The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. The roots are irrational numbers and can only be approximated.
The roots of the quadratic equation 5x² 4x 3 0 are two complex conjugates, which cannot be expression in terms of real numbers. To find the roots, the quadratic formula can be used. The formula requires the coefficients of the equation, which in this case are a=5, b=4, and c=3. When the quadratic formula is applied, the results are two complex roots, which are expressed as x1 = -1/5 + (√16)/5i and x2 = -1/5 - (√16)/5i. These roots are irrational numbers and can only be approximated. Complex roots are often found when the discriminant, which is b²-4ac, is negative. In this case, the discriminant is -64, which is negative, indicating that the equation has complex roots.
Discriminant = b²-4ac = 4²-4(5)(3) = -64
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a and b are positive integers and a-b=2. Evaluate the following:
9^1/2b/3^a
Answer:
[tex] \frac{1}{ 9 }[/tex]
Step-by-step explanation:
[tex] \huge \frac{ {9}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ {( {3}^{2} )}^{ \frac{1}{2}b } }{ {3}^{a} } \\ \\ = \huge \frac{ { {3}}^{2 \times \frac{1}{2}b } }{ {3}^{a} } \\ \\ \huge = \frac{ {3}^{b} }{ {3}^{a} } \\ \\ \huge = \frac{1}{ {3}^{a - b} } \\ \\ \huge= \frac{1}{ {3}^{2} } \\ ( \because \: a - b = 2)\\ \\ \huge = \frac{1}{ 9 }[/tex]
The evaluation of the expression 9^((1/2)b)/3^a is 1/9
What are some basic properties of exponentiation?If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
Now, for this case, we are given that:
a - b = 2
The expression is:
[tex]\dfrac{9^\dfrac{1}{2}b}{3^a}[/tex]
Since we know that [tex]3^2 = 9[/tex], thus:
[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} = \dfrac{(3^2)^{\frac{1}{2}b}}{3^a} = \dfrac{3^{2 \times 1/2 \times b}}{3^a} = \dfrac{3^b}{3^a} = \dfrac{1}{3^{a-b}}[/tex]
Since a-b = 2, therefore, we get:
[tex]\dfrac{9^{\frac{1}{2}b}}{3^a} =\dfrac{1}{3^{a-b}} = \dfrac{1}{3^2}} = \dfrac{1}{9}[/tex]
Thus, the evaluation of the expression 9^((1/2)b)/3^a is 1/9
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what type of association is there ??
Answer:
Negative because the dots travel down away from the positive area
The fare for taxi journeys in a certain town is $2.00 plus $1.00 for each kilometre. Using this information, estimate: (i) The fare for a journey of 3.5 km. (ii) The distance travelled if the fare was $6.00
Answer:
Step-by-step explanation:
Since the journey initially costs $2 (this will be our y-intercept), and the variable (x) is $1 for every additional kilometer. This can be modelled as...
y=1x+2
(i) if we want to know the cost of what 3.5 km would cost, we simply plug it into our equation...
y=1(3.5)+2
Answer: $5.5
(ii) For this question you can set the y value equal to 6 and plug in a random number for x until you get 6 on both sides. In this case...
6=1x+2
6=1(4)+2
The distance traveled if the fare was $6 is 4km
I hope this helps you! When I was younger I used to use this site for help and now I'm paying it forward!
6. True or false: A compass contains a magnet that responds to the geomagnetic field of
earth
The correct answer is true
And expression is shown below f(x)=2x^2-x-10 party what are the X intercepts of the graph of f(x) show your work part B is the vertex of the graph of f(x) going to be a maximum or minimum what are the coordinates of the vertex justify your answer in show your work part C what are the steps you would use to graph f(x) justify that you can use the answer is obtained in part a and part B to draw the graph
Answer:
3
Step-by-step explanation:
Hello everybody please help me (this is 6th grade math)
Answer:
Look at the image.
Step-by-step explanation:
Please please please please please please answer question y<-1/3x+2?
Answer:
Please see the attachment, none of the graphs you showed was correct.
Step-by-step explanation:
Hope it helps :)
Jamal has 16 marbles. Zing has 9. How many fewer marbles does Zing
have than Jamal?
Answer:
7
Step-by-step explanation:
16 - 9 = 7
Answer:
7
Step-by-step explanation:
16-9=7
DhhdhcdchxKhkkjdchjcjjdhc
Evaluate:
Σ18/1 (5n– 4) = [? ]
Basically, you are going to evaluate 5n - 4 from n = 1 to n = 18. Don't forget to add as you evaluate.
I will get you started.
Let n = 1 and then n = 2.
5(1) - 4 + 5(2) - 4 + the rest
5 - 4 + 10 - 4 + the rest
1 + 6 + the rest
7 + the rest
Just continue the pattern. You will then let n be 3, 4, 5, etc all the way to 18.
Solve the 4 letter code please I need it before midnight, it's not a word.
9514 1404 393
Answer:
EAGI
Step-by-step explanation:
Your choices are correct except for "B". Graph 3 has a dashed line, so the inequality symbol is <, not ≤.
Please please can someone help me asap thank you
Answer:
Answers bellow
Step-by-step explanation:
FIGURE A
Decreasing by 1/4 =25%
Figure B
Increase by 1/5 = 20 %
Page 2
b The amount of sunny days this year is 75% of the amount of sunny days last year
c The amount of houses sold this month is 150 % amount of houses sold last month
d The runner's time to complete this marathon was 110% he needed to complete the last marathon(not sure about that one )( it's either 90 % or 110)
» Quinn is a contestant on a quiz show. Quinn's score changes by -15 points for 4 questions in a row. D *) What is the total change in Quinn's score?
Answer:
-60
Step-by-step explanation:
5 people shared 2 pizzas how much do they get
Answer: 2 and a half slices
Step-by-step explanation: 5/2 is 2.5
2(10+p)−20<140 what the answer
Answer:
p<70
Step-by-step explanation:
Answer:
p < 70
Step-by-step explanation:
2(10 + p) - 20 < 140
20 + 2p - 20 < 140
2p < 140
p < 70
two three digit numbers are formed using the same integers and then when they are added they form another three digit number with the same integers find the added number
Answer:
I just cannot find it, so I appologize to the author. ... 2. Sum of all the numbers which can be formed by using the digits (repetition being ... Same is true for the other two digits. ... One more tip: when we add up all the numbers, we can start with the ... (1+5+8)/3 * 111 - another way to write 3-digit number formed from "average
Step-by-step explanation:
What is the domain and range for function A?
Answer:
Domain → (-∞, ∞)
Range → (-∞, 5)
Step-by-step explanation:
Domain of a function is a set of x-values (input values) for which the function is defined.
Function A is a quadratic function (in the form of a parabola) opening downwards.
This function is defined for every input value from negative infinity to positive infinity.
Therefore, domain of the given function A is (-∞, ∞).
Similarly, y-values (output values) vary from negative infinity to 5.
Therefore, range of the given quadratic function will be (-∞, 5).
Avery deposited 1250 in a new savings account. Which amount is closest to the balance of the account at the end of three years
Answer: $1,467.80
Step-by-step explanation:
The formula for the future value given annual compounding is:
= Amount * ( 1 + rate) ^ number of years
The amount after 3 years at 5.5% is therefore:
= 1,250 * ( 1 + 5.5%)³
= 1,250 * 1.174241375
= $1,467.80
pls helpppppppppppppppppppppp
Answer:
∠A = 6x + 4
Step-by-step explanation:
Hello There!
We are given the exterior angle ∠ACD and an interior angle ∠B
If you didn't know this is the rule for exterior angles of a triangle:
An exterior angle is equal to the sum of its opposite interior angles
so ∠ACD = ∠A + ∠B ( ∠A and ∠B being the opposite interior angles)
So with the information that we are given we plug them into their corresponding angle
then we would have
8x+5 = ∠A + 2x + 1
now we solve for A
Well how do we solve for A?
Well we have to isolate the variable
To do so we want to get rid of 2x + 1
We do that by subtract each side by 2x and 1
8x + 5 - (2x + 1 ) = 6x + 4
we're left with
∠A = 6x + 4
Given the vertex of a parabola is (-3,1) and also contains the point (-4,-1). State the exact equation of the parabola in vertex form, show all your work.
Answer:
y = -2(x + 3)^2 - 1
Step-by-step explanation:
The vertex equation of a parabola is y = a(x - h)^2 + k. If the vertex here is (-3, 1), then this equation becomes y = a(x + 3)^2 + 1.
Knowing that the graph passes through (-4, -1), we let y = -1 and x = -4, obtaining:
-1 = a(-4 + 3)^2 - 1, which must be solved for a:
-1 = a - 1. Therefore, a = -2, and the exact equation of this parabola is:
y = -2(x + 3)^2 - 1
y=−x+2 y=3x−4 khan
Answer: 0
Step-by-step explanation:
2y -3x - 4 = 0
Subtract 2y from both sides of the equation.
-3x - 4 = -2y
Add 4 to both sides of the equation.
-3x = -2y + 4
Divide each term by -3 and simplify
5. A right triangle has a hypotenuse that is 13 cm and a leg that is 4 cm.
Determine the length of the unknown leg. Round to the nearest tenth.
Answer:
ok so square 13 cm, and square 4 cm. then you will add those together then take that number and find the square root plz mark brainliest
1-cosx/1+cosx=secx-1/secx+1
Verify the identity. I tried all identities that I could, but could not find how it worked. Can you show me how to verify with all steps?
I usually do not ask on brainly, but I've tried everything else and still got nothing.
Currently in Algebra 2 and in the 9th grade.
Answer:
Sorry cannot help you, I'm only in year 8 (7th grade if I'm correct), and am horrible at Algebra. I'm sorry :(
The sum of two numbers is 52 . The larger number is 2 less than twice the smaller number .What are the numbers
Answer:
35.34 and 16.66
Step-by-step explanation:
Given data
let the numbers be x and y
the smaller number = x
the larger number = y
x+y=52--------1
The larger number is 2 less than twice the smaller number
y=2x-2-------2
put y= 2x-2 in eqn 1
x+2x-2=52
3x-2=52
3x=52-2
3x=50
x= 50/3
x= 16.66
put x=16.66 in eqn 1 to find y
x+y=52
16.66+y= 52
y=52-16.66
y= 35.34
Hence the numbers are
35.34 and 16.66
Check
35.34+16.66= 52
Solve for a
a³ = 100
Answer: 4.641588833612779
Step-by-step explanation:
By using a calculator I was able to find the question answer. I am hoping this was the answer you needed. I hope I helped! :)
PLEASE HELPLPPPpppppp
Answer:
40
Step-by-step explanation:
it could be 40 all I did was subtract 80 from 120 but ¡dk wasn't really good in geometry
Drum Roll Please
Our school band is selling sweatshirts and t
shirts to raise money. The goal is to raise
$1200. The sweat shirts cost $12.50 and will
be sold for $15. The shirts will cost $6.50
and be sold for $8.
a) Write a function to describe the
number of shirts and sweatshirts the band can sell to reach their profit goal.
Explain your reasoning.
Of the last 10 contestants on a game show, 8 won a prize. Considering this data, how many of the next 20 contestants would you expect to win a prize? contestants Submit Type the answer please or don't do it
WHAT IS THE RANGE FOR THIS GRAPH?
PLEASE HELP
Answer:
[0,5] or 0≤ y≤ 5
Step-by-step explanation:
Not 100% certain but all the values are included even though there is an open circle
a b c d ????????? which one is it please hurry im timed . high points
Answer:
0
Step-by-step explanation:
X is greater than -4 which leads to having to technically add 4 getting you to 0.
-4, -3, -2, -1, **0**
I hope this is correct and helps you!!!!
please help :-( !! What is the scale factor of the dilation shown? Round your answer to 2 decimal places if necessary.
Answer: Scale factor is 1.5
Step-by-step explanation:you get scale factor e.g F'G' : FG= 12:8 =1,5