In simplest radical form, what are the solutions to the quadratic equation 0 =3x4x + 5?
Quadratic formula: x= btyb- 4ac
Answers
Given:
The quadratic equation is
[tex]0=-3x^2-4x+5[/tex]
To find:
The simplest radical form of the solution.
Solution:
Quadratic formula:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]0=-3x^2-4x+5[/tex]
Here, a=-3, b=-4 and c=5. Putting these values in the quadratic formula, we get
[tex]x=\dfrac{-(-4)\pm \sqrt{(-4)^2-4(-3)(5)}}{2(-3)}[/tex]
[tex]x=\dfrac{4\pm \sqrt{16+60}}{-6}[/tex]
[tex]x=\dfrac{4\pm \sqrt{76}}{-6}[/tex]
[tex]x=\dfrac{4\pm 2\sqrt{19}}{-6}[/tex]
Taking 2 common, we get
[tex]x=\dfrac{2(2\pm \sqrt{19})}{-6}[/tex]
[tex]x=\dfrac{(2\pm \sqrt{19})}{-3}[/tex]
[tex]x=-\dfrac{(2\pm \sqrt{19})}{3}[/tex]
Therefore, the correct option is A.
Related Questions
Determine whether each sum or product is even or odd.
10,481 + 4,569
Answers
Answer:
even
Step-by-step explanation:
11050 it's even because it ends in a zero
Two dice are rolled; find the probability for total: a) 1, b) 4 or 6; c) <13
Answers
Answer:
0 ; 2/9 ; 1
Step-by-step explanation:
In a roll of two dice ;
The sample space = (Number of faces on die)^number of dice rolled = 6^2 = 36
The total possible outcome = sample space = 36
The probability of an event (A) :
P(A) = number of required outcome / number of total possible outcomes
find the probability for total: a) 1,
P(total of 1)
Number of 1 total = 0
Hence, P(total of 1) = 0
b) 4 or 6;
Number of 4 total = 3
Number of 6 total = 5
3 /36 + 5 / 36 = 8/36 = 2/9
c) <13
P(total < 13)
Number of total < 13 = 36
36 / 36 = 1
Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period.
P0 Q0 P1 Q1 P2 Q2
A 90 100 95 100 95 100
B 50 200 45 200 45 200
C 100 200 110 200 55 400
Required:
Calculate the first-period rates of return on the following indexes of the three stocks: (Do not round intermediate calculations. Round answers to 2 decimal places.)
a. A market value–weighted index
b. An equally weighted index
Answers
evaluate the expression when c=2
c^2-8c-3
Answers
Answer:
-15
Step-by-step explanation:
Replace c with 2,
(2)^2 -8(2) -3 =
4 - 16 -3 + -12
= -15
One-stray Problem Solving
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A population of bacteria is growing at an hourly rate of r so that at the end of each hour the population of the sample is multiplied by the growth factor of
z = 1+r. The beginning population is 800 bacteria, an additional 300 are present after 1 hour, and an additional 400 are present after the following
hour.
Write an expression for the population at the end of three hours in terms of the growth factor.
Answers
Answer:
1500z
Step-by-step explanation:
Given a bacteria population that is multiplied by z every hour, and the population after 2 hours is 1500, you want the population after 3 hours in terms of z.
ApplicationThe problem statement tells you the population is multiplied by z every hour. After 2 hours, the population is 800 +300 +400 = 1500. After 3 hours, that value will be multiplied by z:
1500z . . . . . population after 3 hours
__
Additional comment
The given values of population tell us z = 1100/800 = 1.375 for the first hour, and z = 1500/1100 ≈ 1.364 for the second hour. The average value of z for the two-hour period is √(15/8) ≈ 1.369. The desired expression could be any of ...
800z³ . . . . . . . population 3 hours after the beginning1100z² . . . . . . . population 2 hours after the first hour1500z . . . . . . . population 1 hour after the second hourPresumably z would have different values in each case, and we hesitate to predict what those values might be. Perhaps the population is being rounded to the nearest 10 or 100.
An exponential regression calculation models the population as ...
p = 801.945×1.36812^t . . . . . . . z ≈ 1.36812
Using this formula, we get the given population numbers by rounding to the nearest 10.
Convert 0.45 to a percent. Remember to add the percent sign.
0.45%
4.5%
45%
50%
Answers
Answer:
45%
Step-by-step explanation:
Martine wants to open an after-school tutoring service for students in 6th through 9th grade. How can a thorough knowledge of customers' expectations improve the probability of her success?
Answers
Answer:
it would help her know how to prepare her teaching to match the students learning and expectations
Step-by-step explanation:
This idea of opening this tutoring service for students in these grades would prove a success if if martine has adequate knowledge of her students/customers. That is the learners requirements, their expectations, their experiences, and their strengths and weaknesses in particular subject areas.
Knowledge of these expectations would help to set Martine on the path of tutoring success and this would attract more students. So for her to have a strong tutoring business she has to know the approaches to use to make students strong academically, and how to match learning ability with her teaching.
Suppose a one-year subscription to a magazine costs $12.99 and a three-year subscription costs $25.98. The cost and length of a subscription are related. Write a slope-intercept equation to model the cost of a subscription for any period of time.
Answers
Answer:
[tex]y = 6.495x + 6.495[/tex]
Step-by-step explanation:
Represent years with x and cost with y.
So, we have:
[tex](x_1,y_1)=(1,12.99)[/tex]
[tex](x_2,y_2)=(3,25.98)[/tex]
Required
Determine the slope intercept equation
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{25.98 - 12.99}{3 - 1}[/tex]
[tex]m = \frac{12.99}{2}[/tex]
[tex]m = 6.495[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 6.495[/tex]
[tex](x_1,y_1)=(1,12.99)[/tex]
[tex]y - 12.99 = 6.495(x - 1)[/tex]
[tex]y - 12.99 = 6.495x - 6.495[/tex]
Make y the subject
[tex]y = 6.495x - 6.495 + 12.99[/tex]
[tex]y = 6.495x + 6.495[/tex]
5x – 24 > 26
what is the solution to the inequality?
Answers
Answer:
x > 10
Step-by-step explanation:
5x - 24 > 26
Add 24 on both sides.
5x -24 + 24 > 26 + 24
5x > 50
Divide by 5 on both sides.
x > 50 ÷ 5
Find x.
x > 10
f(x)=2x+3 find the
x-int:
y-int:
Asymptote:
End behavior:
Also put in a table f(x)=2x+3
Answers
A length of a rope is stretched between the top edge of a building
Answers
Answer:
what am i supposed to be answering..?
Step-by-step explanation:
Solve the given equation for x.
2x-B = 10
Answers
Answer:
x=5+b/2
Step-by-step explanation:
move all terms that dont contain x to the right, and solve
Answer:
2 times 6-2+10
Step-by-step explanation:
-1/2 (8+1/3 )
1. -4-1/6
2.-4-1/3
3.-5+1/3
4. -5+1/6
Answers
Answer:4.16667
Step-by-step explanation: 1
Simplify —
3
Equation
0 - (— • (8 + —))
2 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
8 8 • 3
8 = — = —————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
8 • 3 + 1 25
————————— = ——
3 3
Equation at the end of step
2
:
1 25
0 - (— • ——)
2 3
STEP
3
:
1
Simplify —
2
Equation at the end of step
3
:
1 25
0 - (— • ——)
2 3
STEP
4
:
Final result :
-25
——— = -4.16667
6
Terms and topics
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Solve the following equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal places.
A rectangular-shaped parking lot is to have a perimeter of 546 yards. If the width must be 61 yards because of a building code, what will the length need to be?
Answers
The length of the parking lot will be 212 yards
Perimeter of rectangleFrom the question, we are to determine what the length of the parking lot needs to be
From the given information, we have that
"A rectangular-shaped parking lot is to have a perimeter of 546 yards"
and
"the width must be 61 yards"
From the formula for perimeter of a rectangle,
P = 2(l +w)
Where P is the perimeter
l is the length
and w is the width
From the given information,
P = 546 yards
w = 61 yards
Putting the parameters into the equation,
546 = 2(l + 61)
546 = 2l + 122
2l = 546 - 122
2l = 424
l = 424/2
l = 212 yards
Hence, the length of the parking lot will be 212 yards
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expand and simplify root5(root10+root2)
Answers
25(104)
= 1000
According to the Rational Root Theorem, which number is a potential root of f(x) = 938 + 946 – 12x + 7?
Answers
Answer:
938
Step-by-step explanation:
So if you are taking a quiz it's C.
Sophie answered 84% of the questions on her science test correctly. If she answered 21 questions correctly, how many questions were on the test?
Answers
Answer:25
Step-by-step explanation:
Susan has 4 cup of raisins and she is dividing them into 3/8 cup
servings. How many servings will she have?
Answers
Answer:
32/3 servings
Step-by-step explanation:
4 / (3/8) =
(4/1) x (8/3) =
32/3
Does the rule y = 6x7 represent an exponential function?
yes
no
Answers
No , the rule y = 6x ^7 does not represent an exponential function.
The exponential function is a mathematical function of the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The exponential function is defined by the formula f(x) = a^x. where the input variable x is displayed as an exponent. An exponential curve depends on the exponential function and the value of x.
We have given y =6 x^7.
Here the variable is base & the exponent is an integer.
But an exponential function has a constant as its base and a variable as its exponent .
So, it does not represent an exponential function .
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help pleasee :)
In the 1936 Olympics, Jesse Owens won a gold medal for running the 100-meter dash in 10.3 seconds. What was Owens' speed in meters per second, rounded to the nearest tenth?
Answers
Jesse Owen speed is 9.71 meters per seconds.
How to find speed?Speed is a scalar quantity that refers to "how fast an object is moving.
In other words, speed is the distance travelled per unit of time.
Therefore, it can be represented mathematically as follows:
speed = distance / time
Jesse Owen covers 100 meters dash for 10.3 seconds. Therefore, the speed he used for the race can be calculated as follows:
speed = distance / time
distance = 100 meters
time = 10.3 seconds
Hence,
speed = 100 / 10.3
speed = 9.70873786408
speed = 9.71 meters per seconds
Therefore, Jesse Owen speed is 9.71 meters per seconds.
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what is the awnser to y=3/2x-1
Answers
Answer:
On a coordinate graph, make a point at (0, -1)
Move the point up 3 units and right 2 units, and make another point. Continue across the plane and draw the line connecting the dots.
Answer:
Step-by-step explanation:
A scuba diver descends from the surface at a rate of 40 feet per minute.
What is the position of the scuba diver relative to the surface after diving for 4
minutes?
-44 ft
10 ft
-160 ft
36 ft
Answers
The Awsome Bowl Factory makes two kinds of bowls. they produce a basic bowl every 6 minutes and a gigantic bowl every 15 minutes. They start at 8:00 a.m. how many minutes after they start will both bowls be produced together?
Answers
Answer:
21 minutes or 8:21 a.m
Step-by-step explanation:
6+15=21
Lily begins soving the equation 4(x -1) -x =3(x + 5) -
11. Her work is shown bekow.
How can her partial solution be interpreted?
O The equation has one solution: x =0.
O The equation has one solution: x=8.
O The equation has no solution.
O The equation has infinite solutions.
4(x-1) -X= 3(x + 5) -11
4x–4-X=3x + 15-11
3x-4= 3x + 4
PLEASE HURRY
Answers
Answer:4(x - 1) - x = 3(x + 5) - 11
Step-by-step explanation:
Lily's work:
4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
Her partial solution, 3x - 4 = 3x + 4, can be interpreted as a FALSE statement because 3x - 4 does NOT equal 3x + 4.
Since it is a false statement, the equation has no solution.
The number of the solution will be infinity. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
4(x – 1) – x = 3(x + 5) – 11
Simplify the equation, we have
4x – 4 – x = 3x + 15 – 11
3x - 3x = 8
The variable x is eliminated.
Then the number of the solution will be infinity.
Then the correct option is D.
More about the solution of the equation link is given below.
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A card is selected at random from an ordinary deck of 52 cards. What is the probability that it is either an ace or a spade
Answers
Answer: 4/13
Step-by-step explanation:
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
Could y’all PLEASE HELP
Answers
Answer:
should be complementary angles
Solve the system by the elimination method:
-6x + 5y = -11
6x - 11y = -19
A (6,5)
B (-6,-5)
C (5,6)
D (-5, -6)
Answers
Answer:
x = 6, y = 5
Step-by-step explanation:
Solve the following system:
{5 y - 6 x = -11 | (equation 1)
{-11 y + 6 x = -19 | (equation 2)
Add equation 1 to equation 2:
{-(6 x) + 5 y = -11 | (equation 1)
{0 x - 6 y = -30 | (equation 2)
Divide equation 2 by -6:
{-(6 x) + 5 y = -11 | (equation 1)
{0 x + y = 5 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{-(6 x) + 0 y = -36 | (equation 1)
{0 x + y = 5 | (equation 2)
Divide equation 1 by -6:
{x + 0 y = 6 | (equation 1)
{0 x + y = 5 | (equation 2)
Collect results:
Answer: {x = 6, y = 5
HELP ME OUT PLEASE!!!
Answers
Answer:
x=30
Step-by-step explanation:
8x - 3(2x-4) = 3(x-6)
first let's get rid of the brackets:
8x- 3·2x + 3·4 = 3x - 3·6
8x - 6x + 12 = 3x - 18
now group all the x terms and number terms
8x - 6x - 3x = -18 - 12
-x = -30
x = 30
how to explain how you know the midpoint of line segment
Answers
Answerits the point that divides the segment into two congruent segments
Step-by-step explanation:
ex. D————-o————-G
The midpoint would be the O. Mid:means Middle
hehehe hope this helps
(7y-8y)2+14=2 solve for x
Answers
Answer:
y = 6
Step-by-step explanation:
(7y-8y)2+14=2
First, simplify the left side
7y - 8y = -y
2*-y = -2y
Now solve the equation
-2y + 14 = 2
Subtract 14 from both sides
-2y = -12
Take away the negative signs since both sides are negative
2y = 12
Divide both sides by 2
y = 6
(If the variable was x instead of y the variable would still equal 6)