The relative maxima and relative minima of the function
f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6
the relative maxima is -1.871the relative minima is 1.518How to fine the relative maxima and minimaThe relative minima and maxima is calculated
by differentiating the given function find the critical values or roots of the equationdifferentiate the second tiesubstitute the critical value that are real numbersthe critical value that gave a negative value is the maximathe critical value that gave a positive value is minimaThe procedure is done as follows
x^5 - 4x^3 + 3x^2 - 8x - 6
differentiating gives
5x^4 - 12x^2 + 6x - 8
solving the equation for the critical values are
x₁ = 0.176 + 0.73i
x₂ = 0.176 - 0.73i
x₃ = 1.518
x₄ = -1.871
The second derivative
5x^4 - 12x^2 + 6x - 8
differentiating gives
20x^3 - 24x + 6
substituting x = 1.58
20 * 1.58^3 - 24 * 1.58 + 6
= 46.966 (positive hence minima)
substituting x = -1.871
20 * -1.871^3 - 24 * -1.871 + 6
= -169.9 (negative hence maxima)
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A bag contains 150 marbles. Some are blue the rest is white. There are 21 blue marvles for every 4 white marbles. How many blue marbles are there.
There are 126 blue marbles.
Total marbles in the bag=150
There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150
21 blue marbles appear 6 times for every 4 blue marbles
So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles
∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.
a farmer wants to construct a fence around an area of 150 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what dimensions should the fenced area have in order to minimize the length of fencing used?
The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
Let x represent the length of the fence and y represent the width of the fence.
Since the area is 150, hence:
Area = length × width = x × y
150 = xy
y = 150/x
A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:
Amount of fencing needed (P) = x + x + y + y + y = 2x + 3y
Amount of fencing needed (P) = 2x + 3(150/x) = 2x + 450/x
To minimize the amount of fencing needed, dP/dx = 0, hence:
dP/dx = 2 - 450/x²
2 - 450/x² = 0
2 = 450/x²
2x² = 450
x² = 225
x = 15 feet
Let's find the value of y.
y = 1350/x = 1350/15 = 10 feet
Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 15 feet by 10 feet.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
answer this and u a big W if u dont ur a L
Answer:
Part A. (4,5)
Part B. (9,7)
Step-by-step explanation:
Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.
how many degrees in a right angle
Answer:
90 degrees is the amount of degrees in a right angle
Select the correct answer.
What is the domain of function f?
Answer:
D
Step-by-step explanation:
The domain of this function is all real numbers because you can see that there are no endpoints on the graph. The function is going off of the graph, which means it is continuing aka never-ending.
(-∞,∞) aka all real numbers
please help me.
5x + (-y) +8 -6x +9y (Evaluate X=4 and Y=-2)
Answer:
answer: -35
Step-by-step explanation:
if it's not sorry
Answer:
-12
Step-by-step explanation:
5x+(-y)+8-6x+9y
where x=4 and y=-25(4) +(-(2))+8 -6(4) + 9(-2)20+2+8-24-1830-42-12When parallel lines are cut by a transversal, then
Answer:
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
50 POINTS
You are looking at starting a summer business mowing lawns to get started. You already need to purchase some items investing in your business. You already have a lawnmower, but below are the items you still need to purchase.
what is the total amount you plan to invest in your lawn mowing business? [__]
1. You just determined how much you are willing to invest to get your summer job started. Write an inequality to represent when you start making a profit if you charge $15 to mow one lawn.
2. at the end of the summer, you have mowed a total of 16 lawns right in equation that represents your total earnings. How much did you earn? [Show your work]
with investment costs taken into account, did you:
a. lose money
b. make money
Regarding the situation described, it is found that:
The total amount invested is of $25.
1. You start making a profit when 15x - 25 > 0.
2. You earned $215 with this work.
With the investment, you made money (option b).
What is the total amount investment?The investment was as follows:
Pack of 50 lawn bags for $10.Eye protecting glasses for $15.Hence the total amount invested was of:
10 + 15 = $25.
What is the profit inequality?The profit is given by revenue subtracted by costs.
In the context of this problem, the revenue and the cost functions are given as follows:
Revenue: R(x) = 15x (as you charge $15 to mow one lawn).Cost: C(x) = 25. (investment).Hence the profit function is:
P(x) = R(x) - C(x)
P(x) = 15x - 25.
You start making a profit when:
P(x) > 0.
15x - 25 > 0.
The amount you earned mowing 16 lawns is of:
P(16) = 15(16) - 25 = $215.
(positive profit, hence you made money).
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The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the
function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit
of $3,365, what is the value of c?
-1,135
Step-by-step explanation:
The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit of $3,365, what is the value of c?
$3,365 = 225(75) - (165(75) + c)
$3,365 = 16,875 - 165(75) - c
$3,365 = 16,875 - 12,375 - c
$3,365 = 4,500 - c
=1,135 = - c
c = 1,135
Below are different equations, determine whether each equation is quadratic or not quadratic.
Write your answer on the space provided.
1x-5x+3=0
2.2s + 3t = -7
3,8k-3 = 12
4,9²-25=0
5.4m² + 4m + 1 = 0
Answer: calculate these equations
Step-by-step explanation: if you have times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.
You're putting 81 feet of molding
along the walls around a rectangular
room that's 12 feet wide; what is the
area of that room (if you subtracted
3 feet for the width of the door)?
Answer:
360 sq feet
Step-by-step explanation:
The width of the room is given in the question, 12 feet.
We don't know the length. Let's call the length x.
x = length
We were also given the perimeter, 81, that's the distance around the sides...
all the sides added up.
Use x for the long wall.
Use x-3 for the wall with the door in it.
x + 12 + x-3 + 12 = 81
combine like terms
2x + 21 = 81
subtract 21
2x = 60
divide by 2
x = 30
The room is 30 feet long by 12 feet wide.
Area =
length × width
= 30 × 12
= 360
The area of the room is 360sq feet.
∠A=5x−12 ∘ start color #11accd, angle, A, equals, 5, x, minus, 12, degrees, end color #11accd \qquad \green{\angle B=2x + 24^\circ}∠B=2x+24 ∘
The solution to the variable x is 12 and the measure of ∠B is 48°.
How to solve congruent angles?∠A = 5x−12°
∠B = 2x+24°
Angle A and Angle B are congruent angles.
Congruent angles are angles with the same or equal measures.
So,
∠A = ∠B
5x - 12 = 2x + 24
collect like terms5x - 2x = 24 + 12
3x = 36
divide both sides by 3
x = 36/3
x = 12
So therefore,
∠A = 5x−12°
= 5(12) - 12
= 60 - 12
= 48°
∠B = 2x+24°
= 2(12) + 24
= 24 + 24
= 48°
Therefore, since ∠A and ∠B are congruent, the measure of ∠A and ∠B is 48° respectively.
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
0.64 feet
Step-by-step explanation:
make h the subject of this expression
[tex]t = \sqrt{ \frac{h}{16} } [/tex]
[tex] {t}^{2} = \frac{h}{16} [/tex]
[tex]h = 16 {t}^{2} [/tex]
then substitute in the value of t=0.2 into the equation of h:
h = 16 × (0.2)² = 0.64 feet(answer)
SOLVE FOR X answer .
Answer:
31
Step-by-step explanation:
x+10+2x+20+2x-5=180
5x+25=180
5x=155
x=31
pls help asap giving 50 points Farmer A planted green beans and corn at a ratio of 5:3. Farmer B planted green beans and corn at a ratio of 3:2.
Which farmer planted a greater ratio of green beans to corn?
Farmer A planted a greater ratio of green beans to corn
How to find the farmer that planted a greater ratio of green beans to corn?Ratio is defined as the comparison of two quantities (a and b) of the same units which indicates how much of one quantity is present in the other quantity. They are written a / b, where b does not equal 0
Given that: Farmer A planted green beans and corn at a ratio of 5:3 and farmer B planted green beans and corn at a ratio of 3:2
To find the greater ratio treat the ratio as a fraction:
Farmer A => 5:3 and Farmer B => 3:2
5/3 and 3/2 (LCM of 2 and 3 is 6)
10/6 and 9/6
10:6 and 9:6
Since 10:6 is greater than 9:6. Therefore, Farmer A planted a greater ratio of green beans to corn
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Angie bikes for 20 minutes burning 150 calories. How many calories will he burn if he bikes for 25 minutes
Answer:
I think it's 187.5
Step-by-step explanation:
I divided 150 by 20 and got 7.5.
i multiplied 7.5 by 25 and got 187.5
Hop this is correct and helps you.
A student solves the problem 354 divided by 24. The student finds an answer of 13 R40. Explain how you can tell that the answer is incorrect just by looking at the remainder.
Answer:
Step-by-step explanation:
When dividing, you always have to make sure that your remainder
(40) is ALWAYS less than your divisor (24)
24<40, so the students' answer is incorrect.
A hardware store is having a 35%-off sale. If an item has a list price of $16.20, what is the item's sale price?
$12.80
$9.67
$10.53
$12.15
$11.60
Answer:
10.53
Step-by-step explanation:
hope it helps :)
the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that thesum of the four numbers on each face is the same. what is this common sum?
The common sum is 18 as "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same".
What is sum?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. The outcome or conclusion we arrive at when we add two or more numbers is known as the SUM. Addends are the numbers that are added.
Here,
The sum of the numbers on one face of the cube is equal to the sum of the numbers on the opposite face of the cube; these 8 numbers represent all of the vertices of the cube.
=(1+2+3+4+5+6+7+8)/2
=18
Since "the numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same," the common sum is 18.
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What id an equation of a line in point-slope form that passes theough (1,-7) and has a slope of -2/3?
(y + 7) = -2/3(x - 1) is the point-slope form of the equation of a line passing through (1, -7) and having a slope of -2/3.
How to calculate a line's equation in point-slope formThe query revealed information include
a slope of -2/3
point (1, -7)
Describe a linear function.Those functions with exponents of 1 are known as linear functions.
The form represents the equation of a line in point-slope form.
(y - y₁) = m (x - x₁)
Variables in the y direction are described by (y and y₁).
variables in the x direction are described by (x and x₁).
m = slope
substituting into the slope and point (1, -7) equation gives
()y + 7) = -2/3 (x - 1)
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Samuel has a collection of toy cars. His favorites are the 27 red ones, which make up 60%, percent of his collection.
How many toy cars does Samuel have?
Answer:
45
Step-by-step explanation:
The 27 red cars make up 60% of the total collection, here is the equation
to be solved:
27 = 60% of C C is the total cars in the collection
27 = .60 C
27 / .60 = C
45 = C
Hope this helps! :)
What is the slope and equation of a line that is perpendicular to the y-axis and passes through the point (3,12)
A. The slope is undefined and the equation of the line is y=12.
B. The slope is zero and the equation of the line is x=3.
C. The dlope is zero and the equation of the line is y=12.
D. The slope is undefined and the equation of the line is x=3.
Slope equals the change in the vertical (Y value) divided by the change in the horizontal (X value), the slope of a horizontal line is zero and equation of line is Y =12. So option C is correct.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept.
Here,
Since the Y-axis is vertical, a line perpendicular to it would be horizontal.. The slope of a horizontal line is zero, because slope is the change in the vertical (Y value) divided by the change in the horizontal (X value), and the vertical coordinate does not change from the -3 of the point given.
If we start with the slope-intercept form of an equation of a line
Y = mX + b,
we can write Y = 0X + (12)
Y =12
Slope is the vertical change (Y value) divided by the horizontal change (X value); the slope of a horizontal line is zero, and the equation of the line is Y =12.
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please I need help asap
consider the following data set which is the time (in minutes) for students to finish a math test. 34 45 27 33 38 41 45 29 30 39 34 40 28 33 36 50 (a) what is the sample mean? (b) what is the sample standard deviation? (c) construct a 99% confidence interval for the population mean.
a) Sample mean of set is 36.375.
b) Standard deviation of sample is 6.66208.
Define mean and standard deviation.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Given,
a) Mean
Total number of values = 16
= Sum/Total number of values
= 34 +45+ 27 +33 +38+ 41+ 45 +29 +30+ 39 +34 +40 +28 +33 +36+ 50/16
= 582/16
= 36.375
Sample mean of set is 36.375.
b) Sample standard deviation
S² = ∈ (x i - x)²/N-1
S² = 666.75/16-1
S² = 44.383333
S = √44.38333
S = 6.66208
Standard deviation of sample is 6.66208.
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Alvin's bill for dinner at a restaurant was $96. He left a 20% tip. What was the amount of
the tip?
Answer:$ 17.28
Step-by-step explanation:
4 friends want to take a vacation together. Each person has 8 weeks to save $720 for the vacation. Analyze the 4 individual plans below and decide which of the 4 people will reach his or her goal.
a) Friend A: Works 6 hours per week at $13.90 per hour
b) Friend B: Works 7.5 hours per week at $11.70 per hour
c) Friend C: Works 9 hours per week at $10.50 per hour
d) Friend D: Works 5.5 hours per week at $15.60 per hour
The person from the 4 people that will reach his or her goal is Friend C.
How to calculate the amount?Friend A: Works 6 hours per week at $13.90 per hour. The amount in 8 weeks will be:
= 6 × $13.90 × 8
= $667.2
b) Friend B: Works 7.5 hours per week at $11.70 per hour. The amount in 8 weeks will be:
= 7.5 × 11.70 × 8
= $702
c) Friend C: Works 9 hours per week at $10.50 per hour. The amount in 8 weeks will be:
= 9 × $10.50 × 8
= $756
d) Friend D: Works 5.5 hours per week at $15.60 per hour. The amount in 8 weeks will be:
= 5.5 × $15.60 × 8
= $686.40
In this case, C had $756 which is above the amount needed.
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A police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets. Should he be on a perpendicular bisector, a median, an angle bisector, or an altitude?
ALSO… Draw a picture to show solution to this problem and label all parts of your picture and the name of the segment the police officer should use.
A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.
What is a perpendicular bisector?A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.
Perpendicular bisector: A line that bisects a line segment in two equal parts.
Median: The middle number; found by ordering all data points and picking out the one in the middle.
Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.
Therefore, a police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
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In one study of burmese pythons it took a snake an a stage of 25/4 days to gain 1/8 of weight. at that rate how long does it take a snake to gain 1 pound?
At the rate of variation of 50 days/pound the snake gain 1 pound.
The mathematical expression for the percentage difference change over a predetermined period is called the rate of variation, which also denotes the movement of a variable. It allows us to understand how 2 factors that are changing interact with one another.
A snake takes 25 ÷ 4 days to gain 1 ÷ 8 pounds of weight,
a) Gain 1 pound need take: (25 ÷ 4) × 8 = 50 days
b) In one year = 365 days
= (25 ÷ 4) × (1 ÷ 8)
= (25 ÷ 4) × 8
= 50 days/pound.
So, the snake gained(1 ÷ 50) pounds one day.
In one year: (1 ÷ 50) × 365 = 7.3 pound
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A,B and C form a triangle where ∠BAC=90∘.AB=7 mm and BC=13.8 mm. Find the length of AC, giving your answer rounded to 1 decimal place.
The length of AC which is the hypothenuse is equal 15.5mm
Pythagoras TheoremThe Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.
In this question, triangle ABC forms a right-angle triangle at angle B and this makes it possible to use Pythagoras theorem.
AB = leg = 7mmBC = leg = 13.8mmAC = hypothenuse = ?Using the formula;
AC² = AB² + BC²
AC² = 7² + 13.8²
AC = 15.5mm
The length of the hypothenuse is 15..5mm
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