By using the quadratic formula, the roots of the equation are,
⇒ x = 2 ± (√3/2) i
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The quadratic equation is,
⇒ x² - 4x + 13 = 0
Now, By using the quadratic formula, the roots of the equation are,
⇒ x² - 4x + 13 = 0
⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2
⇒ x = 4 ± √16 - 52 / 2
⇒ x = 4 ± √- 36 / 2
⇒ x = 4 ± √6 i / 2
⇒ x = 2 ± (√3/2) i
Thus, We get;
⇒ x = 2 ± (√3/2) i
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Final answer:
The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.
Explanation:
To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:
x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)
This simplifies to:
x = 4 ± √(16 – 52) / 2
x = 4 ± √(-36) / 2
Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:
x = (4 ± 6i) / 2
x = 2 ± 3i
Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.
If you double Lucien’s age and then subtract 6, you get Paul’s age. 2 years ago the sum of their ages was 29. How old is each person?
Answer:
Step-by-step explanation:
In this parallelogram m angle bad =75 so m angle bcd
A university football stadium has 1/6 of its students' seats in the end zones. If tickets are randomly selected and mailed to students, what is the probability that a certain student would get end zone seats at all 5 home games?
Answer:
1/7,776
Step-by-step explanation:
the odds of getting an end zone seat once is 1/6 so you multiply that by itself 5 times to get your answer.
1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6 = (1/6)^5 = 1/7,776.
The probability that a certain student would get end zone seats at all 5 home games is [tex]\frac{1}{7776}[/tex]
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given,
A university football stadium has 1/6 of its students' seats in the end zones
Probability = Number of Favorable outcome / Number of total outcome
Probability that a certain student would get end zone = [tex]\frac{1}{6}[/tex]
Probability that a certain student would get end zone in 5 game = [tex](\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )=\frac{1}{7776}[/tex]
Hence, the probability that a certain student would get end zone seats at all 5 home games [tex]\frac{1}{7776}[/tex]
Learn more about Probability here
https://brainly.com/question/11234923
#SPJ2
What is the approximate area of the shaded sector in the circle shown below?
Answer:
Correct option is B.
Step-by-step explanation:
Given the radius of circle and the angle in sector we have to find the area of shaded region i.e minor sector.
[tex]Radius=r=16 in.[/tex]
[tex]Angle=\theta=110^{\circ}[/tex]
[tex]Area of sector=}\frac{\theta}{360}\times\pi r^2[/tex]
[tex]=\frac{110}{360}\times\frac{22}{7}\times(16)^2[/tex]
[tex]=\frac{11}{36}\times \frac{22}{7}\times 16\times 16=245.841=246(approx.)[/tex]
∴ Area of sector is [tex]246in^2[/tex]
Correct option is B.
Answer:B
Step-by-step explanation:
NICE
How many x intercepts appear on the graph of this polynomial function?
Answer:
B) 2 x-intercepts
What is an equivalent expression to 4+3(5+x)
2. Find x and y, given that line KL and line MN are parallel. Show all work
Answer:
[tex]x=9.5[/tex]
[tex]y=8.8[/tex]
Step-by-step explanation:
We have been given a diagram of triangles. We are asked to find the value of x and y.
We can see that triangle JKL and JMN share same vertex that is angle J. Since line KL is parallel to line MN, therefore, there corresponding angles will be equal.
Therefore, Angle-angle-angle similarity [tex]\Delta JKL\sim \Delta JMN[/tex].
Since corresponding sides of similar triangles are always proportional, so we can set a proportion for the sides of our given triangles as:
[tex]\frac{x-2}{5}=\frac{12}{8}[/tex]
Upon cross multiplying our equation we will get,
[tex]8(x-2)=12*5[/tex]
[tex]8x-16=60[/tex]
Let us add 16 to both sides of our equation.
[tex]8x-16+16=60+16[/tex]
[tex]8x=76[/tex]
Let us divide both sides of our equation by 8.
[tex]\frac{8x}{8}=\frac{76}{8}[/tex]
[tex]x=9.5[/tex]
Therefore, x equals 9.5.
We can also set a proportion to solve for y as:
[tex]\frac{y}{22}=\frac{8}{12+8}[/tex]
[tex]\frac{y}{22}=\frac{8}{20}[/tex]
Upon cross multiplying our equation we will get,
[tex]20y=22*8[/tex]
[tex]20y=176[/tex]
Let us divide both sides of our equation by 20.
[tex]\frac{20y}{20}=\frac{176}{20}[/tex]
[tex]y=8.8[/tex]
Therefore, y equals 8.8.
Which of the binomials below is a factor of this trinomial? 5x2 + 20x + 15
factor X + 1 is the answer
Please helpppp now 99 points
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −15
0 −10
1 −5
g(x)
g(x) = 2x + 8
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
A) Inverse Property of Multiplication
B) Commutative Property of Addition
C) Commutative Property of Multiplication
D) Associative Property of Addition
What is the measure of C to the nearest degree?
Answer:
43
Step-by-step explanation:
I got it right on my quiz.
What is the Value of X? Sin(x+22 degree) = Cos( 2x-7 degree) I might have a idea of what it is but I’m not sure
The value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees) can be found by using the identity sin(90° - x) = cos(x), leading to x = 22.67° (or in radians by converting degrees to radians).
To find the value of x in the equation Sin(x+22 degrees) = Cos(2x-7 degrees), we can utilize the trigonometric identity sin(90° - x) = cos(x). By setting the angle inside the cosine to equal 90° - (x + 22°), we can equate this to (2x - 7°) as both represent the same cosine value.
So we have the equation 90° - (x + 22°) = 2x - 7°. Solving for x, we combine like terms: 68° = 3x, which then gives us x = 68°/3. Therefore, x = 22.67°, which is the angle in degrees.
If we needed to find x in radians, we would have to convert degrees to radians by using the conversion factor: π radians = 180°. This would yield x as x = (22.67°/180°) * π.
Which of the following points are solutions to the system of inequalities shown below? Check all that apply. y -2x + 6 x > 1
A. (3, 0)
B. (2, 1)
C. (2, 11)
D. (0, 6)
E. (5, -6)
F. (1, 4)
The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters. The number of times one needs to use the completely filled cone to completely fill the cylinder with water is ?
Solution:
Let volume of cylinder be K times more than volume of Cone.
⇒K × Volume of Cone = Volume of Cylinder
[tex]K \times \frac{\pi\times r^2 \times h }{3}=\pi \times R^2 \times H\\\\K \times 5^2 \times 10= 3 \times 10^2 \times 20\\\\250 K=3 \times 100 \times 20\\\\K=\frac{6000}{250}\\\\K=24[/tex]
⇒Number of times one needs to use the completely fill cone to completely fill the cylinder with water is=24
A circular rug has a radius of 4.5 feet. What is the circumference of the rug? Use 3.14 for .
answer= 28.26
Step-by-step explanation:
your welcome
evaluate ab - 0.5b when a =1 and b=5
Answer:
ya 2.5
Step-by-step explanation:
PLEASE HELP!! FIRST CORRECT ANSWER GETS BRAINLIEST!!
Elizabeth rode her bike 6 1/2 miles from her house to the library and then another 2 2/5 miles to her friend Milo's house. If Carson's house is 2 1/2 miles beyond Milo's house, how far would she travel from her house to Carson's house?
Answer:
Step-by-step explanation:
11.4
The networking organization you joined is throwing a party. You are in charge of buying the chips, which cost two dollars and fifty cents per bag and salsa, which costs four dollars per jar. The chips & salsa budget you are given totals $60. The inequality 2.5x + 4y 60 represents the possible combinations of chips (x) and salsa (y) you can buy. graph of the inequality 2.5 x plus 4 y is less than or equal to 60 Which of the following does not represent a solution to the inequality?
Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the account balance be after 6 years?
She invests some amount in a saving account of fixed interest compounded half-yearly. It says to find its Future Value after six years.
The principal amount is P = $4,848.
Annual interest rate is 5% i.e. r = 0.05
Compounding period is two times per year i.e. n = 2.
Time of investment is t = 6 years.
We know the formula of Future Value is given by :-
[tex] FV=P*(1+\frac{r}{n})^{nt} [/tex]
We can plug the given values in the formula to calculate the answer.
[tex] FV = 4848*(1+\frac{0.05}{2})^{(2*6)} \\\\
FV = 4848*(1+0.025)^{(12)} \\\\
FV = 4848*(1.025)^{(12)} \\\\
FV = 4848*(1.344888) \\\\
FV = 6520.02102 [/tex]
Hence, future value of investment after six years is 6,520.02 dollars.
The question involves calculation of compound interest. The formula to use is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
Explanation:This question involves the concept of compound interest. Compound interest is calculated each period on the original deposit, or principal, along with any interest previously earned. Unlike simple interest which only takes into account the principal amount, compound interest accounts for the interest that accumulates on the initial amount as well as the interest that has previously been added.
In Brenda's case, as she's benefiting from compounded interest, the formula to use here is A = P (1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, t is the time in years, n is the number of times interest is compounded per year and A is the amount of money accumulated after n years.
So, plug in the given values: P=$4848, r=0.05 (as 5% = 5/100), t=6, and n=2 (since it's compounded semi-annually). This will allow us to find the final account balance after 6 years.
Learn more about Compound Interest here:https://brainly.com/question/14295570
#SPJ3
Match the systems of equations to their solutions. Tiles 2x + y = 12 x = 9 − 2y x + 2y = 9 2x + 4y = 20 x + 3y = 16 2x − y = 11 y = 11 − 2x 4x − 3y = -13 y = 10 + x -3x + 3y = 30 2x + y = 11 x − 2y = -7 Pairs x = 2, y = 7 arrowBoth x = 5, y = 2 arrowBoth x = 3, y = 5 arrowBoth x = 7, y = 3 arrowBoth
PLEASE FULL ANSWERS! need all the help I can get
hepppppppppppppppppppppppppppppp
Answer:
D
Step-by-step explanation:
Can someone graph these 2 equations for me??
y=5(1/2)^x +4
y=4(1/6)^(x+2)
Simplify the expression. 3–9 • 36 • 36
To simplify expressions, one needs to apply rules correctly, such as combining like terms and using exponentiation rules. The process includes correctly applying the rule that simplifies multiplications of the same base by adding their exponents. Cubing exponentials involves multiplying the original exponent by 3.
Explanation:To simplify mathematical expressions, it's crucial to follow the correct rules and operations. In this case, the example provided shows the exponentiation and multiplication rules. Specifically, when dealing with expressions like 3².3⁵, this is equivalent to multiplying 3 x 3 and then taking that result and multiplying it by 3 five more times. According to the rule xPx9 = x(p+q), where x is the base and p and q are the exponents, it simplifies to adding the exponents when the base number is the same and multiplied together.
The process of simplifying expressions involves several steps:
Identifying like terms and combining them.Applying the rules of exponents correctly.Dividing or multiplying to simplify equations as demonstrated with loop equations, dividing by a constant to simplify the equation.Additionally, when cubing exponentials, one should cube the digit normally and multiply the existing exponent by 3, a rule demonstrated in squaring operations as well.
If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct? if a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by guessing?
The probability of getting at least 1 correct answer when guessing on a multiple-choice test can be found by subtracting the probability of getting all answers wrong from 1. Whether it is reasonable to expect to pass by guessing depends on the passing percentage and the probability of getting at least 1 answer correct.
Explanation:To find the probability of getting at least 1 correct answer when making random guesses for 10 multiple-choice test questions, we can look at the probability of getting 0 correct and subtract it from 1. Since each question has 5 possible answers, the probability of getting a question wrong is 4/5. So the probability of getting all 10 questions wrong is (4/5)^10. Therefore, the probability of getting at least 1 correct answer is 1 - (4/5)^10.
To determine if you can reasonably expect to pass the test by guessing, we need to compare the probability of getting at least 1 correct answer to the passing percentage. If the probability of passing is higher than the passing percentage, then it is reasonable to expect to pass by guessing.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
What is the 32nd term of the arithmetic sequence -12 -7?
The municipality of Waterloo needs $915,000 from property tax to meet its budget. The total value of
assessed property in Waterloo is $14,000,000. What is the tax rate per dollar? (Round your answer to the
nearest thousandth.)
A. $.07
B. $.065
C. $.0655
D. $.071
PLEASE!!!!!!!!!!!!!HURRY!!!!!!!!!!!!!!!!!!!!!!!20 points!!!!!!!!!!!!!!!!!!!!!!1
A group of children are asked whether they prefer vanilla or chocolate ice cream. The data are collected in the table.
helppppppppppppppppppppppppppppp