2.4.1 Study: Multiplying PolynomialsA cone has a height, h, and a circular base with a radius of (h - 3). The volumeof the cone is: V=(1/3)pi(h-3)^2hwhich statements about the volume below of the cone are true?select all that applyA. The Area of the base, pi(h-3)^2, is a factor of the volume.B. The height,h, is a factor of the volume of the coneC. The volume does not depend on the height.D. The volume is the sun of the height and the radius,(h-3)
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Explanation
The volume of a cone is given as;
[tex]volume=\frac{1}{3}\times base\text{ are}a\times height=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi(h-3)^2h[/tex]Since a number or algebraic expression that divides another number or expression evenly is a factor. From the above definition, we can see that the base area and the height are factors of the volume.
However, the volume depends on the height, the higher the height the bigger the volume, and vice versa. The volume is also not the sum of the height and the radius.
Answer: Option A and B
Related Questions
The weight of a blue whale is about 200,000 kg, or 2 x 10^5 kg.The weight of a large whale shark is about 20,000 kg, or 2 x 10^4 kg.About how many times heavier is the blue whale than the whale shark?A. 180,000 timesB. 2 timesC. 1x 10^-1 timesO D. 1x10^1 times
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In order to find the relation between the weight of the two whales we need to divide them. We want to know how many times heavier the blue whale is in relation to the whale shark, therefore we need to divide the weight of the blue whale by the weight of the shark. Both weights are given in scientific notation form, this makes things easier for us, because in that form we can divide the base and subtract the expoents. This is done below.
[tex]\begin{gathered} \text{ratio =}\frac{2\cdot10^5}{2\cdot10^4} \\ \text{ratio = 1}\cdot10^{(5-4)} \\ \text{ratio}=1\cdot10^1 \end{gathered}[/tex]Therefore the result is 1*10^1 times, which would be the letter "D".
Which answers are true and which answers are false? These are the 4 possible answers
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SOLUTION
Given the image
For statement 1
The coordinate of point A after a clockwise rotation of 90° about the origin is (3,-1)
Note that a clockwise rotation of 90° is defined as
[tex](x,y)\Rightarrow(y,-x)[/tex]From the image, the coordinate of point A is (1,3)
Therefore the statement is TRUE
STATEMENT 2
The coordinate of Point A after dilation of the scale factor of 2 is (2, 6)
For a dilation of the scale factor of 2, the coordinate will be doubled
Therefore the statement is TRUE
The next two statements are FALSE
tell me the first 100 digits of pi
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SOLUTION:
Step 1:
In this question, we are given the following:
The digits of pi:
The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679.
The value of pi starts with a 3 followed by a decimal point.
Since pi is an irrational number, the digits after the decimal point are infinite.
Find the population in 2017 round to the nearest tenth
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Given:
In 2000, the population was 6.08 billion
rate of increase = 1.5% per year
Required: The population in 2017
The formula for calculating population growth is:
[tex]y(t)\text{ = a\lparen1 + r\rparen}^t[/tex]Where y(t) is the population at a later time t
a is the initial population
r is the annual rate of increase
and t is the number of years
For the given problem,
a = 6.08 billion
r = 1.5%
t = 17 years (2017-2000)
Substituting the given values into the formula:
[tex]\begin{gathered} y(t=17)\text{ =6,080,000,000\lparen1 + }\frac{1.5}{100})^{17} \\ =\text{ 7,831,163,611.683507} \\ \approx\text{ 7,831, 163, 611.7} \end{gathered}[/tex]Hence, the population in 2017 should be 7831163611.7
Find the 52nd term.-3, -12, -48, -92,…
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The given sequence is
[tex]-3,-12,-48,-92,\ldots[/tex]We will find the common ratio by dividing the 2nd term by the 1st term
[tex]\begin{gathered} r=\frac{-12}{-3} \\ r=4 \end{gathered}[/tex]The rule of the nth term of the geometric sequence is
[tex]a_n=ar^{n-1}[/tex]a is the 1st term
r is the common ratio
n is the position of the term
Since the 1st term is -3, then
a = -3
Since the common ratio is 4, then
r = 4
Since we need to find the 52nd term, then
n = 52
Substitute them in the rule above
[tex]\begin{gathered} a_{52}=-3(4)^{52-1} \\ a_{52}=-3(4)^{51} \end{gathered}[/tex]The answer is
[tex]a_{52}=-3(4)^{51}[/tex]Use factoring to solve the polynomial equation:423 + 422 – 482 = 0Answer:
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Now, let's analyze each factor
4x=0
x=0
x-3=0
x=3
x+4=0
x=-4
Answer
x=0, x=3, x=-4
Find the solution to the system of equations 2x + y = 3 and x - y = 3.(-2, 1)(-2, -1)(2, -1)(2, 1)
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Use the elimination method to solve the system of equations:
[tex]\begin{gathered} 2x+y=3 \\ x-y=3 \end{gathered}[/tex]Add both equations to eliminate the variable y. This can be done because the coefficient of y in the first equation is 1, while the coefficient of y in the second equation is -1:
[tex]\begin{gathered} (2x+y)+(x-y)=(3)+(3) \\ \\ \Rightarrow2x+y+x-y=3+3 \\ \\ \Rightarrow2x+x+y-y=6 \\ \\ \Rightarrow3x+0=6 \\ \\ \Rightarrow3x=6 \\ \\ \Rightarrow x=\frac{6}{3} \\ \\ \therefore x=2 \end{gathered}[/tex]Replace x=2 into the first equation and solve for y:
[tex]\begin{gathered} 2x+y=3 \\ \\ \Rightarrow2(2)+y=3 \\ \\ \Rightarrow4+y=3 \\ \\ \Rightarrow y=3-4 \\ \\ \therefore y=-1 \end{gathered}[/tex]Then, the solution to the system is x=2 and y=-1. Using the ordered pair notation (x,y), the solution to the system is (2,-1).
Therefore, the correct choice is:
[tex](2,-1)[/tex]what is the value of x to the nearest tenth on problem 6
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ANSWER:
x = 15
STEP-BY-STEP EXPLANATION:
We can calculate the value of x, with the help of the Pythagorean theorem, we obtain the following equation:
[tex]\left(x+10\right)^2=x^2+20^2[/tex]We solve for x:
[tex]\begin{gathered} \left(x+10\right)^2=x^2+400 \\ \\ x^2+20x+100=x^2+400 \\ \\ x^2-x^2+20x=400-100 \\ \\ 20x=300 \\ \\ x=\frac{300}{20} \\ \\ x=15 \end{gathered}[/tex]The value of x is equal to 15
Write an equation in standard form for the vertical line that passes through (5,-3)
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For the given question, we will write an equation in standard form for the vertical line that passes through (5,-3)
the general equation for the vertical line is:
[tex]x=h[/tex]Where (h) is the x-coordinate of a point lying on the vertical line
given: the vertical line passes through (5, -3)
So, h = 5
And the equation of the vertical line will be:
[tex]x=5[/tex]the national health examination survey reported that in a sample of 13,267 adults, 6634 had high cholesterol (total cholesterol above 200 mg/dl), 8093 were overweight (body mass index above 25), and 4113 were both overweight and had high cholesterol. a person is chosen at random from this study. round all answers to four decimal places. (C) find the probability that the person does not have high cholesterol. The probability that the person does not have high cholesterol is?(D) Find the probability that the person is overweight or has high cholesterol. The probability that the person is overweight or has high cholesterol is?
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The results of the National Health Examination Survey are:
High Cholesterol: 6634
Overweight: 8093
Both overweight and had high cholesterol: 4113
Sample size: 13 267
(C)
We need to calculate the probability that the person does not have high cholesterol. To do that, we need to find the probability that the person does have cholesterol, and then subtract this result from 1. Then:
P[not high cholesterol] = 1 - P[high cholesterol]
P[high cholesterol] = (# people that have high cholesterol) / (Total # of people)
P[not high cholesterol] = 1 - (6634) / (13 267) = 0.499962...
Rounding to four decimal places:
P[not high cholesterol] = 0.5000
(D)
Now, we need to calculate the probability that the person is overweight or has high cholesterol. We define the events:
A: The person has high cholesterol
B: The person is overweight
Then:
P[A ∪ B] = P[A] + P[B] - P[A ∩ B]
Where:
P[A] = 6634/13267
P[B] = 8093/13267
P[A ∩ B] = 4113/13267
Where we defined the probability as:
P[C] = (# of events C) / (# of total events)
Then:
P[A ∪ B] = 6634/13267 + 8093/13267 - 4113/13267 = (6634+8093-4113)/13267
P[A ∪ B] = 10614/13267
Rounding to four decimal places:
P[A ∪ B] = 0.8000
KiteKite StringAltitude : 120 ftGroundA kite is flown at a 55° angle of elevation. That is, the kite stringmakes a 55° angle with the ground.If the altitude of the kite is 120 feet, what is the length of the kitestring used? Round your answer to the nearest foot.
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Given:
The altitude of the kite, h=120 ft.
The angle made by the kite string with the ground, θ=55° .
Let x be the length of the string.
Now, using trigonometric property in the above triangle,
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypotenuse} \\ \sin \theta=\frac{h}{x} \end{gathered}[/tex]Now, substitute the values and solve the equation for x.
[tex]\begin{gathered} \sin 55^{\circ}=\frac{120\text{ ft}}{x} \\ x=\frac{120\text{ ft}}{\sin55^{\circ}} \\ =146.49\text{ ft} \\ \approx146\text{ ft} \end{gathered}[/tex]Therefore, length of the kite string is 146 ft.
Math vocabulary for 1 and 138 and 45 and 77 and 1216 and 112 and 816 and 39 and 12
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1 and 13 are Alternate exterior angles
8 and 4 are Vertical angles
5 and 7 are corresponding angles
7 and 12 are same side interior angles and also Supplementary
16 and 11 are Supplementary angles
2 and 8 are alternate interior angles
16 and 3 are Supplementary angles and also Same side exterior angles
9 and 2 are No relation
can someone help me find the measurement of each angle in the attached assignment.
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The given figure is a polygon with 4 sides. The sum of the interior angles in a polygon is expressed as
(n - 2)180
Where
n represents the number of sides. Given that n = 4, then the sum of the interior angles in the polygon would be
(4 - 2)180 = 2 * 180 = 360 degrees
Thus, we have
4x + 9 + 7x - 5 + 2x + 15 + 5x - 1 = 360
Collecting like terms, we have
4x + 7x + 2x + 5x + 9 - 5 + 15 - 1 =360
18x + 18 = 360
18x = 360 - 18 = 342
x = 342/18
x = 19
To find the measure of each angle, we would substitute x = 19 into each of the angles. Thus, we have
Angle G = 4 * 19 + 9 = 76 + 9 = 85 degrees
angle B = 2 * 19 + 15 = 38 + 15 = 53 degrees
angle M = 5 * 19 - 1 = 95 - 1 = 94 degrees
angle L = 7 * 19 - 5 = 133 - 5 = 128 degrees
4 Raquel earned S105 for baking seven pies one week. The following week she earned$60 for baking four pies. On the third week, she did not bake any pies or earnany moneyPart AUse the graph below to show the relationship between the number of pies Raquelbaked and the amount of money she earned each week. Plot the three data pointsfrom the problem statement and draw a line connecting the points.34 5Ples BakedPart BIs there a proportional relationship between the number of pies Raquel bakes andthe money she earns? Use the graph to explain your answer.
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We are given a relationship between pies and earnings, we are asked wheater the relationship is linear. Let "x" be the number of pies and "y" its cost. Then, according to the statements of the problem we have the following points.
It says that she earned 105 for 7 pies, this means the point:
[tex](x,y)=(7,105)[/tex]It also says that she earned 60 for 4 pies, which means the point:
[tex](x,y)=(4,60)[/tex]It also says that she earned 0 for baking 0 pies, that is the point:
[tex](x,y)=(0,0)[/tex]Since the point passes through the point (0,0) the form of its equation is the following:
[tex]y=mx[/tex]To find the value of "m" we replace one of the given points. Let's pick (4,60), this means that when x = 4, y = 60.
[tex]60=m(4)[/tex]Solving for "m"
[tex]m=15[/tex]Replacing in the equation:
[tex]y=15x[/tex]Now, the relationship is proportional if the given point (7,105) is part of the line. To see that we replace x = 7 and we should get y = 105.
[tex]\begin{gathered} y=15(7) \\ y=105 \end{gathered}[/tex]Since we got y = 105, the relationship is proportional.
The graph of the points looks like this:
determine whether the graph is a complete graph. if not, explain why it is not complete.
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It's denominated a complete graph when all vertices are connected, then this isn't a complete graph because the vertex C is not connected to E.
let y=ln(x^2+y^2) determine y prime at the point -(e^4-16)^1/2
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dy/dx = -2√e⁴ - 16/e⁴ - 8 is differential equation .
The meaning of a differential equation?
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics.The rate of change of a function at a particular moment is determined by the function's derivatives.It is mostly employed in disciplines like biology, engineering, and physics.y = In( x² + y² )
now doing implicit differentiation
dy/dx = d/dx In( x² + y² )
dy/dx = 1/(x² + y² ) × d/dx ( x² + y² )
dy/dx = 1/x² + y² × ( 2x + 2y dy/dx)
(x² + y² )dy/dx = 2x + 2y dy/dx
dy/dx (x² + y² - 2y) = 2x
dy/dx = 2x/(x² + y² - 2y)
we need to calculate dy/dx at ( - √e⁴ - 16 , 4 )
dy/dx =
dy/dx = - 2√e⁴ - 16/e⁴ - 16 + 16 - 8
dy/dx = -2√e⁴ - 16/e⁴ - 8
Learn more about differential equation
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A family records the amount of total savings, in dollars, it has each year and constructs a linearº model to fit the data set. The resulting linear model has equation y = 43,517 + 5,321x where x isthe years from 2015 and y is the total savings.Fill in the blanks with the correct phrases that make the statement true.The value 5.321 represents ( blank )amount of money, in dollars, the family ( Blank )Dropdown 1the exactthe approximateDropdown 2has savings in 2015.currently has in savings.saves each year.
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A linear model, generally, is written as:
y = mx + b
where m is the slope
b is the y-intercept
The given linear model is:
y = 43517 + 5.321x
x represents the number of years since 2015
y represents the total savings
Since x represents the number of years from 2015, the value 5.321 represents the amount of money, in dollar, saved each year from 2015.
what does the slope of the linear equation that models the data indicate
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From the dat, we get that in 1 hour, the car travelled 45 miles.
In 2 hours, the car travelled 104 miles.
2hour-1 hour=1 hour.
104 miles-45 miles=59 miles.
So, the car traveled 59 miles the second hour.
Kyndal wants to buy a lamp thatoriginally cost $82, but went on sale for20% off. The store is having anadditional sale that is 40% off the saleprice. What is the price of the lamp?
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The price of the lamp = $39.36
Explanation:
Original cost = $82
Discount = 20%
The discounted price = $82 × 20% = 82 × 0.2
The discounted price = $16.4
The price to be paid = $82 - $16.4 = $65.6
An additional discount of 40%:
Discounted price = 40% of $65.6 = 0.4 × $65.6
Discounted price = $26.24
The price of the lamp = $65.6 - $26.24
The price of the lamp = $39.36
Is the expression below quadratic?5xsquared(2)- 18A.TrueB.False
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A quadratic expression has the general form:
[tex]\begin{gathered} ax^2+bx+c \\ \text{where }a\ne0 \end{gathered}[/tex]In the expression:
[tex]\begin{gathered} 5x^2-18 \\ a=5,b=0\text{ and c=-18} \end{gathered}[/tex]So, is a quadratic expression beacuase satisfy the general formula with a = 5 (distinc of zero), b=0 and c=-18.
is the SIMPLIFIED form of [tex]2 \sqrt{3} + 3 \sqrt{3} [/tex]rational?
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The given expression is:
[tex]2\sqrt[]{3}+\text{ 3}\sqrt[]{3}[/tex]Note that:
[tex]a\sqrt[]{c}+\text{ b}\sqrt[]{c}=\text{ (a+b)}\sqrt[]{c}[/tex]Therefore, the given expression can be written as:
[tex]undefined[/tex]ug gu g6 6tc6tc6tc6tx6tx
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Find the equation of the line that is perpendicular to 3x -2y = 6 and passes through (1,2)
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first, rearrange the equation 3x-2y=6 to y=mx+b form.
-2y= -3x + 6......... subtract both sides by 3x
y = 3/2x-3.......... divide both sides by -2
considering that the slope of a line that is perpendicular to this line is the opposite reciprocal
3/2 => -2/3
finally, use the point-slope equation to get the final answer
y-2= -2/3 (x-1)
y-2= -2/3x + 2/3
y= -2/3x + 2/3+ 2
y= -2/3x + 8/3
answer: y= -2/3x + 8/3
Kendra is filling cone shaped baskets each with a height of 20 inches and radius of 6 inches to use as table decorations.Part Ain terms of pie, what is the exact volume of each cone shaped basket?
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height = 20 inches
radius of the cone = 6 inches
Therefore,
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\pi r^2h \\ \text{volume}=\frac{1}{3}\times\pi\times6^2\times20 \\ \text{volume}=\frac{1}{3}\times\pi\times36\times20 \\ \text{volume}=\frac{720\pi}{3} \\ \text{volume}=240\pi^{}inches^3 \end{gathered}[/tex]Consider the equation and solution steps shown here. If there is an error, identify the step in which the error occurs.problem: 5^x+3 = 212step A: In 5^x+3 = In 212step B: x + 3(In 5) = In 212step C: x = In 212 - 3(In 5)A) step AB) step BC) step CD) no error
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Solution:
Given the equation;
[tex]5^{x+3}=212[/tex]STEP A: Take the logarithm of both sides;
[tex]\begin{gathered} \ln (5^{x+3_{}})=\ln (212) \\ \end{gathered}[/tex]STEP B: Apply the logarithmic law;
[tex]\log _ba^c=c\log _ba[/tex][tex]\begin{gathered} \ln (5^{x+3_{}})=\ln (212) \\ (x+3)\ln (5)=\ln 212 \end{gathered}[/tex]STEP C: Divide both sides by In(5);
[tex]\begin{gathered} (x+3)\ln (5)=\ln 212 \\ \frac{(x+3)\ln (5)}{\ln (5)}=\frac{\ln 212}{\ln (5)} \\ x+3=\frac{\ln212}{\ln(5)} \end{gathered}[/tex]Thus, there is an error in the solution.
CORRECT OPTION: B
I need help with this I forgot how to do it
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The solution of the system of inequalities is the intersection region of the solutions of two inequalities
for a class of 24,78% of students got a B or better on the tex How many students is this? Round to a wholenumber
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Step 1
Use the ratio of the number to the percentage to get the required answer.
[tex]\frac{Total\text{ number of students}}{\text{The required number of students}}=\frac{Total\text{ percentage of the class}}{\text{Given percentage}}[/tex]Where,
[tex]\begin{gathered} \text{The total number of students = 24} \\ \text{The required number }of\text{ students= x} \\ \text{The total percentage of the class = 100} \\ \text{Given percentage = 78} \end{gathered}[/tex]Step 2
Get the required answer
[tex]\begin{gathered} \frac{24}{x}=\frac{100}{78} \\ 100x=24\times78 \\ 100x=1872 \\ \frac{100x}{100}=\frac{1872}{100} \\ x=\text{ 18.72} \\ \text{Hence} \\ x\approx19students\text{ rounded to a whole number } \end{gathered}[/tex]The number of students that got B or a better grade on the test = 19 students rounded to a whole number.
Y=10/x+7-5 graph the function. State the domain and range
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Classify the following polynomials by degree and number of terms:[tex] {4p}^{3} + {2p}^{2} + 19p - 5 [/tex]
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
4p³ + 2p² + 19p - 5
degree = ?
number of terms = ?
Step 02:
We must analyze the expression to find the solution.
4p³ + 2p² + 19p - 5
degree = 3 = cubic
number of terms = polynomial
The answer is:
degree = cubic
number of terms = polynomial
The rhombus below NL=3, KL=5, and angle JML=60° find angle JLK
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1) When we are dealing with a Rhombus is convenient to recall some properties:
0. Opposite angles are congruent
,1. Consecutive angles are supplementary
,2. Congruent sides
,3. Diagonals bisect angles
,4. Diagonals are perpendicular.
So, we can sketch out the following, to better grasp it:
2) So, based on the properties: Opposite angles are congruent, and the fact that Diagonals bisect angles then we can state the following answer:
[tex]\angle JLK=60^0[/tex]