Answer:
Step-by-step explanation:
The coefficients of the x terms are {1, 3, -3}, so the discriminant, b^2 - 4ac, is 3^2 - 4(1)(-3), or 9 + 12, or 21. The positive nature of the discriminant tells us that there are two real, unequal roots. Following the quadratic formula, we get:
-3 ± √21
x = -----------------
2
What is the mean of 4 and 25?
The geometric mean of 4 and 25 is 10.
When a positive value is repeated in either the means or extremes position of a proportion, that value is referred to as a geometric mean (or mean proportional) between the other two values.
The Geometric Mean (GM) is the average value or mean that, by taking the product of a set of numbers' values as its root, indicates the collection's central tendency.
Let x = the geometric mean.
4/x = x/25 (by the definition of geometric mean)
x²=100
x=√100 (cross-product property)
x=10
Hence, The geometric mean of 4 and 25 is 10.
Complete question: What is the geometric mean of 4 and 25?
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A and B can finish a work in 30 days they worked for it for 20 days and then B left the remaining work was done by alone in 20 more days a alone can finish the work in
Answer:
A could finish the whole work in 60 days
Step-by-step explanation:
Both A and B can finish the work in 30 days.
That means both A and B can finish 1/30 part of the work in 1 day.
So in 20 days, both A and B can finish 20/30 = 2/3 part of the work.
Both A and B worked together for 20 days and completed 2/3 part of the work. Now 1/3 part of the work is remaining.
But after 20 days B left the work. Now A finished the remaining 1/3 part of the work alone.
Given A has completed the remaining 1/3 part of the work in 20 days. We are asked to find in how many days A could finish the whole work.
Let A could finish the whole work in x days.
That means A could finish 1/x part of the work in 1 day.
So in 20 days, A could finish 20(1/x) = 20/x part of the work.
But it's given that A finished the remaining 1/3 part of the work in 20 days.
Thus we are able to equate 20/x and 1/3.
[tex]\longrightarrow\dfrac{20}{x}=\dfrac{1}{3}[/tex]
[tex]\Longrightarrow\underline{\underline{x=60}}[/tex]
Hence A could finish the whole work in 60 days.
A triangular pendant has two sides of length 23 mm and 31 mm. What are the possible lengths (in whole mm) for the third side?.
According to Pythagoras theorem, the value of the third side of the triangle is 38.6mm
In math Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
Here we have given that the triangular pendant has two sides of length 23 mm and 31 mm.
And we need to find the possible lengths (in whole mm) for the third side.
Here in the given question, we have the values of the two sides are 23mm and 31mm.
Then we have to apply the values on the Pythagoras theorem formula,
=> hypotenuse² = adjacent² + opposite²
Now, we have to apply the values as opposite and adjacent on it, then we get,
=> hypotenuse²= 23² + 31²
=> hypotenuse² = 529 + 961
=> hypotenuse² = 1490
Therefore, the value of the third side is 38.6mm
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IN THE FIGURE TRIANGLE ABE IS CONGURENT TO TRIANGLE ACD SHOW THAT TRIANGLE ADE AND TRIANGLE ABC ARE SIMILIAR
The triangle ADE is similar to the triangle ABC.
What are congruent triangles?
The triangles are congruent if two sides and the included angle of one triangle match the corresponding sides and angle of another triangle.
It is given that triangle ABE is congruent to triangle ACD, which can also be written as ΔABE≅ΔACD.
So, according to the Corresponding parts of Congruent triangles (CPCT) property:
AB=AC...........(1)
AE=AD...........(2)
By dividing 2 and 1 we will get:
[tex]\frac{AD}{AB} =\frac{AE}{AC}[/tex]........(3)
In the triangles ADE and ABC, ∠A is the common angle and according to this and 3,
ΔADE is similar to ΔABC by side angle side criterion.
Therefore hence it is proved that ΔADE and ΔABC are similar.
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What are two ways sequences can be defined?
The two ways that sequences can be defined include the following: Arithmetic Sequences and Geometric Sequences.
What is a sequence in mathematics?A sequence is defined as the collection of items in such a way that repetitions can be observed.
There are two major ways the sequence can be defined in arithmetics and this includes the following:
Arithmetic Sequences: This is the type of sequence whereby every term is created by adding or subtracting a definite number to the preceding numberGeometric Sequences: This is the type of sequence whereby every term is obtained by multiplying or dividing a definite number with the preceding number.Learn more about sequence here:
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which expression represents the perimeter of
8x - 43
5x+12
Answer:
Step-by-step explanation:
The perimeter is P = 26x - 62.
P = 2(L + B)
P = 2(5x + 12 + 8x - 43)
P = 2(13x - 31)
P = 26x - 62
Does anyone know the answer to this?
Answer: I think it is between 3rd and 4 lines of number 2 and 3
Step-by-step explanation:
Because it line here is 0.20
so 2.7 will be some where between 3rd and 4 lines of number 2 and 3
Earning Commission Sales Commision Rate Commission $750 3%
The commission for $750 at 3% is:
Commission can be defined as the fees or extra fees that is been paid to someone for a job well done or for rendering a service.
Now let find the commission amount using this formula
Commission = Earnings × rate
Where:
Earnings = $750
Rate =3%
Commission = $750 × 3%
Commission = $22.50
Therefore the commission is $22.50.
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The complete question is:
Find the commission.
Earning Commission
Sales Commission Rate Commission
$750
3%
?
The commission is $
Please help and show work, will give lots of points!
Lourdes is reading a biography for her history class. She reads 30 pages each day. After 9 days, Lourdes has read 3/5 of the biography. Write a linear equation to represent the number of pages Lourdes still has to read after x days.
y = []x + []
(Use above format to write the equation.)
What does the y-intercept of this linear equation represent?
A. Pages already read
B. Pages in book
C. Pages read each day
D. Days to finish
Answer:
The linear equation is y = 450 - 30 x, where y is the number of pages
Lourdes has left to read after x days
Step-by-step explanation:
Each day, Lourdes reads 30 pages of a 450-page book
- We need to write a linear equation to represent the number of pages
Lourdes has left to read after x days
∵ Lourdes reads 30 pages each day
∵ Lourdes will read for x days
∴ The number of pages Lourdes will read in x day = 30 x
- The left pages will be the difference between the total pages of the
book and the pages Lourdes read
∵ The book has 450 pages
∵ Loured will read 30 x in x days
∴ The number of pages left = 450 - 30 x
- Assume that y represents the number of pages Lourdes has left
to read after x days
∴ y = 450 - 30 x
The linear equation is y = 450 - 30 x, where y is the number of
pages Lourdes has left to read after x days
Why is it called linear?
Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation.
Does linear mean straight?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Why differential is called linear?In the variable separation if the unknown function and its derivatives have no exponent larger than one and there are no cross-expressions—that is, terms like f f′ or f′f′′ in which the function or its derivatives appear more than once—the partial differential equation is said to be linear.
Because the equation depicts a straight line in the Cartesian plane, it is called a linear equation. Through the use of logical and mathematical tools, it enables us to solve issues in a variety of scientific fields and academic disciplines as well as in real-world circumstances.
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At which root does the graph of f x x 4 6 * x 7 5 cross the X axis?
The graph of the function f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.
The graph of the function f(x) = x^4 - 6*x^7 + 5 is a polynomial function. The roots of a polynomial are the values of x for which the polynomial is equal to zero. To find the roots of the polynomial, we must solve the equation f(x) = 0. To solve this equation, we will use polynomial division.
We will divide the polynomial by (x - 5), which will give us the following result:
f(x) = x^4 - 6*x^7 + 5 = (x - 5)(x^3 + 7x^2 - 5x + 25).
We can now solve for the roots of the polynomial. Since (x - 5) is a factor of the polynomial, the root is x = 5. We can also solve for the other roots by setting the remainder of the polynomial division equal to 0. This gives us the equation x^3 + 7x^2 - 5x + 25 = 0. This equation can be solved by factoring and the result is x = 0, 1, and 5. Therefore, the graph of f(x) = x^4 - 6*x^7 + 5 crosses the x-axis at x = 0 and x = 5.
f(x) = x^4 - 6*x^7 + 5
Divide f(x) by (x-5):
f(x) = (x-5)*(x^3 + 7x^2 - 5x + 25)
Set remainder equal to 0:
x^3 + 7x^2 - 5x + 25 = 0
Factor:
x^3 + 7x^2 - 5x + 25 = (x - 5)*(x^2 + 5x + 5)
x = 0, 1, 5
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Please help me respond this question
Answer:
y=0
Step-by-step explanation:
Characterize observational study with respect to nature of the sample and treatment.
An observational study is used to answer a research question based purely on what the researcher observes.
What Is an Observational Study?An observational study is a statistical study that does not have any treatment or intervention done by the researchers.
Observational research allows the researcher to see what their subjects really do when confronted with various choices or situations. The term refers to the study of non-experimental situations in which behaviour is observed and recorded.
Statistics is the process of collecting data about a group of objects to draw conclusions about populations of those objects. For example, a statistician may take a sample group of workers from company XYZ and have them rate their job satisfaction with the company. Based on the results of that sample, the statistician can make educated assumptions about all the employees of company XYZ and their job satisfaction.
However, observational studies can only establish that significant associations exist between predictor and outcome variables. Observational studies cannot establish that the associations identified represent cause-and-effect relationships.
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Find the critical numbers of the function on the interval 0≤ θ < 2π.
f(θ) = 2cos(θ) +(sin(θ))^2
Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.
Therefore, the answer is 0 and π.
f(θ) = 2cos(θ) +(sin(θ))²
f'(θ) = -2sin(θ) +2sin(θ)cos(θ)
Critical values of f are points at which f' is zero or not defined.
For all values of θ, we can find that f'(θ) is defined.
f'(θ) = 0
-2sin(θ) +2sin(θ)cos(θ) = 0
cos(θ) - 1 = 0 or sin(θ) = 0
cos(θ) = 1
θ = nπ, n = 0, 1, 2, ...
sin(θ) = 0
θ = nπ, n = 0, 1, 2, ...
Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.
2π is not there as it is not included in the interval.
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A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner.
If the function for the total rental cost for vacuum cleaner is f(x) = 6x + 14 , then the cost for using it for 10 hours is $74 .
A hardware store rents vacuum cleaner for a part of a day ,
the function that models the total rental cost for the vacuum cleaner is given as : f(x) = 6x + 14 ;
where , x is the number of hours the cleaner is used .
given that the vacuum cleaner is used for 10 hours , So x = 10 .
the total cost is f(10) = 6×10 + 14 ;
f(10) = 60 + 14 ;
f(10) = 74 ;
Therefore , the total rental cost for using the vacuum cleaner for 10 hours is $74 .
The given question is incomplete , the complete question is
A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner. What is the total cost for using the vacuum cleaner for 10 hours .
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what is 777777900000/244576575
Answer:
31800.997945142
or
31800 24407400⁄24457657
S
What is the value of K the line?
As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.
What is a line?A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
What is slope of a line?A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.
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Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? responses.
The top 25% of cars have a typical gas mileage of at least 33.5 miles per gallon.
To calculate this, you need to use the interquartile range (IQR) formula.
The IQR is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3).
IQR = Q3 - Q1
In this case, the 25th percentile (Q1) is 28.4, and the 75th percentile (Q3) is 37.9. So:
IQR = 37.9 - 28.4 = 9.5
The top 25% of cars have a gas mileage of 33.5 miles per gallon, which is Q3 + 1.5*IQR.
33.5 = Q3 + 1.5*IQR
33.5 = 37.9 + 1.5*9.5
33.5 = 37.9 + 14.25
33.5 = 52.15
Therefore, the top 25 percent of cars have a typical gas mileage of at least 33.5 miles per gallon.
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A workers earnings E are a function of the number of hours N worked at a rate of $8.75 per hour. Write a function rule that represents each situation
The function rule that represents each situation is $8.75 * n.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here, we have
A worker's earnings E are a function of the number of hours N worked at a rate of $8.75 per hour.
We have to create an incognita that represents a worker's salary based on how many hours he or she works.
G: Worker's salary
n: number of hours worked
G=f(n)
Then using the data that the worker earns $8.75 per hour worked, we must formulate f(n) so that with this data we can calculate G.
G = f(n) = $8.75 * n
If the worker performs 1 hour of work (n=1), then his salary will be:
G = $8.75 * 1 = $8.75
If the worker performs 10 hours of work (n=10), then his salary will be:
G=$8.75 * 10 = $87.5
Hence, the function rule that represents each situation is $8.75 * n.
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Lauren has a 16-foot ladder. The safety instructions recommend the base of
the ladder be placed 6 feet from the base of the wall. How high will the ladder
be able to reach up the wall?
Round your answer to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
You can use Pythagoras theorem for this
[tex]16^{2}[/tex] = [tex]6^{2}[/tex] + [tex]x^{2}[/tex]
256 = 36 + [tex]x^{2}[/tex]
220 = [tex]x^{2}[/tex]
[tex]\sqrt{220}[/tex] = x
14.8323.... = x
we also have to remember that it could be negative, but, negative distances are just the same distance but in the other direction, so they are the same length here.
14.8 feet = x to the nearest 10th
What is the equation in slope-intercept form of the line that passes through the point (2,-2)
and is perpendicular to the line represented by y = 2/5x+ 2?
A y=5/2x-7
в y=5/2x+7
c y=-5/2x-3
D y=-5/2x+3
Answer:
D, [tex]y=\frac{-5}{2x}+3[/tex]
What is the value of |a-b|+|b-a| if a=b-1/2
The value of the absolute expression |a - b| + |b - a| will be 1.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The equation is given below.
a = b - 1/2
The expression is given as,
⇒ |a - b| + |b - a|
The value of (a - b) is given as,
a = b - 1/2
a - b = - 1/2
And the value of (b - a) is given as,
a = b - 1/2
b - a = 1/2
Then the value of the expression is calculated as,
⇒ |a - b| + |b - a|
⇒ |-1/2| + |1/2|
⇒ 1/2 + 1/2
⇒ 1
The worth of the outright articulation |a - b| + |b - a| will be 1.
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Jing just got a new job. She started at a pay rate of $12.50 per hour and will get a $0.50 raise each year. Max started a job where his salary is found by the equation: f(x) = x + 10 , where x is the number of years.
Interpret the rates of change and initial values of the linear functions in terms of the situations they model. Compare the results and what they mean. How many years must they both work for Max to earn more per hour than Jing?
Jing
Initial value:
Rate of change:
Max
Initial value:
Rate of change:
Jing's initial pay rate is $12.50 per hour. She will receive a pay raise of $0.50 per hour every year.
Max's initial pay rate is 10 dollars per hour. He will receive a pay raise of 1 dollar per hour every year.
To determine how many years it will take for Max to earn more per hour than Jing, we need to find the point at which the two linear equations intersect. This can be done by setting the two equations equal to each other and solving for x.
Jing's equation is: $12.50 + 0.50x
Max's equation is: x + 10
Setting the equations equal to each other and solving for x, we get:
$12.50 + 0.50x = x + 10
This simplifies to:
$0.50x = -2.50
Dividing both sides by 0.50, we get:
x = -5
Since the value of x cannot be negative, this means that Max will never earn more per hour than Jing.
What if limit is infinity minus infinity?
If the limit is infinity minus infinity it is undefined because the result would be a number that is not a real number.
In mathematics, a limit is the value that a function approaches as the independent variable approaches a certain value. Limits are used to study the behavior of a function as the independent variable approaches a certain point.When the limit is infinity minus infinity (∞ - ∞), it is undefined because the result is not a real number. Infinity minus infinity is an indeterminate form, which means that the limit could approach any real number or it could approach infinity or negative infinity. In other words, the result of infinity minus infinity is an unknown quantity.To understand why infinity minus infinity is undefined, you must understand the concept of infinity. Infinity is not a number, but rather an idea of something that is larger than any number. Therefore, when subtracting infinity from infinity, there is no set answer since the two concepts are not numbers. To calculate the limit, the two infinities must be replaced with real numbers. In conclusion, when the limit is infinity minus infinity, it is undefined because the result is not a real number. Infinity is an idea and not a number, so the result of infinity minus infinity can not be determined. To calculate the limit, the two infinities must be replaced with real numbers.
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Use elimination method to solve the following system of equations
6x+y=-4
6x+5y=4
Answer:(-1,2)
Step-by-step explanation:
-(6x+y=-4)
6x+5y=4
------------------
-6x-y=4
6x+5y=4
--------------
4y=8
y=2
6x+2=-4
6x=-6
x=-1
What is the linear inequality symbol?
The symbol of a linear inequality is: " ≤ " or " ≥ "
What is a linear inequality equation?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
For example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
Now, the graph becomes according to the slope-intercept form is:
Here we noticed that,
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.
Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.
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What is the domain and range calculator?
The domain and range calculator is a tool that allows us to enter the necessary data and have it compute and output the domain and range.
What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input.
After we enter an x value, the function outputs this sequence of values.
We simply solve the equation y = f to determine the values of the independent variable x and obtain the domain (x).
Simply put, after determining g's domain, x=g(y) will calculate the function's range (y).
The domain and range calculator is a tool in which we put in the required values and it calculates and gives out the domain and range as an output.
Therefore, the domain and range calculator is a tool that allows us to enter the necessary data and have it compute and output the domain and range.
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which point of concurrency is determined by the three altitudes of any triangle?
Answer:
orthocentre
Step-by-step explanation:
A triangle's three altitudes intersect at the orthocentre
5(2x + 1) = 50 I am struggling please help
Answer:
x = 4.5
Step-by-step explanation:
To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we need to get rid of the 5 that is multiplying the expression 2x + 1.
One way to do this is to divide both sides of the equation by 5. This gives us:
(5(2x + 1))/5 = 50/5
Simplifying the left side of the equation gives us:
2x + 1 = 10
Now, we just need to get x by itself on one side of the equation. To do this, we can subtract 1 from both sides of the equation. This gives us:
2x = 9
Finally, we can divide both sides of the equation by 2 to solve for x. This gives us:
x = 9/2
Therefore, the solution to the equation is x = 9/2, or x = 4.5.
I hope this helps! Let me know if you have any other questions.
Answer:
x = 9/2 or 4.5
Step-by-step explanation:
5(2x + 1) = 50
10x + 5 = 50
10x = 50 -5
x = 45 /10
x = 9/2 or 4.5
I hope my answer helps you.
luke went to a blackjack table at the casino. at the table, the dealer has just shuffled a standard deck of 52 cards. luke has had good luck at blackjack in the past, and he actually got three blackjacks with queens in a row the last time he played. because of this lucky run, luke thinks that queens are the luckiest card. the dealer deals the first card to him. in a split second, he can see that it is a face card, but he is unsure if it is a queen. what is the probability of the card being a queen, given that it is a face card? answer choices are in a percentage format, rounded to the nearest whole number.
The probability of the card being a queen, given that it is a face card is; 33%
How to find the probability of selection?The probability of an event is simply the number of favorable outcomes divided by the total number of outcomes possible.
In a standard deck of cards, we know that there are 52 cards in total and that out of those 52 cards, there are 12 face cards.
Now, One-third of those face cards are always queens, due to the fact that there are 4 queens in a deck of cards.
This means that the probability using the formula of;
Probability = number of favorable outcomes/number of expected outcomes
Probability = 4/12 = 1/3 = 0.33 = 33%
Therefore, we conclude that there is a 33% chance that the card Luke holds is a queen.
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