The function f(x)=2x³ 18x²-162x 5, -9 is less than or equal to x is less than or equal to 4, has an absolute minimum value of -475 at x = -9.
What is the absolute minimum value of the function f(x) = 2x³ + 18x² - 162x + 5, where -9 ≤ x ≤ 4?To find the absolute minimum value of the function, we need to find all the critical points and endpoints in the given interval and then evaluate the function at each of those points.
First, we take the derivative of the function:
f'(x) = 6x² + 36x - 162 = 6(x² + 6x - 27)
Setting f'(x) equal to zero, we get:
6(x² + 6x - 27) = 0
Solving for x, we get:
x = -9 or x = 3
Next, we need to check the endpoints of the interval, which are x = -9 and x = 4.
Now we evaluate the function at each of these critical points and endpoints:
f(-9) = -475f(3) = -405f(4) = 1825Therefore, the absolute minimum value of the function is -475, which occurs at x = -9.
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Shara is building a birdhouse. She cuts a 6-foot-long board into sections that are each 1/3 foot long. How many sections of the board will Shara have when she is finished cutting?
A 2
B 6 1/3
C 10 1/3
D 18
Answer:
D
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by its reciprocal.
6 ÷ 1/3
= 6 x 3/1
= 6 x 3
= 18
The number of sections of the board Shara has when she is finished cutting is 18 sections.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Length of the board = 6 feet
Length of the section = 1/3 feet
The number of 1/3 feet sections.
= 6 ÷ 1/3
= 6 x 3
= 18
Thus,
Shara when she is finished cutting will have 18 sections.
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Solve each system by elimination
Answer:
system of equation by elimination
1 write both equation in standard form
2 make the coefficient of one variable opposites
3 add the questions relating from step to eliminate one variable
4 solve for the remaining variable
5 substitute the solution from step for into one of the original equation
In how many ways can max select 3 toppings from 10 available toppings for his
12. pizza?
Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.
Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3
=[tex]\frac{10!}{7!3!}[/tex]
= [tex]\frac{8.9.10}{3!}[/tex]
= 120
Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.
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Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
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If you could help me on 1 and 2 that would be great!!!
The conversion of the vectors into coordinate notation rule are as follows;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)What are the coordinate notation form of the given vectors?It follows from the task content that the vectors given in the task content can be converted to coordinate notation form by mapping x and y to their respective transformation units. It therefore follows that the coordinate notation form of the vectors are;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)Read more on coordinate notation;
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can someone please help me with 17a
Answer:
r=8.74038744 m
and surface area=1303.76211 m2
Step-by-step explanation:
Design your own statistical question that you can ask at least twenty different people. Keep in mind that the question should result in a variety of different numerical answers. What is your statistical question?
Ask at least twenty different people (classmates, family, friends, neighbors, teammates, etc.) your statistical question and record their answers. Describe the people you asked and how you gathered your data.
Organize and list your numerical data in order from least to greatest. Then, determine the values of the five-number summary for your set of data.
Use your five-number summary to create and upload a box plot that displays your data set.
A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
An hypothetical data for the number of pets 20 sixth graders have has been given and the box plot that displays the data set is in the image below.
What is a Statistical Question?A statistical question can be defined as a question that can be answered by collecting a variety of numerical answers that vary. Examples of statistical questions include:
What are the age of students in my class?What are the heights of students in a class?A statistical question you can ask at least 20 different people can be: "How many pets do you have?"
Below is the hypothetical questions that can be assumed you'd get from two people:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
Description of the people you asked can be: 20 sixth graders in your school.
How you gathered your data can be: Asking them to fill a questionnaire or by interview.
The numerical data from least to the greatest, hypothetically would be:
0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5
The five-number summary for the hypothetical data would be:
Minimum: 0 (least data point)
Quartile Q1: 1 (middle of the first half of the data distribution)
Median: 1.5 (center of the data)
Quartile Q3: 2.75 (middle of the second half of the data distribution)
Maximum: 5 (greatest data value).
Using the five-number summary generated, the box plot that displays the data set is shown in the image attached below.
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What are the inputs of the following function?
{(-3, 2), (-4, 2), (8,3), (7, 1)}
A. {-4, -3, 7, 8}
B. {1, 2, 3, 7, 8}
C. {1, 2, 3}
D. {-4,-3, 1, 2, 3, 7, 8}
Answer:
A. {-4, -3, 7, 8}
Step-by-step explanation:
The ordered pairs representing a function are always written ...
(input, output)
InputsThe set of inputs for the given function is the list of first-numbers of the ordered pairs. Those numbers are -3, -4, 8, 7. When we express them as a set, we like to have the elements of the set in increasing order:
inputs = {-4, -3, 7, 8} . . . . . . matches the first choice
Let k be the largest integer such that 343/7^k is an integer. What is the remainder when 343/7^k is divided by 7
Answer:
1
Step-by-step explanation:
The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.
Factors of 343343 = 7·7·7 = 7³
RatioThe value of k is the power of 7 in the factorization of 343, so we have ...
k = 3
and ...
343/7³ = 1
RemainderThe remainder when this ratio is divided by 7 is ...
1 mod 7 = 1
The remainder when 343/7^k is divided by 7 is 1.
Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =
Answer:
[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]
Answer:
Step-by-step explanation:
YOU PLUS ALL OF THEM
Find the equation of a circle with center at (5, 6) and radius 8.
Answer:
(x - 5)^2 + (y - 6)^2 = 64
Step-by-step explanation:
Every circumference is in the form:
(x - xc)^2 + (y - yc)^2 = r^2
Where xc is the x of the center. Yc is the y of the center. r is the radius. We just plug in the values and we're done.
Answer:
[tex](x-5)^2+(y-6)^2=64[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
center = (a, b)radius = rGiven:
center = (5, 6)radius = 8 unitsSubstitute the given values into the formula:
[tex]\implies (x-5)^2+(y-6)^2=8^2[/tex]
[tex]\implies (x-5)^2+(y-6)^2=64[/tex]
Therefore, the equation of a circle with the given values is:
[tex](x-5)^2+(y-6)^2=64[/tex]
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Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
A
B
F
D
C
E AC = BC
ZAZB
Answer:
ASA
Step-by-step explanation:
2x-3y=1 2x+3y=2 describe the process of using addition to show that the lines are intersecting
Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.
2x - 3y = 1
+ 2x + 3y = 2
4x =3 Or x=3/4
Substituting x value in any of the two-equation we can find the corresponding y value .
2x-3y=1
2(3/4) - 3y =1
Solving for y
y= 1/6
The point of intersection of the two lines is ( 3/4, 1/6)
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Find the equation of the line with slope = 6 and passing through (2,20). write your equation in the form y = mx + b.
Answer:
y = 6x + 8
Step-by-step explanation:
y = mx + b
20 = 6(2) + b
b = 8
y = 6x + 8
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A shaded polygon A B C D is graphed in an x y plane, where x axis ranges from 0 to 7 in increments of 1 and y axis ranges from 0 to 6 in increments of 1. The vertices are as follows: A (1, 1), B (2, 3), C (5, 4), and D (4, 2). Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′. The slope of C'D' is___ .
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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Given AB=15cm,BC=20cm.Find AB correct 3 significant
(question refer to a triangle ABC which is right -angled at C)
The length of AB is 25 units
How to determine the length AB?The given parameters are
AC = 15 cm
BC = 20 cm
The triangle is right -angled at C.
So, we have:
AB^2 = AC^2 + BC^2
This gives
AB^2 = 15^2 + 20^2
Evaluate
AB^2 = 625
Take the square roots
AB = 25
Hence, the length of AB is 25 units
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If my savings of $x grows 10% each year. how much will I have in: 2 years
The amount I'll have in two years at the growth rate described is; $1.21x.
How much will I have in 2 years?Since it follows that the savings grow by 10% each year, it can be concluded that the growth factor is; 110% = 1.1
Hence, in two years, we have;
= $x × (1.1)²
= $1.21x.
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Answer:
1.21x
Step-by-step explanation:
on rsm it says its correct
Below is the market for funnel cakes at a small community fair.
a) what is the equilibrium price and quantity of the funnel cakes?
b) What is the total consumer spending on funnel cakes at the equilibrium point?
c) Calculate the producer surplus and consumer surplus at equilibrium. Show your work.
d) What would be the result if the suppliers charged $6? Explain.
e) Cheese pretzels are substitute good for funnel cakes at the same fair. Draw a correctly labeled graph of the market for cheese pretzels. Shade the area of consumer surplus.
f) A large number of new guests enter the fair. Illustrate the effect of this change on the same graph from part E.
g) does the consumer surplus increase, decrease, or stay the same as a result of the change from part F? Explain.
h) A new cheese pretzel stand opens at the same fair. On a new graph, illustrate the market for cheese pretzels at this fair before and after the new stand opened.
i) if the large number of new guests entering the fair happened at the same time that the new cheese pretzel stand open how would the equilibrium price and quantity for cheese pretzels change? Explain.
From the graph given, the equilibrium price and quantities are given respectively as;
Price = $5Quantity = 6 units of funnel cakes.What is the total consumer spending on funnel cakes at the equilibrium point?The total consumer spending(TCS) is achieved by finding the product of the price and the quantities at the equilibrium point.
Hence,
TCS = 5 * 6
= 60
A) The producer surplus is the area of the triangle shaded yellow in the attached image.
Recall that he area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Producer Surplus) =
1/2 * 4 * 6
= 12
B) The Consumer surplus is the area of the triangle shaded Green in the attached image.
Recall that the area of triangle is:
1/2 b * h
b = 4
h = 6
Hence Area of the RA-Triangle (Consumer Surplus) =
1/2 * 4 * 6
= 12
What would be the result if the suppliers charged $6?
If the suppliers charged $6, then the quantity demanded would drop to 4 units of funnel cakes. It is demonstrated graphically. Recall that the law of demand and supply indicates that when prices goes up, demand comes down and vice versa.
Graph II illustrates what would happen if a large number of guests entered the fair. It would result to a right-ward shift in the demand curve.
Does the consumer surplus increase, decrease, or stay the same as a result of the change from part F?Yes, there is an increase in the consumer surplus. Now there are more consumers hence the total amount they are willing to pay as an aggregate sum has increased from what was.
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If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below. . Group of answer choices 1/4 3/7 4/7 1/7
Using it's concept, the probability of D is 4/7.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:
[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]
[tex]P(D) = 1 - \frac{3}{7}[/tex]
[tex]P(D) = \frac{4}{7}[/tex]
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A teacher knows that 80% of her students will score no more than 5 points above or below the class average, 85%, on the test. Which inequality represents the test scores of 80% of her students?
Answer:
[tex]|x-85| \leq 5[/tex]
Step-by-step explanation:
|x-85| represents the 'distance' of the test score than 85, and this distance must be less than or equal to 5.
Find the missing segment in the image below.
Answer:
10.
Step-by-step explanation:
6/9 = x/15
9x = 6*15
9x = 90
x = 10.
Answer:
10
Step-by-step explanation:
[tex]\frac{6}{15} =\frac{x}{x+15}[/tex]
[tex]6(x+15)=15x[/tex]
[tex]6x+90=15x[/tex]
[tex]90=15-6x[/tex]
[tex]90=9x[/tex]
[tex]x=90/9= 10[/tex]
Hope this helps
Which of these numbers is irrational?
-3.5
3.5
ОО
35
√5 help
Answer:
√5 is irrational
Step-by-step explanation:
A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.
ApplicationUsually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.
The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.
__
Additional comment
A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.
The geometry students have designed a hexagonal flowerbed for the Homes for
Humanity landscaping project. The shape indicates the color of the flowers. The
design is composed of two congruent rhombuses (blue), four congruent parallelograms
(red and white), and four congruent trapezoids (red and white). The circular area
surrounding the design is an existing rock bed.
The students have determined the following measurements of each figure:
the bases of the trapezoids are 6 ft and 8 ft,
• the heights of the trapezoid and the parallelogram are 3.5 ft each, and
• the horizontal distances between the left and right vertices of each rhombus is 2
ft.
Trapezoid
[tex]A=\frac{1}{2}(3.5)(6+8)=24.5[/tex]
Parallelogram
[tex]A=(3.5)(6)=21[/tex]
Rhombus
[tex]A=\frac{1}{2}(7 \cdot 2)=7[/tex]
Red Area
[tex]2(21)+2(24.5)=91[/tex]
White Area
[tex]2(21)+2(24.5)=91[/tex]
The circular area surrounding the design is an existing rock bed are 24.5, 21, 27, 91 and 91 ft sq.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
It is given the bases of the trapezoids are 6 ft and 8 ft,
The heights of the trapezoid and the parallelogram are 3.5 ft each, and the horizontal distances between the left and right vertices of each rhombus is 2 ft.
Trapezoid
Area = 1/2(3.5)(6 + 8)
Area = 24.5
Parallelogram
Area = 1/2(3.5)(6)
Area = 21
Rhombus
Area = 1/2(7)(2)
Area = 7
Red Area
Area = 2(21) + 2(2.4)
Area = 91
White Area
Area = 2(21) + 2(2.4)
Area = 91
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15-point question. Pls help
Answer:
44
Step-by-step explanation:
x + (22 - 13) = 53
x + 9 = 53
x = 44
Answer:
44
Step-by-step explanation:
x+(22-13)=53
x+22-13=53
x+9=53
x=44
solve -9 2/7 - (-10 3/7)
A star is estimated to be 150,000,000,000,000 km away from Earth. Write this distance in scientific notation. [?] × 10 km
Answer:
[tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14
Step-by-step explanation:
The answer is [tex](1*10^{15} )(5*10^{14})[/tex] or 1.5×10^14.
Hope this helps!
4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(
Total area=
Help me please, thankss
The Area of given figure is 341.6 square.
According to the statement
we have to find the total area of given figure.
Here a= 10 and h= 11
So, we use the formula is A = a(a + √((a)^2 + 4(h)^2))
where the a represent the base of given solid or sides of the equilateral triangle
And h represent the slant height of the solid.
So, Substitute the values in above formula then
A = 10(10 + √((10)^2 + 4(11)^2))
A = 10(10 + √((100 + 4(121))
A = 10(10 + √(100 + 484)
A = 10(10 + √(584)
A = 10(10 + 24.16)
A = 10(34.16)
A= 341.6
So, The Area of given figure is 341.6 square.
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Dion is 4 years older than Agustina. In 3 years the sum of their ages will be 46. How old is Dion now?
Answer:
22
Step-by-step explanation:
Dion (d) is 4 years older than Agustina (a)
d=a+4
In 3 years the sum of their ages will be 46
d+3+a+3=46
d+a+6=46
d+a=40
d=40-a
d=a+4
a+4=40-a
2a=36
a=18
Plug a back in
18+4=d
22=d
d=22
Sorry if this was a little long.
The population parameters that describe the y-intercept and slope of the line relating y and x, respectively, are _____. Group of answer choices B0 and B1 y and x a and b a and B
B0 AND B1 are the parameters which describes the intercept and slope of the lines.
According to statement
we have to find the parameters which describes the intercept and slopes.
Simple linear regression is a model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
So, B0 AND B1 are the parameters which describes the intercept and slope of the lines.
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