The average rate of change within the function f(x)=[tex]x^{2} -x-1[/tex]is -2.
Given The function f(x)=[tex]x^{2} -x-1[/tex]
We have to search out the typical rate of change of function within the interval (-2,1).Interval is largely a variety between numbers lying on the quantity line which may be a line on which different numbers are plotted.
We know that average rate of change =f(b)-f(a)/(b-a)
we have to first know the values of function at different values of x.
f(x)=[tex]x^{2} -x-1[/tex]
f(1)=1-1-1
=-1
f(-2)=4+2-1
=5
b=-2
a=1
put within the formula:
A=-1-5/1+2
=-6/3
=-2
Hence average rate of change of the function within the interval (-2,1) is -2.
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Simplify the expression. What classification describes the resulting polynomial? (3x^2-11x-4)-(2x^2-x-6)
The expression can be simplified to a polynomial of degree 2.
[tex]x^2 - 10x + 2[/tex]
How to simplify the expression?
Here we have the expression:
[tex](3x^2 -11x - 4) - (2x^2 - x - 6)[/tex]
We can directly simplify this by taking the variable as common factor:
[tex](3 - 2)*x^2 + (-11 + 1)*x + (-4 + 6)\\\\x^2 - 10x + 2[/tex]
This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.
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Write 32.5% as a fraction in simplest form.
Answer:
13/40
Step-by-step explanation:
Rewrite a percentage as a decimal: [tex]\frac{32.5}{100}[/tex]
Convert decimals to integers: [tex]\frac{325}{100}[/tex]
Reduce the fraction: [tex]\frac{13}{40}[/tex]
Answer: [tex]\frac{13}{40}[/tex]
32.5% as a fraction in simplest form is 13/40.
Here we have to find fractional form of 35 percent
Since we knw that,
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
To convert a percentage to a fraction,
we can simply write it as a fraction with a denominator of 100.
Then,
we simplify the resulting fraction to its simplest form.
For 32.5%,
we can write this as,
⇒ 32.5/100
Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).
The GCF of 32.5 and 100 is 12.5,
so we can divide both by 12.5,
⇒ 32.5/100 = (32.5 ÷ 12.5) / (100 ÷ 12.5)
= 13/40
Therefore, 32.5% as a fraction in simplest form is 13/40.
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Do the side lengths 4, 8, and 10 form a triangle? Select the correct answer and reasoning. Question 19 options: A) Yes, because the sum of any two side lengths is greater than the third side length. B) No, because the third side length is greater than the sum of the other two side lengths. C) Yes, because the sum of all three side lengths is greater than 20. D) No, because 4 + 8 is greater than 10.
Answer:
A) Yes, because the sum of any two side lengths is greater than the third side length.
Step-by-step explanation:
All triangles have a property that the sum of two side lengths is greater than the remaining side length.
4 + 8 = 12 > 10, making it a triangle
y=-3x² + 12x - 12 has how many real roots?
A. 0
B. 1
C. cannot be determined
D. 2
The equation has 2 real roots
How to determine the number of real roots?The equation is given as:
[tex]y = 3x^2 + 12x - 12[/tex]
Calculate the determinant using
d = b^2 - 4ac
So, we have:
d = 12^2 - 4 * 3 * (-12)
Evaluate
d = 288
Because d > 0
i.e. 288 is greater than 0
Then it means that the equation has 2 real roots
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Take a rectangular sheet of paper. Fold it in any way and then unfold it. Draw a line on the crease using a ruler and pencil. Repeat this process 7 more times. Mark the points of intersection as A, B, C, D and so on. Identify polygons and identify whether they are convex or concave.
The polygon formed was convex polygon.
What is a Concave and Convex Polygon ?A polygon that has at least one interior angle greater than 180 degree is called concave polygon . It usually has an irregular shape.
A convex polygon has all angles less than 180 degree.
It is given to follow some steps
1. A rectangular sheet of paper is taken .
2. It if folded and unfolded in random directions
3. Lines are drawn on the creases
4. The intersection points are marked A,B,C,D,E,F,G
5. The figure formed is a convex polygon as all the angles measure were less than 180 degree.
Therefore the polygon formed was convex polygon.
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An insurance company has provided you with a sample of paid claims. The sample includes the following claims: 192, 113, 200, 287, and 225. What are the mean and the variance respectively of this sample rounded to nearest whole number?
Review Later
203, 63
203, 3942
210, 63
210, 3942
The required value of mean and variance is 203 and 3942 respectively.
Hence option B is correct.
The sample includes the following claims: 192, 113, 200, 287, and 225.
What is Statistic?The statistic is the study of mathematics which deal with relations between comprehensive data.
Mean(x) = 192+113+200+287+225/5
x = 203
variance =[tex]\frac{\sum(x-x_i)^2}{n^2-1}[/tex]
=summation of squared value/n^2−1
=15769/25−1
=15769/24
=3942
Thus, the required value of mean and variance is 203 and 3942 respectively.
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Denver, Colorado, is 5,183 feet above sea level. Convert the height to miles. Round to two decimal places.
Answer:
0.98 miles
Step-by-step explanation:
Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.
Step-by-step explanation:
1) the difference betwee the terms given is 3-8=-2-3= -5, then
2) for n-th term: aₙ=8-5(n-1);
3) for the 9-th term: a₉=8-5*8=-32.
Sally is using strings to mark parallel rows for a vegetable garden for her house.
House
Step-by-step explanation:
ATTACHED IS THE SOLUTION.
Answer:
m<2=115
m=180-115
=75
your answer is 75 because house is hanged in 180
A person has 100 notes of Rs. 10 and Rs. 20 each. He went to a shop and bought items for Rs. 220. In how many ways can he pay this amount using the notes he has?
Answer:
look below
Step-by-step explanation:
first way ,10 x 22 = 220
second way , 20 x 11 = 220
There are many ways other than this but I cant tell all of them. for example, the person can just give Rs. 1000 to the shopkeeper and receive a change of Rs. 780
There are 12 ways he can pay this amount using the notes he has the answer is 12.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
Let x be the number of Rs10 notes and y be the Rs20 note
10x + 20y = 220
The whole number of x and y which satisfy the above equation:
x = 0, y =11
x = 2, y =10
x = 4, y =9
x = 6, y =8
x = 8, y =7
x = 10, y =6
x = 12, y =5
x = 14, y =4
x = 16, y =3
x = 18, y =2
x = 20, y =1
x = 22, y =0
Total number of ways = 12
Thus, there are 12 ways he can pay this amount using the notes he has the answer is 12.
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Will mark brainliest, need help ASAP!
A radioactive element has a half-life of 55 days. what percentage of the original sample is left after 115 days? round to 4 decimals when necessary.
The percentage of the original sample that is left after 115 days is; 23.4733%
How to calculate the decay percentage?Formula for radioactive decay is;
A = A₀ * (1/2)^(t/t_¹/₂)
where;
A = quantity of the substance remaining
A₀ = initial quantity of the substance
t = time elapsed
t_¹/₂ = half life of the substance
Thus;
A/A₀ = (1/2)^(115/55)
A/A₀ = 0.234733 or 23.4733%
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A wall of a building is 30 inches wide. 14 inches is concrete,10 inches is brick, and 6 inches is like stone. What fraction of the wall is concrete
Answer:
46.67 %
Step-by-step explanation:
Total thickness = 30
14 of this is concrete 14/30 x 100% = 46.67 %
State the domain of the function
F(x)= (x+3)/(x-1)
Answer:
x < 1 or x > 1
Step-by-step explanation:
The domain of a function is the range of values of the input is real and defined
In this particular function, x = 1 is the only value at which the function is not defined since the denominator x -1 becomes 0 and the function is undefined since division by zero is undefined
Flying the SR-71A jet, Capt. Elden W. Joersz, USAF, set a record speed of 2193.16 miles per hour. At this speed, the algebraic expression 2193.16t gives the total distance flown in t hours. Find the distance flown by the SR-71A in 1.7 hours.
Final answer:
The required distance is 3728.372 miles.
Step-by-step explanation:
Step 1
The distance flown is t hours given by:
2193.16t
Step 2
Let distance be represented by d, thus:
d = 2193.16t
Step 3
d = 2193.16t
Substitute t = 1.7 in the relation:
d = 2193.16 x 1.7
Step 4
Solve for d:
d = 2193.16 x 1.7
d = 3728,372
Y is inversely proportional to the square root of x. If Y = 5 when x = 36, find Y, when x is 16. For full credit: 1. Write a proportion. 2. Solve for y. 3. Show work.
Answer: y=7.5
Step-by-step explanation:
Given
y∝(1/√x)
this implies that
y=k/√x eq(*)
when y=5 and x=36 then
5=k/√36
5=k/6
30=k eq(1)
to find y when x is 16
put values in eq(*)
y=30/√16
y=30/4
y=7.5
The mean of the Normal distribution determines the ___________ of the distribution. Please complete the sentence by selecting one of the word below:
A) location
B) percentage
C)Spread
D) proportion
Step-by-step explanation:
location
of the distribution.
Show all work pleaseee and thank you
Work is attached. Hope it helped!
Your little brother just learned how to flip and catch a coin. He believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. Based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.
By performing two experiments a lot of times, your brother will see that catching the coin mid-air does not affect the probability.
How to explain that the theory is false?We assume that the probability of each outcome of the coin is equal, so the probability of getting tails is 0.5 and the probability of getting heads is 0.5
Then, you can say to your brother to perform his experiment a lot of times. In two ways.
First, he lets the coin came down to his hand around 100 times.
Then, he catches the coin in mid-air another 100 times.
He will see that the probability of getting heads (or tails) is (almost) the same in both cases, this will mean that his theory is false.
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f(x)=-2x+4
find domain and range
Domain: All real numbers
Range: All real numbers
Since the function is linear it is a continuous straight line meaning that the domain and range are all real numbers.
Which is the best definition of closure?
Number sets are closed under an operation when you perform the operation and the result is a number that is not a real number.
Number sets are closed under an operation when you perform the operation and the result is a member of the opposite number set.
Number sets are closed under an operation when you perform the operation and the result is a member of a related number set.
Number sets are closed under an operation when you perform the operation and the result is another member of the same number set
Answer:
Number sets are closed under an operation when you perform the operation and the result is another member of the same number set
Tom changed the rotating speed of his cement mixer from 6 1/3 rpms to 10 rpms . By how many revolutions per minute did the speed of the mixer increase
Answer:
3 2/3
Step-by-step explanation:
10 rpms - 6 1/3 rpms = 3 2/3
Evaluate functions from their graph f(−3)=
See the Correct answer attached!
Considering the given graph, it is found that f(-3) = 1.
How to verify the value of f(x) from a graph?First we identity x on the horizontal axis, then we look at the value of y on the vertical axis for which the function is marked at this point.
At this graph, when the horizontal axis is of -3, the vertical axis is of 1, hence f(-3) = 1.
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Which number could be added to
both sides of this quadratic equation
to complete the square?
1=x²-3x
er the value that belongs in both of these green boxes.
[2]+1=x²-3x+
Hint: Use ()²
The number which could be added to both sides of the equation to complete the square is; -2.25.
Which number could be added to both sides of this quadratic equation to complete the square?The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;
1 - 2.25 = (x -3/2)² - 2.25
Hence, the number which should be added to both sides of the equation is; -2.25.
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PLEASE HELP MEEEE!!!!!
Using proportions, it is found that the meaning of 1 + x is the percent of original price being paid.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the total cost of the toy is given by:
15.85(1 + x).
In which x is the sales tax.
We have that:
15.85 is the base cost.15.85(1 + x) is the cost considering sales tax.Hence (1 + x) is the percent of original price being paid.More can be learned about proportions at https://brainly.com/question/24372153
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Kurt has $9,000 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much will he have in 1 year? Kurt has $ 9,000 in an account . The interest rate is 5 % compounded annually . To the nearest cent , how much will he have in 1 year ?
Answer:
$9450
Step-by-step explanation:
Answer:
A = $9,450.00
A = P + I where
P (principal) = $9,000.00
I (interest) = $450.00
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,000.00(1 + 0.05/1)(1)(1)
A = 9,000.00(1 + 0.05)(1)
A = $9,450.00
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $9,000.00 at a rate of 5% per year compounded 1 times per year over 1 years is $9,450.00.
Please help with this pre algebra question
Answer:
(2) / ((x + 5)(x - 1))
&
(3x) / ((x - 6)(x - 1))
Step-by-step explanation:
The question is asking you to factor the denominator. In this case, you cannot simplify either of the numerators. You can factor the denominator by asking yourself the question: which two numbers multiply to equal the final number in the quadratic and add to equal the middle number in the quadratic?
1.) 2 / (x² + 4x - 5)
-----> Which two numbers multiply to -5 and add to 4? These numbers are 5 and -1. This makes the factors (x + 5) and (x - 1). The fully simplified answer: (2) / ((x + 5)(x - 1))
2.) 3x / (x² - 7x + 6)
------> Which two numbers multiply to 6 and add to -7? These numbers are -6 and -1. This makes the factors (x - 6) and (x - 1). The fully simplified answer: (3x) / ((x - 6)(x - 1))
*Please let me know if I misinterpreted the question or you need further clarification <3
7(x + 1) -2 =5 (x + 1) +2
Answer:
x = 1
Step-by-step explanation:
Simplifying
7(x + 1) + -2 = 5(x + 1) + 2
Reorder the terms:
7(1 + x) + -2 = 5(x + 1) + 2
(1 * 7 + x * 7) + -2 = 5(x + 1) + 2
(7 + 7x) + -2 = 5(x + 1) + 2
Reorder the terms:
7 + -2 + 7x = 5(x + 1) + 2
Combine like terms: 7 + -2 = 5
5 + 7x = 5(x + 1) + 2
Reorder the terms:
5 + 7x = 5(1 + x) + 2
5 + 7x = (1 * 5 + x * 5) + 2
5 + 7x = (5 + 5x) + 2
Reorder the terms:
5 + 7x = 5 + 2 + 5x
Combine like terms: 5 + 2 = 7
5 + 7x = 7 + 5x
Solving
5 + 7x = 7 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
5 + 7x + -5x = 7 + 5x + -5x
Combine like terms: 7x + -5x = 2x
5 + 2x = 7 + 5x + -5x
Combine like terms: 5x + -5x = 0
5 + 2x = 7 + 0
5 + 2x = 7
Add '-5' to each side of the equation.
5 + -5 + 2x = 7 + -5
Combine like terms: 5 + -5 = 0
0 + 2x = 7 + -5
2x = 7 + -5
Combine like terms: 7 + -5 = 2
2x = 2
Divide each side by '2'.
x = 1
Simplifying
x = 1
Answer:
Hello! The answer is x = 1.
Step-by-step explanation:
To solve this equation, we need to find x.
The first step in approaching this problem would be to use the distributive property:
7(x + 1) - 2 = 5(x + 1) + 2 will turn into:
7x + 7 - 2 = 5x + 5 + 2
Now, you can combine like terms on each side of the equation:
7x + 5 = 5x + 7
Now, you want to get the x's on one side and the whole numbers on the other side. In order to do this, we will subtract 5 from both sides and subtract 5x from both sides:
7x + 5 = 5x + 7
-5x -5 -5x -5
This will leave us with:
2x = 2
We will have to now divide both sides by 2 to get x by itself:
2x = 2
-- --
2 2
This leaves us with the result: x = 1
if the following data were transformed, and points with the coordinates (x, log) y)) were plotted, what points would be plotted? round log(y) to three decimal places.
x y
3 125
4 625
5 3125
A. (3, 2.097), (4, 2.796), (5, 3.495)
B. (2.097, 3), (2.796, 4), (3.495, 5)
C, (125, 2.097), (625, 2.796), (3125, 3.495)
D. (2.097, 125), (2.796, 625), (3.495, 3125)
Option A is accurate. The points were plotted with the coordinates (x, log) y), and they are (3, 2.097), (4, 2.796), and (5, 3.495).
What is the definition of a logarithm?
Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
Identity used;
[tex]\rm log_x (y) = z \\\\ z^x=y[/tex]
From the data we obtained;
[tex]\rm log_3(125) = 5 \\\\ 5^3 = 125[/tex]
[tex]\rm log_5 625 = 4 \\\\ 5^4 = 625[/tex]
[tex]\rm log_5 (3125) = 5 \\\\ 5^5 = 3125[/tex]
The points with the coordinates (x, log) y)) were plotted, the points are (3, 2.097), (4, 2.796), (5, 3.495)
Hence, option A is correct.
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Review the equation used in writing a partial fraction decomposition.
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
or, [tex]\frac{-15x+10}{(5x-2)^2} = \frac{A}{5x-2} + \frac{B}{(5x-2)^2}[/tex]
Which system of equations can be used to determine the values of A and B?
(answer choices in attached image)
Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:
5A = -15.-2A + B = 10.What is the partial fraction?The partial fraction is given as follows:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]
Applying the least common multiple at the right side, we have that:
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}[/tex]
[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}[/tex]
Hence, comparing both sides of the equality:
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Answer:
The answer is Be
Step-by-step explanation:
5A=-15
-2A+B=10
According to the graph, what is the value of the constant in the equation
below?
Height = Constant - Width
Answer:
B) 0.5
Step-by-step explanation:
The given formula is:
Height = Constant * Width
You may now choose any point on the graph (the horizontal line represents a point for width, and the vertical line represents a point for height) and put it into the specified formula. Let's test the two supplied points (2, 1):
Now, 2 is on the horizontal line, so we put it in for width, and 1 is on the vertical line, so we plug that in for height. When we do it, we get:
1 = C * 2
(In the expression above we need to solve for C, and we can do that by dividing both sides by 2)
C= 1/2 = 0.5
So, the answer is 0.5 or option B.