What ordered lair is closest to a local minimum of the function, f(x)?A. (-1, -3)B. (0, -2)C. (1, 4)D. (2, 1)
Answers
We have the following function given:
x f(y)
-2 -8
-1 -3
0 -2
1 4
2 1
3 3
And we can see that the minimum of the function is for the lowest f(y) value on this case -8
And the closest pair to this local minimum is:
A. (-1,3)
Related Questions
6.Landscaping Calculate the area (in square feet) of a flower garden shaped like a circularsector with radius 60 ft and central angle 40 degrees.
Answers
The area of the circular sector is given as:
[tex]\begin{gathered} \text{Area}=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}[/tex]Given that, radius= 60ft and angle =40 degrees
[tex]\begin{gathered} \text{Area}=\frac{40}{360}\times3.14\times60\times60 \\ \text{Area}=\frac{452160}{360} \\ \text{Area}=1256\text{square f}eet \end{gathered}[/tex]Achromycin is to be administered 11mg per pound in 4 equal doses to a patient weighing 34kg. Oral suspension is available 125mg per 5mL. How many millilitres should you give per dose? Use 1 kg = 2.2 lbs and round your final answer to 1 decimal place.
Answers
We are told that 11 mg of Achromycin per patient pound must be administered, we are also given the weight of the patient as 34 kg, in order to properly use this weight we must convert it from kg to pounds by multiplying the weight in kg by 2.2, like this:
34×2.2 = 74.8
Then, the patient weight is 74.8 lbs, by multiplying this by the 11 mg per pound of Achromycin that have to be administered we can determine the mg of Achromycin, like this:
74.8×11 = 822.8
Then, 822.8 mg of Achromycin has to be administered, by dividing this amount by 4, we can determine the amount for each dose:
822.8/4 = 205.7
Then 205.7 mg are given per dose, since 5 mL contains 125 mg, we can take the ratio of mL to mg to get:
5/125 = 1/25
By multiplying the above ratio by 205.7 we can determine the milliliters that should be given per dose, like this:
205.7×1/25 = 8.2
Then, 8.2 mL must be given per dose
Fill in the blank to correctly complete the sentence.
Consider the following function.
f(x)
=
2x4+6x3−4x2+2x+12
=
x−2)2x3+10x2+16x+34+80
By inspection, we can state that f(2)=
Answers
The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The given function below is:
f(x) = 2x⁴ + 6x³ −4x² +2x + 12
f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
We have to determine the value of f(2).
⇒ f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80
Substitute the value of x = 2 in the given function,
⇒ f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80
⇒ f(x) = 0 + 80
⇒ f(x) = 80
Therefore, the value of f(2) would be 80.
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Evaluate the expression.3 – 5 (11 + 4) = 52
Answers
In order to evaluate this expression, let's calculate the operations in the left side and compare the final value with the value in the right side:
[tex]\begin{gathered} 3-5(11+4)=52 \\ 3-5\cdot15=52 \\ 3-75=52 \\ -72=52 \end{gathered}[/tex]Since the values don't match, so the expression is FALSE.
The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $72.How much is each allowance?
you [][][][][]
friend[][][][]
Answers
The allowance of each person is
You: $40Friend: $32How to determine the amount of each person's allowance?From the question, the tape diagram that can be used in our computation is given as
you [][][][][]
friend[][][][]
Counting the number of boxes, we have
You = 5
Friend = 4
Next, we represent the boxes as a ratio
So, we have
You : Friend = 5 : 4
This means that
You = 5/9 * Total allowance
Friend = 4/9 * Total allowance
From the question, we have
Total allowance = $72
Substitute the known values in the above equation
So, we have the following equation
You = 5/9 * 72
Friend = 4/9 * 72
Evaluate the products
You = 40
Friend = 32
Hence, the amount of each person's allowance is $40 and $32, respectively
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11 – 8 (5 – 2) help
Answers
Answer
11 - 8 (5 -2) = -13
Explanation
11 - 8 (5 -2)
To solve this, we will first solve the one in the bracket
11 - 8 (5 -2)
= 11 - 8 (3)
= 11 - 24
= -13
Hope this Helps!!!
Can someone pls help me find the equation for the arithmetic sequence and help me fill out the graph
Answers
Solution
- The question gives us the following arithmetic sequence:
[tex]t(n+1)=t(n)-4[/tex]- We are asked to write out the explicit function for the sequence.
- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.
- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:
[tex]\begin{gathered} t(m)=a+(m-1)d \\ \text{where,} \\ a=\text{first term of the sequence} \\ d=\text{common difference} \\ m=\text{ number of terms} \\ \\ (\text{Note that: }m=n+1\text{, since the formula starts assumes that the sequence starts from the 1st term not zeroth term} \end{gathered}[/tex]- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.
[tex]\begin{gathered} \text{Let n=2} \\ \text{The formula becomes} \\ t(2+1)=t(2)-4 \\ t(3)=t(2)-4 \\ \\ \text{But we know that }t(2)=10 \\ \therefore t(3)=10-4 \\ t(3)=6 \\ \\ \text{Let n=3} \\ t(3+1)=t(3)-4 \\ t(4)=6-4 \\ t(4)=2 \\ \\ \text{Let n=4} \\ t(4+1)=t(4)-4 \\ t(5)=2-4 \\ t(5)=-2 \\ \\ \text{Thus, we can write out the terms of the sequence as follows:} \\ \ldots,t(2),t(3),t(4),t(5),\ldots=\ldots10,6,2,-2\ldots \\ \\ \text{ We can observe that the common difference is -4 since,} \\ 6-10=-4 \\ 2-6=-4 \\ -2-2=-4 \\ \text{And so on}\ldots \\ \\ \text{Thus, we can trace our sequence back to its first term as follows:} \\ t(2)-t(1)=-4 \\ 10-t(1)=-4 \\ \text{Subtract 10 from both sides} \\ -t(1)=-4-10 \\ \therefore t(1)=14 \\ \\ t(1)-t(0)=-4 \\ 14-t(0)=-4 \\ \text{Subtract 14 from both sides} \\ -t(0)=-4-14=-18 \\ \therefore t(0)=18. \\ \\ \text{Thus, the first term }t(0)=18 \end{gathered}[/tex]- Let us now apply the formula for the nth term of a sequence to find the explicit formula:
[tex]\begin{gathered} first\text{ term =}t(0)=a=18 \\ \text{common difference}=d=-4 \\ t(m)=a+(m-1)d \\ \\ t(m)=18+(m-1)(-4) \\ \text{Expand the bracket} \\ t(m)=18+m(-4)-1(-4) \\ t(m)=18-4m+4 \\ \\ \therefore t(m)=22-4m \\ \\ \text{Let us write the sequence in terms of n} \\ m=n+1 \\ t(n)=22-4(n+1) \\ t(n)=22-4n-4 \\ t(n)=18-4n \\ \\ \text{Thus, the explicit function is:} \\ t(n)=18-4n \end{gathered}[/tex]- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.
[tex]\begin{gathered} t(n)=18-4n \\ \\ \text{when n = 0} \\ t(0)=18-4(0) \\ t(0)=18 \\ \\ \text{when n= 1} \\ t(1)=18-4(1) \\ t(1)=14 \\ \\ \text{when n=2} \\ t(2)=18-4(2) \\ t(2)=10 \\ \\ \text{when n = 3} \\ t(3)=18-4(3) \\ t(3)=18-12=6 \\ \\ \text{when n = 4} \\ t(4)=18-4(4) \\ t(4)=2 \\ \\ \text{when n = 5} \\ t(5)=18-4(5) \\ t(5)=-2 \end{gathered}[/tex]- On the table, we have the values filled in below:
Final Answer
The explicit form of the sequence is:
[tex]t(n)=18-4n[/tex]Use the inverse trigonometric keyson a calculator to find the measureof angle A
Answers
ANSWER
A = 51°
EXPLANATION
ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,
[tex]\cos A=\frac{AC}{AB}[/tex]Solving for A,
[tex]A=\cos^{-1}\left(\frac{AC}{AB}\right)[/tex]Replace with the known values and solve,
[tex]A=\cos^{-1}\left(\frac{28}{44}\right)=\cos^{-1}\left(\frac{7}{11}\right)\approx50.4788\degree\approx51\degree[/tex]Hence, the measure of angle A is 51°, rounded to the nearest whole number.
Roots of Quadratics 50 PTS!!!
Answers
The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
k < 1/24b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
k = 3/5ci the equation -x² + 3x + (k + 1) = 0 has real roots
k > -3.25d the equation 3kx² - 3x + 2 = 0 has no real solutions
k < ± 1.633How to solve quadratic equations to get different answersQuadratic equations of the form ax² + bx + c = 0 is solved using the formula
[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex] OR [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
b² - 4ac > 0substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
b² - 4ac = 0substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
b² - 4ac > 0substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
b² - 4ac < 0substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
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Answer:
ax² + bx + c = 0 is solved using the formula
Step-by-step explanation:
The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.
(a) domain=
(b) range =
Answers
Range = -3 (< or =) Y (< or =) 5
Can someone tell me how to solve it with a picture on how you did it. Teacher told me to show my work. It hard pls Helppp
Answers
The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3
How to solve the given inequality?In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:
(2 × |4v + 6|)/3 - 2/1 ≤ 10
[(2 × |4v + 6|) - (3)2]/3 ≤ 10
[(2 × |4v + 6|) - 6]/3 ≤ 10
Cross-multiplying, we have:
(2 × |4v + 6|) - 6 ≤ 10 × 3
(2 × |4v + 6|) - 6 ≤ 30
Adding 6 to both sides, we have:
(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6
(2 × |4v + 6|) ≤ 36
Dividing both sides by 2, we have:
(2 × |4v + 6|)/2 ≤ 36/2
|4v + 6| ≤ 18
Evaluating the absolute value function, we have:
4v + 6 ≤ ±18
For the positive interval, we have:
4v ≤ 18 - 6
4v ≤ 12
v ≤ 12/4
v ≤ 3.
For the negative interval, we have:
4v ≥ -18 - 6
4v ≥ -24
v ≥ -24/4
v ≥ -6
Lastly, we would express the solution as an interval notation as follows:
-6 ≤ v ≤ 3
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A person invests $6,750 in an account that earns 5.25% annual interest compounded continuously. Findwhen the value of the investment reaches $15,000. If necessary round to the nearest tenth.The investment will be reach $15,000 in approximatelyyears.
Answers
Recall the formula for the Future value of a principal amount, compounded continuously.
[tex]\begin{gathered} A=Pe^{rt} \\ \text{where} \\ A\text{ is the Future Value} \\ P\text{ is the Principal amount} \\ r\text{ is the rate in decimals} \\ t\text{ is time in years} \end{gathered}[/tex]Rearrange the equation so that we can solve for time t.
[tex]\begin{gathered} A=Pe^{rt}^{} \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=e^{rt} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt\ln e^{}=\ln \mleft(\frac{A}{P}\mright) \\ rt^{}=\ln \mleft(\frac{A}{P}\mright) \\ \frac{rt}{r}=\frac{\ln (\frac{A}{P})}{r} \\ t=\frac{\ln(\frac{A}{P})}{r} \end{gathered}[/tex]Now substitute the following given and we have
[tex]\begin{gathered} t=\frac{\ln(\frac{A}{P})}{r} \\ t=\frac{\ln (\frac{15000}{6750})}{0.0525} \\ t=\frac{\ln (\frac{20}{9})}{0.0525} \\ t=15.2096704\text{ years} \end{gathered}[/tex]Rounding the answer to the nearest tenth, the investment will reach $15000, in approximately 15.2 years.
9m^2 - 49factor each expression. Be sure to check for the greatest common factor first.
Answers
We need to factor the following polynomial:
[tex]9m^2-49[/tex]We can see that:
[tex]9m^2=3^2m^2=(3m)^2[/tex]And
[tex]49=7^2[/tex]Then, we can use the following factor rule:
[tex]x^2-y^2=(x-y)(x+y)[/tex]We have that:
[tex]x=3m,y=7[/tex]Then, we can factor the polynomial as follows:
[tex]9m^2-49=(3m)^2-(7)^2=(3m-7)(3m+7)[/tex]In summary, we have:
[tex]9m^2-49=(3m-7)(3m+7)[/tex]which number is a rational number?A. √3B. √36C. √7D. π
Answers
We have to identify the rational number.
Any number that can be expressed as a fraction is a rational number.
In this case the options are:
A. The square root of 3. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.
B. The square root of 36, unlike the square root of 3, does have a rational solution: 6. So the square root of 36 is a rational number.
C. The square root of 7. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.
D. The number π has an infinite number of decimals, so it can not be represented as a fraction. Thn, it is not a rational number.
nswer: O√36 [ption B]
Find sin S, sin R, cos S, cos R.sin S =sin R =cos S =cos R =
Answers
From the basic knowledge of Trignometry,
We are meant to find sin S , sin R , cos S and cos R:
sin S = opposite / Hypoteuse = 18 / 26
sin R = opposite / Hypotenuse = 16 / 26
cos S = Adjacent / Hypotenuse = 16 / 26
cos R = Adjacent / Hypotenuse = 18 / 26
m^2+5mn+5n^2factor each polynomial completely. If a polynomial is prime, state this.
Answers
m²+5mn+5n²
To factor the above, we need two factors of 5n², such the sum gives 5n and the product gives 5n²
No such factors exists, hence the polynomial is prime.
a crew can clear 1/2 ton of dirt in 30 minutes. how many tons can they clear in 4 hours
Answers
Answer: 4 tons
Step-by-step explanation:
Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4
Answer: 4 tons
Step-by-step explanation:
30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.
a student measures which method of taking notes improves grades more, using a computer or a pencil and paper. what type of study is described?Sample StudyExperiment Observational Study Cluster Study
Answers
Since the student is meausuring something we conclude that this is an experiment.
Catalina is moving to a new house. Her old house is 3.5 miles away from her new house. How many feet are between Catalina’s old and new house?
Answers
18480 feet are between her old and new house
The sales tax in Arizona is 7.5%. The price tag on a T-shirt in Arizona says $11.50. What is the sales tax, in dollars, for this item?
Answers
Answer:
$0.8625
Explanation:
The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:
[tex]\text{ \$11.50 }\times\text{ 7.5\% = 11.50}\times\frac{7.5}{100}=\text{ \$0.8625}[/tex]So, the sales tax for this item is $0.8625
which of the relations has a domain of (-5, 0, 5)
Answers
Choice A
Is the answer
The tree diagram represents an experiment consisting of two trials
What is P(A)
Answers
The value of probability P(A) is 0.60
How to determine the probability?The clear tree diagram is added as an attachment
The given parameters from the tree diagram are:
Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7The probability is calculated using the following probability formula
P(A) = P(A and D) + P(A and C)
Substitute the known values in the above equation
P(A) = 0.6 * 0.7 + 0.6 * 0.3
Evaluate the products
P(A) = 0.42 + 0.18
Evaluate the sum
P(A) = 0.60
Hence, the value is 0.60
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PLS HELP ME WITH THIS QUESTION ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The value of (x) will be equal to → x = 16 - K.
What is the perimeter?
Perimeter is the measure of the length of the boundary of any two dimensional shape.
Given is a quadrilateral with its sides given.
The perimeter of this quadrilateral will be the sum of the length of its sides. Since, in the question, the final value of perimeter is not given, therefore we will assume it as K. The perimeter will be equal to -
(7x - 1) + (- 8x - 5x) + (6x + 13) + (4 - x) = K
7x - 1 - 8x - 5x + 6x + 13 + 4 - x = K
16 - x = K
x = 16 - K
Therefore, the value of (x) will be equal to → x = 16 - K.
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I'll give brainliest!
Answers
Answer:
=1/1024
Step-by-step explanation:
4^-5
=1/4^5
=1/1024
Rate as brainliest
Here is it step-by-step:
4^-5
=1/4^5
and 1/1=1024
2 PointsMULTIPLE CHOICEQuestion 42: PracticeWhich statements are true for the decimals 0.04 and 0.004?Choose two correct answers.in Base TenA0.04 is 10 times as much as 0.004.B.0.04 is 100 times as much as 0.004.Etice Solvingс0.004 is 10 the amount of 0.04.uizD0.004 is 100 the amount of 0.04
Answers
From the question;
we are given the decimal numbers
[tex]0.04\text{ and 0.004}[/tex]If we consider dividing 0.04 by 0.004 we will have
[tex]\frac{0.04}{0.004}=10[/tex]Therefore, 0.04 is 10 times as much as 0.004
Also, if we consider dividing 0.004 by 0.04 we will get
[tex]\frac{0.004}{0.04}=0.1=\frac{1}{10}[/tex]Therefore, 0.004 is 1/10 the amount of 0.04
Hence
Given the decimals 0.04 and 0.004 we have
1. 0.04 is 10 times as much as 0.004
2. 0.004 is 1/10 the amount of 0.04
I need this answered From my prep guid, pre calc
Answers
Given:
The equation of the ellipse is,
[tex]\frac{(x-2)^2}{36}+\frac{(y+3)^2}{12}=1[/tex]Explanation:
The general equation of ellipse with center (h,k) is,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]The center of te given ellipse is (2,-3).
Determine the value of a and b.
[tex]\begin{gathered} a=\sqrt[]{36} \\ =6 \end{gathered}[/tex][tex]\begin{gathered} b=\sqrt[]{12} \\ =2\sqrt[]{3} \end{gathered}[/tex]The value of a is more than b. so major axis is horiontal and minor axis is vertical.
The coordinates of endpoints of major axis are,
[tex](2+6,3)=(8,-3)[/tex]and
[tex](2-6,3)=(-4,-3)[/tex]The coordinates of endpoints of minor axis,
[tex](2,-3+2\sqrt[]{3})[/tex]and
[tex](2,-3-2\sqrt[]{3})[/tex]or we can expressed coordinates of endpoints of minor axis as,
[tex](2,-3\pm2\sqrt[]{3})[/tex]Look Ahead To find the new temperature, you found the sum of a positive anda negative integer. You can use a number line to help you think about addinga. During the day, the temperature at another weather station is 4°C. Overnight,it changes by-9°C Enrico models the situation on the number line below.Hasina says she can model it with one arrow. How can she model the situationLook Back whalHow do you know?positive and negative numbers.with just one arrow?434520 1-3 -2 -1
Answers
Let's begin by listing out the information given to us:
How do scatter plots and histograms differ from line graphs?
None of the above
All three are used synonymously
Scatter plots and histograms show trends, or how data changes over time while line
graphs show how data is distributed.
Scatter plots and histograms show how data is distributed while line graphs show
trends, or how data changes over time.
Answers
Answer: Scatter plots, to show relationships among numerical variables. Line graphs, to show change over time. Histograms, to show data distributions.
Step-by-step explanation: I looked it up
What percent of 90 is 200?
Answers
What is the equation of the
line that goes through
(-1, 3) and is perpendicular
to y = 4x - 7?
Answers
Answer:
Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.
For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.
For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4
There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?
Your answer would be something like: y = -1/4 x + b
b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.