The nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0 is complex number.
The nature of roots of a quadratic equation is determined by the discriminant, which is the value of b² - 4ac. In this case, the quadratic equation is 5x^2 - 2x + 3 = 0.
To find the discriminant, we can use the formula: b² - 4ac. In this case, a = 5, b = -2 and c = 3, so the discriminant is:
Discriminant = (-2)² - 4*5*3 = 4 - 60 = -56
The discriminant can be used to determine the nature of the roots:
If the discriminant is greater than 0, the roots are real and distinct.
If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).
If the discriminant is less than 0, the roots are complex and not real numbers.
In this case, the discriminant is negative, so the roots of the equation 5x^2 - 2x + 3 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).
--The question is incomplete, answering to the question below--
"What is the nature of roots of the quadratic equation 5x^2 - 2x + 3 = 0?"
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- You have a total of 10 coins consisting of nickels and dimes in your
pocket. The value of the coins is $0.70. Write and solve a system of linear
equations to find the numbers of nickels and dimes in your pocket.
Answer:The value of the coins is $0.70. Write and solve a system of linear equations to find the numbers of nickels and dimes in your pocket. There are 6 nickels and 4 dimes.
Step-by-step explanation:
How do you change log base 2 to base 10?.
To change the log base 2 to log base 10, we can use the change of base formula for logarithms.
We know that the change of base formula for logarithms.
The formula to change the base of a logarithm from base 'a' to base 'b' is:
[tex]log_a(m)=\frac{log_b(m)}{log_b(a)}[/tex]
Here, we need to change log base 2 to base 10
By using this change of base formula, we can change the log base 2 to log base 10.
We know that log base 10 is called the common logarithm.
We denote [tex]log_{10} (x)[/tex] as log(x).
Let us assume that we want to change a number log of x to the base 2 to log of x to the base 10
From above formula of change of base we get,
[tex]log_2(x)\\\\=\frac{log_{10}(x)}{log_{10}(2)}\\\\=\frac{log(x)}{log(2)}[/tex]
Thus, we can use the change of base formula for logarithms to change the log base 2 to log base 10,
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Q.10 Multiply
What is (f. g)(x)?
f(x) = 4x + 1
g(x) = x + 6
Write your answer as a polynomial or a rational function in simplest form.
A polynomial or a rational function in simplest form is (f. g)(x) is 4x² + 25x + 6.
What is Polynomial?The exponents of all the variables of an algebraic statement known as a polynomial must all be whole numbers. In any polynomial, the exponents of the variables must be non-negative integers.By identifying which phrases only contain the processes of adding, subtract, multiplying, and non-negative integer exponents, the polynomials can be located. Expressions with additional processing are considered as non expressions.
Given, f(x) = 4x + 1
g(x) = x + 6
Now, (f. g)(x) = f(x).g(x)
= (4x + 1)(x + 6)
= 4x² + 24x + x + 6
= 4x² + 25x + 6
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I need help fast please!!
f(-2) = 3 (value on y axis)
if f(x) = -1, x = 0 (when y = -1)
1) At a factory the basic week is 40 hours.
During a particular week Mr. Riley earned a gross
Wage of $513.88, however 159.48 was for
Overtime
Calculate Mr. Riley's basic rate of Payment.
If overtime was paid for a time and a half
determine how many hours Mr. Riley worked
Overtime
If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.
what is unitary method ?By first figuring out the value of a single unit and then multiplying that value to get the requisite value, a problem can be solved using the unitary technique. For multiplication and dividing by fractions, the unitary strategy is frequently beneficial because it makes sense immediately and can be executed mentally if the numbers add up. Since written methods for fractions are frequently employed, notably division by a fraction, it is useful to explain or defend these algorithms. The unitary method's formula is to get the value of one unit, multiply it by the number of units, and then divide the result by the desired value.
given
The standard workweek is 40 hours.
Gross wages totaled $490.15.
Pay for overtime: $156.75
Total compensation based on a basic week = Total Gross salaries minus overtime pay
Total wages calculated based on a standard week are $490.15 - $156.75 = $334.
Let the basic hourly salary be $8.36 ($x = x).
Let y hours equal the number of overtime hours.
Due to the fact that overtime pay is time-and-a-quarter.
According to the calculation: Equals 15 hours
If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.
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What is the result when this equation is solved for y? 4x²+6x-2y = 10 O A. y= 2x² + 3x-5 O B. y= 4x² + 6x - 10 C. y=-4x² - 6x + 10 O D. y=-2x²-3x+5
Answer: y=2x²+3x-5
Step-by-step explanation:
Solve 4x²+6x-2y=10
1. subtract 4x² and 6x from both sides
(you do this to leave y by itself)
-2y=10-4x²-6x
2. divide -2 on both sides
y= -5+2x²+3x
This is technically the right answer but you still need to put the numbers and variables in the right order.
y=2x²+3x-5
(variables w/ exponents go first, then the variable, then the number)
Hope this helps! Good luck!
Does a square root graph have an inverse?.
A square root function is the inverse of a quadratic function. If a function f is the inverse of another function f1, then f is the inverse of f1.
The order of positive integers is preserved by the square function: greater numbers have larger squares. The square, then, is a monotonic function on the range [0, +]. Since negative integers have squares that are proportional to their absolute values, the square on [(,0] is a monotonically declining function.
The horizontal line test determines whether or not f has an inverse if any horizontal line crosses its graph more than once.
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How do you write more than 50?.
The greater than sign is '>'. If one value is greater than the other, use greater than. Therefore, we can write more than 50 as x > 50.
Greater Than:
In mathematics, the greater than sign is placed between two values where the first number is greater than the second number.
Example: 60 > 50, where 60 is greater than 50.
In inequalities, the greater-than sign always refers to the greater value, and the sign consists of two equal length dashes joined at an acute angle on the right increase (>).
The greater than sign is used in linear inequalities when the value of a variable is not known to be greater than to a certain value. This symbol is a greater-than symbol (>) with a sleep line below it.
Here are some more examples.
x > 100 means the value of x is greater than to 100.
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You are going to exercise at the indoor track. Your friend is going to exercise at the pool. What is the first step in determining where you should park to minimize the distance you both will walk?
The answer is option (D) : Find the midpoint of segment NP.
What is Midpoint?
The midpoint of a line segment is a point that lies exactly halfway between two points. It is the same distance from each endpoint of the straight line segment. Midpoint formula is a mathematical equation that is used to locate the halfway point between two data points. The midpoint formula is applied when one is required to find the exact center point between two defined points.
As Shown in below diagram given below,
suppose need to park at point M (i.e. midpoint of NP)
distance = NM + MP
so, when M is the midpoint of NP and has the minimum distance.
Therefore, the answer is option (D) : Find the midpoint of segment NP.
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Mi White i renting a van for one week in a few additional day D. He doe not have to pay a per mile fee. Evaluate the expreion 440130 D to find how much he will pay for the nine day rental
For the nine-day rental, the expression for the same sum will be charged as $1,610
The formula combines numerical elements and operations symbolised by the signs for addition, subtraction, multiplication, and division.
Expression are the Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping in addition to numbers (constants). The operation order and other characteristics of the logical syntax can also be indicated by them.
Given that Mr. White will be leasing an enormous vehicle for a week plus a few more days, He is not required to pay a per-mile charge. The formula is 440 + 130d.
The sum will be computed as follows by the expression:
A = 440 + 130d
A = 440 + ( 130 x 9 ) ( 130 x 9 )
A = 440+ 1170
A = 1,610
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find the volume of a square pyramid with a base length 14.2 cm and a height of 3.9 cm
A: 18.5 cm
B 71. 0cm
C 262.1cm
D 786.4cm
Answer:
c
Step-by-step explanation:
V=a2h
3=14.22·3.9
3=262.132cm³
If f(x) = g(x) = 2x² - 4x + 4 and f(x) = 3x² - 2x + 1, what is
g(x)?
g(x) must be equal to f(x).
What is equivalent function?An equivalent function is a mathematical expression that produces the same result as another expression. It is a function that is mathematically equivalent to a given function, meaning that its graph is the same as that of the given function. Equivalent functions are useful in problem solving as they can be used to simplify a problem or to show a relationship between two functions.
g(x) = 3x² - 2x + 1. This means that f(x) and g(x) are equivalent functions, and thus have the same output for any given input. This means that when x is plugged in to both equations, the resulting output will be the same. Therefore, g(x) must be equal to f(x).
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Is it possible to construct a triangle whose sides are 10. 2 cm 5. 8 cm and 4. 5 cm which result did you use to verify this?.
Yes, it is possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(4.5cm + 5.8cm) =10.2cm
10.3cm = 10.2cm
LHS>RHS
A triangle is possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Question 3(Multiple Choice Worth 2 points)
(Slope LC)
What is the slope of the linear relationship?
A graph of a linear function that decreases from left to right passing through the points 1 comma 0 and 3 comma negative 3.
negative three halves
three halves
negative two thirds
two thirds
Answer:
(a) negative three halves (-3/2)
Step-by-step explanation:
You want the slope of the line through points (1, 0) and (3, -3).
Slope formulaThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-3 -0)/(3 -1) = -3/2
(a) The slope of the line is -3/2.
<95141404393>
Geometry
A drawer contains 12 white socks and 8 black socks. You randomly choose 1 sock and do not replace it. Then you randomly choose another sock.
a. What is the probability of selecting a white sock first and then a black sock?
b. What is the probability of selecting two white socks?
c. What is the probability of selecting two black socks?
12 white socks, 8 black socks, 20 total socks:
a.
[tex]\dfrac{12}{20}\cdot\dfrac{8}{19}\approx 0.252631578947\approx 25.3\%[/tex]
b.
[tex]\dfrac{12}{20}\cdot\dfrac{11}{19}\approx 0.347368421053\approx 34.7\%[/tex]
c.
[tex]\dfrac{8}{20}\cdot\dfrac{7}{19}\approx 0.147368421053 \approx 14.7\%[/tex]
Evaluate −xyz
if x= −2/3
, y= 0.6
, and z= 1 7/8
Write your answer as a fraction in simplest form.
Answer:
17/20
Step-by-step explanation:
_(_2/3)*6/10*17/8
2/3×6/10×17/8
=17/20
At Chocolatier Incorporated, there are two factors that determine the cost of health
care. If an employee makes less than $65,000 per year, he pays
$52 per month for
individual coverage and $98 per month for family coverage. If an employee makes at
least $65,000 per year, individual coverage is $67 per month and family coverage is
$122 per month.
a) Graham makes $62,800 per year. He has individual health care. His yearly contribution
is 10% of the total cost. How much does his employer contribute?
b) Claudia s annual salary is $75,400. She has family health care. Her employer
contributes $1,052 per month toward her total coverage cost. What percent does
Claudia contribute toward the total coverage? Round to the nearest tenth of a percent.
a) Graham's employer contributes $561.60 per year towards his coverage.
b) Claudia contributes 28.2% towards the total coverage cost.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is typically represented by the symbol "%", and is often used to express a change or a part of a whole.
a) Graham makes $62,800 per year, which is less than $65,000, so he pays $52 per month for individual coverage. His yearly contribution is 10% of the total cost, so his employer contributes 90% of the total cost. To find the total cost, we can multiply the monthly cost by 12: $52/month * 12 months/year = $624/year. So Graham's employer contributes $624 * 90% = $561.60 per year towards his coverage.
b) Claudia's annual salary is $75,400, which is at least $65,000, so she pays $122 per month for family coverage. Her employer contributes $1,052 per month towards her total coverage cost. To find the total cost, we can multiply the monthly cost by 12: $122/month * 12 months/year = $1,464/year. To find the percentage Claudia contributes, we divide her contribution by the total cost and multiply by 100: $1,464-$1,052 / $1,464 * 100 = 28.2%. So Claudia contributes 28.2% towards the total coverage cost.
Hence,
a) Graham's employer contributes $561.60 per year towards his coverage.
b) Claudia contributes 28.2% towards the total coverage cost.
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A front-end loader is to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd. , calculate the total cycle time for the loader if it can move 55 cu. Yd. Of in-bank material in 1 hr. With an efficiency of 48 min. /hr
A front-end loader to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd. the total cycle time for the loader, if it can move 55 cu, is 16.2 hours( 55 cu. Yd. / 10 cu. Yd. (heaped capacity) * 15% (swell factor) * 48 min. /hr)
The total cycle time for a front-end loader to load trucks with granular material with a swell factor of 15% can be calculated by taking the total amount of in-bank material to be loaded and dividing it by the heaped capacity of the loader. This will give us the total number of cycles the loader must complete. Once we have this number, we must multiply it by the swell factor. This gives us the total number of heaped cycles the loader will have to complete.
Finally, we must multiply the total number of heaped cycles by the efficiency of the loader. Efficiency is the amount of time it takes for the loader to complete one heaped cycle. In this case, the total cycle time for the loader to load is 55 cu. Yd. Of in-bank material with a swell factor of 15% and a heaped capacity of 10 cu. Yd. Is 16.2 hours, assuming the loader has an efficiency of 48 min. /hr.
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Find the equation of the line joining the points A (1,2) and 8(-1,8)
First, you need to find the slope between the two points:
[tex]\begin{aligned}\dfrac{8-2}{-1-1} & = \dfrac{6}{-2}\\[0.5em]&=-3\endaligned}[/tex]
Now, you use one of the points to find the equation.
You can use point-slope form:
y - 1 = -3 (x-2)
Or you can use slope-intercept form:
y = -3x + 5
Note:
You can find the slope-intercept form by taking y = mx + b and substituting in the slope and a point and solving for b:
2 = -3 (1) + b
Find the measure of the base angle in an isosceles triangle that has a base length of 6 and a leg length of 5. Round your answer to the nearest whole degree.
The base angle for the isosceles triangle is 53°.
What is an isosceles triangle?Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.
Given base length = 6 and leg length = 5
draw a perpendicular to the base that divides the base into equal parts,
as shown in the image attached
let the base angle be Ф,
and using a cosine formula for the base angle
cosФ = base/hypotenuse
from construction base = 3 and hypotenuse = 5
cosФ = 3/5
Ф = cos⁻¹(3/5)
Ф = 53.13°
Ф = 53° (approx)
Hence the base angle is 53°
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What is the sum of the polynomials (- X² 9 (- 3x² 11x 4?.
The sum of the polynomials (-x² + 9) + (-3x² - 11x + 4) is -4x² - 11x - 5.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the sum of the polynomials (-x² + 9) + (-3x² - 11x + 4)?
To have $8,250 for a child’ education in 10 year, what amount hould a parent depoit in a aving account which earn 12 percent, compounded quarterly?
By applying the future values, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is $2,529.09
A current asset's future value, abbreviated as FV, is the value that asset is expected to have at some point in the future, based on a projected rate of growth. The future value is essential for investors and financial planners because they use it to estimate how much money an investment made now will be worth in the future.
To find the future values, we can use this following formula:
FV = I x (1 + R)^T
Where:
I = investment amount
R = interest rate
T = number of years
In this case, we are given that:
Future values (FV) = $8,250
The periodic rate = 12% : 4 = 0.03 (compounded quarterly)
Number of period = 10 years x 4 = 40
Hence, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is:
8,250 = I x (1 + 0.03)⁴⁰
I = 8,250: ((1 + 0.03)⁴⁰)
I = $2,529.09
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a football stadium can seat 62,005 people. if there were 59,319 people in attendance at the game, how many seats were empty?
bag a has 2 yellow marbles,2 red marbles,and 3 blue marbles picking from bag a is certain,likely,unlikely,impossible
Picking a green marble from bag A is D. impossible.
What is an impossible probability ?The probability of an impossible occurrence is the likelihood that an event won't occur at all and won't have any chance of happening in the future. As a result, the likelihood of such an event is always zero. An impossible event is one that doesn't take place. There is no chance that it may occur. Therefore, there is no chance of that happening.
There are no green marbles in Bag A which means that it is not possible to pick a green marble from Bag A. The probability of picking a green marble is 0 and the likelihood is impossible.
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The full question is:
Bag a has 2 yellow marbles,2 red marbles, and 3 blue marbles picking a green marble from bag a is certain,likely,unlikely,impossible
a cylinder with a radius of 6 cm has a volume of 432 pi cm3. What is the height of the cylinder
The height of the cylinder is given by the equation h = 12 cm
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the cylinder be represented as A
Now , the radius of the cylinder be r = 6 cm
Let the height of the cylinder be h
Let the volume of the cylinder be V = 432π cm³
Volume of Cylinder = πr²h
Substituting the values in the equation , we get
432π = π ( 6 )² x h
On simplifying the equation , we get
432 = 36h
Divide by 36 on both sides of the equation , we get
h = 12 cm
Hence , the height of the cylinder is 12 cm
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i need help with finishing this ASAP
Answer: Look at the image below.
Step-by-step explanation: I traced it out and did the math for you.
Hope this helps! :)
???
HELPOOOOOPPPPPPPPPPPPPOPPPPPPPP
Answer:
-13, -22, -31, -40
Step-by-step explanation:
substitute n for each term
Kate's food budget for the month is R700. The first week she spent R189,75, the second week she spent R203,20 and the third week she spent R146,95. How much does she have left for the last week?
Answer: R160.10
Step-by-step explanation:
R700-R189.75=R510.25
R510.25-R203.20=R307.05
R307.05-R146.95=R160.10
which equation represents the graph below?
Answer:
linear equation represents the graph below
When triangle ABC with A(5,-1), B(0,4), and C(-2,2) is rotate 90 degrees counterclockwise about point A, what are the coordinates of the vertices of the image?
The coordinates of the vertices of the image are:
A' = (-1, 5)
B' = (-4, 0)
C' = (-2, -2)
Option A is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Counterclockwise means the coordinates will interchange and the sign will be depending on the quadrants.
The coordinates of the triangle ABC.
A = (5, -1)
This is in the 4th quadrant.
If rotated 90 degrees counterclockwise A will be in the 1st quadrant.
A' = (-1, 5)
B = (0, 4)
This is in the first quadrant.
If rotated 90 degrees counterclockwise B will be in the 2nd quadrant.
B = (-4, 0)
C = (-2, 2)
This is in the 2nd quadrant.
If rotated 90 degrees counterclockwise C will be in the 3rd quadrant.
C = (-2, -2)
Thus,
The coordinates of the image are:
A' = (-1, 5)
B' = (-4, 0)
C' = (-2, -2)
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