Find the average rate of change of the given function on the interval [1,6]. g(x)=2x2−x
Answer:13
Step-by-step explanation:
g(1)=2(1)^2-1= 1
g(6)=2(6)^2-6=66
66-1/6-1=13
I need help with this problem. Please and thank you.
The correct option; B. Two irrational numbers, are the two roots found for the given quadratic equation.
What is defined as the discriminant?In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its categorization or solution. The discriminant for the quadratic equation ax² + bx + c = 0 is b² - 4ac.If the discriminant is positive, the roots of such a quadratic or cubic equation having real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots have included a conjugate pair of complex roots.For the given question;
The quadratic equation is give as;
x² + 5x + 3 = 0
discriminant D = b² - 4ac
b = 5, a = 1 and c = 3
D = 25 - 4(1)(3)
D = 25 - 12
D = 13
√D = √13
As, number is real, there will be two real roots.
As, root of discriminant √D = √13 is a irrational number, the solutions of the given quadratic equation will be two irrational number.
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¿Cuántas personas podrán ir sentadas en 5 buses si en cada uno se suben 85 personas y solo van sentados tres quintas partes de esas personas?
The number of people that are seated in the buses is 425
How to calculate the number of people?From the information, there are 5 buses and there are 85 people in each. Therefore, the total number of people will be:
= 85 × 5.
= 425
Since 3/5 of those people are seated, the number of people seated will be:
= Fraction of those seated × Total number of people.
= 3/5 × 425
= 255
Therefore, there are 255 people.
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Which graph represents an odd function?
There are 6 points on a coordinate plane. The points are (negative 5, 3), (negative 3, 1), (negative 1, 1), (1, 3), (3, negative 5), (5, negative 1).
There are 8 points on a coordinate plane. The points are (negative 4, 2), (negative 3, negative 1), (negative 1, negative 3), (0, 1), (1, 0), (2, negative 4), (4, 5), (5, 4).
There are 8 points on a coordinate plane. The points are (negative 4, 0), (negative 3, 1), (negative 2, negative 3), (negative 1, negative 2), (1, 2), (2, 3), (3, negative 1), (4, 0)
There are 11 points on a coordinate plane. The points are (negative 4, 3), (negative 4, 4), (negative 3, 5), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 1), (2, 1), (3, 5), (4, 3), (4, 4).
Answer: first graph
Step-by-step explanation:
Find the intercepts and use them to graph the equation y=x-6
Answer:
x intercepts= (6,0)
y intercepts= (0,-6)
Step-by-step explanation:
I graphed the points.
What is 804082 written in expanded form
Answer:
Step-by-step explanation:
(8 x 100000) + (0 x 10000) + (4 x 1000) + (0 x 100) + (8 x 10) + (2 x 1) = 804082
Find which are the errors and solve correctly the problem:
Answer:
[tex]f^{-1}(y) = \sqrt{x-5}[/tex]
Step-by-step explanation:
You have to switch the f(x) to x and the x's to y's
[tex]x = y^2 + 5[/tex]
[tex]\sqrt{x-5} = \sqrt{y^2}[/tex]
[tex]y = \sqrt{x - 5}[/tex]
I need this for today !!!
Answer:
1. reflection
2.translation
3.rotation
4.translation
5.translation
6.reflection
7.rotation
8.reflection
Hope this helps
have a good day
God bless you!
if Tn =5n +2 which term will have a value of 52
Answer:
10th term
Step-by-step explanation:
given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
Question 2 (1 point) Find the area of a triangle with two sides measuring 6 meters and 8 meters with an included angle of 137 degrees. D. 15.8 m² OB. 12. 7m² Oc 16.4m² A. 14.3 m²
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
Which equation represents a line which is parallel to the line y = -2x - 7?
y = -2x is line parallel to given line.
What is line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.
Main body:
The slope-intercept form is
y=mx+b, where
m is the slope and b is the y-intercept.
y=mx+b
Using the slope-intercept form, the slope is −2.
m=−2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope −2 and a given point (0,0) to substitute for
x₁ and y₁ in the point-slope form
y−y₁=m(x−x₁)
, which is derived from the slope equation
m=(y₂−y₁)/(x₂−x₁).
y−(0)=−2*(x−(0))
Simplify the equation and keep it in point-slope form.
y+0=−2⋅(x+0)
Solve for y.
y=−2x
Hence y = -2x is line parallel to given line.
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Using the calculator below, substitute the values to calculate the interest amount on a the loan using the compound interest formula. Principal: $4,000 time: 10 years rate: 7% number of compounding periods: 4 What is the amount of the compound interest? (interest only)
a. 2,800
b. 4,757
c. 4,006
d. 59,897
A firm manufactured 1000 Tv sets during its first year.the total firms production during the 10 year of operationis 29035 sets .
For each the level of output for 15th year using per year constant increase in production .
Answer:
6922 TV sets
Step-by-step explanation:
You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.
Arithmetic seriesAn arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...
an = a1 +d(n -1)
And the sum of n terms is ...
Sn = (2a1 +d(n-1))(n/2)
ApplicationTo find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.
S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000
29035 = 10000 +45d . . . . . . . . . . . simplified
d = (29035 -10000)/45 = 423 . . . . the increase in production each year
Production in the 15th year is ...
a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922
The output in the 15th year was 6922 TV sets.
It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?
The distance between the eyes and the distance to the image of the toes will be 273.80 cm.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that It is 163 cm from your eyes to your toes. You're standing 220 cm in front of a tall mirror.
The distance between the image of toes and eyes will be calculated as,
H² = P² + B²
H= √(P² + B²)
H = √(163² + 220²)
H = √(26569+48400)
H = √74969
H = 273.80 cm
Therefore, the distance between the eyes and the distance to the image of the toes will be 273.80 cm.
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What is the equation of the line that passes through the point (-3,-8) and has a slope of 4?
Answer:
[tex]y-8=4(x+3)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
Find a point on the line only.
Answer:
Step-by-step explanation:
this is very complicated and i suggest you to go to einstin
Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answer:
Step-by-step explanation:
She needs to sell 65 necklaces.
A scientist mixes water (containing no salt) with a solution that contains 20% salt. she wants to obtain 120 ounces of the mixture that is 15 % salt. How many ounces of water and how many ounces of the 20% salt solution should she use?
Answer:Say w= the amount of water in oz, then the 60% of the solution is 250 - w
Set up the equation:
Use distributive property first
0.60(250-w) = 0.15 x 250
Isolate to solve for w
150- 0.60w= 37.5
-0.60w= 37.5-150
0.60w= -112.5
w= 187.5 ounces
250-187.5= 62.5 ounces salt solution
Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.
Hope this helps!
Step-by-step explanation:
Emmett is planning a party at an escape room. The escape room will charge Emmett a
booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Answer:
B. After the booking fee the party will cost $20 per person
Pls help asap maths
32/3
Step-by-step explanation:
5 = 3(x-9)
5 = 3x - 27
5 + 27 = 3x
32 = 3x
x = 32/3
System of Equations Question:
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month. How much can John spend on food for each cow per month?
The amount John will spend on food for each cow per month is approximately 15.08 dollars
How to find the how much each cow feed per month?John is in charge of feeding the pigs and cows on the farm.
The cow's food costs twice as much as the pig's food.
Let
x = cost of pigs food
y = cost cow's food
Hence,
y = 2x
There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month.
46y + 22x = 860
Therefore, let's combine the system of equation.
y = 2x
46y + 22x = 860
46(2x) + 22x = 860
92x + 22x = 860
114x = 860
x = 860 / 114
x = 7.5 dollars
y = 2(7.54) = 15.08 dollars
Therefore, the cost of food for each cow is 15.08 dollars
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what is the vaule of 2 × 4^2 + 5 enter the answer in the box
The value of the expression 2 x 4² + 5 will be 37
What is expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given is the following expression -
2 x 4² + 5
On solving the expression, we get -
2 x 4² + 5
2 x 4 x 4 + 5
32 + 5
37
The value of the expression 2 x 4² + 5 will be 37
Therefore, the value of the expression 2 x 4² + 5 will be 37
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PLEASE HELP!! PLEASE I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
LMNP is rotated 180° clockwise about the origin.
What are the coordinates of M' ?
Answer:
M'(-3, -4)
Step-by-step explanation:
the coordinate rules for a rotation of 180 degrees is (x, y) --> (-x, -y)
Basically, you just change both values (x and y) of M to negative. Then bam, u got the coordinates for M'
Comet Lee borrowed $16,000 on a 6%, 90-day note. After 20 days, Comet paid $2,000 on the note. On day 50, Comet paid $4,000 on the note. What are the total interest and ending balance due by the U.S. Rule? Use ordinary interest. (Use 360 days. Do not round the denominator in your calculation and round your final answers to the nearest cent.)
The total amount of interest and the final debt owed under the US Rule is $191.09.
Given that,
Comet Lee took out a $16,000 loan with a 90-day, 6% note. Comet settled the note for $2,000 after 20 days. Comet settled the note for $4,000 on day 50.
We have to find what is the total amount of interest and the final debt owed under the US Rule.
First,
To calculate $2000 per 20 days.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $1600
r is 6%
t is 20 days is 20/360
So,
i= 1600×0.06×20/360
i= $53.33
Apply partial payment to interest due,
$2000-$53.33= $1946.67
Next,
Subtract remainder of payment from principal is adjusted balance
Adjusted balance =$16000-$1946.67
Adjusted balance =$14053.33
Now, Second,
To calculate $4000 per 50 days.
We know that,
i=p×r×t
So, p is $14053.33
r is 6%
t is 50 days is 30/360
So,
i= 14053.33×0.06×30/360
i= $70.27
Apply partial payment to interest due,
$4000-$70.27= $3929.73
Next,
Subtract remainder of payment from principal is adjusted balance
Adjusted balance =$14053.33-$3929.73
Adjusted balance =$10123.6
Now, for 40 days
i= 10123.6×0.06×40/360
i= $67.49
So, balance is 10123.6+67.49= $10191.09
When max make two makes partial payments,
The total interest is $53.33+$70.27+$67.49= $191.09
Therefore, the total amount of interest and the final debt owed under the US Rule is $191.09.
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Quill works for a newspaper. He was hired
five years ago. When he was hired, he was
given three vacation days. For each year he
works with the company, he earns two
additional vacation days up to a maximum
of 20 days. How many paid vacation days
does he now get at the end of five years of
employment. If his annual salary is
$64,480, how much does he make during his
vacation?
He got 11 vacation days in five years. If his annual salary is $64,480 he earned during his vacation days $2277
How much vacation time should employee get?The average nationwide is 10, however it varies a little by industry and area. These days off—generally regarded as vacation time—usually get longer the longer an employee works. For the majority of businesses, an employee can receive an additional three to four days per year every five years based on longevity.
The normal recommendation is to wait three to six months. However, the organization and its culture have a big impact. He continued by saying that many businesses make it very clear what their vacation policy is. Some employers allow you to accumulate additional vacation time the longer you work
64,480/12 =5373.33
5373.33/26 = 207
207 x 11 =2277
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He got 11 vacation days in five years. If his annual salary is $64,480 he earned during his vacation days $2277
How much vacation time should employee get?The average across the country is 10, but it varies slightly by region and industry. The length of these vacation days typically increases with an employee's length of service. Based on longevity, most companies allow employees to get an extra three to four days per year every five years.
The usual advice is to hold off for three to six months. The organization and its culture, however, play a significant role. He went on to remark that a lot of companies are quite explicit about their vacation policies. The longer you work for some employers, the more vacation time you can accrue.
64,480/12 =5373.33
5373.33/26 = 207
207 x 11 =2277
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how to find the area with a circumfernece of 18
The area of the circle with the circumference 18 units is 25.80 square units
How to calculate the area of the circle?The given parameters are
Circumference = 18 units
As a general rule, circumference are represented by the variable C
So, we have the following representation equation
C = 18
The circumference of the circle can be calculated as
C = 2πr
Next, we substitute the value of the variable C in the above equation
i.e. C = 18
So, we have the following equation
2π * r = 18
Divide both sides by 2π
r = 9/π
The area of the circle can then be calculated using the following area formula
A = πr²
Next, we substitute the value of the variable r in the above equation
i.e. r = 9/π
A = π * (9/π)²
Evaluate the exponents
This gives
A = π * 81/π²
Evaluate the products
So, we have
A = 81/π
As a general notation, π = 3.14
So, we have the following equation
A = 81/3.14
Evaluate the quotient
A = 25.80
Hence, the area is 25.80 square units
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State whether the following variables have a positive correlation, negative correlation, or no correlation.
3.)
(a.)Height of a person and how often he or she attends religious services. __________________________________
(b.)Average property tax in a school district and salary of teachers __________________________
(c.)Weight of a person and shoe size. ____________________________
The types of correlation seen between positive correlation, negative correlation, or no correlation, in the variables is:
a. Height of a person and how often he or she attends religious services. - No correlation (b.)Average property tax in a school district and salary of teachers - Positive correlation (c.)Weight of a person and shoe size. - Positive correlation What is the correlation between property taxes and teacher salaries?One of the main sources of funding for school districts is the property tax charged. This means that increased property taxes will lead to more money being available for teacher salaries which might then increase. There is therefore a positive correlation between the two.
The same is true for the weight of a person and shoe size. This is because the heavier a person is, the larger their shoe size according to research.
There is however no correlation between the height of a person and their attendance of religious services.
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Translate each phrase into a variable expression. Use n for the variable.
Nine increased by twice a number
The expression of the phrase " Nine increased by twice a number " is 2n + 9
The given phrase is
Nine increased by twice a number
We have to convert the the phrase to the expression
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.
Consider the number as n
Twice the number = 2n
nine increased by twice a number = 2n + 9
Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9
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The population of city A is 24% less than the population of city B, so city A's population is _____% of city B's.
Answer:
76%
Step-by-step explanation:
100%-24%=76%
Deion plans to repaint some classroom bookcases. He has 3 5 /1 gallons of paint. All of the bookcases are the same size and each requires 1/5 gallon of paint. How many bookcases will he be able to paint?
The bookcases that Deion will be able to paint is 16.
What is a fraction?It should be noted that a fraction is a part of a whole number that has a numerator and denominator.
In this case, Deion has 3 1/5 gallons of paint and all of the bookcases are the same size and each requires 1/5 gallon of paint.
The number of bookcase needed will be:
= Total gallons / Gallons for each
= 3 1/5 ÷ 1/5
= 16/5 ÷ 1/5
= 16/5 × 5/1
= 16
He can paint 16 cases.
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