Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.)
Answers
Before we can determine the absolute extrema of the function, let's graph the given function first. f(x) = x² - 6x.
For the interval [-1, 6], we can see that the maximum value would be at x = -1.
Let's replace x with -1 in the function above.
[tex]\begin{gathered} f(x)=x^2-6x \\ f(-1)=(-1)^2-6(-1) \\ f(-1)=1+6 \\ f(-1)=7 \end{gathered}[/tex]Therefore, the maximum between the interval [-1, 6] is at (-1, 7).
On the other hand, looking at the interval (3, 7] in the graph, the maximum is found at x = 7. To determine the maximum point, replace "x" with 7 in the function above.
[tex]\begin{gathered} f(7)=7^2-6(7) \\ f(7)=49-42 \\ f(7)=7 \end{gathered}[/tex]Therefore, the maximum at the interval (3, 7] is at point (7, 7).
Related Questions
I really need help with number 6find the value of x that makes abcd a parallelogram.
Answers
Given:
The adjacent angles of the parallelogram are,
[tex]28,\text{ and }3x[/tex]To find:
The value of x.
Explanation:
We know that,
The sum of the two adjacent angles between the parallel lines is supplementary.
So, we write,
[tex]\begin{gathered} 28+3x=180 \\ 3x=180-28 \\ 3x=152 \\ x=50.66 \\ x\approx50.7 \end{gathered}[/tex]Thus, the value of x is 50.7.
Final answer:
The value of x is 50.7.
A real estate agent believes that most of the home prices are low with few homes have very high prices in a certain area in his county. If his description on home prices in this area is accurate, which of the following shape best describe the distribution of home prices in this area?SymmetricalNormalNegatively skewedPositively skewe
Answers
GIVEN:
We are told that a real estate agent believes that most of the home prices are low with very few homes having very high prices in a certain area.
Required;
If his description is accurate, which shape best describes the distribution of home prices in this area?
Explanation;
For data distribution, the graph can take on different shapes dpending on how the data is distributed. In this particular instance, most of the data is lying on the left side of the graph. In other words, the curve is more elevated on the left side while its very low towards the right side.
The following picture is an illustration of this scenario;
This is "Positively skewed data distribution."
ANSWER:
Positively skewed.
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 6 and AD = 2, what is the length of AC? (Note: the figure is not drawn to scale.) B 6 2 D Answer: Submit Answer
Answers
The first step is to make a sketch of the triangle
The altitude (h= BD) of the triangle divides it into two similar right triangles and the hypothenuse, AC, into two line segments n= AD and m= DC.
The relationship between the altitude and the parts of the hypothenuse follows the ratios:
[tex]\frac{n}{h}=\frac{h}{m}[/tex]So, the first step is to determine the altitude of the triangle. To do so, you have to work with ΔABD, "h" is one of the sides of the triangle. Using the Pythagorean theorem you can determine the measure of the missing side:
[tex]a^2+b^2=c^2[/tex]Write the expression for the missing side:
[tex]\begin{gathered} b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Replace c=6 and a=2
[tex]\begin{gathered} h=\sqrt[]{6^2-2^2} \\ h=\sqrt[]{36-4} \\ h=\sqrt[]{32} \\ h=4\sqrt[]{2} \end{gathered}[/tex]Now that we have determined the value of the altitude, we can calculate the value of m
[tex]\frac{n}{h}=\frac{h}{m}[/tex]Write the expression for m:
-Multiply both sides by m to take it from the denominators place:
[tex]\begin{gathered} m\cdot\frac{n}{h}=m\cdot\frac{h}{m} \\ m\cdot\frac{n}{h}=h \end{gathered}[/tex]-Multiply both sides of the equal sign by the reciprocal of n/h
[tex]\begin{gathered} m(\frac{n}{h}\cdot\frac{h}{n})=h\cdot\frac{h}{n} \\ m=\frac{h\cdot h}{n} \\ m=\frac{h^2}{n} \end{gathered}[/tex]Replace the expression with h=4√2 and n=2 and calculate the value of m
[tex]\begin{gathered} m=\frac{h^2}{n} \\ m=\frac{(4\sqrt[]{2})^2}{2} \\ m=\frac{32}{2} \\ m=16 \end{gathered}[/tex]So DC=m= 16cm and AD=n= 2cm, now you can determine the measure of the hypothenuse:
[tex]\begin{gathered} AC=AD+DC \\ AC=2+16 \\ AC=18 \end{gathered}[/tex]The hypothenuse is AC=18cm
A box has s snack bags in it. Each snack bag contains c carrot sticks.Which equation can be used to find b , the number of carrot sticks in one box?Ab = s/cB b = scCb = s+c Db = c/s
Answers
Solution
For this case we have s snacks and each snack with c carrot sticks
So then if we want to find the total of carrot sticks in one box we can do the following operation:
B. b = sc
Which of the following are possible sidelengths for a triangle?A. 16, 8, 10B. 4, 12,6C. 6, 9, 17
Answers
Step-by-step explanation:
Triangle rule
a + b > c
This implies that the summation of first and second leg must be greaterthan the third leg
For Option A
a = 16, b = 8, and c = 10
16 + 8 > 10
A quadrilateral is formed by the points A(1,-1), B(0,3), C(5,5), and D(6, 1). Plot the points and use the distance formula to find the lengths of all 4 sides. What type of quadrilateral is this?
Answers
If we have the given points on a cartesian point, the result would be:
It is not difficult to see that these points will form a rhombus. In this case, we do expect that the opposite sides have the same size. To verify it, we will use the following formula to calculate the distance among the given points:
[tex]d_{P1-P2}=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Substituting each pair, we have:
AB
[tex]\begin{gathered} d_{AB}=\sqrt[]{(1-0)^2+(-1-3)^2}=\sqrt[]{1^2+(-4)^2}=\sqrt[]{1+16}_{} \\ d_{AB}=\sqrt[]{17} \end{gathered}[/tex]BC
[tex]undefined[/tex]a student's can sit at 1 cafeteria table about how many tables are needed for 231 students explain
Answers
We can solve this question by means of the rule of three:
[tex]\begin{gathered} 1\text{ student ------- 1 table} \\ 231\text{ students ------ x} \end{gathered}[/tex]then, x is given by
[tex]undefined[/tex]You invested $9000 between two accounts paying 4% and 7% annual interest. If the total interest earned for the year was $510, how much was invested at each rate?
Answers
Let x represent the amount invested at 7%.
Then 9000-x is the amount invested at 4%
total interest earned is:
0.07x + 0.04(9000-x) = 510
0.07x + 360 - 0.04x = 510
0.03x = 150
x = 5000 the amount invested at 7%
9000 - 5000 = 4000 the amount invested at 4%
A file that is 284 megabytes is being downloaded. If the download Is 17.5% complete, how many megabytes have been downloaded? Round your answer to thenearest tenth.megabytesх5?
Answers
We are given the size of a file to download is 284 megabytes. If 17.5% has complete,
We want to find the megabytes that has been downloaded
Solution
We have
[tex]284mb[/tex]The 17.5% of 284mb will be
[tex]\begin{gathered} \frac{17.5}{100}\times284 \\ =\frac{497}{10} \\ =49.7mb \end{gathered}[/tex]Therefore, the megabytes that have been downloaded is 49.7mb (to the nearest tenth)
What is the constant of proportionality of the tablex 5 8 11y 35 56 77
Answers
y =kx
Where:
k = Constant of proportionality
If x = 5, y = 35
35 = k5
Solving for k:
k = 35/5 = 7
Verify the answer:
If x = 8 , y = 56
y = kx = 7*8 = 56
The constant of proportionality is 7
7.4.PS-13 Question Help David drew this diagram of a picture frame he is going to make. Each square represents 1 square inch. What is the area of the picture frame? 12- 10- 0 2 4 6 8 10 12 14 16 18 The area is Enter your answer in the answer box and then click Check Answer. Clear All Check Ans All parts showing of 10 Next → Back Question 7 Review progress
Answers
52
1) In this question, since we need to calculate the shaded region or the frame. We'll calculate the whole picture, and then subtract the white rectangle from it.
2) Examining the picture, we can see that the whole larger shape has a width of
14 -4 = 10 units Horizontal (width)
7-1 = 6 units Vertical (height)
3) Let`s use now the formula for the Rectangle Area
[tex]\begin{gathered} A_{\text{Whole Rectangle}}=w\cdot l \\ A_{\text{Whole Rectangle}}=6\times10=60units^2 \\ A_{\text{White Rectangle}}=2\times4=8u^2 \\ A_{\text{FRAME}}=60-8=52units^2 \end{gathered}[/tex]Hence the area of the frame is 52 square units.
F(x) = x^3 + x^2 + 9x + 9 Find all zeros including irrational and/ or complexFactor f completely into linear factors Part of it completed: The zeros are -1, 3i, and -3i
Answers
Given:
[tex]F\left(x\right)=x^3+x^2+9x+9[/tex]To find:
The zeros
Explanation:
Factorizing by grouping method,
[tex]\begin{gathered} F\left(x\right)=x^3+x^2+9x+9 \\ =x^2(x+1)+9(x+1) \\ =(x+1)(x^2+9) \end{gathered}[/tex]The zeros are found by equating the factors with zero.
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex]And we have,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\pm\sqrt{-9} \\ x=\pm3i \end{gathered}[/tex]So, the zeros are,
[tex]-1,3i,-3i[/tex]Final answer:
The zeros are,
[tex]-1,3i,-3i[/tex]The graph in the figure shows the Smith family's driving plan for their vacation. If they want to stop and eat lunch after they've driven for 4 hours, how far will they have driven by lunchtime?Question 17 options:A) 120 milesB) 90 milesC) 60 milesD) 180 miles
Answers
ANSWER:
A) 120 miles
STEP-BY-STEP EXPLANATION:
We can determine at a distance through the graph, just like this:
This means that at 4 hours they have driven 120 miles.
Therefore, the correct answer is: A) 120 miles
Find the number of degrees in the acute angle formed by the intersection of walnut street and elm street
Answers
Given two parallel lines and a transversal
So, the angles (2x + 33) and ( 5x - 15 ) are congruent because they are corresponding angles
So, 5x - 15 = 2x + 33
Solve to find x
[tex]5x-15=2x+33[/tex]Combine like terms:
[tex]\begin{gathered} 5x-2x=33+15 \\ 3x=48 \\ x=\frac{48}{3}=16 \end{gathered}[/tex]So, the required angle = 2x + 33 = 2 * 16 + 33 = 32 + 33 = 65
So, the angle is 65
Hello I just need the answer for “What is the inverse for the equation y=x^2+16”
Answers
Given:
The given equation is
[tex]y=x^2+16[/tex]Required:
We need to find the inverse for the equation.
Explanation:
[tex]\text{ Let y=f\lparen x\rparen and }x=f^{-1}(y)\text{ and substitute }x=f^{-1}(y)\text{ in the given equation.}[/tex][tex]y=(f^{-1}(y))^2+16[/tex]Substract 16 from both sides of the equation.
[tex]y-16=(f^{-1}(y))^2+16-16[/tex][tex]y-16=(f^{-1}(y))^2[/tex]Take square root on both sides of the equation.
[tex]\pm\sqrt{(y-16)}=f^{-1}(y)[/tex][tex]f^{-1}(y)=\pm\sqrt{(y-16)}[/tex]Replace y=x in the equation.
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]Final answer:
[tex]f^{-1}(x)=\pm\sqrt{x-16}[/tex]3С21In the similaritytransformation of AABCto ADEF, AABC was dilated bya scale factor of [? ], reflectedacross the J, and movedthrough the translation [ ].BА-7-6-5-4m, 002-1 0.12.39ShoesDA. 2B. 1/2C. 3D. 1/3
Answers
Scale factor is the ratio of corresponding sides in two(2) similar geometric figures.
Taking one similar side of the two(2) figures, we have:
[tex]\begin{gathered} \frac{DF}{CA}=\frac{2}{1}=2 \\ \text{Thus, scale factor is 2} \end{gathered}[/tex]Hence, the correct option is option A
It is reflected across the x-axis and moved through the translation (3, 1)
Let n =2. Evaluate the following (nn)n
Answers
We have the following:
[tex](nn)n[/tex]n=2
[tex]2\cdot2\cdot2=8[/tex]1. Use the image below to find the midpoint of segments BD and AC B 5 С D -5 4 3 2 1 1 2 3 4 5 2. Classify triangle ABC as either equilateral, right, isosceles, or none. 5 C B 2 A -3 -2 -1 2 3 4 5 6 -2
Answers
1. We have that B (-2,4) and D (2,1), then the midpoint has coordinates
[tex]\begin{gathered} x=\frac{-2+2}{2}=0 \\ y=\frac{4+1}{2}=\frac{5}{2} \end{gathered}[/tex]and the midpoint is (0,5/2).
On the other hand A (-4,1) and C (4,4), so the midpoint has coordinates
[tex]\begin{gathered} x=\frac{-4+4}{2}=0 \\ y=\frac{1+4}{2}=\frac{5}{2} \end{gathered}[/tex]and the midpoint is (0, 5/2).
In conclusion, the midpoint of segments BD and AC is (0,5/2).
2. To classify the triangle we need to know the length of its sides
[tex]\begin{gathered} \bar{AB}=\sqrt[]{(3-(-2))^2+\mleft(0+2\mright)^2}=\sqrt[]{25+4}=\sqrt[]{29} \\ \bar{BC}=\sqrt[]{(2-(-2))^2+(4-2)^2}=\sqrt[]{16+4}=\sqrt[]{20} \\ \bar{AC}=\sqrt[]{(3-2)^2+(4-0)^2}=\sqrt[]{1+16}=\sqrt[]{17} \end{gathered}[/tex]Since neither of its sides has equal length, then it is not equilateral os isosceles. Besides,
[tex]17^2+20^2\ne29^2[/tex]Then it is not a right triangle.
In conclusion the answer is none of the options
How do I relation in amplitude compared to parent function of sine?How do I describe the relation in period compared to parent function of sine?
Answers
At his new job, Manuel expects to make about $37,850 per year. He is paid bi-weekly. 15% of his gross pay will be withheld for federal income tax, 4% for state income tax and 7.65% for Social Security and Medicare taxes. Calculate his net pay, and how much he will pay in taxes each paycheck. a. Convert the Annual Pay to Biweekly Pay b. How much money will he pay in taxes each paycheck? c. What is the Net Pay (take-home pay)?
Answers
Answer:
(a)$1455.77
(b)$387.97
(c)$1067.80
Explanation:
(a)Manuel's proposed annual income = $37,850
There are 52 weeks in a year, this means that if he is paid bi-weekly (every two weeks), he will receive his salary 26 times a year.
His Biweekly pay will be:
[tex]\begin{gathered} =\frac{37,850}{26} \\ =\$1455.77 \end{gathered}[/tex](b)
Federal Income Tax = 15% of his gross pay
[tex]\begin{gathered} =\frac{15}{100}\times1455.77 \\ Federal\; Income\; Tax=\$218.37 \end{gathered}[/tex]State Income Tax = 4% of his gross pay
[tex]\begin{gathered} =\frac{4}{100}\times1455.77 \\ State\; Income\; Tax=\$58.23 \end{gathered}[/tex]Social Security and Medicare taxes = 7.65% of his gross pay
[tex]\begin{gathered} =\frac{7.65}{100}\times1455.77 \\ =\$111.37 \end{gathered}[/tex]The total taxes paid will be:
[tex]\begin{gathered} Taxes=218.37+58.23+111.37 \\ =\$387.97 \end{gathered}[/tex](c)
Therefore, his net pay (take-home pay) will be:
[tex]\begin{gathered} \text{Net Pay==}1455.77-387.97 \\ =\$1067.80 \end{gathered}[/tex]
I need help in math can you please help me please
Answers
Trigonometric Equations
Solve:
[tex]9\tan ^3x=3\tan x[/tex]In the interval [0,2pi)
We have to find all the values of x that make equality stand. First, divide by 3:
[tex]3\tan ^3x=\tan x[/tex]Subtract tan x
[tex]3\tan ^3x-\tan x=0[/tex]Factor tan x out:
[tex]\tan x(3\tan ^2x-1)=0[/tex]One solution comes immediately:
tan x = 0
There are two angles whose tangent is 0:
[tex]x=0\text{ , x=}\pi[/tex]The other solutions come when equating:
[tex]3\tan ^2x-1=0[/tex]Adding 1, and dividing by 3:
[tex]\tan ^2x=\frac{1}{3}[/tex]Taking the square root:
[tex]\tan x=\sqrt[\square]{\frac{1}{3}}=\pm\frac{\sqrt[]{3}}{3}[/tex]The positive answer gives us two solutions:
[tex]\tan x=\frac{\sqrt[]{3}}{3}[/tex]x=pi/6 and x=7pi/6
The negative answer also gives us two solutions:
[tex]\tan x=-\frac{\sqrt[]{3}}{3}[/tex]x=5pi/6, 11pi/6
Summarizing the solutions are:
{
Find the circumference with a diameter of 10 feet long. I missed the notes for this section, so I don't know what I'm doing.
Answers
We need to find the circumference using the diameter.
The equation for the circumference is given by:
[tex]C=\pi d[/tex]Where d represents the diameter.
Replace d=10 ft
[tex]\begin{gathered} C=\pi10ft \\ \text{Then, the circumference is:} \\ C=10\pi\text{ }ft \end{gathered}[/tex]• An ice cube is slowly melting, losing 3cm^3 of water each hour. If it is always a perfect cube, (V=s^3), what is the rate of change of its side length when it has 8 cm^3 of ice left?
Answers
Given:
The volume is decreasing at the rate of 3 cm^3 per hour.
The volume of the left ice is 8 cm^3.
Aim:
We need to find the rate of change of the side of the cube.
Explanation:
Let the length of the cube is denoted as s.
Consider the volume of the cube.
[tex]V=s^3[/tex]Since the volume is decreasing at the rate of 3 cm^3 per hour. we can write,
[tex]\frac{dV}{dt}=-3cm^3\/h[/tex]where t represents time and the negative sign represents decreasing.
Differentiate the volume with respect to s.
[tex]\frac{dV}{ds}=\frac{d}{ds}(s^3)=3s^2[/tex]To find the rate of change of the side length, we use the chain rule.
[tex]\frac{dV}{dt}=\frac{dV}{ds}\frac{ds}{dt}[/tex][tex]\text{ Substitute }\frac{dV}{dt}=-3\text{ and }\frac{dV}{ds}=3s^2\text{ in the equation.}[/tex][tex]-3=\frac{ds}{dt}(3s^2)[/tex][tex]-\frac{3}{3s^2}=\frac{ds}{dt}[/tex][tex]-\frac{1}{s^2}=\frac{ds}{dt}[/tex]Since the left ice is 8 cm ^3.
[tex]V=(s)^3=8[/tex][tex]s^3=2^3[/tex][tex]s=2cm[/tex][tex]Substitute\text{ s =2 in the equation}-\frac{1}{s^2}=\frac{ds}{dt}.[/tex][tex]-\frac{1}{2^2}=\frac{ds}{dt}.[/tex][tex]\frac{ds}{dt}=-\frac{1}{4}[/tex][tex]\frac{ds}{dt}=-0.25cm\text{ per hour}[/tex]Verification:
Let s =2 cm, then the volume is 8cm^3.
Let s =1.75cm, the volume is
What is the solution to the equation?3+√3x- 5 = x A. -2 and -7B.2 and 7C. -2D. 7
Answers
Given the equation:
[tex]3+\sqrt[\placeholder{⬚}]{3x-5}=x[/tex]Isolating the square root:
[tex][/tex]Which shows the graph of x - 4y=-4?5O1 2 3 4 5 x433-2+4-5-4-3-2-12-لنا -343-51543212-A
Answers
Explanation
Using a graphing calculator, the graph of x-4y =-4 can be seen below.
Jessica furniture store is trying to figure out if she bought a couch at wholesale price for $113 and she mark up by 45%. what price should she sell the couch
Answers
original price = $113
MArkup = 45% = 45/100 = 0.45 ( decimal form)
Sell price = 113 (1 + 0.45) = 113 * 1.45 = $163.85
At Orangefield Junior High 40% ofthe seventh graders participate in extra-curricular activities a such as athletics, band, and drama. If there are 80 seventh graders participating in extra-curricular activities how many seventh graders are in the class.
Answers
Answer:
200
Explanation:
To know the total number of graders, we will use the rule of three. Where we know that 40% is equivalent to 80 graders and we want to know how many graders are equivalent to 100%. Then:
40% -------- 80 seventh graders
100% -------- x
Where x is the number of seventh graders in the class.
So, solving for x, we get:
[tex]x=\frac{100\text{ \% }\cdot\text{ 80}}{40\text{ \%}}=200\text{ seventh graders}[/tex]Then, there are 200 seventh graders in the class.
-1/4÷ (x/y) = -1/2what is the missing fraction
Answers
-1/4 / (x/y) = -1/2
Cross fractions
-1/4 / (-1/2) = x/y
-1/4 (-2/1) = x/y
2/4 = x/y
1/2 = x/y
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Answers
As per the unitary method, they need to save $106.25 each week.
Unitary method:
Basically, the unitary method is a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.
Given,
The Hudson family is saving for a family vacation to Disney World. They determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Here we need to find the amount they need to save for each week if they leave in 16 weeks.
While we looking into the given question,
Total amount of Saving = $3,200.
Amount in hand = $1,500
So, the amount need is calculated as,
=> 3200 - 1500
=> 1700
Here we have the 16 week time,
So, the saving for each week is calculated as,
=> 1700/16
=> 106.25
Therefore, the family have to save $106.25 for each week.
To know more about Unitary method here.
https://brainly.com/question/28276953
#SPJ1
Convert from degrees-minutes-seconds to decimal degrees.Round your answer to the nearest thousandth.
Answers
Given:
[tex]25\degree46^{\prime}11^{\prime}^{\prime}[/tex]Required:
To convert the given degrees-minutes-seconds to decimal degrees.
Explanation:
Consider
[tex]25\degree46^{\prime}11^{\prime}^{\prime}[/tex]Now
[tex]\begin{gathered} 11\div3600=0.00305 \\ \\ 46\div60=0.76666 \\ \\ 25\div1=25 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} =25+0.76666+0.00305 \\ =25.76971\degree \end{gathered}[/tex]Final Answer:
[tex][/tex]