The required distinct roots of the following equation using the quadratic formula is x = -3±√5i.
What is the quadratic formula?Any quadratic problem can be solved using the quadratic formula.
The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients.
After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
So, the quadratic formula:
x = -b±√b²-4ac/2a
Now, insert values and calculate for roots as follows:
x = -b±√b²-4ac/2a
x = -b±√b²-4*4(1)*14/2(1)
x = -b±√36/56/2
x = -b±√-20/2
Discriminant: b² - 4ac < 0
Now,
x = -6± 2√5i/2
x = -6/2 ± 2√5i/2
x = -3±√5i
Therefore, the required distinct roots of the following equation using the quadratic formula is x = -3±√5i.
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At Dubble High School, 42% of the students play sports, 34% of the
students play a musical instrument, and 24% do both. What is the
probability that a randomly selected student at Dubble High School
plays a sport or a musical instrument?
Solve each system of equations below by graphing
Solution !
Y= -2/3x + 3
y = 2x-5
On solving the provided question, we can say that in these equation Y= -2/3x + 3 and y = 2x-5 let x = 1, Y = 7/3 and y = -3
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
in these equation
Y= -2/3x + 3
y = 2x-5
let x = 1
Y = 7/3
y = -3
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What is one way a market economy affects the lives of private citizens?Citizens can change jobs relatively easily.Citizens cannot choose their own careers.Citizens do not have to pay for their housing.Citizens have little freedom and independence.
Citizens have the freedom and independence to choose their own career paths, as well as the ability to change jobs relatively easily if they desire.
What is the equation of the graph below?
The solution ax2 + bx + c = 0 can be solved using quadratic equation
x = (-b (b2 - 4ac))/2a to get the roots of the problem.
Quadratic equations: what are they?Just using equations x = ax2 + bx + c = 0 and a 0, a quadratic function is a 2nd polynomial problem in one variable. It is a third polynomial problem, hence the foundational theorem of algebra guarantees that there is least one solution. There may also be real or sophisticated solutions. The quadratic formula makes solving any quadratic equation easier for us. In order to solve this equation, we must first change its form to appear as ax2+bx+c=0, in which a, b, and d are the coefficients. Therefore, we add these coefficients to the method: (-b(b2-4ac))/ (2a).
Here,
The problem ax2 + bx + c = 0 can be solved using
the method x = (-b (b2 - 4ac))/2a to get the roots of the problem.
D = b² - 4ac provides the discriminant value. If D > 0, the equation has two genuine, separate roots.
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Sketch the area represented by g(x). g(x)t4 dt Then find g'(x) in two of the following ways (a) by using Part 1 of the Fundamental Theorem g(x) (b) by evaluating the integral using Part 2 and then differentiating g'(x)
The area represented by g(x) is the definite integral of g(x) with respect to t from t=0 to t=x:
g(x) = ∫(t^4) dt from 0 to x
To find g'(x) using Part 1 of the Fundamental Theorem of Calculus, we know that:
g'(x) = d/dx (∫(t^4) dt from 0 to x) = (t^4) evaluated at x = x^4
To find g'(x) using Part 2 of the Fundamental Theorem of Calculus, we can evaluate the integral:
g(x) = ∫(t^4) dt = (1/5)t^5 evaluated from 0 to x = (1/5)x^5
then take the derivative of g(x) with respect to x:
g'(x) = d/dx ((1/5) x^5) = (1/5) * 5x^4 = x^4
Both ways give the same result of g'(x) = x^4
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How much of a 14% ethanol fuel mixture should be mixed with 8 gal of 3% ethanol fuel mixture to get a mixture that is 12% ethanol?
(blank) gal of 14% ethanol solution is needed to produce a 12% ethanol solution.
Answer:
Step-by-step explanation:
A = x 14%=.14x
B=8 (4%)=.04(8)
=8x 12%= .12*8x
.14x+.04(8)=.12(8x)
.14x+.32=96x-.14x
.32=.82x/x
.32/.82=.39
The amount of 14 % of ethanol that needs to mixed is A = 36 gallons
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
14% ethanol fuel mixture should be mixed with 8 gal of 3% ethanol fuel mixture to get a mixture that is 12% ethanol
So , the equation is
A ( 14 % ) + ( 8 ) ( 3 % ) = ( A + 8 ) ( 12 % )
On simplifying , we get
14A + 24 = 12A + 96
Subtracting 12A on both sides , we get
2A + 24 = 96
Subtracting 24 on both sides , we get
2A = 72
Divide by 2 on both sides , we get
A = 36 gallons
Therefore , the value of A is 36 gallons
Hence , the equation is A = 36 gallons
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the checking account fees for banks a b c d are shown below on the table
Therefore, when comparing all the banks, Bank B has the lowest fees. Bank B is the best choice, thus.
what is linear equations?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
Charges are equal to $13.25 when 23 checks are signed from bank A.
Charges will be equal to $11.50 when 23 checks are signed from bank B.
Charges are equal to $15 when 23 checks are signed from bank C.
Charges are equal to $12.30 when 23 checks are signed from bank D.
Therefore, when comparing all the banks, Bank B has the lowest fees. Bank B is the best choice, thus.
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The complete question is :-
The checking account fees for Banks A, B, C, and D are shown in the table below.
Monthly Service Fee Per-Check Fee
Bank A $7.50 $0.25
Bank B None $0.50
Bank C $15.00 None
Bank D $10.00 $0.10
If a customer writes 23 checks per month, which bank will charge her the least in fees? Show your work.
5 por ciento es un número entero
Los números enteros están constituidos por todos los números que no tienen cifras decimales, por lo que sería verdadero afirmar que 5% es un numero entero.
¿Qué son los números enteros?
Los números enteros son un conjunto de números que se caracterizan por no tener cifras decimales. En general, los números enteros incluyen los positivos, negativos y el cero.
De acuerdo con lo anterior, podemos inferir que es verdadero afirmar que el 5% es un numero entero debido a que no tiene cifras decimales y es un número positivo. Por otra parte, si fuera 5.2% u otro valor con cifras decimales sería falsa la respuesta.
Nota: Esta pregunta está incompleta debido a que tiene información faltante. Aquí está la información faltante:
De acuerdo a reglas sobre los números, se puede concluir que 5 por ciento si es un número entero.
Opciones
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Jimmy asked his friends in his lunch period
what their favorite pizza toppings were. The
graph shows these results.
30
25
20
15
10
Favorite Pizza Toppings
Cheese Mushrooms Sausage Pepperoni
and olives
What is the approximate difference in the
percentage of people that liked pepperoni on
their pizza and the percentage of people that
only liked cheese pizza?
un
To find the approximate difference in the percentage of people that liked pepperoni on their pizza and the percentage of people that only liked cheese pizza, we need to find the percentage of people that liked pepperoni and the percentage of people that only liked cheese, and then subtract the smaller percentage from the larger percentage.
From the graph, we can see that 30 people liked pepperoni, 20 people liked mushrooms, 15 people liked sausage, and 10 people liked cheese and olives.
The total number of people Jimmy asked is 30+20+15+10 = 75
The percentage of people that liked pepperoni is 30/75*100 = 40%
The percentage of people that only liked cheese is 10/75*100 = 13.33%
The difference between 40 and 13.33 is 26.67%.
So, the approximate difference in the percentage of people that liked pepperoni on their pizza and the percentage of people that only liked cheese pizza is 26.67%.
HELP PLSSSSSSS GOD BLESS ILL GIVE BRAINLIEST
Jackson digs a hole at a rate of 3/5 feet every 10 minutes. After digging for 40 minutes, Jackson places a plant in the hole that fills exactly 9/10 feet of the hole. Relative to ground level, what is the elevation of the hole after placing the plant in the hole? Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex]2 \, \dfrac{4}{25} \textrm{ ft}[/tex]
Step-by-step explanation:
First, solve for how many feet Jason has dug after 40 minutes:
[tex]\dfrac{\dfrac{3}{5} \textrm{ ft}}{10 \textrm{ min}} \times 40 \, \textrm{min} = 2 \dfrac{2}{5} \, \textrm{ft}[/tex]
So, the hole he has dug is 2 2/5 ft deep.
Next, we can solve for how deep the hole will be after placing a plant in by simply multiplying 9/10 by the depth of the hole dug.
[tex]2\, \dfrac{2}{5} \times \dfrac{9}{10} = \dfrac{12}{5} \times \dfrac{9}{10} = \dfrac{6 \times 9}{5 \times 5} = \dfrac{54}{25} = 2 \, \dfrac{4}{25} \textrm{ ft}[/tex]
In the diagram below, m is the perpendicular bisector of BC.
Is ΔABK ≅ ΔACK? Justify.
so far i have this, angle APB is a right angle- perpendicular bisectors form right angles. angle APC is a right angle- perpendicular bisectors form right angles. angle APB is congruent to angle APC- all right angles are congruent. But I don't know if this is right
literally the last question on my test. Please please please help
Answer:
yes 5=89
Step-by-step explanation:
12. Look at the picture. Write and solve an
equation to model the picture. Show
your answer as a multiplication equation
as a factor.
with
1/2 as a factor
The expression y = 1/2x is required a multiplication equation as a factor with 1/2.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Given multiplication factor between the value is given as 1/2, So it is assumed that one of the dependent variables is equal to 1/2 times the independent variable. expression is given as,
y = 1/2x.
Thus, the expression y = 1/2x is required a multiplication equation as a factor with 1/2.
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A pound of blueberries costs `\$3.50` and a pound of clementines costs `\$2.50`.
What is the total cost of `0.6` pounds of blueberries and `1.8` pounds of clementines?
The total cost of 0.6 pounds of blueberries and 1.8 pounds of clementine's is, $6.6.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A pound of blueberries costs $3.50 and a pound of clementine's costs $2.50.
Hence, We get;
The total cost of 0.6 pounds of blueberries and 1.8 pounds of clementine's is,
⇒ 0.6 × $3.50 + 1.8 × $2.50
⇒ $2.1 + $4.5
⇒ $6.6
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JTHF monitors offices for tax preparation fee averages, and considers averages greater than $625.00 to be excessive. Offices that consistently charge excessive fees may be subject to which of the following corrective actions? Select one: a. The office will immediately be terminated from the Program. b. The office will be fee capped, which will result in all Financial Product Applications with fees greater than $625.00 to be rejected. c. The office will be fee capped from charging any tax preparation fees. d. None of the above – the office can charge whatever tax preparation fees it wants. Incorrect
The corrective action that offices that consistently charged excessive fees would be subject to by JTFH is a. The office will immediately be terminated from the Program.
What is JTFH ?JTH Financial, LLC (JTHF) is a company that was formed in 2010 in Virginia and their goal and mode of operation is to help customers with tax settlement products that can help them get the best amount to pay for taxes.
JTH Financial, LLC has affiliate offices that engage in tax preparation for clients around the United States but they monitor these offices to ensure that their tax preparation fee averages is not excessive. If an office consistently has excessive fees charged to its customers, then JTH Financial terminates them from the program to protect its customers.
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Help meeeee plssss I need to pass this by tmr
The statement means "whenever x is close to (but not equal to) a, then f(x) is a large positive number.
How do you find the limit of x approaches 0?When x is close to (but not equal to) a, then f(x) is a large positive number, according to the expression limxaf(x)=. In other words, f(x) grows larger and larger without bound as x approaches a.
For a rational function, we divide the numerator and denominator by the highest power of x that appears in the denominator to get the limits at infinity. This establishes which term in the overall expression controls how the function behaves at high x values.
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Find the equation of the linear function represented by the table below in slope-intercept form.
x y
-3 -12
2 13
7 38
12 63
Answer:
[tex]y=5x+3[/tex]
Step-by-step explanation:
Consider the points [tex](-3,-12)[/tex] and [tex](2,13)[/tex].
[tex]m=\frac{-12-13}{-3-2}=5 \\ \\ y-13=5(x-2) \\ \\ y-13=5x-10 \\ \\ y=5x+3[/tex]
Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. Determine the price of each bag of popcorn and the price of each drink.
The price of each bag of popcorn and the price of each drink is $7.5 and $4 respectively.
How to calculate the equation?Let the drinks be represented as d.
Let the popcorn be represented as p.
From the information, Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:
6p + 4d = 65
Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:
9p + 8d = 107.50
Equating the equation
6p + 4d = 65 ..... i
9p + 8d = 107.50 ..... ii
Multiply equation i by 8
Multiply equation ii by 4
48p + 32d = 520
36p + 32d = 430
12p = 90
Divide
p = 90/12
= 7.5
6p + 4d = 65 .
6(7.5) + 4d = 65
4d = 65 - 45
4d = 20
d = 20/4
drink = 5
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what is the general form of the equation for the given circle?
The general form of the equation for the given circle is:
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
Define Circle.A circle is a closed shape consisting of all points that are a fixed distance, called the radius, away from a single point, called the center. It is a two-dimensional geometric shape and is defined by its diameter, which is the distance between two points on the circle that are opposite each other and pass through the center.
What do you mean by equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown numbers or values, and one or more constants, which are fixed numbers. The most common type of equation is an algebraic equation, which uses mathematical operations such as addition, subtraction, multiplication, and division to relate the variables and constants.
The general form of the equation for a circle is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where,
(a,b) is the center of the circle and
r is the radius of the circle.
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BRAINLIEST EASY PROBLEM!!!!!!!!!!! 7th grade) find x and y.
Answer:
x = 20
y = 20
Step-by-step explanation:
In the given triangle, we can deduce that angle x is congruent to angle y using the Isosceles Triangle Theorem. Hence, we can construct the equation xº = yº.
We also know that the measures of the interior angles of a triangle add to 180º. Hence, we can construct the equation xº + yº + 140º = 180º.
We now have a system of equations, and since we already have an identity for xº (and also for yº), we can solve the system using the substitution method.
xº + yº + 140º = 180º
↓ substituting xº for yº
xº + xº + 140º = 180º
↓ subtraction 140º from both sides
2xº = 40º
↓ dividing both sides by 2
xº = 20º
↓ removing degree sign from both sides
x = 20
Now that we have solved for x, we have also essentially solved for y, as plugging this x-value into the equation xº = yº will just yield:
20 = y
y = 20
what is the value of the exponential expression below?
36 1/2
Which unit of length would a microscope best help to see?
Answer:
The unit of length that a microscope best helps to see is 1 millimeter.
Step-by-step explanation:
Microscopes are instruments used for viewing objects that cannot be seen with eyes. The unit length of an object that a microscope can view should be a length that is very small
Many students choose to take courses in statistics and computer science as elective. Suppose that in a certain university 41% take computer science, 48% take statistics, and 63% take at least one of these two courses. What is the probability a randomly selected student takes both a computer science and a statistics courses as elective? Round your answer to two decimal places.
The probability that a randomly selected student takes both computer science and statistics courses as electives is 0.26
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We can use the formula for the probability of the intersection of two events:
P(A and B) = P(A) + P(B) - P(A or B)
where A and B are the events of taking computer science and statistics courses as electives, respectively.
Given:
P(A) = 0.41 (probability of taking computer science)
P(B) = 0.48 (probability of taking statistics)
P(A or B) = 0.63 (probability of taking at least one of these two courses)
So,
P(A and B) = 0.41 + 0.48 - 0.63 = 0.26
Therefore, the probability is 0.26, rounded to two decimal places.
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Ms. McCarty cuts
1
2
of a piece of construction paper. She uses
1
5
of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower?
Ms. McCarty uses 1/10 fraction of the sheet of paper to make a flower
How to calculate the fraction of the sheet of paper that was used to make the flower?Ms.McCarty uses 1/2 of a piece of construction paper
She uses 1/5 of this quantity to make a flower
Therefore the fraction of the sheet of paper used to make the flower can be calculated as follows
1/2 × 1/5
= 1/10
Hence she uses 1/10 of the sheet of paper to produce the flower
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Please help me !!!!!!!!
Answer: y = 40deg, x = 80deg
Step-by-step explanation:
1. Because we see that there are parallel lines in the triangle to the left, we know that two of the angles of that triangle are 50deg
2. using the fact that triangles have a total of 180deg we get x = 80deg
To solve for y, we also know that there are two angles in that triangle which are the same, and one of them is y, therefore 2y + 100deg = 180deg, meaning 7 = 40deg
Write and solve the system of equations for each of the following problems. You have to write two equations for each problem PLEASE
1. A plane makes a 600 mile trip in 3 hours flying with the wind, but the return trip against the same wind takes 4 hours.
What is the rate of the plane in still air and the rate of the wind?
2. Two pizzas and four sandwiches cost $62. Four pizzas and 10 sandwiches cost $140. How much does each pizza
and sandwich cost?
Consequently, the airplane's speed in still air 250 mph and Therefore, the wind's speed is 50 mph.
what is equation ?Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two spherical geometry and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0.
given
Now solve any problem for one variable. In the first equation, I'll find the value of x:
200mph = p - w
On both sides, add w:
p = 200mph Plus w
Now that we have the x from the first equation, we can use it to solve for w in the second equation:
200 mph + w + w Equals 300 mph
Add related phrases together for 300 mph: 200 mph plus two
200 mph on both sides are subtracted:
100mph = 2w
50 mph divided by two is w.
Therefore, the wind's speed is 50 mph.
To find the plane's speed, enter the value we just discovered back into either equation. I'll enter it into the first equation.
200 mph = (p - 50 mph)
50 mph extra on both sides
250mph = p
Consequently, the airplane's speed in still air 250 mph .
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Find the mode for the Following sets of numbers 83,97,85,84,96,80,87,91,80
Answer:
80
Step-by-step explanation:
80,80,83,84,85,87,91,96,97
in this numbers there is one mode which is 80 . it is mono.
Solve each system of equations below by graphing
y = -1/2x +4
x + 2y = 8
Answer:
enter this equation in desmos or symbolab, i cant do it here
Step-by-step explanation:
the sum of the squares of a and b
Answer:
[tex]a^2+b^2[/tex]
Step-by-step explanation:
The SUM of the SQUARES of a and b
The square of a is a^2
The square of b is b^2
The sum of them is: a^2 + b^2
Answer:
well if its about a right triangle its c^2 if not its just a^2+b^2
Step-by-step explanation:
Lesson 13 Practice Pro Lesson 13 Practice Problems 1. a. How can you find 50% of a number quickly in your head? b. Andre lives 1.6 km from school. What is 50% of 1.6 km? c. Diego lives mile from school. What is 50% of mile?
50% of 1.6 km, or 0.8 km, is how far Andre lives from school, which is 1.6 km away.
what is percentage ?A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.
given
Of means multiply and is means equals
W = 50% of 1.6
Change to decimal form
W = .50 * 1.6
W = .8 km
50% of 1.6 km, or 0.8 km, is how far Andre lives from school, which is 1.6 km away.
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The table shows monthly costs for two different internet service providers. What will be the difference in cost of the two plans after 18 months
Answer: 240
Step-by-step explanation:
The difference in cost between the two plans after 18 months is $240.
This is because the cost of Company A is consistently $35 more per month than that of Company B, which therefore would add up to $630 after 18 months.
The linear equation representing the cost of Company A is Y = 35X + 40, while the linear equation representing the cost of Company B is Y = 50X.
After 18 months, X would equal 18, and substituting this value into the two equations, we get the following for Company A:
Y = 35X + 40 Y = 35 * 18 + 40 Y = 630Meanwhile, for Company B, we get:
Y = 50X Y = 50 * 18 Y = 900The difference between these two values for different internet service providers is:
= $900 - $630 = $240This question should be provided with this following data:
Company A
Month, X : 1, 2, 3, 4
Total Cost ($), Y: 75, 110, 145, 180
Company B
Month, X : 1, 2, 3, 4
Total Cost ($), Y: 60, 110, 160, 210
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