me posted picture of question
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There are 50 total patrons. 16 like lattes, 12 like espressos, and 8 like both drinks.
Add the two totals for patrons that like either lattes or espressos:
[tex] 16 + 12 = 28 [/tex]
8 patrons like both drinks, so subtract this from the amount of patrons that like either drink:
[tex] 28 - 8 = 20 [/tex]
20 patrons like at least one drink.
Subtract the amount of patrons that like a drink from the total amount of patrons:
[tex] 50 - 20 = \boxed{30} [/tex]
30 patrons like neither drink.
n(L) = 16
n(E) = 12
n(L and E) = 8
n(L or E) = n(L) + n(E) - n(L and E)
n(L or E) = 16 + 12 - 8 = 20
Thus 20 like Either of the coffee drinks.
The patrons don't like either of the drinks will be = 50 - 20 = 30
So, option D gives the correct answer
Solve the given differential equation. y' = 5x^2 − 1/ 5 + 4y
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In a class, 12 out of 25 students are female. what percent of students are female?
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12 females
25 total students
12 / 25 = 0.48 = 48%
Which expression below gives the average rate of change of the function g(x)= -x^2 -4x on the interval 6 ≤ x ≤ 8?
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[tex]Average\ rate\ of\ change= \frac{g(b)-g(a)}{b-a} [/tex]
Thus, the average rate of change of [tex]g(x)=-x^2-4x[/tex] over the interval [tex]6\leq x\leq8[/tex] is given by:
[tex]Average\ rate\ of\ change= \frac{[-(8)^2-4(8)]-[-(6)^2-4(6)]}{8-6} \\ \\ = \frac{(-64-32)-(-36-24)}{2} = \frac{-96-(-60)}{2} = \frac{-96+60}{2} = \frac{-36}{2} \\ \\ -18[/tex]
describe a situation where it is easier to use decimals than fractions and explain why
Answers
When you must multiply non whole numbers, decimals are easier to manipulate in the sense that setting up a multiplication problem with decimals rather than fractions is much simpler and easier to calculate.
What is the equation of the line written in general form? -x+y-2=0
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_____
Personally, I would rewrite it to have a positive leading coefficient.
x -y +2 = 0
can someone help with this
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In Set Notation, this might be written as
{x | (x ≤ 0) ∪ (x ≥ 23)}
In Interval Notation, this might be written as
(-∞, 0] ∪ [23, ∞)
Lila draws a 145 degree angle. then she divides it into three smaller angles. One of the smaller angles measures 65 degrees, then the other two are equal in measure. What is the measure of the other two.
Answers
Let each of the equal small angles be x.
The sum of three small angles is 145 degrees. One of these small angles is 65 degrees.
Now let us substitute the given information in an equation.
[tex]2x+65=145[/tex]
After subtracting 65 from both sides of equation we get
[tex]2x=80[/tex]
Dividing both sides of equation with 2 we get
[tex]x=\frac{80}{2}=40[/tex]
Therefore measure of each of the remaining angles is 40 degrees.
The measure of the other two smaller angles, given that they are equal would be 40 degrees.
How to find the measure of angles ?Let's denote the measure of the other two smaller angles as "x."
We know that the sum of the three angles should be equal to the original 145-degree angle. Therefore, we can set up the equation:
65 + x + x = 145
Simplifying the equation:
65 + 2x = 145
Next, we can isolate "x" by subtracting 65 from both sides of the equation:
2x = 145 - 65
2x = 80
Finally, we divide both sides of the equation by 2 to solve for "x":
x = 80 / 2
x = 40
So, the measure of the other two smaller angles is 40 degrees each.
Find out more on angle measure at
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A Spanish class has 28 a total of students. The number of females is 4 less than the number of males. How many males and how many females are in the class?
Answers
F + M = 28
F = M - 4
Now we can solve for M by substitution. In the first equation, replace F with (M - 4):
(M - 4) + M = 28
Combine like terms and solve for M:
2M - 4 = 28
2M = 32
M = 16
If there are 16 males, we can solve for the number of females by plugging 16 back into one of the equations:
F = 16 - 4 = 12
There are 16 males and 12 females.
[tex]x + y = 28[/tex]
[tex]x = y + 4[/tex]
x represents the males in the class, and y represents the females in the class.
Because x = y + 4, we can substitute x in the first equation:
[tex]x = y + 4[/tex]
[tex]y + 4 + y = 28[/tex]
Combine like terms.
[tex]2y + 4 = 28[/tex]
Subtract 4 from both sides.
[tex]2y = 24[/tex]
Divide both sides by 2 to get y by itself.
[tex]y = 12[/tex]
Because we know what y is, we can plug in its value into the first equation:
[tex]x + 12 = 28[/tex]
Subtract 12 from both sides to get x by itself.
[tex]x = 16[/tex]
There are 16 males and 12 females in the class.
What is the opposite or addictive inverse of 43
Answers
The opposite of a number is simply found by dividing by 1. If it were a negative number, it would become positive, and vice versa.
I hope this helps!
Omg I am stuck please help
Answers
Once the minimum population of insects reaches 2 million:
P>=2, then possible options: Third or fourth
The minimum number of the species, in milions, is constantly decreasing at a rate of 7.9% each year.
When the exponent of "e" is positive, the function is increasing.
When the exponent of "e" is negative, the function is decreasing.
Answer: Fourth option:
P>= 26 e^(-0.079t)
P>= 2
Please please help!!
Answers
x must be different to zero, then x=0 is an asymptote
When x tends to -infinite or x tends to + Infinite, the function f(x) tends to zero, then y=0 is an asymptote.
In g(x):
x-1 must be different to zero, then x=1 is an asymptote
When x tends to -infinite or x tends to + Infinite, the function g(x) tends to zero, then y=0 is an asymptote.
Answers:
Third option: y=0
x=0 is an asymptote
The answer for the question is the 3rd option y= 0
Eric leans a ladder against the roof of his house so that the ladder forms a 2004-04-02-01-00_files/i0260000.jpg angle with the ground. The roof of the house is 13 feet above the ground. How far is the bottom of the ladder from the base of the house? Round the answer to the nearest tenth.
Answers
We have a perpendicular(opposite side), the measure of angle and we are interested in finding the hypotenuse.
sine of the angle relates its perpendicular side to hypotenuse as:
sin(x) = perpendicular/hypotenuse
⇒
Hypotenuse = Perpendicular/sin(x) = 13/sin(70) = 13.8 feet
This means, the length of the ladder is 13.8 feet, rounded to nearest tenth.
Answer:
4.7 ft.
Step-by-step explanation:
Let x represent the distance of the bottom of the ladder from the base of the house.
We have been given that Eric leans a ladder against the roof of his house so that the ladder forms a 70 angle with the ground. The roof of the house is 13 feet above the ground.
Upon looking at our attached graph we can see that ladder and wall of house forms a right triangle with respect to ground, where x is adjacent and side with 13 ft length is opposite side to the angle of 70 degrees.
We know that tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(70^{\circ})=\frac{13}{x}[/tex]
[tex]x=\frac{13}{\text{tan}(70^{\circ})}[/tex]
[tex]x=\frac{13}{2.747477419455}[/tex]
[tex]x=4.7316\approx 4.7[/tex]
Therefore, the bottom of ladder is 4.7 feet away from the base of the house.
Daisies cost $0.99 each and tulips cost $1.15 each. Maria bought a boquet of daisies and tulips. It contained 12 flowers and cost $12.52. Find the number of daisies and the number tulips in the bouquet
Answers
Maria bought 8 daisies and 4 tulips in the bouquet.
Explanation:Let's assume that Maria bought x daisies and y tulips. Since the total number of flowers in the bouquet is 12, we can write the equation: x + y = 12.
Also, the total cost of the bouquet is $12.52. Using the cost per flower, we can write another equation: 0.99x + 1.15y = 12.52.
Now we have a system of equations that we can solve. Multiplying the first equation by 0.99, we get 0.99x + 0.99y = 11.88. Subtracting this equation from the second equation eliminates the x term, giving us 0.16y = 0.64. Dividing both sides by 0.16, we find that y = 4.
Substituting this value back into the first equation, we can solve for x: x + 4 = 12, x = 8.
Therefore, Maria bought 8 daisies and 4 tulips in the bouquet.
sophina brought 3 yards of trim to put around a rectangular scarf she wants the width of the scarf to be a whole number that is at least 6 in and at most 12in if she uses all of the trim what are the possible dimensions of her scar write your answers in inches
Answers
Solve 5x 2 - 7x + 2 = 0 by completing the square. What is the constant added on to form the perfect square trinomial?
Answers
Answer: 49/100 is correct
( that other answer was bothering me )
Now evaluate f(x) = 2x4 - 4x3-11x2+3x-6 for x=-2 f (-2) =
Answers
The answer to the given solution is 8.
Given that,
The equation is [tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6[/tex].The x = -2.Based on the above information, the calculation is as follows:
[tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6\\\\= 2(-2)^4 - 4(-2)^3-11(-2)^2+3(-2)-6\\\\= 2\times 16 - 4\times -8 - 11\times 4+ 3 \times -2 - 6\\\\[/tex]
= 32 + 32 - 44 - 6 - 6
= 8
Therefore we can conclude that the answer is 8
Learn more: brainly.com/question/17429689
You have a bag full of 17 marbles. of those marbles, 3 are black. what is the probability that a marble chosen is not black? brainly
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-----------------------
Total number of marbles that are not black = 17 - 3 = 14
P(not black) = 14/17
Answer: 14/17
What is the midpoint between the points (1, 3) and (5, 7)?
A. (4, 4)
B. (7, 9)
C. (3, 5)
D. (2, 2)
Answers
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have [tex]A(1;\ 3);\ B(5;\ 7)[/tex]
Therefore
[tex]M_{AB}\left(\dfrac{1+5}{2};\ \dfrac{3+7}{2}\right)\to M_{AB}\left(\dfrac{6}{2};\ \dfrac{10}{2}\right)\to M_{AB}(3;\ 5)[/tex]
Answer: C. (3; 5)
a golf course charges $10 to golf or $150 for a summer pass. Write an inequality to represent the number of times you would need to golf in order for the summer pass to be a better deal
Answers
We have then:
x: the number of times you would need to golf
We write now the inequality:
10x> 150
Answer:
An inequality to represent the number of times you would need to golf in order for the summer pass to be a better deal is:
10x> 150
Answer:I
Step-by-step explanation:
What is the gcf of 108 and 132
Answers
Answer:
12
Explanation:
The greatest common factor (GCF) is the largest factor two numbers share within their respective factor trees. In order to find the GCF, list factors of each number and then select the biggest one they have in common.
Factors of 108 are:
1, 108; 2, 54; 4, 27; 6, 18; 9, 12
Factors of 132 are:
1, 132; 2, 66; 3, 44; 4, 33; 6, 22; 11, 12
As can be observed, the largest number they have in common is 12. Therefore the GCF of 108 and 132 is 12.
In your drawer you have 10 white socks, 6 black socks, 4 brown socks and 2 blue socks. your roomate is still asleep, and you cannot turn the light on while you get dressed. you reach in blindly and grab two socks. what is the probability of pulling out a matching pair of black socks?
Answers
the number of black socks is 6 and in one pair of sock, there are 2 socks.
so, 6/22 = 3/11 which means out of 6 black socks I pulled out 3/11 pair of black socks.
Hey can you please help me posted picture of question
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So, shifting to right by 9 units means, subtracting 9 from x.
G(x) = F(x - 9)
G(x) = |x - 9|
So, option D is the correct answer
What is the GCF
135, 189 , 297
Answers
I would say the answer is 27.
Pls, give brainliest.
If the question is multiple choice, next time, you should put all the possible answers down to make it easier for the viewers
edit: nevermind I checked, and it's 27. sorry :(((
How does tan 135 degrees compare to tan -135 degrees
Answers
tan 135=tan(135+180)=tan 315=-1
next:
tan -135=tan(180-135)=tan 45=1
thus comparing the two we see that tan 135 is negative while tan -135 is positive
Tan(135°) is -1 because it lies in the second quadrant with sine positive and cosine negative, whereas tan(-135°) is 1 as it falls in the third quadrant with both sine and cosine negative. Thus, tan(135°) = -1 and tan(-135°) = 1.
1. The tangent of an angle is defined as the ratio of the sine to the cosine of that angle: tan(θ) = sin(θ) / cos(θ). The tangent function is also periodic with a period of 180 degrees, meaning tan(θ) = tan(θ + 180°).
2. First, let’s find the value of tan(135°). Since 135° is in the second quadrant where sine is positive and cosine is negative:
sin(135°) = sin(180° - 45°) = sin(45°) = √2/2cos(135°) = cos(180° - 45°) = -cos(45°) = -√2/23. Therefore, tan(135°) = (√2/2) / (-√2/2) = -1.
4. Next, we consider tan(-135°). Since -135° is in the third quadrant where both sine and cosine are negative:
sin(-135°) = -sin(135°) = -√2/2cos(-135°) = cos(225°) = -√2/25. So, tan(-135°) = (-√2/2) / (-√2/2) = 1.
In summary, tan(135°) = -1 and tan(-135°) = 1.
convert from radians to degrees -7pi/2
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-7π/2=(-7*180)/2=-7*90=-630⁰
-7π/2= -630⁰
hey can you please help me posted picture of question
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subtract the number taking both, so you don't count the same student twice: 34-7 = 27
now subtract that amount from total students: 60 - 27 = 33
The answer is C. 33
-6x- 17/4 is less than or equal to 79/4
please please please solve and show work
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Tree a lived for 6 decades and 5 years. Tree b lived for 58 years. Which tree lived longer
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Final answer:
Tree A, which lived for 65 years (6 decades and 5 years), lived longer than Tree B, which lived for 58 years.
Explanation:
To answer which tree lived longer, we can calculate the age of both trees. Tree A lived for 6 decades and 5 years. Since one decade is equal to 10 years, 6 decades would be 6 x 10 years, which is 60 years. Adding the additional 5 years, Tree A lived for a total of 60 + 5 = 65 years.
Tree B lived for 58 years. Comparing both ages, Tree A lived for 65 years while Tree B lived for 58 years. Therefore, Tree A lived longer than Tree B.