The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
What is inflection points ?
An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.
First find the extrema (zeros of the derivative).
f (x) = 12x^5 - 5x^4
f '(x) = 60x^4 -20x^3
= 20x^3(3x - 1)
x = 0 x =1/3
So the extrema occur at x = 0 and x =1/3.
Now find the inflection points (zeros of the 2ndderivative).
f '(x) = 60x^4 -20x3^
f ''(x) = 240x^3 -60x^2
= 60x^2(4x - 1)
x = 0 x =1/4
The inflection points occur at x = 0 and x =1/4.
Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
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The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
What is inflection points ?
An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.
First find the extrema (zeros of the derivative).
f (x) = 12x^5 - 5x^4
f '(x) = 60x^4 -20x^3
= 20x^3(3x - 1)
x = 0 x =1/3
So the extrema occur at x = 0 and x =1/3.
Now find the inflection points (zeros of the 2ndderivative).
f '(x) = 60x^4 -20x3^
f ''(x) = 240x^3 -60x^2
= 60x^2(4x - 1)
x = 0 x =1/4
The inflection points occur at x = 0 and x =1/4.
Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
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This graph shows all the key characteristics of a particular polynomial function. Drag tiles to complete the function rule that could be represented by the graph
The function that can be represented by this graph is defined as follows:
f(x) = 2x³ + x - 3.
How to define the function?
The function is defined looking at the features of the graph.
The first feature which we look at is the y-intercept, as the graph of the function crosses the y-axis at y = -3, hence the function can be defined as follows:
f(x) = ax^n + x - 3.
The function has an inflection point, as it has a change in it's concavity, thus the function has a second derivative of the first degree, meaning that the function is of the third degree, that is:
n = 3.
The x-intercept is when the function crosses the x-axis, meaning that when x = 1, y = 0, then the leading coefficient a is obtained as follows:
0 = a + 1 - 3
a = 2.
Which means that the function rule can be given by:
f(x) = 2x³ + x - 3.
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at 2 p.m., two cars leave eagle river, wi, one headed east and one headed west. if the car traveling east averages 55 mph and the car traveling west averages 40 mph, when will the cars be 237.5 miles apart?
After 2.5 hours cars be 237.5 miles apart.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common usage can refer to a physical length or an estimation based on other factors.
First to write equation for each car
[tex]d_1=r_1t_1 (east bound)\\d_2 = r_2t_2 (west bound)[/tex]
They both start at the same time, and I will stop them both when they are 165 mi apart.
So, [tex]t_1=t_2[/tex] call just t.
⇒
[tex]d_1 = r_1t\\d_2=r_2t[/tex]
[tex]t = \frac{d_1}{r_1} \\t= \frac{d_2}{r_2}[/tex]
⇒
[tex]\frac{d_1}{r_1} = \frac{d_2}{r_2} \\d_1r_2 = d_2r_1[/tex] ..(1)
We also know that
[tex]d_1 + d_2 = 237.5[/tex]
[tex]d_2 = 237.5 - d_1[/tex]
[tex]r_1 = 55, r_2 = 40[/tex]
So, equation (1) becomes,
[tex]40d_1 = 55d_2[/tex]
Plug the value of [tex]d_2[/tex].
[tex]40d_1 = 55(237.5 - d_1)\\40d_1 = 13,062.5 - 55d_1\\40d_1 + 55d_1 = 13062.5\\95d_1 = 13062.5\\d_1 = 137.5[/tex]
[tex]d_1 = 137.5 mi[/tex]
Now,
[tex]t = \frac{d_1}{r_1} = \frac{137.5}{55} = 2.5[/tex]
Hence, after 2.5 hours cars be 237.5 miles apart.
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Ben has a barrel in his garden to collect rainwater. The barrel can hold less than 42 gallons of water. Which inequality represents this situation? Ow> 42 Ow< 42 w² 42 Ow≤ 42
Answer: The barrel can only hold less than 42 gallons of water, which means w<42.
the correlation between cost and distance is 0.791. describe the relationship between cost of damage and distance from the nearest fire station.
According to the question,
Given data,
The correlation between cost and distance is 0.791.
The farther the house is from a first station, the higher cost of damage tends to be.
the correlation between cost and distance
The largest single cost of liver transplantation is the cost of organ acquisition, with the variable portion of that amount being associated travel costs. We assessed the proportion of donors using ground, air, and jet transport and compared the transport costs of these three types of transport and their impact on organ procurement costs for transplant centers.
How is correlation measured?
The sample correlation coefficient r quantifies the strength of the relationship. Correlations are also tested for statistical significance.
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find the slope of the line thst passes through (10,2) and (1,3)
Answer: -7/1
Step-by-step explanation: When graphing both points and drawing a line through it, count how many times it goes up or down and then count how many times it goes left or right.
if anyone can help me solve this i will give you 20 points!!
Answer:137
Step-by-step explanation:
The sum of two numbers is 26:Two-fifths of the first number plus
three-eighths of the second number is 10. Find the numbers.
The two numbers are x = 3.43 and y = 22.57.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Let the first number be x and the second number be y. Then we can write the given information as a system of equations:
x + y = 26
(2/5)x + (3/8)y = 10
To solve this system, we can eliminate one of the variables by multiplying the first equation by 8 and the second equation by 5, then subtracting the resulting equations:
8x + 8y = 208
10x + 15y = 50
Subtracting these equations gives us:
-2x - 7y = -158
Dividing both sides by -7, we get:
x + y = 22.57
Substituting this back into the first equation, we get:
x + 22.57 = 26
Solving for x, we get:
x = 26 - 22.57
= 3.43
Substituting this back into the original equation x + y = 26, we get:
3.43 + y = 26
Solving for y, we get:
y = 26 - 3.43
= 22.57
Hence, the two numbers are x = 3.43 and y = 22.57.
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Which one multiple choice
The transformation describing the function is a translation 5 units to the right.
What is transformation?Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects".
Given that, a function f(x) = x² translated to g(x) = (x-5)²
We know,
h(x) = A(x - h)² + k
Where
A represent the vertical stretch (by factor of A)
h represent the horizontal shift (positive = Right, negative = Left)
k represent the vertical shift (positive = Up, negative = Down)
f(x) = x²
g(x) = (x - +5)²
Where, positive shows to the right.
Hence, the translation is 5 units to the right.
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If anyone can help me ill give you 20 points !!!
Answer:
26
Step-by-step explanation:
Mr Ford has 78 cattle
so Mrs Metcalf has 78/3 = 26
Answer:
26
Explanation:
No of cattle Mr. Ford has= 78
Then, no of cattle Mrs. Metcalf will have:
= 78/3
=26
What is the value of the expression below?
The value of the expression [tex]- \frac{2}{3} x \frac{5}{-6}[/tex] is 10/18
What is an ExpressionAn expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between
Simplify the expression
[tex]- \frac{2}{3} x \frac{5}{-6}[/tex]
multiply the numerator by numerator and also multiply the denominator
10/ 18
Therefore, solution to the expression is 10/18
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If anyone can help me on the #14 please
4(4÷2+4)
Answer:24
Step-by-step explanation: 4(4÷2 + 4) = 24/1 = 24
Spelled result in words is twenty-four.
Divide: 4 / 2 = 2
Add: the result of step No. 1 + 4 = 2 + 4 = 6
Multiple: 4 * the result of step No. 2 = 4 * 6 = 24
This calculator adds two fractions. When fractions have the same denominators calculator simply adds the numerators and place the result over the common denominator. Then simplify the result to the lowest terms or a mixed number.
Answer:
24
Step-by-step explanation:
We have to solve this according to BODMAS Theorem.
That is,
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Let us solve it now.
4 ( 4 ÷ 2 + 4 )
4 ( 2 + 4 )
4 × 6
24
Convert 3/4 to a decimal
Answer: 0.75
Step-by-step explanation:
0.75
watch your cholesterol: the mean serum cholesterol level for u.s. adults was 196 , with a standard deviation of 36 (the units are milligrams per deciliter). a simple random sample of 104 adults is chosen. use the ti-84 calculator. round the answers to four decimal places. what is the probability that the sample mean cholesterol level is greater than 205 ? the probability that the sample mean cholesterol level is greater than 205 is
The probability that the sample mean cholesterol level is greater than 205 is 0.62%.
To find the probability that the sample mean cholesterol level is greater than 205, we need to use the standard normal distribution and the formula for a normal distribution.
The sample mean cholesterol level, μ, is the population mean cholesterol level, 196, and the standard deviation of the sample mean, σ, is the standard deviation of the population divided by the square root of the sample size:
μ = 196
σ = 36 / √104 = 3.17
We want to find the probability that the sample mean cholesterol level is greater than 205, so we need to find the area under the curve of the standard normal distribution to the right of z = (205 - 196) / 3.17 = 2.5.
We can use the TI-84 calculator to find this probability by using the normal cdf function. In the function, we enter 2.5 as the lower bound and infinity as the upper bound to find the area under the curve to the right of z = 2.5.
The probability that the sample mean cholesterol level is greater than 205 is about 0.0062, or 0.62%.
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What is the value for y?
The value of the variable, y as represented in the image attached to the task content is; 14.
What is the value of the variable y as in the attached image?By observation; it follows that the lines CA and CB have equal length measures and hence, angles CAB and ABC are congruent (base angles of an isosceles triangle).
On this note;
50 = 2x.
Therefore; 2x = 50°.
Consequently, since the sum of interior angles of a triangle is; 180°; it follows that;
50 + 50 + 5y + 10 = 180
5y + 110 = 180
5y = 180 - 110
5y = 70
y = 70 / 5
y = 14.
On this note, the value of variable, y as required in the task content is; 14.
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Can someone help me out with this questions please?!?!
The simplified form of inequality -3x - 1 ≥ 20 is x ≤ -7.
The correct option is option (A).
What is number line?A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.
The given inequality is,
-3x - 1 ≥ 20.
To find the right number line from the options
Solve the inequality,
Add 1 to both the sides,
-3x -1 + 1 ≥ 20 + 1
-3x ≥ 21
-x ≥ 21 / 3
-x ≥ 7
x ≤ -7
The value of x are less than or equal to -7. Implies that, in number line graph close circle.
The number line in option (A), is correct option.
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The proof that ΔACB ≅ ΔECD is shown.
Given: AE and DB bisect each other at C.
Prove: ΔACB ≅ ΔECD
Triangles A B C and C D E share common point C.
A flow chart has 5 boxes with arrows facing downward connecting the boxes. Each of the boxes are labeled. Box 1 contains line segment A E and line segment B E bisect each other at C and is labeled given. Box 2 contains line segment A C is-congruent-to line segment E C and is labeled definition of bisector. Box 3 contains question mark and is labeled vertical angles theorem. Box 4 contains line segment D C is-congruent-to line segment B C and is labeled definition of bisector. Box 5 contains triangle A C B is-congruent-to triangle E C D and is labeled SAS.
What is the missing statement in the proof?
∠BAC ≅ ∠DEC
∠ACD ≅ ∠ECB
∠ACB ≅ ∠ECD
∠BCA ≅ ∠DCA
The statement that completes the proof is ΔACB ≅ ΔECD.
What is the statement in the proof?Triangles that are congruent have the same size and shape as similar triangles, albeit their shapes may differ. " is used to represent congruent triangles.Congruent triangles are similar triangles.The statement that completes the proof is ΔACB ≅ ΔECDFrom the complete question (see attachment), we have the following highlightsAC ≅ CE
BC ≅ CD.
The angle at point C of both triangles are congruenti.e. ΔACB ≅ ΔECD
This means that the missing statement of the proof is that the angles at C of both triangles are congruent.Hence, the statement that completes the proof is ΔACB ≅ ΔECD.To Learn more About completes the proof refer to:
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Select the correct answer.
If vector u = <-3.5, -1.5> and vector v=<-1.25, 2.25>, which graph shows the resulting vector for 2v-u?
If vector u = <-3.5, -1.5> and vector v=<-1.25, 2.25>, the graph given in attachment shows the resulting vector for 2v-u
What do you mean by vector?In mathematics, a vector is an object that has both magnitude and direction. size defines the size of the vector. This is represented by a line with an arrow. The length of the line is the magnitude of the vector and the arrow indicates the direction. It is also known as Euclidean his vector, geometric vector, space vector, or simply "vector".
Given vectors:
vector u = <-3.5, -1.5> and vector v=<-1.25, 2.25>
Now, 2v - u = 2<-1.25,2.25> - <-3.5,-1.5> = <-2.5,4.5> - <-3.5,-1.5>
= <(-2.5 + 3.5) , (4.5 + 1.5)>
= < 1 , 6.0>
θ = tan⁻¹ (6/1) = 80.5° ≈ 81 degree
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Which method could you use to eliminate one
of the variables from the following system of
equations?
4x - 6y = 18
3x + 4y = 5
A. Multiply the first equation by 2 and the second
equation by 3. Then add the equations.
B. Multiply the first equation by 3 and the second
equation by 4. Then add the equations.
C. Multiply the first equation by 4 and the second
equation by -6. Then add the equations.
D. Multiply the first equation by 5 and the second
equation by 18. Then add the equations.
Answer:
B
Step-by-step explanation:
To eliminate one of the variables from a system of equations, we can multiply one or both equations by constants and then add the equations together. In this case, the correct method to use is to multiply the first equation by 3 and the second equation by 4, and then add the equations together. This will eliminate the y-variable from the system of equations. Thus, the correct answer is option B: multiply the first equation by 3 and the second equation by 4, and then add the equations together.
The correct is option B (i.e.Multiply the first equation by 3 and the second
the equation by 4. Then add the equations.)
multiplying the first equation by 3 and the second equation by 4:
12x - 18y = 54
12x + 16y = 20
subtracting the first equation from the second equation:
( 12x - 18y = 54) - (12x + 16y = 20)
-2y = -34
y = 17
substituting y = 17 in the first equation:
4x - 6(17) = 18
4x = 106
x = 26.5
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The radius of a circle is 5 feet. What is the length of an arc that subtends an angle of
radians?
3л/2
5 ft
Give the exact answer in simplest form.
feet
The radius of a circle is 5 feet, 23.55 feet is the length of an arc.
What is arc length?The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc.
The arc length formula may be used to get a circle's arc length from its radius and central angle.
The distance between two places in a curve's section is known as the arc length of a circle. Any portion of a circle's circumference is an arc. An arc's angle at any given location is the angle created by the two line segments connecting that point to the arc's endpoints.
Given that,
radius (r) = 5 feet
angle (θ) = 3π/2
Now as we know,
Arc length = radius x subtended angle in radians
or, Arc length = 5 feet x (3π/2 radians)
or, Arc length = 15π/2
or, Arc length = 23.55 feet
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a friend of yours who works in the it department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., monday through saturday. what is this restriction an example of?
Given restriction is an example of Time-of-day restrictions
The correct answer is an option (C)
In this question we have been given a friend tells you that tellers
are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday through Saturday.
We need to identify the type of restriction in this example.
We know that time-of-day restrictions are the restrictions that often used to limit the hours during which a user is allowed to log into or access a system.
This type of restrictions helps prevent unauthorized access outside that user's normal working hours .
Therefore, given restriction present in this example: Time-of-day restrictions
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The complete question is:
A friend of yours who works in the IT department of a bank tells you that tellers are allowed to log in to their terminals only from 9 a.m. to 5 p.m., Monday
through Saturday. What is this restriction an example of?
A. User auditing
B. Least privilege
C. Time-of-day restrictions
D. Account verification
can someone solve: Layla wants to build a wooden box with a volume of 454545 cubic centimeters.
She started with a width of 3\text{ cm}3 cm3, start text, space, c, m, end text and a height of 3\text{ cm}3 cm3, start text, space, c, m, end text.
How long should Layla make the box? if someone could kindly do so, please put an answer AND comment by copying and pasting the answer! omg tysm
Layla can make the box up to 5centimeter long.
How to calculate volume of a box?Rectangles have a volume that is equal to their length, breadth, and height. If your box is a cube or a rectangular prism, all you need to know is its size in terms of length, width, and height. Then, to calculate volume, multiply them all together.V = l x w x h
Measure the box's length. If you look up at your box from the bottom, the top appears to be a flat rectangle with the longest side being the height. This number should be noted as "length." If you measure one side in inches, you must measure them all in inches. Be sure to use the same measurement for each side.Next to the length, gauge the box's breadth. The box's other edge, adjacent to the length, is its breadth. The breadth is the side that forms a "L" with the length when you look at one side of the box. This measurement should be noted as "width." The side that is shorter is always the width.The box's height should be measured. The distance from the top of the box to the ground is the last side you haven't measured. This measurement should be noted as "height." Add the three sides together and multiply. Remember that the formula for volume is V = length x width x height, therefore to calculate volume, simply multiply the three sides by one another. Include the measurement units you used as well, so you don't misinterpret your results.Units should be added to your volume. Volume is a measurement, but if you don't know the system used to measure it, your result won't signify anything. Your form of measurement cubed is the proper way to write out volume.Here it is given that,
volume= 45cm³
width= 3cm
height=3cm
volume = width × height × length
45cm³=3cm×3cm×length
45cm³=9cm²×length
length=45cm³÷9cm²
=5cm.
Hence, Layla can make the box up to 5centimeter long.
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The answers are
A. Statement: FDC≈FAB Reason: SAS
B. Statement FDC~FBA Reason: AA
C. Statement FDC≈FBA Reason: SAS
D. Statement FDC~FAB Reason: AA
Can I get an answer as well as how it makes sense?
Answer:
Step-by-step explanatihelpson:
is c hope it
In triangle xyz, m∠y = 38.25° and m∠z = 74.3°. determine the measure of the exterior angle to ∠x. 152.05° 112.55° 98.60° 62.05°
Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.
How to Apply the Exterior Angle Theorem?In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.
In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:
Measure of angle Y = 38.25°
Measure of angle Z = 74.3°
Therefore:
The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z
Substitute
The measure of the exterior angle to angle X = 38.25° + 74.3°
The measure of the exterior angle to angle X = 112.55°
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Is this statement true or false?
TRUE: The given condition is correct that m ≤ 10 and m > 4.
Explain the term inequality of the numbers?An inequality in mathematics depicts the relationship between these two values in an unbalanced algebraic expression. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to some other value.Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two parameters are not equal. But several inequalities are utilized to compare the numbers, either it is less than or higher than.For the given statement;
m ≤ 10 and m > 4, the number for the value of m be;
m = 5, 6, 7, 8, 9, 10.
Thus, the given condition is correct that m ≤ 10 and m > 4.
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To find the mass in grams, ______ the number of kilograms by the unit rate, _____ grams per kilogram.
PLEASE HELP
Answer:
To find the mass in grams, multiply the number of kilograms by the unit rate, 1000 grams per kilogram.
Explanation:
For every kilogram, there are 1000 grams. So, if you have 12 kilograms, you have 12,000 grams.
PLEASE HELLPPPP
The White Chuck Glacier is in the Cascade Range of western North America. In 1958 it covered 3.1 km?.
By 2002 it had lost about 70% of its area. What was the area of the glacier in 2002? Show your thinking.
Answer:
0.93 km
Step-by-step explanation:
The White Chuck Glacier lost 70% of its area between 1958 and 2002, which means that its area was reduced by 70/100 = <<70/100=0.7>>0.7.
Since the glacier-covered 3.1 km. in 1958, its area was reduced by 0.7 * 3.1 km? = <<0.7*3.1=2.17>>2.17 km.
Therefore, the area of the White Chuck Glacier in 2002 was 3.1 km. - 2.17 km? = <<3.1-2.17=0.93>>0.93 km.
10.
Manny took AABC and translated it according to (x,y)→(x+2,y-3).
What are the points of AA'B'C'?
the points of AA'B'C' is A'(4,0) B'(5,-1) C'(7,-2)
What are the points of AA'B'C'?Solution:
x, y = 0
(x + 2, y - 3) = 0
x + 2 = 0
x = -2
y - 3 = 0
y = 3
AABC
A(2,3) B(3,2) C(5,1)
A: (2,3) → (2+2,3-3) = (4,0)
B: (3,2) → (3+2,2-3) = (5,-1)
C: (5,1) → (5+2,1-3) = (7,-2)
AABC and A'B'C are equivalent. A student attempts to identify which of these straightforward transformations converted AABC into AA'B'C'. Points A and Bare are situated on sides CE and ED, respectively, in the CED as shown below. Given that AE = 3.75, AC = 5, EB = 4.5, and BD = 6, line segment AB is drawn. A"B"C" is a triangle congruent to ABC if T is the identity or a translation. A"B"C" is a triangle if T is a rotation by angle x but not a halfturn.To learn more about points refer to:
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pls help
write the equation that gives the proportional relationship of the graph
a. y=7x
b.y=35x
c.y=5x
d.y=1/7x
Answer:
y=7x
Step-by-step explanation:
NEED THIS ANSWERED ASAP!! NEED ALL ANSWERS! FIRST GETS BRAINLIEST!!
Answer:
AGDB
Step-by-step explanation:
1: 1 is alternate interior because the angles are on opposite sides of the interior of the transversal. (A)
2: 2 is alternate exterior because the angles are on opposite sides of the exterior of the transversal. (G)
3: 3 is same-side interior because the angles are on the same side of the interior of the transversal. (D)
4: 4 is same-side exterior because the angles are on the same side of the exterior of the transversal. (B)
Please help me with my geometry work
In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. ,m∠2 = 40°.
What is a straight line?An unending, one-dimensional figure with no breadth is a straight line. It consists of an infinite number of points connected on either side of a point. A straight line has a 180° measurement.
Definition of angle bisector.In geometry, the ray, line, or segment that splits a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. Alternatively said, it divides two smaller congruent angles. Given below is an image of an angle bisector of ∠AOB.
The graphic XYQ is the straight line, m∠3 = 40°, and m∠4 = 25°. YZ is the angle bisector of ∠s.
m∠2 = 40° the reason is YZ is the angle bisector of ∠s
∠s = m∠2 + m∠3
m∠2 = m∠3
therefore m∠2 = 40°
m∠1 + m∠2 + m∠3 + m∠4 = 180° the reason is XYQ is the straight line.
substitution of all values
m∠1 + 40° + 25° + 40° = 180°
m∠1 + 105° = 180°
m∠1 = 75° (straight line, substitution of all values )
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