Answer: The behavior of the function can be checked by finding the derivative of it and evaluating it at the two specified points:
\(\begin{gathered} f(x)=|x^2-9| \\ \\ \\ \frac{df(x)}{dx}=\frac{|x^2-9|}{x^2-9}(2x) \end{gathered}\)The behaviour at x = -3 and x = 3.
\(\begin{gathered} \frac{df(x)}{dx}=\frac{\lvert x^{2}-9\rvert}{x^{2}-9}(2x) \\ \\ \\ x=3\rightarrow\frac{\lvert3^2-9\rvert}{3^2-9}(2\times3)=\frac{0}{0}\times6=0\rightarrow\text{ Not possible} \\ \\ x=-3\rightarrow\frac{\lvert(-3)^2-9\rvert}{(-3)^2-9}(2\times-3)=\frac{0}{0}(-6)\rightarrow\text{ Not possible} \\ \end{gathered}\)The answer therefore is:
\(\text{ Option\lparen D\rparen}\rightarrow\text{ Continuous but non-Differentiable }\)Plot for the function:
Not that the f(x) is indeed Differentiable function
, but there can not be any slope at x = -3 and x = 3.
Evaluate the expression 2x-7 for x = -4
Answer:
-15
Step-by-step explanation:
The solution of expression for x = - 4 is,
⇒ - 15
We have to given that,
An expression is,
⇒ 2x - 7
Now, We can simplify the expression for x = - 4 as,
An expression is,
⇒ 2x - 7
Plug x = - 4;
⇒ 2 × - 4 - 7
⇒ - 8 - 7
⇒ - 15
Thus, The solution of expression for x = - 4 is,
⇒ - 15
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A classmate said that the vertex of g(x) = -5(x + 2)^2 - 4 is (2, 4). Is your classmate correct? If not, what is the correct vertex?
Answer: Classmate is wrong. Vertex = (-2, -4)
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k where
"a" is the vertical stretch-a is a reflection over the x-axish is the horizontal shift (positive = right, negative = left)k is the vertical shift (positive = up, negative = down)Given: g(x) = -5(x + 2)² - 4
↓ ↓
h= -2 k= -4
Vertex = (-2, -4)
-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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If a and b are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is
9 8 7 6
A 3 2
B 1 (A). 4 (B). 5 (C). 6
(D). 9
(E). Depends on the values of A and B
If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B that is option E.
What is digit?In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of the ten numbers from 0 to 9. If a and b are nonzero digits, the number of digits (which may or may not be different) in the sum of the three whole numbers is determined by the values of A and B. A digit can be any of the following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a measurement of something. It can be written with one, two, three, or more digits.
Here,
If a and b are nonzero digits, the number of digits (which does not have to be the same) in the sum of the three whole numbers is determined by the values of A and B that is option E.
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Choose the kind(s) of symmetry in the 2D number. (Select all that apply.)
plane
point
line
none
Answer:
plane
point
line
Step-by-step explanation:
Based on the options provided, the kinds of symmetry in a 2D number can be:
Plane symmetry: This refers to a symmetry where a figure can be divided into two identical parts by a plane. This symmetry is also known as reflectional symmetry.Point symmetry: This refers to a symmetry where a figure can be rotated 180 degrees around a central point to produce the same figure. This symmetry is also known as rotational symmetry.Line symmetry: This refers to a symmetry where a figure can be divided into two identical parts by a straight line. This symmetry is also known as bilateral symmetry.Therefore, the possible kinds of symmetry in a 2D number can be
plane symmetry,
point symmetry, or
line symmetry.
Given the conditional statement ~p q, which statement is logically equivalent? p ~q. ~p ~q. ~q ~p. ~q p.
Answer: contrapositive ⌝Q→⌝P.
A quiz consists of multiple choice questions. each question has 4 possible answers (a-d) and only one answer is correct. if the student guesses the answer to each question, then what is the probability that the student answer correctly for that question?
Answer:
Answers - 4
Correct Answer - 1
Probability - 1/4
A copy machine makes 44 copies per minute . how many copies does it make in 3 minutes and 45 seconds
Answer:
165
Step-by-step explanation:
Please answer this before friday
Answer: 21:9 and 42:18
Step-by-step explanation:
14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.
21:9 is our simplified ratio multiplied by 3 on both sides.
42:18 is our simplified ratio multiplied by 6 on both sides.
But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.
What’s the correct answer answer asap
Answer:
The answer should be B.
consider the system of linear equations
consider the system of linear equations
6x+2y – z=4
X +5y+z=3
2x+y+4z=27
A, solve the system by
I. Gassian elimination method,
II. LU- decomposition method
III. Gauss- Jacobi method,and
IV. Gauss-seidel method,
I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.
II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.
III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.
IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.
I. Gaussian Elimination Method:
To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:
| 6 2 -1 | 4 |
| 1 5 1 | 3 |
| 2 1 4 |27 |
We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.
After performing the necessary row operations, we obtain the following reduced row-echelon form:
| 6 2 -1 | 4 |
| 0 4 2 | -1 |
| 0 0 3 | 6 |
From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.
II. LU-Decomposition Method:
LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.
III. Gauss-Jacobi Method:
The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.
IV. Gauss-Seidel Method:
Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.
Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.
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1. Kelly bounces a basketball 30 times in 50 seconds. At that rate,
approximately how many times will Kelly bounce the ball in 150
seconds?
Answer:
kelly would of hit the ball 90 times in 150 seconds
Step-by-step explanation:
you take 30 and divide it by 50 and you get 0.6.
then you take 0.6 and times it be 150
Answer:
90 times
Step-by-step explanation:
The equation set-up for if she bounces a basketball 30 times in 50 seconds is 30x=50. This means that she bounced the ball every 1 2/3 second. According to this, our next equation set-up would be 1 2/3x=150. If we divide 150 by 1 2/3, we get 90. This means that Kelly bounced the basketball 90 times in 150 seconds.
Can anyone help me solve this question?
x = e^y
Step-by-step explanation:
Pick any point on the graph below for a solution:
Which of the following best describes the graph of the logarithmic function
given below?
F(x) = logo.316 %
O A. Translation
O B. Decreasing
C. Reflection
O D. Increasing
Answer:
decreasing
Step-by-step explanation:
The graph gives the curve is decreasing.
Option B is the correct answer.
What are logarithms?The logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be raised to obtain x is the logarithm of a number x to the base b.
The given logarithmic function is .
log (base 0.316)x
Graph the logarithm using the vertical asymptote and a few selected points.
Vertical Asymptote: x=0
The coordinate points to plot on graph are (1, 0), (2, -0.6016) and
(3, -0.9536).
If we plot these points on the graph then we can see the curve is decreasing.
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At a school, 40% of the sixth-grade students said that hip-hop is their favorite kind of music. If there are 275 sixth-grade students at the school, how many sixth-grade students prefer hip hop music?
Answer:
Around 80 students
Step by step explaining:
My big brain
Simplify the expression below.
12a−8−5a+12
Step-by-step explanation:
Given
12a - 8 - 5a + 12
= 7a + 4
Hope it will help :)
Answer:
7a + 4
Step-by-step explanation:
First, let's rewrite this expression to combine like terms:
12a – 8 – 5a + 12 — I bolded the constants and underlined the expressions with variables
12a – 5a – 8 + 12 — it looks a little easier regrouped, doesn't it?
The last two terms are easy, right?
12 – 8 = 4 — simplify with subtraction
We'll focus on the first two terms now. Let's rewrite the terms with variables attached to make the subtraction easier:
a(12 – 5) = a(7) = 7a
We could also think of it this way: multiplication is just repeated addition.
12a = a + a + a + a + a + a + a + a + a + a + a + a (we just add a to itself 12 times)
5a = a + a + a + a + a (we just add a to itself 5 times)
Subtracting this expression would then look like this:
a + a + a + a + a + a + a + a + a + a + a + a – (a + a + a + a + a)
a + a + a + a + a + a + a + a + a + a + a + a – a – a – a – a – a
Five of the a values will cancel out, and to show this, we can rewrite the expression once more, like this:
a – a + a – a + a – a + a – a + a – a + a + a + a + a + a + a + a
The five a values cancel out and leave us with this:
a + a + a + a + a + a + a
How many a values are added together now? Seven of them, right? We add a to itself 7 times. We can then rewrite that expression as 7a.
Using the [12 – 8 = 4] expression from above, we add the 4 to the 7a to find our final answer: 7a + 4
I hope this helps increase your understanding of the concept! Have a great day!
Can somebody please help me with this..? Thanks a lot btw if u do!
Answer:
The answer is c 2580/6
Step-by-step explanation:
The answer is c because the ounces are trying to be separated into the 6 jars so it makes sense that they will divide
The following frequency data shows the number of states, including the District of Columbia, that
favored each party in the presidential popular vote in 1976 and in 2012.
What percent voted Republican in 1976? What type of frequency is this?
2012 Election
1976 Election Democrat Republican
Total
Democrat
12 = 23.5% 12 = 23.5% 24 = 47.1%
Republican
15 = 29.4% 12 = 23.5% 27 = 52.9%
Total
27 = 52.9% 24 = 47.1951 = 100%
1
% voted Republican in 1976.
This is a (select)
Answer: 52.9% vote Republican in 1976
This is a marginal relative frequency.
Let's complete the table for 1976 elections as well as subsequently then for 2021 elections. It can also be done vice-versa.
1976 elections:
Democrat voting will be:
= \((\frac{12}{27}\times 100+ \frac{12}{24}\times 100)\)
= \(44.45+50\)
= \(94.45\) (%)
Republic voting will be:
= \((\frac{15}{27}\times 100 + \frac{12}{24}\times 100 )\)
= \(55.55+50\)
= \(105.55\) (%)
Total will be:
= \(\frac{27+24}{51}\times 100\)
= \(100\) (%)
2012 elections:
Democrat voting will be:
= \((\frac{12}{24}\times 100 +\frac{12}{24}\times 100 )\)
= \(50+50\)
= \(100\) (%)
Republic voting will be:
= \((\frac{15}{27}\times 100+\frac{12}{27}\times 100 )\)
= \(55.55+44.45\)
= \(100\) (%)
Total will be:
= \(\frac{27+24}{51}\times 100\)
= \(100\) (%)
Thus the solution above is right.
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Round 38 to the nearest ten. Enter your answer in the box below.
Answer:
40
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Here are the rules;
• If the number undergoing the rounding is followed by 5, 6, 7, 8, or 9, round the number up
• If the number undergoing the rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Example: 32 and 38 rounded to the nearest ten is 30 and 40 respectively.
On January 1, Year 1, Jana started a small flower merchandising business that she named Jana’s Flowers. The company experienced the following events during the first year of operation: Started the business by issuing common stock for $43,000 cash. Paid $28,000 cash to purchase inventory. Sold merchandise that cost $20,000 for $42,000 on account. Collected $37,000 cash from accounts receivable. Paid $9,800 for operating expenses. Required a. Organize ledger accounts under an accounting equation and record the events in the accounts. In the last column of the table, provide appropriate account titles for the Retained Earnings amounts. b-1. Prepare an income statement. b-2. Prepare a balance sheet. b-3. Prepare a statement of cash flows. c. Since Jana sold inventory for $42,000, she will be able to recover more than half of the $43,000 she invested in the stock. Do you agree with this statement?
a) The organization of ledger accounts under an accounting equation and journal entries are as follows:
Accounting Equation:Assets = Liabilities + Equity
Cash + Inventory + A/Receivable C.Stock R/Earnings
1. $43,000 $43,000
2. -28,000 $28,000
3. $42,000 42,000 S/Revenue
4. -20,000 -20,000 COGS
5. 37,000 -37,000
6. -9,800 -9,800 Op Exp.
Bal. $42,200 $8,000 $5,000 $43,000 $12,200
Journal Entries:Debit Cash $43,000
Credit Common Stock $43,000
Debit Inventory $28,000
Credit Cash $28,000
Debit Accounts Receivable $42,000
Credit Sales Revenue $42,000
Debit Cost of goods sold $20,000
Credit Inventory $20,000
Debit Cash $37,000
Credit Accounts Receivable $37,000
Debit Operating expenses $9,800
Credit Cash $9,800
b1)
Jana's Flowers
Income StatementFor the year ended December 31, Year 1
Sales Revenue $42,000
Cost of goods sold $20,000
Gross profit $22,000
Operating expenses $9,800
Net income $12,200
b2) Jana's Flowers
Balance SheetDecember 31, Year 1
Cash $42,200
Accounts Receivable $5,000
Inventory $8,000
Total assets $55,200
Common Stock $43,000
Retained Earnings 12,200
Total equity $55,200
b3) Jana's Flowers
Statement of Cash FlowsFor the year ended December 31, Year 1
Net income $12,200
Changes in working capital:
Accounts Receivable (5,000)
Inventory (8,000)
Operating cash flow ($800)
Financing activities:
Common Stock $43,000
Cash flows $42,200
c) I do not agree with this statement. It does not necessarily flow that Jana selling $42,000 in goods will be able to recover more than half of the $43,000 she invested in her business. So far, she has made $12,200 from her investment.
Data Analysis:Cash $43,000 Common Stock $43,000
Inventory $28,000 cash $28,000
Accounts Receivable $42,000 Sales Revenue $42,000
Cost of goods sold $20,000 Inventory $20,000
Cash $37,000 Accounts Receivable $37,000
Operating expenses $9,800 Cash $9,800
Thus, it will take time for Jana to recover her investment in the business.
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What is the next term of the geometric sequence?
250, 50, 10
Answer:
c
Step-by-step explanation:
your welcome
4/7 and 12/71 Are these ratios proprtional?yes or no?
No
Explanation
Step 1
simplify the fractions and compare
\(\begin{gathered} \frac{4}{7}\rightarrow\frac{4}{7} \\ \frac{12}{71}\rightarrow this\text{ fraction can not be simplied} \end{gathered}\)so, as the simplified fractions are differents , teh ratios are not proportional.
i hope this helps you
If A=[-3,2),B=(0,4]then A-B=?
\(A - B = [-3, 0]\)
Katie has 52 cups. she pours juice into 3/4 of her cups. in how many cups does Katie pour juice? Show your work.
Answer:
39cups
Step-by-step explanation:
Katie has 52 cups
she poured juice to 3/4×52 of the cups
=13×3 =39
she poured juice to 39cups
please, write an equation in point-slope form of the line through point J(4,1) with slope -4
Answer:
\(y=-4x+17\)
Step-by-step explanation:
slope (\(m\)) \(= -4\)
Using equation: \(y-y_1=m(x-x_1)\)
Substituting \(m=-4\) and point (4, 1): \(y-1=-4(x-4)\)
Therefore: \(y=-4x+17\)
Find the set of the solutions of each of the following absolute value inequalities. Check your answers. |(x+1)/2 - x/2|<1/2
Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1
Explain about the absolute value inequalities:The comparison of the connection here between variable and its value is a compound inequality. In a compound inequality, a variable is compared across two ranges which may provide the variable's range by satisfying either one or both of the limitations .
The given absolute value inequalities :
|(x+1)/2 - x/2| < 1/2
Removing the modulus sign will for 2 equations:
(x+1)/2 - x/2 < 1/2 and (x+1)/2 - x/2 < - 1/2
Simplifying each:
(x+1)/2 - x/2 < 1/2
x/2 + 1/2 - x/2 < 1/2
Both values will get cancelled:
0 < 0
But 0 = 0
and (x+1)/2 - x/2 > - 1/2
x/2 + 1/2 - x/2 > -1/2
0 > -1 (correct)
here also the terms are getting completely cancelled to
Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1
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Complete question:
Find the set of the solutions of the following absolute value inequalities.
|(x+1)/2 - x/2| < 1/2
Help please! Confused on this
the closing price of the fast food restaurant stock was $32.5 per share, and the closing price of the toy company stock was $5.5 per share on that day.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
We know that Norman and Suzanne own 27 shares of the fast food restaurant stock and 63 shares of the toy company stock, so the value of their fast food restaurant stock holdings is:
The total value of their stock portfolio is given as $1224.00, so we can write: 27x + 729 + 63x = 1224
Combining like terms:
90x + 729 = 1224
Subtracting 729 from both sides:
90x = 495
Dividing by 90 on both sides:
x = 5.5
Therefore, the closing price of the toy company stock on that day was $5.5 per share, and the closing price of the fast food restaurant stock was:
x + 27 = 5.5 + 27 = $32.5 per share
So, the closing price of the fast food restaurant stock was $32.5 per share, and the closing price of the toy company stock was $5.5 per share on that day.
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Customer pays $0.035 per minute for local calls, if the customer made 60 local calls that all lasted 3 minutes, how much will the customer pay?
The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.
To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30
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Enter a positive value for d that makes this statement true: 34×d is less than 34 but greater than zero HELP PLSS FASTT
Answer:
0.5 (any number between 0 and 1)
Step-by-step explanation:
34 * 0.5 = 17
34 > 17 > 0
What is the multiplicative rate of change of 1,6 2,4 3,8/3 and 4,16/9
The multiplicative rate of change of the function is 2/3
How to determine the multiplicative rate of change?From the question, we have the following parameters that can be used in our computation:
1,6 2,4 3,8/3 and 4,16/9
These can be represented as
(1,6) (2,4) (3,8/3) and (4,16/9)
The multiplicative rate of change is then calculated as
Rate = f(2)/f(1)
Substitute the known values in the above equation, so, we have the following representation
Rate = 4/6
Evaluate
Rate =2/3
Hence, the rate is 2/3
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