The maximum number of turning points based on the degree of the polynomial is 2.
What is the turning point?A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.A turning point is a point in the graph where the graph changes from increasing to decreasing or decreasing to increasing.Turning point = n-1, where n is the degree of the polynomial.
The highest order of the polynomial is 3.n = 3Turning point = 3 - 1 = 2Therefore, the maximum number of turning points based on the degree of the polynomial is 2.
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A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
Which fraction is less than 3/5 is it 5/7, 9/15, 4/6, 7/12
Answer: 7/12
Step-by-step explanation:
3/5=0.6
5/7=0.71428571428
9/15=0.6
4/6=0.66666
7/12=0.583333
Answer: 7/12
Step-by-step explanation:
I have attached my work.
Triangle XYZ is rotated 90° counterclockwise about the origin.The result is Triangle X'Y'Z', as shown below.
A shortcut for a 90° counterclockwise rotation:
• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).
Answer:
Therefore the coordinates would be:
• X,(-5, 3) → ,X',(-3, -5)
,• Y,(-1, 1) → ,Y',(-1, -1)
,• Z,(-8, -4) → ,Z',(4, -8)
Then, the rule is (x, y) → (-y, x).
X-1 what is the answer
Answer:
x - 1 = x - 1
Step-by-step explanation:
If you were expecting a singular solution, you won’t get it. You’ll likely instead get a lot of smart alecks snidely answer your question. Looks like you already have actually.
But they speak true. x – 1 on its own like that wont really get you anything. Now if you asked something along the lines of “What is x – 1 equal to if x is equal to 5?” then you’d get one solid definitive solution: 4.
Answer:
YES!!!!!
Step-by-step explanation:
LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLLOLOLOLOLOLOLOLOL
What is the amplitude of the graph g(x)=f(x)+2 Where f(x)=cos x
In the cosine equation
[tex]y=AcosB(x-C)+D[/tex]A is the amplitude
B is using it to find the period
C is the phase shift
D is the vertical shift
Since the given function is
[tex]g(x)=cos(x)+2[/tex]A = 1
B = 1
C = 0
D = 2
The amplitude is 1
The answer is 1
Can someone help me out??
The correct option for the missing sides of given triangles is-
Part 1: x = 30Part 2: x = 21Part 3: x = 49Part 4: x = 22What is termed as the similar triangles?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size.For the given question,
The dimension of the two triangles are given with the missing sides.
Part 1: In the given rectangles;
5/3 = x/18
x = 30
Part 2: In the given rectangles;
9/x = 3/7
x = 21
Part 3: In the given triangles;
x/63 = 7/9
x = 49
Part 4: In the given triangles;
16/x = 8/11
x = 22
Thus, the missing sides of the given shapes are found.
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What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
URGENT TWO WAY TABLES
Answer: A) 6 B) 19.5
Step-by-step explanation:
A) 2,4,6,8,10
B) 8+16+30+24=78
78/4=19.5
Let me known if question b was right
Write using set-builder notation: -2x + 1 < 27
Instead of describing the constituents of a set, a set-builder notation describes them. The set-builder notation exists A = {x: x is a natural number less than 27}.
What is meant by set-builder notation?A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Set-builder notation is a mathematical notation for defining a set by enumerating its elements or by specifying the properties that each of its members must satisfy. It is used in set theory and its applications to logic, mathematics, and computer science.
Let the given inequality be 2x+1 < 27
Subtract 1 from both sides, we get
-2x+1-1 < 27-1
Simplifying the above equation, we get
-2 x < 26
Multiply both sides by - 1 (reverse the inequality)
(-2 x)(-1) > 26(-1)
Simplifying the above equation, we get
2x > -26
Divide both sides by 2
[tex]$\frac{2 x}{2} > \frac{-26}{2}[/tex]
x > -13
Therefore, the set-builder notation exists
A = {x: x is a natural number less than 27}.
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Please help I'm not sure what should I substitute the variable (x) by
From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
figure0123456vehicles4122028364452linear ?pattern ?constant?
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
Which sequence of transformations will change figure PQRS to figure P'Q'R'S'?
Explanation:
A counterclockwise rotation about the origin by 90 degrees rule is:
[tex](x,y)\rightarrow(-y,x)[/tex]The reflection about the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]If we take for example point P (-3, -2) we can see it ends at P'(2,3). The counterclockwise rotation about the origin by 90º gives:
[tex](-3,-2)\rightarrow(2,-3)[/tex]And now with a reflection about the x-axis:
[tex](2,-3)\rightarrow(2,3)[/tex]Which is point P'
Answer:
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
1. Evaluate the following expressions if a = 2. b = 3, x = 4, and y = 5.+3(27-»
When a=2, b=3, x=4, and y=5,
evaluate:
[tex]b^2+3(2x-y)[/tex]Let's replace b, x and y by the appropriate values:
[tex](3)^2+3(2(4)-5)[/tex]now let's solve what is inside the parenthesis:
[tex]9+3(8-5)[/tex]again more solving inside the second parenthesis:
[tex]9+3(3)[/tex]and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:
[tex]9+9=18[/tex]You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.
Like:
[tex]ab+ya^3[/tex]and then evaluate:
[tex]\frac{y+ab}{b+x}[/tex]Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.
The triangle formed is shown in the diagram below
The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
opposite side = 150
adjacent side = 40
Tan x = 150/40 = 3.75
x = Tan^-1(3.75)
x = 75.069
To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees
Margo borrows $1200, agreeing to pay it back with 4% annual interest after 17 months. How much interest will she pay?
Answer:
$68
Step-by-step explanation:
P = $1200
R = 4%
T = 17months (Convert to years; 17 months ÷ 12 months)
Formular for Interest; I = PRT
100
I = $1200 × 4 × 17
100 × 12
I = $68
sketch the graph of and identify the axis of symmetry
Given the following equation:
[tex]y=(x-1)^2+2[/tex]We will sketch the graph and identify the axis of symmetry.
the given function is a quadratic function with a vertex at (1, 2)
the graph of the function will be as follows:
As shown, the graph of the function has an axis of symmetry at x = 1
So, the answer will be option 3) x = 1
Make a tree diagramPlease be quick, I am in a hurry.
Explanation
The question wants us to obtain all the outcomes possible when a coin and a cube is tossed
A coin has two possible outcomes
[tex]\mleft\lbrace\text{Head, Tail}\mright\rbrace[/tex]A cube has 6 surfaces, so the outcomes are
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Thus, we can have the diagram showing the outcomes to be
It goes from -1 to 1 on the x axis.
ANSWER :
EXPLANATION :
there are 66 utensils in the cafeteria. 22 of them are spoons and the rest are Forks. what is the ratio of the number of spoons to the total number of utensils?And what is the ratio of the number of forks to the number of spoons?
Let's begin by listing out the information given to us:
Total utensils = 66
Spoons = 22
Forks = 66 - 22 = 44
The ratio of spoons to the total utensil is given by the ratio of spoons to total utensils. We have:
22:66 ⇒ 1:3
Therefore, the ratio of spoons to total utensils is 1 spoon is to 3 utensils
The ratio of the number of forks to spoon is given by the ratio of forks to spoon. We have:
44:22 ⇒ 2:1
Therefore, the ratio of forks to spoon is 2 to 1. For every 2 forks, there is 1 spoon
Christian buys a $3500 computer using an installment plan that requires 17% down and a 3.7% interest rate. How much is the down payment?
1) Gathering the data
$3500 computer
17% down
3.7% interest rate.
2) Since we want to know how much is that down payment, we must turn that 17% into decimal form, then multiply it by the computer value:
17%=0.17
3500 x 0.17 = $595
3) So Christian must pay $595 as the down payment
A cubic function has turning points at (-1,2) and (1,-2). Which could be its graph?
ANSWER
Graph D is the correct option
EXPLANATION
The turning points of a function are the points where its derivative changes sign - therefore the slope of the function changes sign. In other words, the turning points are the local maximums and local minimums of the function.
From these options, the one that has a local maximum/minimum at point (-1, 2) and another at point (1, -2) is option D.
A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone's volume lies inside the cylinder? Express your answer as a common fraction.
The fraction of the cone's volume that lies inside the cylinder would be; V = 44/21 r^4
How to find the volume of a right circular cone?Suppose that the radius of the considered right circular cone is 'r' units.
And let its height be 'h' units. The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Then, its volume is given :
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Let the radius of the cylinder is r
The height of the cylinder is h = 3r
The height of the cone is h = 6r
The fraction of the cone's volume that lies inside the cylinder would be;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 3.14 \times r^3 \times 6r \: \rm unit^3[/tex]
V = 44/21 [tex]r^{4}[/tex]
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Answer:
4/9
Step-by-step explanation:
Identify the minimum from the tableType your answer as an ordered pair (x,y)
By definition, a function is a relation in which each input value has one and only one output value.
The input values are also known as x-values and the output values are also called y-values.
By definition, the Minimum is the lower point of the function.
Having the table shown in the exercise, you can identify the following points:
[tex]\begin{gathered} (-2,10) \\ (-1,8) \\ (0,6) \\ (1,4) \end{gathered}[/tex]You can identify that the lower y-value of all those points is:
[tex]y=4[/tex]Therefore, you can determine that the lower point of the function is:
[tex](1,4)[/tex]The answer is:
[tex](1,4)[/tex]An exam has 2 papers each scored differently. one is out of 120 and another is out of 80. Maryam scores 65% on the first and 80% on the second. work Maryam's total percentage score for her exam.
Maryam's total percentage score on her exam is 71%.
What is the total percentage score?
Percentage is the ratio of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
The first step is to determine the score on each paper.
Score on the first test = 65% x 120
(65 / 100) x 120 = 78
Score on the second test = 80% x 80
0.80 x 80 = 64
Total percentage score = (sum of scores / total score) x 100
Sum of scores = 64 + 78 = 142
Total score = 120 + 80 = 200
(142 / 200) x 100 = 71%
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Angles A and B are adjacent on a straight line. Angle A has a measure of (2r +20) and angle B has a measure of 130.. What is the measure of r?
When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;
[tex]\begin{gathered} (2r+20)+130=180 \\ \text{Subtract 130 from both sides and you'll have} \\ 2r+20=50 \\ \text{Subtract 20 from both sides and you'll have} \\ 2r=30 \\ \text{Divide both sides by 2 and you'll have} \\ r=15 \end{gathered}[/tex]The measure of r is 15
1.- (picture) 2.-Assuming that the global population is seven billion and that no person receives the letter more than once, the maximum number of mailings is fourteen. Suppose that you are one of the recipients of mailing number 8 and there are ten names on the list (so your five outgoing letters will be in mailing number 9 and there will be nine names above yours on the list). If everyone who receives the letter participates, how much money will you receive?$
Kindly check below
Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.
2) Therefore, we can fill in those gaps with the following:
[tex]\begin{gathered} Number\:of\:mailings|\:Number\:of\:recipients \\ 1\:|\:5 \\ 2\:|\:25 \\ 3\:|\:125 \\ 4\:|\:625 \\ 5\:|\:3125 \\ 6\:|\:15625 \\ 7\:|\:78125 \\ 8\:|\:390625 \\ 9\:|\:1953125 \\ 10\:|\:9765625 \\ 11\:|\:48828125 \\ 12\:|\:244140625 \\ 13\:|\:1220703125 \\ 14\:|\:6103515625 \\ \\ % \end{gathered}[/tex]3) Thus is the table.
is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19
3x+2y= 3 (a)
3x+2y= 19 (b)
Subtract (b) to (a) ; elimination method.
3x+ 2y = 3
-
3x+2y= 19
_________
0 = 19
Since both variables were eliminated, the system has no solutions.
option c.
Find m∠1 I need help please
Answer: 70
Step-by-step explanation: 180-110=70
because of isosceles, so ∠1=70
